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A Reachability Tree-Based Algorithm for Robot Task and Motion Planning

Kanghyun Kim, Daehyung Park, Min Jun Kim

TL;DR

The paper addresses the challenge of integrating abstract task planning with geometric motion feasibility in TAMP by introducing a reachability-tree framework with three hierarchical layers: TP (abstract action sequence sampling via MCTS and symbolic planning), SS (subgoal and attachment sampling), and MP (geometric trajectory sampling). It leverages rewards from MP to bias MCTS in TP and pre-generates geometrically feasible goal candidates to accelerate search. Empirical evaluation on Kitchen, Non-monotonic, and Blocktower benchmarks shows the method achieving higher success rates and faster planning than baselines and PDDLStream, especially in geometry-tight or task-constrained scenarios. This approach preserves task constraints in the abstract domain while efficiently exploring the geometric space, offering practical improvements for scalable TAMP in complex manipulation scenarios.

Abstract

This paper presents a novel algorithm for robot task and motion planning (TAMP) problems by utilizing a reachability tree. While tree-based algorithms are known for their speed and simplicity in motion planning (MP), they are not well-suited for TAMP problems that involve both abstracted and geometrical state variables. To address this challenge, we propose a hierarchical sampling strategy, which first generates an abstracted task plan using Monte Carlo tree search (MCTS) and then fills in the details with a geometrically feasible motion trajectory. Moreover, we show that the performance of the proposed method can be significantly enhanced by selecting an appropriate reward for MCTS and by using a pre-generated goal state that is guaranteed to be geometrically feasible. A comparative study using TAMP benchmark problems demonstrates the effectiveness of the proposed approach.

A Reachability Tree-Based Algorithm for Robot Task and Motion Planning

TL;DR

The paper addresses the challenge of integrating abstract task planning with geometric motion feasibility in TAMP by introducing a reachability-tree framework with three hierarchical layers: TP (abstract action sequence sampling via MCTS and symbolic planning), SS (subgoal and attachment sampling), and MP (geometric trajectory sampling). It leverages rewards from MP to bias MCTS in TP and pre-generates geometrically feasible goal candidates to accelerate search. Empirical evaluation on Kitchen, Non-monotonic, and Blocktower benchmarks shows the method achieving higher success rates and faster planning than baselines and PDDLStream, especially in geometry-tight or task-constrained scenarios. This approach preserves task constraints in the abstract domain while efficiently exploring the geometric space, offering practical improvements for scalable TAMP in complex manipulation scenarios.

Abstract

This paper presents a novel algorithm for robot task and motion planning (TAMP) problems by utilizing a reachability tree. While tree-based algorithms are known for their speed and simplicity in motion planning (MP), they are not well-suited for TAMP problems that involve both abstracted and geometrical state variables. To address this challenge, we propose a hierarchical sampling strategy, which first generates an abstracted task plan using Monte Carlo tree search (MCTS) and then fills in the details with a geometrically feasible motion trajectory. Moreover, we show that the performance of the proposed method can be significantly enhanced by selecting an appropriate reward for MCTS and by using a pre-generated goal state that is guaranteed to be geometrically feasible. A comparative study using TAMP benchmark problems demonstrates the effectiveness of the proposed approach.
Paper Structure (20 sections, 6 equations, 5 figures, 4 algorithms)

This paper contains 20 sections, 6 equations, 5 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Manipulation Planning Problem
  4. Problem Definition
  5. Notations
  6. Object $o$, Movable object $m$, Robot $r$
  7. Attachment $\alpha$
  8. Mode $\sigma$
  9. Abstract state $s$
  10. Abstract action $a$
  11. Hybrid state $x$
  12. State transition
  13. Our Planning Algorithm$^*$
  14. Task Planning Layer (Alg. \ref{['tplayer']})
  15. Action Sequence Sampler (Alg. \ref{['acseqsampler']})
  16. ...and 5 more sections

Figures (5)

  • Figure 1: Manipulation planning problems often involve tight geometric constraints as well as task-level planning. (a) In the kitchen domain, the robot needs to cook a given food block after washing it. (b) We propose an algorithm to build a reachability tree with hybrid states using three layers of planning hierarchies towards task and motion planning problems.
  • Figure 2: Our algorithm maintains two trees: (a) The reachability tree (RT) tracks all reachable states from the initial state, and (b) the abstract reachability tree (ART) is an abstraction of the reachability tree, with each node containing multiple RT nodes.
  • Figure 3: (a) TP layer utilizes MCTS and a symbolic planner to sample an action sequence. (b) The RT extension is guided by the sampled action sequence. When the extension fails, the SS layer calculates a reward.
  • Figure 4: (a) Non-monotonic domain. (b) Blocktower domain.
  • Figure 5: The comparison result of the proposed planner, two baseline planners (no-reward, no-rejection), and PDDLStream. The results are expressed as a cumulative distribution function.