You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Many planning applications involve complex relationships defined on high-dimensional, continuous variables. For example, robotic manipulation requires planning with kinematic, collision, and motion constraints involving robot configurations, object transforms, and robot trajectories. These constraints typically require specialized procedures to sample satisfying values. We extend the STRIPS planning language to support a generic, declarative specification for these procedures while treating their implementation as blackboxes. We provide several domain-independent algorithms that reduce STRIPStream problems to a sequence of finite-domain STRIPS planning problems. Additionally, we describe cost-sensitive planning within this framework. Finally, we evaluate our algorithms on three robotic task and motion planning domains.

Cited Abstract(s):
[1]: Planning with numeric state variables has been a challenge for many years, and was a part of the 3rd International Planning Competition (IPC-3). Currently one of the most popular and successful algorithmic techniques in STRIPS planning is to guide search by a heuristic function, where the heuristic is based on relaxing the planning task by ignoring the delete lists of the available actions. We present a natural extension of "ignoring delete lists" to numeric state variables, preserving the relevant theoretical properties of the STRIPS relaxation under the condition that the numeric task at hand is "monotonic". We then identify a subset of the numeric IPC-3 competition language, "linear tasks", where monotonicity can be achieved by pre-processing. Based on that, we extend the algorithms used in the heuristic planning system FF to linear tasks. The resulting system Metric-FF is, according to the IPC-3 results which we discuss, one of the two currently most efficient numeric planners.

[2]: Planning with hybrid domains modelled in PDDL+ has been gaining research interest in the Automated Planning community in recent years. Hybrid domain models capture a more accurate representation of real world problems that involve continuous processes than is possible using discrete systems. However, solving problems represented as PDDL+ domains is very challenging due to the construction of complex system dynamics, including non-linear processes and events. In this paper we introduce DiNo, a new planner capable of tackling complex problems with non-linear system dynamics governing the continuous evolution of states. DiNo is based on the discretise-and-validate approach and uses the novel Staged Relaxed Planning Graph+ (SRPG+) heuristic, which is introduced in this paper. Although several planners have been developed to work with subsets of PDDL+ features, or restricted forms of processes, DiNo is currently the only heuristic planner capable of handling non-linear system dynamics combined with the full PDDL+ feature set.

[3]: PDDL+ planning involves reasoning about mixed discrete-continuous change over time. Nearly all PDDL+ planners assume that continuous change is linear. We present a new technique that accommodates nonlinear change by encoding problems as nonlinear hybrid systems. Using this encoding, we apply a Satisfiability Modulo Theories (SMT) solver to find plans. We show that it is important to use novel planning-specific heuristics for variable and value selection for SMT solving, which is inspired by recent advances in planning as SAT. We show the promising performance of the resulting solver on challenging nonlinear problems.

[4]: In this paper we present PDDL+, a planning domain description language for modelling mixed discrete-continuous planning domains. We describe the syntax and modelling style of PDDL+, showing that the language makes convenient the modelling of complex time-dependent effects. We provide a formal semantics for PDDL+ by mapping planning instances into constructs of hybrid automata. Using the syntax of HAs as our semantic model we construct a semantic mapping to labelled transition systems to complete the formal interpretation of PDDL+ planning instances. An advantage of building a mapping from PDDL+ to HA theory is that it forms a bridge between the Planning and Real Time Systems research communities. One consequence is that we can expect to make use of some of the theoretical properties of HAs. For example, for a restricted class of HAs the Reachability problem (which is equivalent to Plan Existence) is decidable. PDDL+ provides an alternative to the continuous durative action model of PDDL2.1, adding a more flexible and robust model of time-dependent behaviour.

[5]: Planning in hybrid systems is important for dealing with real-world applications. PDDL+ supports this representation of domains with mixed discrete and continuous dynamics, and supports events and processes modelling exogenous change. Motivated by numerous SAT-based planning approaches, we propose an approach to PDDL+ planning through SMT, describing an SMT encoding that captures all the features of the PDDL+ problem as published by Fox and Long (2006). The encoding can be applied on domains with nonlinear continuous change. We apply this encoding in a simple planning algorithm, demonstrating excellent results on a set of benchmark problems.

[6]: In recent years research in the planning community has moved increasingly towards application of planners to realistic problems involving both time and many types of resources. For example, interest in planning demonstrated by the space research community has inspired work in observation scheduling, planetary rover exploration and spacecraft control domains. Other temporal and resource-intensive domains including logistics planning, plant control and manufacturing have also helped to focus the community on the modelling and reasoning issues that must be confronted to make planning technology meet the challenges of application. The International Planning Competitions have acted as an important motivating force behind the progress that has been made in planning since 1998. The third competition (held in 2002) set the planning community the challenge of handling time and numeric resources. This necessitated the development of a modelling language capable of expressing temporal and numeric properties of planning domains. In this paper we describe the language, PDDL2.1, that was used in the competition. We describe the syntax of the language, its formal semantics and the validation of concurrent plans. We observe that PDDL2.1 has considerable modelling power -- exceeding the capabilities of current planning technology -- and presents a number of important challenges to the research community.

[7]: Systems subject to (continuous) physical effects and controlled by (discrete) digital equipments, are today very common. Thus, many realistic domains where planning is required are represented by hybrid systems, i.e., systems containing both discrete and continuous values, with possibly a nonlinear continuous dynamics. The PDDL+ language allows one to model these domains, however the current tools can generally handle only planning problems on (possibly hybrid) systems with linear dynamics. Therefore, universal planning applied to hybrid systems and, in general, to nonlinear systems is completely out of scope for such tools. In this paper, we propose the use of explicit model checking-based techniques to solve universal planning problems on such hardly-approachable domains.
Several PDDL extensions such as PDDL2.1 [6] and PDDL+ [4] support planning with numeric variables that evolve as a function of time. Most planners are restricted to problems with linear or polynomial dynamics governing these variables [1] [3] [5] ; however, some planners can handle non-polynomial dynamics by discretizing time [7] [2] . While it may be technically possible to analytically model, for example, collision constraints among three-dimensional meshes using PDDL+, the resulting encoding would be enormous, far exceeding the demonstrated capabilities of current numeric planners.