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Optimal Task and Motion Planning for Autonomous Systems Using Petri Nets

Zhou He, Shilong Yuan, Ning Ran, Dimitri Lefebvre

TL;DR

This paper tackles task and motion planning (TAMP) for autonomous systems subject to Boolean specifications by modeling the problem with Petri nets (TAMP‑PN). It introduces a two‑stage approach: offline model simplification to a compact simplified PN and offline construction of an extended basis reachability graph (EBRG), followed by online planning that uses an ILP to select a target marking and backtracks on the EBRG to recover an optimal transition sequence with minimal cost $w^T\cdot \mathbf{y}_{\sigma}$. The authors prove that the offline reduced model preserves optimality via projection, and that online planning remains efficient due to the compact EBRG representation. Experiments on a realistic factory-like scenario and scalability tests demonstrate substantially improved computational efficiency and scalability compared with ILP and simulated annealing approaches, enabling real-time TAMP as the environment and agent count grow.

Abstract

This study deals with the problem of task and motion planning of autonomous systems within the context of high-level tasks. Specifically, a task comprises logical requirements (conjunctions, disjunctions, and negations) on the trajectories and final states of agents in certain regions of interest. We propose an optimal planning approach that combines offline computation and online planning. First, a simplified Petri net system is proposed to model the autonomous system. Then, indicating places are designed to implement the logical requirements of the specifications. Building upon this, a compact representation of the state space called extended basis reachability graph is constructed and an efficient online planning algorithm is developed to obtain the optimal plan. It is shown that the most burdensome part of the planning procedure may be removed offline, thanks to the construction of the extended basis reachability graph. Finally, series of simulations are conducted to demonstrate the computational efficiency and scalability of our developed method.

Optimal Task and Motion Planning for Autonomous Systems Using Petri Nets

TL;DR

This paper tackles task and motion planning (TAMP) for autonomous systems subject to Boolean specifications by modeling the problem with Petri nets (TAMP‑PN). It introduces a two‑stage approach: offline model simplification to a compact simplified PN and offline construction of an extended basis reachability graph (EBRG), followed by online planning that uses an ILP to select a target marking and backtracks on the EBRG to recover an optimal transition sequence with minimal cost . The authors prove that the offline reduced model preserves optimality via projection, and that online planning remains efficient due to the compact EBRG representation. Experiments on a realistic factory-like scenario and scalability tests demonstrate substantially improved computational efficiency and scalability compared with ILP and simulated annealing approaches, enabling real-time TAMP as the environment and agent count grow.

Abstract

This study deals with the problem of task and motion planning of autonomous systems within the context of high-level tasks. Specifically, a task comprises logical requirements (conjunctions, disjunctions, and negations) on the trajectories and final states of agents in certain regions of interest. We propose an optimal planning approach that combines offline computation and online planning. First, a simplified Petri net system is proposed to model the autonomous system. Then, indicating places are designed to implement the logical requirements of the specifications. Building upon this, a compact representation of the state space called extended basis reachability graph is constructed and an efficient online planning algorithm is developed to obtain the optimal plan. It is shown that the most burdensome part of the planning procedure may be removed offline, thanks to the construction of the extended basis reachability graph. Finally, series of simulations are conducted to demonstrate the computational efficiency and scalability of our developed method.
Paper Structure (15 sections, 5 theorems, 4 equations, 2 figures, 3 tables, 2 algorithms)

This paper contains 15 sections, 5 theorems, 4 equations, 2 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. State of the art
  3. Preliminary
  4. Petri net model for TAMP
  5. Task specification
  6. Problem formulation
  7. Model simplification
  8. Planning procedure
  9. Monitored PN model
  10. Off-line computation of extended basis reachability graph
  11. On-line planning strategy
  12. Experiment Results
  13. Case study
  14. Scalability results
  15. Conclusion

Key Result

Lemma 1

There exists a solution $\sigma^\star$ to Problem problem1 iff there exists a sequence $\sigma_s^\star$ in $Q^s$ such that

Figures (2)

  • Figure 1: PN model for TAMP.
  • Figure 2: Planning results for task $\varphi_1$.

Theorems & Definitions (11)

  • Example 1
  • Definition 1
  • Lemma 1
  • Definition 2
  • Lemma 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Proposition 1
  • Proposition 2
  • ...and 1 more