Combined Task and Motion Planning Via Sketch Decompositions (Extended Version with Supplementary Material)

TL;DR

This work addresses the challenge of integrating symbolic task planning with continuous motion planning in TAMP by introducing a width-1 sketch-based decomposition that enables interleaved problem solving. The approach uses SIW$_R$ with a hand-crafted four-rule sketch to partition tasks into subproblems that are solved via IW(1) and local sampling, with MoveIt!-driven feasibility checks (InArmWorkspace, InverseKinematics, MotionPlan) guiding ground actions. Key contributions include a general sketch width-1 formulation for pick-and-place TAMP, adaptive sampling, lazy action-validation, and an incremental IW variant ( Lazy-SIIW$_R$ ), demonstrated on benchmarks like Sorting Objects, Non-Monotonic, and Words, where it outperforms several PDDLStream-based and planning methods in planning time and scalability. The results show complete solving of benchmark instances with favorable plan quality and emphasize the practical benefit of local subproblem sampling and backtracking restricted to subproblems, enabling ROS-integrated, scalable interleaved TAMP. The work also outlines extensions to learning sketches, partial observability, and post-processing optimizations for motion planning.

Abstract

The challenge in combined task and motion planning (TAMP) is the effective integration of a search over a combinatorial space, usually carried out by a task planner, and a search over a continuous configuration space, carried out by a motion planner. Using motion planners for testing the feasibility of task plans and filling out the details is not effective because it makes the geometrical constraints play a passive role. This work introduces a new interleaved approach for integrating the two dimensions of TAMP that makes use of sketches, a recent simple but powerful language for expressing the decomposition of problems into subproblems. A sketch has width 1 if it decomposes the problem into subproblems that can be solved greedily in linear time. In the paper, a general sketch is introduced for several classes of TAMP problems which has width 1 under suitable assumptions. While sketch decompositions have been developed for classical planning, they offer two important benefits in the context of TAMP. First, when a task plan is found to be unfeasible due to the geometric constraints, the combinatorial search resumes in a specific sub-problem. Second, the sampling of object configurations is not done once, globally, at the start of the search, but locally, at the start of each subproblem. Optimizations of this basic setting are also considered and experimental results over existing and new pick-and-place benchmarks are reported.

Figures (2)

• Figure 1: Examples of TAMP considered in this work: Sorting Objects (left), Non-Monotonic (middle), and Words (right).
• Figure 2: Different grasps (a), SOPs (b), and calls to InArmWorkspace (c), InverseKinematics (d), and MotionPlan (e) functions.