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Parallel decomposition and concurrent satisfaction for heterogeneous multi-robot task and motion planning under temporal logic specifications

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Abstract

This paper presents an automaton-based task and motion planning framework for multi-robot systems (MRS) to satisfy finite words of linear temporal logic (LTL) task specifications in parallel and concurrently. A parallel decomposition algorithm is developed to iteratively decompose a global task specification into a set of smaller subtask automata. Robots are assigned to the smallest task component in each subtask automaton. The capability transition system of the assigned robots and these subtask automata synthesize a corresponding set of subtask planning automata (SPA), each of which is either an independent satisfaction of an individual subtask automaton or a concurrent satisfaction of multiple subtask automata. The overall robot assignments and SPA can guarantee the MRS to satisfy all the subtask automata. Each SPA can generate a minimal cost task plan by taking into account the costs of multi-robot tasking. The robots then plan motions to execute the tasks associated with the minimal cost task plans. The proposed framework is demonstrated with a multi-robot experiment for manufacturing tasks in a lab setting. Extensive numerical simulations are also performed to evaluate the scalability, computational complexity, and execution efficiency of the proposed framework and show its advantages over the centralized task and motion planning strategy.

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Code Availability

The source code of the framework and experiment is shown in the repository of the link https://github.com/huanfez/Parallel_Task_Decomposition_Planning

Notes

  1. A co-safety LTL specification can be converted into a DFA by first using open source toolboxes “spot”: https://spot.lrde.epita.fr/app/ to derive a deterministic Büchi automaton (DBA) and further removing the suffix satisfying LTL for infinite times.

  2. The cost depends on the task objective and can be in different forms, such as the estimated time or energy consumption to complete a task. In (Wang et al. 2018; Zheng et al. 2018), we associated the estimated human trust in robots, a multi-dimensional metrics composed value, to evaluate the cost.

  3. Note that we assume the optimal robot assignment is an effective assignment, which means the assignment can synthesize a non-empty SPA and provide a task planning solution. In the actual application, the system with a robot assignment may not output a viable task planning solution. We will not consider such an assignment as an effective one. More details can be found in the experiment section.

  4. We perform the offline triangulation for the working environment with the package in the link: https://www.cs.cmu.edu/~quake/triangle.html

  5. The robot assignments {r3}, {r4} output an empty task planning solution for subtask automaton G1. Hence, they will not be the effective assignments of subtask automaton G1.

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Funding

This work was partially supported by the Air Force Office of Scientific Research (AFOSR) Young Investigator Research Program (YIP) under grant no. FA9550-17-1-0050.

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Authors and Affiliations

  1. Clemson University, Mechanical Engineering Department, Clemson, SC, 29634, USA

    Huanfei Zheng & Yue Wang

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  1. Huanfei Zheng
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  2. Yue Wang
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Huanfei Zheng. The first draft of the manuscript was written by Huanfei Zheng and Yue Wang.

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Correspondence to Yue Wang.

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This work was partially supported by the Air Force Office of Scientific Research (AFOSR) Young Investigator Research Program (YIP) under grant no. FA9550-17-1-0050.

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Zheng, H., Wang, Y. Parallel decomposition and concurrent satisfaction for heterogeneous multi-robot task and motion planning under temporal logic specifications. Discrete Event Dyn Syst 32, 195–230 (2022). https://doi.org/10.1007/s10626-021-00355-z

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