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]: Considerable effort has been spent extending the scope of planning beyond propositional domains to include, for example, time and numbers. Each extension has been designed as a separate specific semantic enrichment of the underlying planning model, with its own syntax and customised integration into a planning algorithm. Inspired by work on SAT Modulo Theories (SMT) in the SAT community, we develop a modelling language and planner that treat arbitrary first order theories as parameters. We call the approach Planning Modulo Theories (PMT). We introduce a modular language to represent PMT problems and demonstrate its benefits over PDDL in expressivity and compactness. We present a generalisation of the hmax heuristic that allows our planner, PMTPlan, to automatically reason about arbitrary theories added as modules. Over several new and existing benchmarks, exploiting different theories, we show that PMTPlan can significantly out-perform an existing planner using PDDL models.

[2]: Mobile manipulation requires to solve multiple subproblems. One is planning in high-dimensional configuration spaces, that we approach in this work. We decompose the manipulation problem into a symbolic and a geometric part. The symbolic part is implemented as a classical symbolic planner that tightly integrates a geometric planner enabling us to efficiently generate correct plans. A probabilistic roadmap planner constitutes the geometric part. During the computation of the roadmap we utilize proximity queries to determine non-colliding configurations and to verify collision-free paths between configurations accurately and efficiently. We demonstrate experiments in two scenarios, one of these being the manipulator dexterity test scenario that was used in NIST's response robot evaluation in Disaster City.

[3]: Solving real-world problems using symbolic planning often requires a simplified formulation of the original problem, since certain subproblems cannot be represented at all or only in a way leading to inefficiency. For example, manipulation planning may appear as a subproblem in a robotic planning context or a packing problem can be part of a logistics task. In this paper we propose an extension of PDDL for specifying semantic attachments. This allows the evaluation of grounded predicates as well as the change of fluents by externally specified functions. Furthermore, we describe a general schema of integrating semantic attachments into a forward-chaining planner and report on our experience of adding this extension to the planners FF and Temporal Fast Downward. Finally, we present some preliminary experiments using semantic attachments.
Semantic attachments [3] [2] , functions computed by an external module, are an existing way of integrating blackbox procedures and PDDL planners. Condition-checker modules are used to test operator preconditions, and effect-applicator modules modify numeric state variables. Operators must be parameterized by variables with finite types, restricting the technique to domains with finite branching factors. Semantic attachments can only produce a single tuple of numeric outputs. Planning with semantic attachments requires modifying existing PDDL planners to evaluate the attachments during the search. This also results in many unneeded procedure calls, resulting in poor planner performance when the attachments are expensive. Planning Modulo Theories (PMT) [1] generalizes semantic attachments by supporting the composition of several modules through custom first-order theories.