I would like to start out by saying that we are all deeply saddened by the absence of Kirk Osborn on this very emotional day. Kirk stood by my side from the very beginning of this travesty and did all that he could to proclaim my innocence. Not only has North Carolina lost one of its finest attorneys, it has lost a man who embodied the words honor and integrity. We will never forget his sacrifices and our thoughts and prayers are with his family.
Today marks the end of a year long nightmare that has been a destructive force in so many peoples lives. The dark cloud of injustice that hung above our heads has finally cleared and we can now all look forward to continuing the life that has been taken from us. My family appreciates the efforts of Attorney General Roy Cooper and Special Prosecutors Jim Coman and Mary Winstead for their thorough investigation. While this day is long overdue, we recognize their diligence and perseverance to uncovering the truth in order to show the world that we have always been 100% innocent of these charges.
This past year has been the most difficult and painful period of my life and I would like to credit my family and friends for keeping me focused and bolstering my spirit throughout this agonizing journey. My Mom and Dad are the toughest, most loving parents anyone could ask for and it is because of there relentless will to defend my name that we were able to make it through the storm. I have been inspired by the courage and strength of both my parents and three brothers who have provided me with so much love, guidance and unquestionable faith in my innocence. I love you all so much.
I must also thank all of my attorneys. Kirk Osborn, Buddy Connor, Antonio Lewis, and Jim Cooney, along with the other defense teams. All of these men have worked tirelessly to ensure that three innocent men did not spend thirty years in prison for a hoax. I would like to specifically thank Jim Cooney for restoring my faith in the legal system. Through his bold leadership, incredible work ethic and sincere concern for my well being, we were finally able to achieve justice.
To the Evans's and Finnerty's, I will never forget your tremendous bravery and unwavering resolve throughout this unbearable ordeal. I wish you all the best in the future as we all move on with our lives and hope that we can repair the damage that was done.
I am forever grateful for all of the care, concern, and encouragement I received from my remarkable girlfriend Brooke and her family, the Delbarton community, the town of Essex Fells, KC Johnson , and everyone else who chose to stand up, use their voice and challenge the actions of a rogue district attorney.
This entire experience has opened my eyes up to a tragic world of injustice I never knew existed. If it is possible for law enforcement officials to systematically railroad us with no evidence whatsoever, it is frightening to think what they could do to those who do not to have the resources to defend themselves. So rather than relying on disparaging stereotypes, or creating political and racial conflicts, we must all take a step back from this case and learn from it. This tragedy has revealed that our society has lost site of the core principle of our legal system, the presumption of innocence.
For everyone who chose to speak out against us before the facts were known, I sincerely hope that you are never put in a position where you experience the same pain and heartache that you have caused our families. While your hurtful words and outrageous lies will forever be associated with this tragedy, everyone will always remember that we told the truth, and in the words of Abraham Lincoln, "truth is the best vindication against slander'. If our case can bring to light the some of the flaws in our judicial system as well as discourage people from rushing to judgment, than the hardships we have endured over this past year will not have been in vain.
As the healing process begins for our families, I feel as though it is my responsibility to create something positive out of this experience. During my time away from school I got the chance to learn a lot about myself: Who I am and who I want to be. This case has shown me what the important things in life really are as my entire perspective on the world has changed. I view this situation as a unique opportunity to make a difference and I know that there are many people who can benefit from the lessons I have learned.
I fully intend on continuing my education and look forward to pursuing the goals I have set for myself. I have the deepest appreciation for my educational and athletic opportunities and my dream is to return to both by this fall. My ultimate aspiration moving forward, is to live a life that will make all of those who stood by my side throughout this injustice, proud to know that they defended the truth.


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"Fusion Fiber" - A Stronger, Smoother Rolling Rim from Revel... And It's Recyclable
Posted Feb 27, 2020 by Dan Perl
The RW-30
You can't re-invent the wheel, but with this rim, Revel has revolutionized it. In March of 2019, Adam Miller, the founder of Revel Bikes, was approached by his long-time friend Joe Stanish, former VP at ENVE and COO at Alchemy, with a new carbon composite material. Called "Fusion Fiber, and produced and manufactured by CSS Composites in Utah, this new carbon composite replaces the epoxy that is used in normal pre-impregnated (pre-preg) carbon with a nylon polymer.
What does this do for a bike rim?
Normal carbon fiber, saturated with epoxy, is extremely brittle. It is not good at dissipating the energy from point impacts, like a rock strike to a rim bead flange. With nylon fibers replacing that epoxy, Fusion-Fiber is more flexible and better able to handle the types of forces and impacts that a bike wheel undergoes.
The RW30 out on the trails.
Increased strength allows Revel to make the entire rim lighter, which, as a rotating mass, is arguably the most significant place to remove weight from on a bicycle. A 29" RW30 rim weighs 470 grams, whereas a comparable Enve rim, the M730, weighs 580 grams - over three ounces. This decreased brittleness compared to regular carbon also gives the rims a desirable ride feel. Described as being "quiet" by our employees, they have something of a damped sensation compared to much of the competition. It's not that they are noodly or don't track well, but that they don't transmit as many vibrations through to you. This results in less pain in your hands and increased awareness of the trail beneath you.
Rich doing some "product testing" on a Revel Rail sporting the RW30 rims
Okay, but "revolutionized?"
It's lighter, it's stronger, it feels better… okay, but that's what they all say. Where this rim, and the material it is made of, really changes the game is in how it's made and what we do with it after it is no longer a usable wheel.
Firstly, Fusion Fiber does not have to be refrigerated. Huh? Yup, pre-preg fiber has to be kept in the fridge before its use, and has a limited shelf life. That is a ton of energy spent in refrigeration, and the possibility of a lot of waste should manufacturing timelines go wrong. Secondarily, Fusion Fiber is flash cooked. 20 seconds in the oven and it's done. Traditional carbon, on the other hand, sits in the oven for an hour. That's a whole bunch more energy consumed. Lastly, the RW30 rims come out of the mold in their final form (except for drilling the holes). Because there isn't a bunch of epoxy all over, they aren't sanded or painted. That eliminates a number of potential health hazards for employees, as well as potential inconsistencies in the final product.
Speaking of inconsistencies, because the carbon strips that these rims are made of are laid up by robots in Utah, the possibility of missing an important piece of the construction is far lower. Fewer mess-ups, less waste, and a better final product. What more can you ask for? I'll tell you. Tradition carbon fiber goes in the landfill when it is no longer in use. You can't melt it down, you can't re-use it.. nothing. Fusion Fiber, on the other hand, can be! That sounds too good to be true. I thought so too. But no. When there is scrap material from manufacturing, or when you back over your wheel in your car and use your lifetime warranty to get a new one, Revel takes the old material, puts it in their wood-chipper, and cuts it down into little chunks. The makers of Fusion Fiber take those chucks, melt and press them into a block, and can then stamp and carve a new airplane/bicycle/car component out of it. Think bottle cages, chain-guide back-plates, tool holders, and more.
Our master wheel builder Joey, tensioning up an RW30 wheel.
The RW30 comes in both 29" and 27.5" sizes, has a 29mm inner width (perfect for 2.4-2.6" tires), has a lifetime warranty, and best of all, has customizable graphics. It is designed for all-mountain/enduro riding, and was designed by guys who call Carbondale, Colorado their home. That means that sharp-edged rocks won't phase this rim. It looks good, it feels good, and it's good (i.e. not as bad) for the planet. What more could you ask for.
Revel Wheels
RW30 27.5" Fusion-Fiber Rim
RW30 29" Fusion-Fiber Rim
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redpajama_set_name: RedPajamaCommonCrawl


In addition to one-off training courses, we have been providing in-depth training for three cohorts of museums in the East of England. Working with six museums in each cohort, we have been providing training and support to help museums improve their fundraising from Trusts and Foundations (one cohort) and Individual Giving and Legacies (two cohorts).
To find out more about SHARED Enterprise, click here.
Can Apollo Fundraising help your organisation?


If you're replacing or installing a new window, there are many decisions that you'll need to make. One of these is which frame material you're going to use.
uPVC is a popular window frame material. It's a type of plastic that's easy to source, low maintenance and durable.
But are uPVC frames right for your windows?
To help you decide, we've come up with a list of uPVC's pros and cons.
uPVC is low maintenance. uPVC windows can be easily wiped clean with a damp cloth, and don't need treating with anything.
uPVC is rot and corrosion resistant. It won't rot in wet conditions, and isn't susceptible to corrosion.
uPVC is durable. It won't get damaged by extreme weather and won't fade or degrade under UV light.
uPVC is energy efficient. It's a very good insulator as it doesn't conduct heat. So uPVC windows will keep the heat in your home and save you energy and money.
uPVC is long-lasting. If uPVC windows are good quality and have been installed correctly, they can last over 35 years.
uPVC is affordable. uPVC frames are generally cheaper than other window frames, as plastic is less expensive than wood or aluminium.
uPVC is versatile. Many people choose to install white window frames because they look sharp and bright. But you can also get uPVC frames in lots of different colours, which can be handy if you want to coordinate your windows with your property.
Although it's generally very durable, uPVC can become brittle over time. This means that it can shatter or splinter when put under extreme pressure.
uPVC is not particularly environmentally friendly. Its production contributes to the amount of carbon dioxide in the atmosphere. uPVC frames also contribute to waste levels, as uPVC isn't biodegradable.
uPVC can look cheap. Compared to other window frame materials, like wood and aluminium, uPVC can look poor quality and low value.
So uPVC window frames have a range of advantages and disadvantages. If you decide you want uPVC window frames, and need to find a professional to source and fit them, we can help. Fill in our online form and we'll connect you with up to 4 local contractors. Or to find out about other types of window frame, take a look at our information on wood and aluminium.


text:
Rolex Sydney Hobart Race – Left field, handshakes and buckets Pt. II
by John Curnow on 23 Dec 2016
The DSS foils look amazing and are quite well aft compared with other vessels that carry the system - CQS Media Launch Beth Morley - Sport Sailing Photography http://www.sportsailingphotography.com
The 100-foot experiment? Four supermaxis are contesting the J.H. Illingworth Trophy for Line Honours in this year's 628 nautical mile dash from Sydney to Hobart. The outright favourite is once again the Oatley family's Wild Oats XI. WOXI has taken line honours seven times and Mark Richards and his seasoned crew is looking for another win after a split mainsail caused them to abandon the race during the vigorous, first night, southerly buster last year.
Two boats with known potential are Anthony Bell's Perpetual Loyal, the former Speedboat, and then after that, Rambler 100. Bell and the crew won in 2011 on Investec Loyal, which was Maximus originally (2005), and subsequently went on to become Ragamuffin 100. That very boat is now the Hong Kong entry, Scallywag, owned by Seng Huang Lee. She was the third boat into Hobart in 2014 and second in 2015, just behind the great Comanche.
Perpetual Loyal crosses in front of Wild Oats XI and Scallywag. - SOLAS Big Boat Challenge © Andrea Francolini
Now the most unknown of the four is also the phoenix of the fleet. Just like WOXI and Maximus, the 90-footer that was until recently known as Nicorette, has undergone some changes, modifications, additions and alterations. Only thing is, hers are far, far more radical – just look at the pictures of the new CQS, as she is now called.
The boat was the winner (Line Honours) of the 2004 Rolex Sydney Hobart Yacht Race. She is now extended to 100 foot, and will be campaigned by Ludde Ingvall and his billionaire cousin, Sir Michael Hintze. She has a host of profound features that could, in theory, blow the race wide open, or just blow up.
Sir Michael Hintze and Ludde Ingvall at today's launch. - CQS Media Launch © Beth Morley - Sport Sailing Photography http://www.sportsailingphotography.com
We talked at length to the dual Hobart winner, Ludde Ingvall, and following is the second of this three-part series. In Part I, Ingvall explained how he and his cousin, Sir Michael Hintze, began the campaign that will see the radical 100-footer CQS on the start line at 1300hrs on Boxing Day.
Specifically, Ingvall detailed how they came up with the key elements of the rebuilt boat; the DSS system, the Dreadnought bow, the wings to reduce the mast compression forces, and the stern cockpit extension for sheeting angles and crew weight.
Now the Swedish born Australian sailor continues. "Naval Architect, Brett Bakewell-White, and I met with New Zealand America's Cup winning skipper, Chris Dickson. He would have to be one of the ultimate technocrats in yachting, and we explained the project. Dickson said exactly what we had hoped for, 'Ludde I have to be on this boat!"
All smiles with Ludde Ingvall and Chris Dickinson - CQS Media Launch © Beth Morley - Sport Sailing Photography http://www.sportsailingphotography.com
"Chris is focusing purely on what things are needed to make sure the boat performs the way it should. That's tweaking and so forth on the boat, and also the foils and related systems."
"We also have Chris Main, who is an extremely good sailor, and he's focusing on the crew work. How the crew needs to operate, and how we set up the systems to furl and unfold these huge sails, because we have no spinnaker. There is not a single analysis showing the boat will ever have the wind aft of the beam. It might be at 70, but probably never aft of 75 degrees."
"That means we have only five sails on the bow, and now all but the smallest one can be furled, so we can open and close any slots. With 17.5 metres from the mast to the end of the bowsprit, we can set those five different sails set up, pretty much equal distances from the mast to the bow. It means we choose to go with number one, and three or five, and you can go number two and four. Because most of them are on furlers, we can change gears rather quickly", explained Ingvall.
Watch Captain Rodney Keenan at the helm of CQS - CQS Media Launch © Beth Morley - Sport Sailing Photography http://www.sportsailingphotography.com
"However, as Rodney Keenan from Evolution Sails New Zealand, who is our sail master and sail maker reminds us, the reality is we are a less than a week from the start of the Hobart race, and only now are we finding out what sail combination works and at what angle, let alone how to make her really fly!"
"We already know she does some pretty cool stuff, but now we have to make her fly for mile after mile. It is a little bit like powerboat development. You remember when we used to have good old-fashioned powerboats, and then someone came up with stepped hulls, and when air hit the under part of the hull, the powerboat took off, with decreased resistance."
"We are feeling the same thing here. There is a moment where the foils are kicking in, and the boat starts lifting with less wetted surface area allowing the boat to accelerate. Right now we can't tell you whether we can maintain that. We are already on our second foil design, and our learning curve is very steep."
CQS finishes White Island Race 2016 and sets monohull record © Suellen Hurling
"We did the White Island Race without the DSS foil because I wasn't prepared to break the shaft by catching a crab pot while we were close tacking along the East coast of New Zealand. Instead we sent the DSS foil to the factory to start the Mark II testing."
"When using the foil, and as we get faster, we get more waves and generate even more lift. The bow and everything comes further out of the water and the boat sails more upright. Our optimal heel angle will be no more than 15 degrees, whereas Comanche probably heels at over 30 to get her massive hull out of the water." (Editor's note, Ken Read has said previously their optimum is 25+)
"So far the wings have not proven to be any issue for us. Not much happens when the wings hit the water. The first thing you have, of course, is that they generate stability. So you have the wing on the leeward side, and when it cuts into the water you can feel it is there. However, the way it is designed it is almost like an upside wing that serves us our purposes."
CQS in action at Royal Akarana Yacht Club Round White Island Race © Big Boat Racing bigboatracing.com
"Every now and then, particularly without the DSS, they did punch the water or hit a wave, and we get some spray, but that is about it. Part of it is that if you heel over and they are touching, then that basically generates some lift. The big benefit of the wings is that they allow us to have a much lighter mast, as the wide base reduces the compression loads. Our rig is only 1000 kilograms, and I would think that the others are probably double."
"This is all new territory, and in fact we will see on the long track to Hobart what really happens with the wings and DSS. There is, I understand, a flat rating penalty of 2% for DSS under IRC, but we think that is certainly worth it."
"It's really a trade-off between lift and drag. The lift it generates in the water will be well over ten times a similar size wing would do if it was in air. We have gone for a totally different configuration to anybody else, in that our wing looks like an aircraft's wing to provide less drag, and there is a flap at the back allowing us to have variable lift."
Those new DSS foils CQS sports - CQS Media Launch © Beth Morley - Sport Sailing Photography http://www.sportsailingphotography.com
"We can also minimise drag, as we can push the whole the thing out half way, all the way out, or pull it in. Of course the shape changes such that we can put in out half way and we have half a wing, which is still functional. If we push it out all the way, then the last quarter of the wing would probably have about less than 30% of the drag of the complete wing being deployed because of its shape."
"We are expecting that the wing will start giving us benefits (lift), rather than drag, from about eight knots of boat speed upwards. Importantly, I can tell you that we have not yet sailed the boat going less than eight knots!"
"Our biggest A1 is 738 square metres. It doesn't need a lot of air for that thing to start moving, with the hull being so skinny and so long. As soon as we reach eight knots, the expectations are that the lift that the DSS gives us will be better than the drag that it causes", explained Ingvall.
"If you want to fly like we are trying to, you need to be very weight conscious. Of course, if we built a brand-new boat with all we know today it would be significantly lighter, and the gains would be even greater, but we have got what we want, and we are learning as much we can."
Will this be the view many will see on Boxing Day? - CYCA Trophy Passage Series © Andrea Francolini
"We are quite open about it, and just seeing where it takes us. If we were to do another boat based on the data that we already know, it would be quite a different boat. Realistically, with all the radical features on this boat, which have not been proven yet, if we actually get to Hobart it will be a major accomplishment!"
Ingvall concludes this section by saying, "If nothing breaks I will be absolutely amazed. Sir Michael is going to sit at the back with me and have a gin and tonic, and then watch what happens." To which we say, and so will we all!!!
There are plenty more interesting revelations, explanations and comments in part three, the final, of 'Left field, handshakes and buckets'. They will be here on Sail-World for you to read before the Rolex Sydney Hobart sets off.
Ludde Ingvall at the helm of CQS - CQS Media Launch © Beth Morley - Sport Sailing Photography http://www.sportsailingphotography.com
Current routing, which has to be viewed in light of the changes that can and do occur on the East coast of Australia, especially at this time of year, has the supermaxis at 1 day and 15 hours, which means they will have to work hard to be on record pace, which is 1:18 and some change. Note that this puts you at the Iron Pot at/near sunrise, which is not ideal for getting up the River Derwent, but certainly better than in the dark. The maxis are at 1:21, the TPs 2:4, displacement 40-Somethings at 2:23, older craft at 3:2 and small at 3:20. We'll have more on all of this as the super all-important weather window first gets a frame, then panes of glass, well before any paint gets applied, let alone any internal dressings, as the next few days unfold.
Ultimately then if you are looking for smiles yourself, then do keep a weather eye here on Sail-World.com for all the latest intel on the great, inspiring, captivating and very historic, blue water classic… The Rolex Sydney Hobart Yacht Race.
If you want to link to this article then please use this URL: www.sail-world.com/150622
Hempel Youth Sailing Worlds day 2
Maltese consistency hands them slender advantage Maltese sisters Antonia and Victoria Schultheis found the right note at the Hempel Youth Sailing World Championships as the Girl's 29er fleet commenced their competition.
Posted today at 4:14 am The Ocean Race: Plans for Hong Kong entry
Sun Hung Kai/Scallywag skipper David Witt is keen to take on another round-the-world Ocean Race One week after celebrating one of his biggest international successes, Sun Hung Kai/Scallywag skipper David Witt said he was keen to take on another round-the-world Ocean Race and win it, according to a report in the South China Morning Post.
Posted today at 3:36 am Hamilton Island Race Week: 200 entries & climbing
200 entries for Hamilton Island Race Week A yacht with a name that says it all for its now retired owner is the 200th entry for Hamilton Island Race Week, which will be staged on the picturesque tropical waters of the Whitsundays next month.
Posted today at 3:35 am America's Cup: Construction Update for June 2019
All 84 piles for the Hobson Wharf extension (Luna Rossa base) have been installed, with 12 remaining The Wynyard Edge Alliance, a consortium charged with the construction of the America's Cup bases in Auckland is making good progress as detailed in their report as of the end of June 2019.
Posted today at 12:56 am Dates for 2020 Auckland Fiji Race confirmed
On Saturday 30th May 2020, a fleet of competitive yachts and multihulls will start the 1,100nm race The dates have been set for the next Royal Akarana Yacht Club major bluewater race, with the club sticking to tradition and racing from Auckland to Fiji.
Posted on 16 Jul Cascais 52 Super Series Sailing Week day 1
Quantum Racing execute a typical Cascais race-winning strategy Quantum Racing's three-point aggregate sees them three points clear of three boats - Provezza, Bronenosec and Azzurra - after the first day of racing at this renowned high-wind venue where last year they won the Rolex TP52 World Championship.
Posted on 16 Jul Cascais 52 Super Series Sailing Week preview
Alegre looking for a repeat performance Cascais and the Rolex TP52 World Championship was the best regatta last year for Andy Soriano's Alegre and as the British-flagged team return this week to the famous Portuguese strong wind racing arena for the Cascais 52 Super Series Sailing Week
Posted on 16 Jul Transpac News, 12 Metre Words, AC Hall of Fame
Latest Sail-World USA newsletter from David Schmidt While summer isn't even half over, the sailing world is being treated to some great offshore racing, starting with the Transatlantic Race 2019, and followed by the Transpacific Yacht Race, which began in a series of pursuit-style starts on July 10.
Posted on 16 Jul Cape Panwa Hotel Phuket Raceweek preview
Over 450 sailors ready for 16th edition of award-winning regatta Over 450 sailors, families and friends from more than 20 countries are set to make Cape Panwa Hotel their home this week as they head to Phuket to take part in the Cape Panwa Hotel Phuket Raceweek, 17 - 21 July.
Posted on 16 Jul Mirabaud Yacht Racing Image Award jury announced
A prestigious international jury will preside over the 10th Mirabaud Yacht Racing Image Award The Mirabaud Yacht Racing Image photo competition has announced the composition of its international jury 2019. Ricardo Pinto, professional sailing photographer and winner of the previous edition, Rob Hodgetts, international sports journalist
Posted on 16 Jul
This site and its contents are Copyright © 2019 Sail-World Sail-World Australia and/or the original author, photographer etc. All Rights Reserved. Photographs are copyright by law. If you wish to use or buy a photograph contact the photographer directly.


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'It Is A Shame And Very Disappointing, BBC Should Investigate Its Journalists' – Says Dr Saravanamuttu
By Colombo Telegraph –
"It is a shame and very disappointing – it seems that some journalists are being supported by tax payers in two countries and with notions of conflict of interest and professional ethics and integrity thrown to the winds. The relevant authorities in both countries -this includes the BBC- should investigate as to how this could happen." says Dr Paikiasothy Saravanamuttu.
Dr Paikiasothy Saravanamuttu
Dr Paikiasothy Saravanamuttu, the Executive Director of the Centre for Policy Alternatives and founder member of the Board of the Sri Lanka Chapter of Transparency International made the above remarks when asked how he saw the issue of senior journalists, particularly BBC World Service journalists applying for and receiving Rs. 1,200,000/- as an interest free loan from the state banks to purchase cars or vans. According to the Ministry of Finance Sri Lanka, the Treasury will pump in the interest due to the state banks for the loans under this scheme.
BBC Sinhala Service Colombo reporter Elmo Fernando and the Londoner BBC World Service – Sinhala senior producer Chandana Keerthi Bandara both applied the interest free loan from the Sri Lankan Government.
Meanwhile the Opposition and UNP Leader Ranil Wickremesinghe said yesterday that some media personnel who had received laptops and obtained vehicle loans, had defamed him in their publications the very next day.
"Last Sunday BBC Sinhala Service Colombo Reporter filed a distorted report on the Opposition Leader's press conference and attacked him" a senior opposition legislator told Colombo Telegraph, asking for anonymity because he didn't want to be targeted by the 'laptop and interest free loan' media. The BBC didn't report what the leader said in full and just criticised him for not answering BBC questions. The BBC even failed to report what the questions were.
Listen to BBC Sinhala reporting on Ranil Wickremesinghe here at minutes 7.37 – 11.20.
Addressing new IT recruits at Sirikotha, Wickremesinghe said that the gifting of laptops and interest free loan to journalists and cartoonists, which coincided with the budget was no mere coincidence. It had been calculated to prevent the media from highlighting the burdens placed by the budget on the poor suffering masses.
"I see this interest-free motor vehicle loan as a sort of a 'bribe'. I don't think it's appropriate at all for a BBC journalist to take this. Obviously it will damage their credibility." the former head of the BBC Sinhala Service Vasantha Raja told Colombo Telegraph.
BBC guidelines says; "A conflict of interest may arise when the external activities of anyone involved in making our content affects the BBC's reputation for integrity, independence and high standards, or may be reasonably perceived to do so. Our audiences must be able to trust the BBC and be confident that our editorial decisions are not influenced by outside interests, political or commercial pressures, or any personal interests.There is a danger of conflict of interest in every area of programme or content making. Each department or team must be aware of its area of vulnerability. There may be particular sensitivities for on-air talent."
"The BBC's reputation for impartiality and objectivity is crucial. The public must be able to trust the integrity of BBC programmes and services. Our audiences need to be confident that the BBC's editorial decisions are not influenced by the outside activities or personal or commercial interests of programme makers or those who appear on air."
Related posts;
Applying And Receiving An Interest-Free Motor Vehicle Loan Will Damage BBC's Credibility Says The Former Head
'BBC World Service Journalist's Interest-Free Loan Application 'On The Waiting List' Says Sri Lankan Government
The Struggles Of Identity In Sri Lanka
Exclusive: Investigate Your Journalists! - Opposition Leader Ranil Wickremesinghe To BBC's Lord Chris Patten
Safa / November 23, 2012
It is disappointing that a journalist from the BBC has stooped to this level. Maybe BBC should appoint a more reliable person and give him a laptop or at least pay him enough. Beggars cannot be choosers.
Wuliangguobinjiu / November 23, 2012
It's the Graft Indian virus spreading into Sri Lanka or vice versa or both ways.
BBC cut some Foreign Service programs in its structural restructuring but not salaries so for a mere £6000 it is despicable.
If channel 4's John Snow and other big guys at BBC with all their personal wealth can cycle to work and fro what problems do these two creeps have?
Isn't it quicker to cycle when there are traffic jams?
White Hall / November 23, 2012
Yes Dr Saravanamuttu, agree with you, YES It is a shame and very disappointing, but also disgusting .
Lakshan / November 23, 2012
BBC should not allow two corrupt bastard to undermine its integrity
Bedrock Barney / November 23, 2012
Anyone watching BBC during the Iraq invasion would not have guessed that the BBC had a "reputation for impartiality and objectivity". Apparently though, they have one.
Controlling the media through the influence of friends and family used to be the exclusive preserve of Mr Wickremasinghe. Now someone has broken in and one-upped him.[Edited out]
Part of this comment was removed by a moderator because it didn't abide by our Comment policy.For more detail see our Comment policy
http://colombotelegraph.com/comments-policy/
Hela / November 24, 2012
So it is ok for these NGO kaakas to receive dollars from their overseas benefactors to persue their agenda (of regime change & destabilisation) and journalists should not ask loans (not grants mind you).
What a hypocracy! Who is trying to fool whom?
Naga / November 24, 2012
I do not know about the BBC Sinhala Service, but I do know that the BBC Tamil Service is a bastion of pro-LTTE elements. BBC's Tamil Service reporting is highly unbalanced and anti-Sri Lankan government. At the time LTTE was controlling North East Sri Lanka,BBC Tamil Service never reported anything bad about the LTTE. Their Vavuniya correspondent Manikavasagam who these days always report the travails of the Vanni refugees was conspicous by his silence on the mass scale child recruitment and other atrocities committed by the LTTE against the Tamil civilians and Sinhalese alike. Now he has become the champion to the cause of human rights of the Sri Lankan Tamils.
Also do not forget the former BBC Tamil Service Producer Ananthi Sivapragasam who was very fond of LTTE. I understand she later after her retirement from BBC became an important personality in a pro-LTTE organisation based in London.
In any case BBC,similar to the VOA for the Americans, is an organisation floated and still maintained at British taxpayers'expense as a propaganda voice of the British to spread its ideals and views. Hence there cannot be any neutrality in its news reporing or program content.
As for the Sri Lankan government providing goodies to the Sri Lankan journalists, there is nothing wrong in those poor journalists accepting them because in any case they work for organisations by design or choice that are either pro-government or anti-government. If they are working for a pro-government organisation they should always be filing stories to put the government in good light, whereas, if they are working for an anti-government media they should seek out anti-government stories. This is the inescapable unwritten rule among the Sri Lankan journalists. An anti-government journalist after acccepting the government goodies cannot be writing pro-government stories to his media as these stories will obviously end up in the dustbin. In effect, the goodies provided by the Rajapakse government are not going to bring out any change in the highly polarised Sri Lankan journalist world. Let those poor bastards enjoy the goodies given by Rajapakse government. Good luck to them.
dicky Bird / November 24, 2012
Pakaya Saravanamuththu….
This comment was removed by a moderator because it didn't abide by our Comment policy.For more detail see our Comment policy
peter casie chetty / November 26, 2014
You will never ever be published if you do not agree with this two faced and biased website. Saravanamuttu is being investigated for ,any years. "Thambi" has been part of CBK's undergarment crew so he escaped punishment because the investigations never complete.
Javi. / November 26, 2014
I gather Ranil never got an answer from BBC chief Patton because the value of laptop once it reaches the first user is £30 just enough to visit a local pub and they are found in skips awaiting the recycle van. Short distance away is RNIB and on this matter he commented `they have eyes but don't see`
Have you heard of biodegradable office buildings they were displayed in China Expo Shanghai by the Swiss and last 20 years (no carbon imprint) so they come on lease and the full value is depreciated?
When you wear Parana coat and like to be a vicious politician from court house (registrar office) supporting the `Boo`ts government and working for a few coins your comments are understandable.
I refrain from giving you the knowledge of where to find brand new for free with no strings attached because you have no imagination.
GTMVK - Navala / November 25, 2012
The BBC has been unfairly criticized by the Sinhala extremists for being anti Sri Lankan and pro Tamil. Moderates have defended it as a reliable source of news and impartial analysis. The applications of some BBC journalists for money from the Rajapaksa government compromises seriously the credibility of the BBC, and makes it impossible for those who trust the BBC to defend it. If the BBC is to maintain the credibility it so far enjoyed, it has only one choice, to demand the resignation of those who have lined up to receive the tainted Rajapaksa money.
Muhunthan / November 26, 2012
BBC correspondence must refrain from any conflict of interest. We expect the reporting of the BBC to be accurate, precise and unbiased. It would damage the reputation of the BBC and its public perception, if its correspondence in Sri Lanka, had applied for an interest free loan, and decided to take the perks given by the government which was with intention to stop reporting of anti government news.
BBC you need to do more.
Peter Casie Chetty / September 15, 2014
The BBC has been despicable on many issues and events they have reported. In the present Scottish referendum that have blatantly ignored the rules of proper journalism and taken sides. Alex Salmond has complained and sadly will not be the last person to have complaints about biased BBC reporting.
Saravanamuttu [Edited out]
Native Vedda / September 15, 2014
Peter Casie Chetty
"The BBC has been despicable on many issues and events they have reported."
Spotting these biases makes you the senior journalists. You deserve it.
Well done Peter.
Snowdon Asange / November 17, 2013
Why would these Journalist LQQk for perks elsewhere IF the BBC had a scheme to assist its journalists than be offered goodies by others… IF ethics is the yardstick, there WONT be any journalists working for BBC in UK or anywhere else..


Wednesday night I posted this picture to capture my anxiousness about going on my first youth camp trip as a leader.
How am I going to survive?
The annual camp trip to Kansas has none of the amenities that a spoiled glamper (fancy camping) like me is used to. Add to that, I volunteered to teach the youth on sin. Thursday morning, I put on my bravest face and began the 3 hr car trip to St Francis, Kansas. We camp out on some land on the edge of the town. This town has a population of 1300. Here's what camp looks like.
I was able to adjust to the "bathroom", which was a toilet seat elevated over a hole, surrounded by a tarp. I didn't even mind being with 37 kids, some of whom I knew, and some of whom I would grow to know. While I thought I would dislike losing my privacy, I liked being around the kids. There was always someone to talk to.
Thursday night, the wind was so strong, it nearly blew my tent off the ground. It made having a fire impossible, and kicked up all kinds of allergens. I barely slept that night, the wind was too much.
Friday's fun was playing at the park in town, where the kids had a ridiculous time playing Slip N Slide kickball. The pictures show giant smiles on everyone's face. Friday night was my turn to teach. I was blessed to have the leaders lay hands on me to pray. I opened by telling them I was so nervous about teaching that I felt like I could either puke or pee. With that icebreaker, I gave an abbreviated version of my testimony, then broke into Scripture and teaching on how hard it is to surrender sin. I was relieved when it was over. While it felt like I had only taught for 5 minutes, I'm sure it was longer.
Unfortunately, one of our girls (K) fell ill that night. The allergies were far too much for her, and her breathing was very labored. She was taken away to the hospital in town, by one of the families from the church who has a home in St Francis. They come out every year to help us with all the meals.
Saturday we woke earlier than usual to get our teaching in before we went into town for a service project. We visited a retirement community to do some chores (window washing, painting, cleaning). It was a blessing to them, and to us. We returned to camp for lunch then went off to Frogland, one of the town's bigger ponds. Here we could play in the water, or just chill on the beach. This was also our day to visit Dairy King.
I spent my time at Frogland in the shade, but was coaxed out to play some beach volleyball. Volleyball is not my sport, but I had a blast getting silly with the group playing. I think my team even won.
Saturday night is when things got wonderful and weird. During worship, one of the girls starting showing symptoms similar to what K had experienced. It was determined she should go get checked out at the hospital. Larry was in charge of teaching that night, and he did awesome. 5 kids ended up giving their lives to Christ. It was a huge blessing. Larry's teaching was followed by more worship, and prayer time. I prayed with one of my HS girls who was overwhelmed with joy at the news of kids being saved. But during the worship, K and another girl had to go to the hospital. That made it 3 girls in the ER. The leaders met and talked about what the plan should be. We determined that we were under attack by the enemy, and we were going to stand our ground and rebuke anything trying to distract from what we were doing. We prayed loud and hard, then broke into small groups. Two of the HS boys went around camp praying over the youth for protection (it was a cool thing). Not even ten minutes into small group time, we were told by the hospital that we should evacuate camp. Clearly something was in the air at our camp, and we needed to leave. We grabbed sleeping bags, and some grabbed a few items, and we fled to the homes of the two families from church who have places in St Francis. By this time it was about 10:30pm.
Morale was pretty good, considering what was going on. As we waited to find out our next move, another girl fell ill and was sent to the ER. We then got word the hospital wanted us to all shower and ditch our "contaminated" clothing. The local high school was opened up for us to shower and change. Hospital gowns were sent over, as well clothes donated by the two families, also clothes from a church. Some of the kids were also sent to the thrift store, which opened up to us, and donated items.
We were at the high school for some time, because it takes a while for everyone to shower, especially if there are only two bottles of shampoo. The school provided towels for us. All our clothes were put into trash bags, to be dealt with later. While we waited at the high school, a 5th girl fell ill and was sent to the hospital.
Once everyone was showered, we split the boys and girls between the two houses. Pretty much everyone fell asleep right away. We resolved that a group would go out to the land Sunday morning to pack up all the tents and belongings.
Sunday morning we did just that, breaking down camp in less than 90 minutes. All the girls that had been hospitalized were released with an epi pen and had received nebulizer treatment. While we still are unsure what had happened, the symptoms were dizziness, shakes and breathing problems. We tried to keep the hospitalized girls in vehicles without people who broke camp, as a precaution. The drive home was fairly uneventful, although one girl had a stomach bug and had to pull over to be sick.
Once we returned to Aurora, all the belongings were laid out on the lawn of the school to be collected. Everyone was told to wash all their clothes, and all girls had to discard any makeup, lotions or sprays.
Three of the five girls had return trips to the ER/Urgent Care after their return to CO Sunday. We're praying hard that this is the end of whatever is attacking their systems.
So, that was Kansas Youth Camp. In the end, it was interesting. There was laughter, tears, and stories to share. Lives were changed, bonds were formed, and God moved.
Day Two, and our last full day, meant cramming in as much as we possibly could. We visited Old Faithful and we could not have timed our visit better. We arrived within ten minutes of the eruption. Hundreds of visitors lined the boardwalk, and watched (or timed) the geyser do its thing. The length of the eruption will tell you when the next one will go off. If it lasts less than 2 1/2 minutes, the next time it goes off will be in one hour. If it's longer than 2 1/2 minutes, you have a 90 minute wait.
There is more to see at Old Faithful, you can check out other geysers, hot springs and fumeroles. We did the 1.3 mile walk around the Geyser Hill Loop, then headed inside to check out the Visitor Center. We were pretty impressed with the children's area, which explained all the hydrothermic features. After a quick picnic lunch, we headed back towards Canyon intending to make a few stops. First stop was Midway Geyser Basin, to view Yellowstone's largest hot spring, Grand Prismatic Spring. Geoff & Miles did this hike, while Elijah said the smell of sulphur was giving him a headache, so we hung out in the shade near the trailhead.
Next stop was Artists Paintpots. Geoff wanted to see mudpots, and this short hike gave great views of our surroundings plus mudpots. The kids were amused by the size and sounds the bubbling mud produced.
Last stop before heading back to camp was snagging a letterbox. I thought it was fate that a box was planted just a few weeks before my visit, and so close to our campsite. We drove back to the Grand Canyon of the Yellowstone River, but this time on the other side of the falls we visited the day before. I had not printed the picture that went with the clue, which proved to be the key for me finding my prize. Thank God for cell signal, I pulled up AQ and used the picture to locate the box. All the while I was doing this, the boys heading on a hike on Uncle Tom's Trail. The hike led them to a rickety metal staircase of 300 steps "attached" to the rock face. But the view of Lower Falls made it worthwhile for them.
The rest of the afternoon was resting from all our adventures. After dinner, we treated ourselves to some ice cream in the village. I indulged in Moose Tracks.
Moose Tracks, the finest of flavors.
It was time to part company, but the memories we made were amazing.
Was it worth the drive? Yes.
Worth the cost? It was definitely one of our most expensive camping trips when you add up gas and park fees. But since we don't plan to do it every year, and it was our family vacation for the year, I'm going to say yes.
Should you go? Absolutely! Yellowstone was awesome. We hope to go back in a few years, next time checking out Grand Tetons and the parts of Yellowstone we missed.
For more information, visit Yellowstone's website.
There seems to be something so Americana about taking a family trip to Yellowstone. A road trip, with two kids, all our camping gear and heading to Wyoming. We settled on this idea a year ago, and made the actual reservations 6 months in advance of our stay. Depending on what accommodations you are looking for, 6 months out is a good marker.
Yellowstone is about a 9 hour drive, if you take the East entrance. We opted to split this into two days driving, staying in Casper, WY the first night. This gave us more time to set up our campsite the next day, and not arrive grumpy or in the dark.
Passing Yellowstone Lake on our way to Canyon.
We've never been to Yellowstone before, so we were unsure what campground we wanted. We decided on Canyon, because it was kind of center of the park, and equal distance for us, and my mom and her husband Gary, driving down from Canada. The campground had all the amenities I require (flush toilets) and with the Canyon Village so close, it was practically glamping.
I'm not exaggerating- we may have had the best site in the campground. We had a water pump right at our site, the bathrooms were over the hill from us, and we had a ton of space between us and the next site. This gave the boys a lot of freedom to play, run, and explore.
Miles shows off our campsite.
My mom and Gary stayed at Canyon Village, in one of the cabins. The sparse rooms offered beds and a bathroom. They loved coming to visit us, hang out by the fire, and eat fire cooked food. I can't say what the other rooms looked like.
The boys and I went to the ranger talk that night, which was about bears. The talk was very educational, but did not allow for interaction, which disappointed Elijah. Still he learned a lot. Miles got bored early, so we headed back, leaving Elijah to come later with Gramma.
After lunch, Geoff and I went to the Village to see what was there. A lot of shops, selling EVERYTHING and ANYTHING you could need. It was crazy. We also checked out all the dining options, because we knew we wanted to eat breakfast there our last morning, to make the packing up of the campsite go faster. I was able to procure some souvenirs and mail off some postcards (they have a post office there!).
The rest of the day was chilling. Playing games, and just enjoying being in Yellowstone. As luck would have it, one of my friends from Denver was also camping Yellowstone the same dates as us, so her family joined us for running around and s'more making. This is just what my kids loved, having friends around, even new friends.
Tomorrow's post, what we did with our last full day in Yellowstone.
I love the month of June. When all that waiting through winter pays off, and it is finally time to camp!
We are tent campers, and our favorite place to camp in Colorado is Golden Gate Canyon State Park. We've been going there every year for the last 4 years. You have to make reservations early if you want a site on the weekend, and I made our Sunday through Tuesday reservation back in March. Geoff really wanted a walk in site (your car is NOT next to your site), and that afforded us an amazing view.
But it also meant a bit of a walk to the bathroom, and to put our food in the car at night. Still, we liked the privacy, and the space for the kids to run and play.
With only two days in the park, we crammed both fishing and hiking into our Monday plans. Fishing at Dude's Fishing Hole, where I caught our first fish (who neither survived, nor became dinner) and a hike up Coyote Trail.
A successful camping adventure, with perfect weather to boot. Already looking forward to booking another site for September!
With the boys getting bigger, and becoming more experienced campers, Geoff was anxious to see if we could attempt to hike all of the Raccoon Trail. It's a 2.5 mile hike round trip, that begins in Reverend's Ridge campground and takes you up to Panorama Point. The hike is marked as moderate, and both kids did great completing it. The timing of our trip offered great fall colors, mostly yellows, and great temps.
Other noteworthy events were the boys learning to build a fire, and Elijah becoming a Jr Ranger.
We'll be back again next summer. If you want to camp there next year, I would suggest you book early!
Summer. It means we're out camping. Our favorite spot is Golden Gate Canyon State Park. Just outside of Golden, it's a real gem. We booked our site in March, allowing us to know we'd have a spot come June.
We really lucked out with the weather, it was perfect. Perhaps we can put the Armstrong curse (rain!) to rest.
We even took advantage of the talks put on by the naturalist. The first night, we learned about black bears. Prizes were awarded for correct answers, and we helped the boys score some granola bars.
The next day, the boys & I planted a letterbox, and attended the talk on pollinators. We went back that night to hear some stories, such as the Navajo story of the night sky creation.
On our last day, I convinced the family to hike up Mt Galbraith to hunt for a letterbox. The views it afforded made it worth while!
Enough words, here are some pics.
Normally I'd be moaning to you about how it rained the whole time, and we had a rough time camping.
Nana & Grampy joined us for a wonderful 3 days camp in Rocky Mountain National Park. I was nervous we'd have a hard time getting a site in Longs Peak Campground, since it only has 26 tent sites. But arriving on a Monday, we nearly had our pick of the sites. We settled in the inner sites, sites 15 and 16 (but for fantastic views try to secure sites 1-4). The weather couldn't have been better, and the food and company were great.
The highlight for me was the lovely hike around Lily Lake.
The views from up high and me figuring out macro photos for wildflowers make me eager to go back. The highlight for the boys was having Nana & Grampy to play with as well as daily conversations with Mr. Bill. He was the camp host, and with him set up across the road from us, the boys could say hello to him several times a day.
The future plan is for us to all tackle Longs Peak, one of the famous 14ers in Colorado. For now, we just enjoyed it from afar.
A trip in Estes Park provided me with an awesome souvenir, trail tags. You can obtain them from Brownfield's Trading Post (on Elkhorn Ave), and the different colored border signify the length of hike you completed. This will be something I hope the boys enjoy earning. I got them the trail tag for the hike we did at Sprague Lake earlier this year.
With so much more of the National Park to explore, I hope get back real soon.
We took a few days to get away and do the first camping trip of the year. We love the Reverend's Ridge Campground near Golden, in Golden Gate Canyon State Park. It's about an hour's drive from our house, and you avoid the I-70 traffic.
The downside to making reservations, is you can't bail due to foul weather. And the weather on Sunday was foul! We were able to set up camp in the breaks from rain. But it made that first day hard on everyone. The highlight was a new recipe we tried, polenta pizza. Basically, you make a polenta crust, then top with your fav toppings. Hot pizza made the cold a little better. Sadly, nothing would drag Miles out of his bad mood. He was cold, and refused to eat dinner. We tried to get some food in him, knowing the cold night would be harder on him without it.
We all slept great, and woke to a block of ice on top of the tent. Monday's rainy clouds didn't clear until midday, and then we still had an afternoon rain shower. We took in the beauty at Panarama Point while the sun was shining. Tuesday was by far the nicest day, and naturally it was the day we planned to go home. We debated staying an extra day, but since we already have another camping trip planned this month, we figured we should leave on a high note. We did do one last hike in the area before we headed home. We all can't wait to get back out into nature, you know, once we get the smell of campfire out of everything.
Pictures of us enjoying the sunshine & camping can be found on Shutterfly.


text:
Become a Volunteer

GDG PH Droids

Google Developer Group Philippines is opening a new initiative of group of volunteers. We are currently looking for:

an active, hyper volunteer and aspiring leaders of the future.

anyone uses any Google technologies or apps.

anyone who wants to share their knowledge about Google technologies

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redpajama_set_name: RedPajamaGithub


In this series, I examine inventory using a simple rule of thumb: Inventory increases ought to roughly parallel revenue increases. If inventory bloats more quickly than sales grow, this might be a sign that expected sales haven't materialized. Is the current inventory situation at Sensata Technologies Holding (NYS: ST) out of line? To figure that out, start by comparing the company's inventory growth to sales growth. How is Sensata Technologies Holding doing by this quick checkup? At first glance, pretty well. Trailing-12-month revenue increased 4.8%, and inventory decreased 10.8%. Comparing the latest quarter to the prior-year quarter, the story looks decent. Revenue dropped 1.8%, and inventory dropped 10.8%. Over the sequential quarterly period, the trend looks OK but not great. Revenue dropped 5.6%, and inventory dropped 5.2%.
What's going on with the inventory at Sensata Technologies Holding? I chart the details below for both quarterly and 12-month periods.
Let's dig into the inventory specifics. On a trailing-12-month basis, each segment of inventory decreased. On a sequential-quarter basis, finished goods inventory was the fastest-growing segment, up 5.1%. That can be a warning sign, so investors should check in with Sensata Technologies Holding's filings to make sure there's a good reason for packing the storeroom for this period. Sensata Technologies Holding seems to be handling inventory well enough, but the individual segments don't provide a clear signal.
If you're interested in companies like Sensata Technologies Holding, you might want to check out the jaw-dropping technology that's about to put 100 million Chinese factory workers out on the street - and the 3 companies that control it. We'll tell you all about them in "The Future is Made in America." Click here for instant access to this free report.
Add Sensata Technologies Holding to My Watchlist.
The article Don't Get Too Worked Up Over Sensata Technologies Holding's Latest Numbers originally appeared on Fool.com.


text:
\section{Introduction}

Physics engines enable the accurate prediction of dynamical behavior of systems for which an analytical model has been implemented. Given such models, Bayesian estimation approaches~\cite{ramos2019bayessim} can be used to find the simulation parameters that best fit the real-world observations of the given system. While the estimation of simulation parameters for traditional simulators via black-box optimization or likelihood-free inference algorithms often requires a large number of training data and model evaluations, differentiable simulators allow the use of gradient-based optimizers that can significantly improve the speed of parameter inference approaches~\cite{murthy2021gradsim}.

\begin{figure}
    \centering
    \includegraphics[width=\columnwidth]{fig/neural_qp_mpc.pdf}\\\vspace{0.5em}
    \includegraphics[width=\columnwidth]{fig/real_qp_mpc.pdf}
    \caption{\textit{Top:} Snapshots from a few seconds of the locomotion trajectories generated by the QP-based model-predictive controller (first row) and the neural network controller imitating the QP solver (second row) in our differentiable simulator running the Laikago quadruped.
    \textit{Bottom:} model-predictive control using the neural network (third row) and OSQP (fourth row) running on a real Unitree A1 robot.}
    \label{fig:neural-qp}
\vspace{-1em}
\end{figure}

\begin{table*}[t]
    \centering
\begin{threeparttable}
    \begin{tabular}{p{7cm}cccc}
    \toprule
    & \bf Analytical & \bf Data-driven & \bf End-to-end $\nabla$ & \bf Hybrid \\\midrule
    Physics engine~\cite{coumans2013bullet,todorov2012mujoco,lee2018dart} & \checkmark \\
    Residual physics~\cite{hwangbo2019learning,anurag2018hybrid,zeng2019tossingbot,golemo2018neuralaugsim} & \checkmark & \checkmark & & \checkmark \\
    Learned physics~\cite{sanchez2020learning,battaglia2016interaction,li2018learning,jiang2018datacontact} & & \checkmark & \checkmark \\
    Differentiable simulators~\cite{giftthaler2017autodiff,hu2020difftaichi,carpentier2018analytical,peres2018lcp,geilinger2020add,Qiao2020Scalable,murthy2021gradsim} & \checkmark & & \checkmark \\
    Our approach & \checkmark & \checkmark & \checkmark & \checkmark \\
\bottomrule
    \end{tabular}
    \caption{Comparison of dynamics modeling approaches (selected works) along the axes of analytical and data-driven modeling, end-to-end differentiability, and hybrid approaches.}
    \label{tab:comparison}
\end{threeparttable}
\vspace{-1em}
\end{table*}

Nonetheless, a sim-to-real gap remains for most systems we use in the real world. For example, in typical simulations used in robotics, the robot is assumed to be an articulated mechanism with perfectly rigid links, even though they actually bend under heavy loads. Motions are often optimized without accounting for air resistance. In this work, we focus on overcoming such errors due to unmodeled effects by implementing a differentiable rigid-body simulator that is enriched by fine-grained data-driven models.

Instead of learning the error correction between the simulated and the measured states, as is done in residual physics models, our augmentations are embedded inside the physics engine. They depend on physically meaningful quantities and actively influence the dynamics by modulating forces and other state variables in the simulation. Thanks to the end-to-end differentiability of our simulator, we can efficiently train such neural networks via gradient-based optimization.

Our experiments demonstrate that the hybrid simulation approach, where data-driven models augment an analytical physics engine at a fine-grained level, outperforms deep learning baselines in training efficiency and generalizability. The hybrid simulator is able to learn a model for the drag forces for a swimmer mechanism in a viscous medium with orders of magnitude less data compared to a sequence learning model. When unrolled beyond the time steps of the training regime, the augmented simulator significantly outperforms the baselines in prediction accuracy. Such capability is further beneficial to closing the sim-to-real gap. We present results for planar pushing where the contact friction model is enriched by neural networks to closely match the observed motion of an object being pushed in the real world. Leveraging techniques from sparse regression, we can identify which inputs to the data-driven models are the most relevant, giving the opportunity to discover places where to insert such neural augmentations.

Besides reducing the modeling error or learning entirely unmodeled effects, introducing neural networks to the computation pipeline can have computational benefits. In real-robot experiments on a Unitree A1 quadruped we show that when the quadratic programming (QP) solver of a model-predictive gait controller is replaced by a neural network, the inference time can be reduced by an order of magnitude.

We release our novel, open-source physics engine, Tiny Differentiable Simulator (TDS)\footnote{Open-source release of TDS: \url{https://github.com/google-research/tiny-differentiable-simulator}}, which implements articulated rigid-body dynamics and contact models, and supports various methods of automatic differentiation to compute gradients w.r.t. any quantity inside the engine.

\section{Related Work}
\label{sec:citations}

\begin{figure*}[ht!]
    \centering
    \includegraphics[height=4.5cm]{fig/system_comparison.pdf}\hfill
    \includegraphics[height=4.5cm]{fig/nn_scalar.pdf}
    \caption{\textit{Left:} comparison of various model architectures (cf.~Anurag et al.~\cite{anurag2018hybrid}). \textit{Right:} augmentation of differentiable simulators with our proposed neural scalar type where variable $e$ becomes a combination of an analytical model $\phi(\cdot,\cdot)$ with inputs $a$ and $b$, and a neural network whose inputs are $a$, $c$, and $d$.}
    \label{fig:approaches}
\end{figure*}

Various methods have been proposed to learn system dynamics from time series data of real systems (see \autoref{tab:comparison} and \autoref{fig:approaches} left). Early works include Locally Weighted Regression~\cite{schaal1994lwr} and Forward Models~\cite{moore1991fm}.  Modern ``intuitive physics'' models often use deep graph neural networks to discover constraints between particles or bodies~(\cite{battaglia2016interaction, xu2019physics, he2019physics, raissi2018physics, mrowca2018physics, chen2018neural, li2018learning, sanchezgonzalez2020learning}). Physics-based machine learning approaches introduce a physics-informed inductive bias to the problem of learning models for dynamical systems from data~\cite{chen2018ode,long2018pde,raissi2019physics,lutter2019delan,greydanus2019hnn,sutanto20rnea}.
We propose a general-purpose hybrid simulation approach that combines analytical models of dynamical systems with data-driven residual models that learn parts of the dynamics unaccounted for by the analytical simulation models.

Originating from traditional physics engines (examples include~\cite{coumans2013bullet,todorov2012mujoco,lee2018dart}), differentiable simulators have been introduced that leverage automatic, symbolic or implicit differentiation to calculate parameter gradients through the analytical Newton-Euler equations and contact models for rigid-body dynamics~\cite{giftthaler2017autodiff,carpentier2018analytical,peres2018lcp, koolen2019rbd-julia, heiden2019ids,  heiden2019real2sim,geilinger2020add,lelidec2021diffsim,lutter2020differentiable}. Simulations for other physical processes, such as light propagation~\cite{NimierDavidVicini2019Mitsuba2, heiden2020lidar} and continuum mechanics~\cite{hu2019chainqueen,liang2019differentiable,hu2020difftaichi,Qiao2020Scalable,murthy2021gradsim} have been made differentiable as well.

Residual physics models~\cite{zeng2019tossingbot,anurag2018hybrid,hwangbo2019learning,golemo2018neuralaugsim} augment physics engines with learned models to reduce the sim-to-real gap. Most of them introduce residual learning applied from the outside to the predicted state of the physics engine, while we propose a more fine-grained approach, similar to~\cite{hwangbo2019learning}, where data-driven models are introduced only at some parts in the simulator. While in~\cite{hwangbo2019learning} the network for actuator dynamics is trained through supervised learning, our end-to-end differentiable model allows backpropagation of gradients from high-level states to any part of the computation graph, including neural network weights, so that these parameters can be optimized efficiently, for example from end-effector trajectories.

\begin{figure}
    \centering
    \includegraphics[width=0.7\columnwidth]{fig/neural_golf.pdf}
    \caption{Exemplar architecture of our hybrid simulator where a neural network learns passive forces $\tau$ given joint velocities $\mathbf{\dot{q}}$ (MLP biases and joint positions $\mathbf{q}$ are not shown). }
    \label{fig:golf}
\vspace{-0.25in}
\end{figure}

\section{Approach}
\label{sec:approach}

Our simulator implements the Articulated Body Algorithm (ABA)~\cite{featherstone2007rbda} to compute the forward dynamics (FD) for articulated rigid-body mechanisms. Given joint positions $\mathbf{q}$, velocities $\mathbf{\dot{q}}$, torques $\tau$ in generalized  coordinates, and external forces $\mathbf{f}_\text{ext}$, ABA calculates the joint accelerations $\mathbf{\ddot{q}}$. We use semi-implicit Euler integration to advance the system dynamics in time. We support two types of contact models: an impulse-level solver that uses a form of the Projected Gauss Seidel algorithm~\cite{stewart2000implicit,horak2019similarities} to solve a nonlinear complementarity problem (NCP) to compute contact impulses for multiple simultaneous points of contact, and a penalty-based contact model that computes joint forces individually per contact point via the Hunt-Crossley~\cite{hunt1975coefficient} nonlinear spring-damper system. In addition to the contact normal force, the NCP-based model resolves lateral friction following Coulomb's law, whereas the spring-based model implements a nonlinear friction force model following Brown et al.~\cite{brown2018friction}.

Each link $i$ in a rigid-body system has a mass value $m_i$, an inertia tensor $\mathbf{I}_i \in \mathbb{R}^{6 \times 6}$, and a center of mass $\mathbf{h}_i \in \mathbb{R}^{6 \times 6}$. Each corresponding $n_d$ degree of freedom joint $i$ between link $i$ and its parent $\lambda(i)$ has a spring stiffness coefficient $k_i$, a damping coefficient $d_i$, a transformation from its axis to its parent ${}^{\lambda(i)}\mathbf{X}_i \in \mathbb{SE}(3)$, and a motion subspace matrix $\mathbf{S}_i \in \mathbb{R}^{6 \times {n_d}}$.

For problems involving $n_c$ possible contacts, each possible pair $j$ of contacts has a friction coefficient $\mu_j \in \mathbb{R}$ describing the shape of the Coulomb friction cone. Additionally, to maintain contact constraints during dynamics integration, we use Baumgarte stabilization~\cite{baumgarte1972stabilization} with parameters $\alpha_j, \beta_j \in \mathbb{R}$. To soften the shape of the contact NCP, we use Constraint Force Mixing (CFM), a regularization technique with parameters $\mathbf{R}_j \in \mathbb{R}^{n_c}$.
$$
\theta_{AM} = \{m_i, \mathbf{I}_i, \mathbf{h}_i, {}^{\lambda(i)}\mathbf{X}_i, \mathbf{S}_i\}_i \; \cup \; \{\mu_j, \alpha_j, \beta_j, \mathbf{R}_j\}_j
$$
are the \emph{analytical model parameters} of the system, which have an understandable and physically relevant effect on the computed dynamics. Any of the parameters in $\theta_{AM}$ may be measurable with certainty a priori, or can be optimized as part of a system identification problem according to some data-driven loss function.

With these parameters, we view the dynamics of the system as
\begin{align}
\label{eqn:augmented-manipulator-equation}
\mathbf{\tau} = \mathbf{H}_{\theta_{AM}}(\mathbf{q})\mathbf{\ddot{q}} + \mathbf{C}_{\theta_{AM}}(\mathbf{q}, \mathbf{\dot{q}}) + \mathbf{g}_{\theta_{AM}}(\mathbf{q})
\end{align}
where $\mathbf{H}_{\theta_{AM}}$ computes the generalized inertia matrix of the system, $\mathbf{C}_{\theta_{AM}}$ computes nonlinear Coriolis and centrifugal effects, and $\mathbf{g}_{\theta_{AM}}$ describes passive forces and forces due to gravity.

\subsection{Hybrid Simulation}
\label{sec:hybrid-sim}

Even if the best-fitting analytical model parameters have been determined, rigid-body dynamics alone often does not exactly predict the motion of mechanisms in the real world. To address this, we propose a technique for hybrid simulation that leverages differentiable physics models and neural networks to allow the efficient reduction of the simulation-to-reality gap. By enabling any part of the simulation to be replaced or augmented by neural networks with parameters $\theta_{NN}$, we can learn unmodeled effects from data which the analytical models do not account for.

Our physics engine allows any variable participating in the simulation to be augmented by neural networks that accept input connections from any other variable. In the simulation code, such \emph{neural scalars} (\autoref{fig:approaches} right) are assigned a unique name, so that in a separate experiment code a ``neural blueprint'' is defined that declares the neural network architectures and sets the network weights.

\subsection{Overcoming Local Minima}
\label{sec:basin-hopping}

For problems involving nonlinear or discontinuous systems, such as rigid-body mechanisms undergoing contact, our strategy yields highly nonlinear loss landscape which is fraught with local minima. As such, we employ global optimization strategies, such as the parallel basin hopping strategy~\cite{mccarty2018parallel} and population-based techniques from the Pagmo library~\cite{Biscani2020}. These global approaches run a gradient-based optimizer, such as L-BFGS in our case, locally in each individual thread. After each evolution of a population of local optimizers, the best solutions are combined and mutated so that in the next evolution each optimizer starts from a newly generated parameter vector. As can be seen in \autoref{fig:local-vs-pbh}, a system identification problem as basic as estimating the link lengths of a double pendulum from a trajectory of joint positions, results in a complex loss landscape where a purely local optimizer often only finds suboptimal parameters (left). Parallel Basin Hopping (right), on the other hand, restarts multiple local optimizers with an initial value around the currently best found solution, thereby overcoming poor local minima in the loss landscape.

\begin{figure}
    \centering
    \includegraphics[width=0.9\columnwidth]{fig/local_vs_global_opt.pdf}

    \caption{

    Comparison of system identification results from local optimization (left) and the parallel basin hopping strategy (right), where the grid cells indicate the initial parameters from which the optimization was started. The link lengths of a double pendulum are the two simulation parameters to be estimated from joint position trajectories. The true parameters are 3 and 4 (indicated by a star), and the colors indicate the $\ell2$ distance between the ground truth and the parameters obtained after optimization (darker shade indicates lower error).

    }
    \label{fig:local-vs-pbh}
\vspace{-0.25in}
\end{figure}

\subsection{Implementation Details}
\label{sec:implementation}

We implement our physics engine \emph{Tiny Differentiable Simulator} (TDS) in C++ while keeping the computations agnostic to the implementation of linear algebra structures and operations.
Via template meta-programming, various math libraries, such as Eigen~\cite{eigenweb} and Enoki~\cite{Enoki} are supported without requiring changes to the experiment code. Mechanisms can be imported into TDS from Universal Robot Description Format (URDF) files.

To compute gradients, we currently support the following third-party automatic differentiation (AD) frameworks: the ``Jet'' implementation from the Ceres solver~\cite{ceres-solver} that evaluates the partial derivatives for multiple parameters in forward mode, as well as the libraries Stan Math~\cite{carpenter2015stan}, CppAD~\cite{cppadweb}, and CppADCodeGen~\cite{cppadcodegen} that support both forward- and reverse-mode AD. We supply operators for taking gradients through conditionals such that these constructs can be traced by the tape recording mechanism in CppAD. We further exploit code generation not only to compile the gradient pass but to additionally speed up the regular simulation and loss evaluation by compiling models to non-allocating C code.

In our benchmark shown in \autoref{fig:adbench}, we compare the gradient computation runtimes (excluding compilation time for CppADCodeGen) on evaluating a 175-parameter neural network, simulating 5000 steps of a 5-link pendulum falling on the ground via the NCP contact model, and simulating 500 steps of a double pendulum without contact. Similar to Giftthaler et al.~\cite{giftthaler2017autodiff}, we observe orders of magnitude in speed-up by leveraging CppADCodeGen to precompile the gradient pass of the cost function that rolls out the system with the current parameters and computes the loss.

\begin{figure}
    \centering
    \includegraphics[width=0.85\columnwidth]{fig/adbench.pdf}
    \caption{Runtime comparison of finite differences (blue) against the various automatic differentiation frameworks supported by our physics engine. Note the log scale for the time (in seconds).}
    \label{fig:adbench}
\vspace{-0.25in}
\end{figure}

\section{Experimental Results}
\label{sec:result}

\subsection{Friction Dynamics in Planar Pushing}
\label{sec:exp-pushing}

Combining a differentiable physics engine with learned, data-driven models can help reduce the simulation-to-reality gap.
Based on the Push Dataset released by the MCube lab~\cite{yu2016more}, we demonstrate how an analytical contact model can be augmented by neural networks to predict complex frictional contact dynamics.

The dataset contains a variety of planar shapes that are pushed by a robot arm equipped with a cylindrical tip on different types of surface materials. Numerous trajectories of planar pushes with different velocities and accelerations have been recorded, from which we select trajectories with constant velocity. We model the contact between the tip and the object via the NCP-based contact solver (\autoref{sec:approach}). For the ground, we use a nonlinear spring-damper contact model that computes the contact forces at predefined contact points for each of the shapes. We pre-processed each shape to add contact points along a uniform grid with a resolution of \SI{2}{\cm} (\autoref{fig:push-butter-plywood} right). Since the NCP-based contact model involves solving a nonlinear complementarity problem, we found the force-level contact model easier to augment by neural networks in this scenario since the normal and friction forces are computed independently for each contact point.

As shown in \autoref{fig:push-butter-plywood} (left), even when these two contact models and their analytical parameters (e.g. friction coefficient, Baumgarte stabilization gains, etc.) have been tuned over a variety of demonstrated trajectories, a significant error between the ground truth and simulated pose of the object remains. By augmenting the lateral 2D friction force of the object being pushed, we achieve a significantly closer match to the real-world ground truth (cf. \autoref{fig:push-rollout}). The neural network inputs are given by the object's current pose, its velocity, as well as the normal and the penetration depth at the point of contact between the tip and the object. Such contact-related variables are influenced by the friction force correction that the neural network provides. Unique to our differentiable simulation approach is the ability to compute gradients for the neural network weights from the trajectories of the object poses compared against the ground truth, since the influence of the friction force on the object pose becomes apparent only after the forward dynamics equations have been applied and integrated.

\begin{figure}
    \centering
    \includegraphics[width=0.55\columnwidth,trim=3em 0 0 3em,clip]{fig/butter_plywood.jpg}\hfill
    \includegraphics[width=0.40\columnwidth, trim=0 0 2em 0]{fig/shape_plots/butter.pdf}
    \caption{\textit{Left:} example setup for the push experiment (\autoref{sec:exp-pushing}) where the rounded object is pushed by the black cylindrical tip at a constant velocity on a plywood surface. Without tuning the analytical physics engine, a deviation between the pose of the object in the real world (green) and in the simulator (metallic) becomes apparent.
    \textit{Right:} predefined contact points (red dots) for one of the shapes in the push dataset.}
    \label{fig:push-butter-plywood}
\end{figure}

\begin{figure}
    \centering
    \includegraphics[width=0.6\columnwidth,trim=3em 3em 3em 3em]{fig/push_rollout.pdf}
    \caption{Trajectories of pushing an ellipsoid object from our hybrid simulator (blue) and the non-augmented rigid-body simulation (orange) compared against the real-world ground truth from the MCube push dataset~\cite{yu2016more}. The shaded ellipsoids indicate the final object poses.}
    \label{fig:push-rollout}
    \vspace*{-1em}
\end{figure}

\subsection{Passive Frictional Forces for Articulated Systems}
\label{sec:exp-swimmer}

\begin{figure}
    \centering
    \includegraphics[width=0.65\columnwidth,trim={0cm -1cm 1cm 0},clip]{fig/mujoco_swimmer05_bg.png}\hfill
    \includegraphics[width=0.33\columnwidth]{fig/swimmer_loss.pdf}
    \caption{\textit{Left:} Model of a swimmer in MuJoCo with five revolute joints connecting its links simulated as capsules interacting with ambient fluid.
    \textit{Right:} Evolution of the cost function during the training of the neural-augmented simulator for the swimmer in different media.}
    \label{fig:swimmer05-render}
    \vspace*{-1em}
\end{figure}

\begin{figure*}
    \centering
    \includegraphics[width=\textwidth]{fig/q_qd_swimmer02_water25c.pdf}
    \caption{Trajectory of positions $\mathbf{q}$ and velocities $\mathbf{\dot{q}}$ of a swimmer in water at 25 ${}^\circ$C temperature actuated by random control inputs. In a low-data regime, our approach (orange) generates accurate predictions, even past the training cutoff (vertical black bar), while an entirely data-driven model (green) regresses to the mean. The behavior of the unaugmented analytical model, which corresponds to a swimmer in vacuum, is shown for comparison.}
    \label{fig:swimmer02-trajectory}
    \vspace*{-1em}
\end{figure*}

\begin{table}[]
    \centering
    \begin{tabular}{lSS}
    \toprule
    \bf Medium & \bf Dynamic Viscosity $\mu$ [Pa$\cdot$s] & \bf Density $\rho$ [kg / m${}^3$] \\\midrule
        Vacuum & 0 & 0 \\

        Water (5 ${}^\circ$C) & 0.001518 & 1000 \\
        Water (25 ${}^\circ$C) & 0.00089 & 997 \\

        Air (25 ${}^\circ$C) & 0.00001849 & 1.184 \\\bottomrule\\
    \end{tabular}
    \vspace*{-1em}
    \caption{Physical properties of media used in the swimmer experiment.}
    \label{tab:media}
\vspace{-1em}
\end{table}

While in the previous experiment an existing contact model has been enriched by neural networks to compute more realistic friction forces, in this experiment we investigate how such augmentation can learn entirely new phenomena which were not accounted for in the analytical model. Given simulated trajectories of a multi-link robot swimming through an unidentified viscous medium (\autoref{fig:swimmer05-render}), the augmentation is supposed to learn a model for the passive forces that describe the effects of viscous friction and damping encountered in the fluid. Since the passive forces exerted by a viscous medium are dependent on the angle of attack of each link, as well as the velocity, we add a neural augmentation to $\mathbf{\tau}$, $\mathbf{\psi}_\theta(\mathbf{q}, \mathbf{\dot{q}})$, analogous to \autoref{fig:golf}.

Using our hybrid physics engine, and given a set of generalized control forces $u$, we integrate \autoref{eqn:augmented-manipulator-equation} to form a trajectory $\hat{T} = \{\mathbf{\hat{q}}_i, \mathbf{\hat{\dot{q}}}_i\}_i$, and compute an MSE loss $\mathcal{L}(T, \hat{T})$ against $T$, a ground truth trajectory of generalized states and velocities recorded using the MuJoCo~\cite{todorov2012mujoco} simulator. We are able to compute exact gradients $\nabla_\theta \mathcal{L}$ end-to-end through the entire trajectory, given the differentiable nature of our simulator, integrator, and function approximator.

We train the hybrid simulator under different ground-truth inputs. We consider water at 5 ${}^\circ$C and 25 ${}^\circ$C temperature, plus air at 25 ${}^\circ$C, as media, which have different properties for dynamic viscosity and density (see \autoref{tab:media}).

Leveraging the mechanical structure of problems aids in long-term physically relevant predictive power, especially in the extremely sparse data regimes common in learning for robotics. As shown in \autoref{fig:swimmer02-trajectory}, our approach, trained end-to-end on the initial 200 timesteps of 10 trajectories of a 2-link swimmer moving in water at 25 ${}^\circ$C, exhibits more accurate long-term rollout prediction over 900 timesteps than a deep long short-term memory (LSTM) network. In this experiment, the augmentation networks for TDS have 1637 trainable parameters, while the LSTM has 1900.

\subsection{Discovering Neural Augmentations}
\label{sec:discovery}

\begin{figure}[t]
    \centering
    \includegraphics[width=0.3\columnwidth]{fig/neural_discovery.pdf}\hfill
    \includegraphics[width=0.68\columnwidth,trim=0 0 1.5cm 0]{fig/pendulum_mse.pdf}
    \caption{\textit{Left:} Neural augmentation for a double pendulum that learns joint damping. Given the fully connected neural network (top), after 15 optimization steps using the sparse group lasso cost function (\autoref{eq:spinn}) (bottom), the input layer (light green) is sparsified to only the relevant quantities that influence the dynamics of the observed system.  \textit{Right:} Final mean squared error (MSE) on test data after training a feed-forward neural network and our hybrid physics engine.}
    \label{fig:pendulum}
    \vspace*{-1em}
\end{figure}

In our previous experiments we carefully selected which simulation quantities to augment by neural networks. While it is expected that air resistance and friction result in passive forces that need to be applied to the simulated mechanism, it is often difficult to foresee which dynamical quantities actually influence the dynamics of the observed system. Since we aim to find minimally invasive data-driven models, we focus on neural network augmentations that have the least possible effect while achieving the goal of high predictive accuracy and generalizability. Inspired by Sparse Input Neural Networks (SPINN)~\cite{feng2019spinn}, we adapt the sparse-group lasso~\cite{simon2013sparse} penalty for the cost function:
\begin{align}
    \label{eq:spinn}
    \mathcal{L} = \sum_t ||f_\theta(s_{t-1}) - s^*_t||_2^2 + \kappa ||\theta_{[:1]}||_1 + \lambda ||\theta_{[1:]}||_2^2,
\end{align}
given weighting coefficients $\kappa,\lambda>0$, where $f_\theta(s_{t-1})$ is the state predicted by the hybrid simulator given the previous simulation state $s_{t-1}$ (consisting of $\mathbf{q},\mathbf{\dot{q}}$), $s^*_t$ is the state from the observed system, $\theta_{[:1]}$ are the network weights of the first layer, and $\theta_{[1:]}$ are the weights of the upper layers. Such cost function sparsifies the input weights so that the augmentation depends on only a small subset of physical quantities, which is desirable when simpler models are to be found that potentially overfit less to the training data while maintaining high accuracy (Occam's razor). In addition, the $L2$ loss on the weights from the upper network layers penalizes the overall contribution of the neural augmentation to the predicted dynamics since we only want to augment the simulation where the analytical model is unable to match the real system.

We demonstrate the approach on a double pendulum system that is modeled as a frictionless mechanism in our analytical physics engine. The reference system, on the other hand, is assumed to exhibit joint friction, i.e., a force proportional to and opposed to the joint velocity. As expected, compared to a fully learned dynamics model, our hybrid simulator outperforms the baselines significantly (\autoref{fig:pendulum}). As shown on the right, convergence is achieved while requiring orders of magnitude less training samples.
At the same time, the resulting neural network augmentation converges to weights that clearly show that the joint velocity $\mathbf{\dot{q}}_i$ influences the residual joint force $\tau_i$ that explains the observed effects of joint friction in joint $i$ (\autoref{fig:pendulum} left).

\subsection{Imitation Learning from MPC}
\label{sec:laikago}

Starting from a rigid-body simulation and augmenting it by neural networks has shown significant improvements in closing the sim-to-real gap and learning entirely new effects, such as viscous friction that has not been modeled analytically.
In our final experiment, we investigate how the use of learned models can benefit a control pipeline for a quadruped robot.
We simulate a Laikago quadruped robot and use a model-predictive controller (MPC) to generate walking gaits. The MPC implements~\cite{kim2019highly} and uses a quadratic programming (QP) solver leveraging the OSQP library~\cite{osqp} that computes the desired contact forces at the feet, given the current measured state of the robot (center of mass (COM), linear and angular velocity, COM estimated position (roll, pitch and yaw), foot contact state as well as the desired COM position and velocity). The swing feet are controlled using PD position control, while the stance feet are torque-controlled using the QP solver to satisfy the motion constraints. This controller has been open-sourced as part of the quadruped animal motion imitation project~\cite{RoboImitationPeng20}\footnote{The implementation of the QP-based MPC is available open-source at \url{https://github.com/google-research/motion_imitation}}.

We train a neural network policy to imitate the QP solver, taking the same system state as inputs, and predicting the contact forces at the feet which are provided to the IK solver and PD controller.
As training dataset we recorded 10k state transitions generated by the QP solver, using random linear and angular MPC control targets of the motion of the torso. We choose a fully connected neural network with 41-dimensional input and two hidden layers of 192 nodes that outputs the 12 joint torques, all using ELU activation~\cite{clevert2016fast}.

The neural network controller is able to produce extensive walking gaits in simulation for the Laikago robot, and in-place trotting gaits on a real Unitree A1 quadruped (see \autoref{fig:neural-qp}). The learned QP solver is an order of magnitude faster than the original QP solver (\SI{0.2}{\ms} inference time versus \SI{2}{\ms} on an AMD 3090 Ryzen CPU).

Thanks to improved performance, the control frequency increased from \SI{160}{\Hz} to \SI{300}{\Hz}. Since the model was trained using data only acquired in simulation, there is some sim-to-real gap, causing the robot to trot with a slightly lower torso height. In future work, we plan to leverage our end-to-end differentiable simulator to fine-tune the policy while closing the simulation-to-reality gap from real-world sensor measurements. Furthermore, the use of differentiable simulators, such as in~\cite{um2020sol}, to train data-driven models with faster inference times is an exciting direction to speed up conventional physics engines.

\section{Conclusion}
\label{sec:conclusion}

We presented a differentiable simulator for articulated rigid-body dynamics that allows the insertion of neural networks at any point in the computation graph. Such neural augmentation can learn dynamical effects that the analytical model does not account for, while requiring significantly less training data from the real system. Our experiments demonstrate benefits for sim-to-real transfer, for example in planar pushing where, contrary to the given model, the friction force depends not only on the objects velocity but also on its position on the surface. Effects that have not been present altogether in the rigid-body simulator, such as drag forces due to fluid viscosity, can also be learned from demonstration. Throughout our experiments, the efficient computation of gradients that our implemented simulator facilitates, has considerably sped up the training process. Furthermore, replacing conventional components, such as the QP-based controller in our quadruped locomotion experiments, has resulted in an order of magnitude computation speed-up.

In future work we plan to investigate how physically meaningful constraints, such as the law of conservation of energy, can be incorporated into the training of the neural networks. We will further our preliminary investigation of discovering neural network connections and the viability of such techniques on real-world systems, where hybrid simulation can play a key role in model-based control.

\section*{Acknowledgments}
We thank Carolina Parada and Ken Caluwaerts for their helpful feedback and suggestions.

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


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This summer, with a collective of Black Canadian artists, critics and curators, I attended the opening of the 10th Berlin Biennale, curated by four people of African descent. Being in Berlin, the art city, in art spaces whose audiences were responsive to new stewardship, was a unique experience. In other words, it was really nice to be around so many Black people, from across Europe and all over the world, who work in the arts. It is rare to come together in this way to look, and to celebrate. The challenges of inclusion, of negotiating institutional support, and of working toward equitable practices of representation, seemed to be shared by many of these art workers; from our respective contexts we had similar stories. Being there gave me renewed energy to both witness, and support, the immense sea change that has been happening for Black artists in Canada in the recent past. I've been writing about art for half a decade, and I've seen a dramatic change in the past year. Black artists are invited to show more, they are written about more frequently, and their efforts are demonstrably recognized. Looking back at the interviews, essays, videos and features Canadian Art has commissioned and published this year, one finds Black writers and artists and curators addressing the activities and concerns of Black arts in Canada, and in the diaspora at large. Though Black art in Canada is not new, the critical discourses around it are still in formation. We are negotiating how to speak about these practices, and how to give ethical, and nuanced, attention to its practitioners.
As an understanding of the diverse and entrenched histories of Black Canada becomes a part of our everyday, we will increasingly allow for new ways of being.
Another approach exists in the practice of the sculptor Tau Lewis, who maintains a special, intimate relationship to her artworks; one that is unbroken by the strictures of the art market. "I would normally spend up to two months producing one of them, so it's been really emotional and really intense. Not just the process of creating them but also being with them at the fair [after]… all the time that I've spent getting to know and getting to love these things for what they are," the artist said after winning the Frame Prize at Frieze New York last spring. Lewis stays in touch with her works, giving herself permission to visit them if ever she needs to, in whichever collection they may be. "I'm lucky to be able to be transparent with my collectors about how I want these things to exist, and how I want these things to live." Lewis, in her way, redefines the relationship between artists and artwork. A similar intimacy exists in the works of Scarborough artist Erika de Freitas. The mourning gestures in her abstract sculptures are traces of her complex emotions about losing her mother.
We still don't have a comprehensive vocabulary to address—and critique—the range of Black art practices in Canada, but we are getting there.
In her article "Ethics Beyond Language," the writer Nasrin Himada exposes the ethical disaster of appropriation in her study of how NourbeSe Philip's Zong! was used by a Prix de Rome-winning artist without permission, or reprisal. "[O]ur actions," she finds, "are conditioned by the ways in which we position ourselves in relation to others." Himada's writing is a great example of how to hold people accountable for intangible wrongs. We still don't have a comprehensive vocabulary to address—and critique—the range of Black art practices in Canada, but we are getting there. Next, it will be important to look back at Black artistic production over the past half-century, and beyond. This will give us context for understanding current practices, and shed light on senior artists who have been working for a long time without institutional support or recognition. Hopefully, in the years to come—following the example set by BAND with their Michael Chambers retrospective—these artists will be honoured in retrospectives in major institutions. As an understanding of the diverse and entrenched histories of Black Canada becomes a part of our everyday, we will increasingly allow for new ways of being.
Black women curators have shaped a distinct conversation—responsive to settler-colonial histories and the unique experiences of the Black diaspora.