Multi-robot Motion Planning based on Nets-within-Nets Modeling and Simulation

TL;DR

This work tackles motion planning for a heterogeneous multi-robot team under a global mission specified in a co-safe LTL formula. It introduces the High-Level robot team Petri Net (HLrtPN) within the Nets-within-Nets framework, with SpecOPN for the mission and RobotOPNs for each robot, all synchronized through a System net via a Global Enabling Function (GEF). The approach is implemented and validated through Renew-based simulations across two case studies, including a hospital scenario, demonstrating scalability to eight robots and favorable comparison with alternative DES methods. The HLrtPN offers a modular, simulation-based path-planning framework that accommodates heterogeneity and complex task ordering, though it is not guaranteed to be globally optimal and may require further work on time constraints and deadlock avoidance.

Abstract

This paper focuses on designing motion plans for a heterogeneous team of robots that must cooperate to fulfill a global mission. Robots move in an environment that contains some regions of interest, while the specification for the entire team can include avoidance, visits, or sequencing of these regions of interest. The mission is expressed in terms of a Petri net corresponding to an automaton, while each robot is also modeled by a state machine Petri net. The current work brings about the following contributions with respect to existing solutions for related problems. First, we propose a novel model, denoted High-Level robot team Petri Net (HLrtPN) system, to incorporate the specification and robot models into the Nets-within-Nets paradigm. A guard function, named Global Enabling Function, is designed to synchronize the firing of transitions so that robot motions do not violate the specification. Then, the solution is found by simulating the HLrtPN system in a specific software tool that accommodates Nets-within-Nets. Illustrative examples based on Linear Temporal Logic missions support the computational feasibility of the proposed framework.

Figures (5)

• Figure 1: Illustrative example supporting the intuitive explanation of the Nets-within-nets formalism, portraying the (ii) System net including 2 types of object nets: (i) Specification Object Petri net and (iii) Robotic Object Petri net
• Figure 2: Example of a partitioned environment into 5 cells in set $\mathcal{P}$ including 4 ROIs ($y_1$ - purple, $y_2$ - blue, $y_3$ - green, and the free space $y_4$ - white) and 3 robots initially placed in $y_4$. The orange line represents the robotic trajectories for the mission $\varphi = \diamondsuit b_1 \wedge \diamondsuit b_2 \wedge \diamondsuit b_3 \wedge \left(\neg b_1~\mathcal{U}~b_3\right)$ (meaning to visit $y_1, y_2, y_3$, with $y_3$ before $y_1$)
• Figure 3: The Global Enabling Function (GEF)
• Figure 4: The object nets of the HLrtPN: (a) RobotOPN modeling the robots evolving in the environment in Fig. \ref{['fig:env']}: two of the robots ($r_1$ and $r_2$) can move freely in the workspace, thus being represented by the entire Petri net with all 5 places; robot $r_3$ is not allowed to enter the overlapped region between $y_2$ and $y_3$ (the Petri net representation is based only on 4 places, by removing the place, arcs and transitions with red border); (b) SpecOPN: the marked path (with dark orange) corresponds to the shortest solution for ensuring the robot mission) considering
• Figure 5: Environment layout for the Case-study 2 considering a hospital scenario with three floors and 12 rooms ($q = 12$) for a multi-robot system with 8 robots ($n = 8$). The synchronous movements of the robots are highlighted by the same color of the rooms, considering the MRI procedure, i.e., yellow ($y_3, y_6$), green ($y_1, y_2$), blue ($y_4, y_6$).

Theorems & Definitions (5)

• Definition 3.1
• Definition 5.1: SpecOPN
• Definition 5.2: RobotOPN
• Definition 6.1
• Example 6.2