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Effort Allocation for Deadline-Aware Task and Motion Planning: A Metareasoning Approach

Yoonchang Sung, Shahaf S. Shperberg, Qi Wang, Peter Stone

TL;DR

This work proposes an effort allocation problem, formulated as a Markov decision process (MDP), to find a plan that can be executed within the deadline despite uncertain planning and execution times, and formally proves the NP-hardness of the problem by reducing it from the knapsack problem.

Abstract

In robot planning, tasks can often be achieved through multiple options, each consisting of several actions. This work specifically addresses deadline constraints in task and motion planning, aiming to find a plan that can be executed within the deadline despite uncertain planning and execution times. We propose an effort allocation problem, formulated as a Markov decision process (MDP), to find such a plan by leveraging metareasoning perspectives to allocate computational resources among the given options. We formally prove the NP-hardness of the problem by reducing it from the knapsack problem. Both a model-based approach, where transition models are learned from past experience, and a model-free approach, which overcomes the unavailability of prior data acquisition through reinforcement learning, are explored. For the model-based approach, we investigate Monte Carlo tree search (MCTS) to approximately solve the proposed MDP and further design heuristic schemes to tackle NP-hardness, leading to the approximate yet efficient algorithm called DP_Rerun. In experiments, DP_Rerun demonstrates promising performance comparable to MCTS while requiring negligible computation time.

Effort Allocation for Deadline-Aware Task and Motion Planning: A Metareasoning Approach

TL;DR

This work proposes an effort allocation problem, formulated as a Markov decision process (MDP), to find a plan that can be executed within the deadline despite uncertain planning and execution times, and formally proves the NP-hardness of the problem by reducing it from the knapsack problem.

Abstract

In robot planning, tasks can often be achieved through multiple options, each consisting of several actions. This work specifically addresses deadline constraints in task and motion planning, aiming to find a plan that can be executed within the deadline despite uncertain planning and execution times. We propose an effort allocation problem, formulated as a Markov decision process (MDP), to find such a plan by leveraging metareasoning perspectives to allocate computational resources among the given options. We formally prove the NP-hardness of the problem by reducing it from the knapsack problem. Both a model-based approach, where transition models are learned from past experience, and a model-free approach, which overcomes the unavailability of prior data acquisition through reinforcement learning, are explored. For the model-based approach, we investigate Monte Carlo tree search (MCTS) to approximately solve the proposed MDP and further design heuristic schemes to tackle NP-hardness, leading to the approximate yet efficient algorithm called DP_Rerun. In experiments, DP_Rerun demonstrates promising performance comparable to MCTS while requiring negligible computation time.
Paper Structure (26 sections, 1 theorem, 10 equations, 6 figures, 2 tables, 1 algorithm)

This paper contains 26 sections, 1 theorem, 10 equations, 6 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Task and motion planning
  4. Resource-constrained planning
  5. Metareasoning
  6. Problem Formulation
  7. TAMP formulation
  8. Effort allocation for deadline-aware TAMP problems
  9. An MDP model
  10. Theoretical Analysis
  11. Model-Based Approach
  12. Monte Carlo Tree Search
  13. Heuristics
  14. Model-Free Approach
  15. Example Scenarios
  16. ...and 11 more sections

Key Result

Theorem 1

Finding the optimal policy for the effort allocation problem is NP-hard.

Figures (6)

  • Figure 1: Example of an effort allocation problem.
  • Figure 2: Visualization of domains used in the example scenarios.
  • Figure 3: Problem instances designed for the experiments.
  • Figure 4: Total computation time comparison between MCTS and DP_Rerun.
  • Figure 5: Performance comparison between MCTS and DP_Rerun when both methods are given the same computation time.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Definition 1: Knapsack problem GareyJohnsson