Cooperative Periodic Coverage With Collision Avoidance

TL;DR

The paper addresses persistent, periodic coverage of a finite set of points by a multi-agent team under collision constraints, formulating a scalable solution that combines path planning, coverage-time optimization, and collision-free scheduling. It introduces a three-step divide-and-conquer approach: (i) plan individual closed paths, (ii) solve a quadratically constrained linear program to obtain optimal coverage times and actions, and (iii) solve a MILP to synchronize and schedule team plans while guaranteeing collision avoidance, with the results expressed relative to a period $T$ and using $Z(\\mathbf{q},t)$ and $Z^*(\\mathbf{q},t)$ to frame the coverage objective. The contributions include generalizing prior work to jointly determine paths, times, and actions, delivering a complete scheduling framework with collision guarantees, and validating the method both in simulation and through real-world experiments on mobile induction heating, demonstrating practical feasibility and tractability for meaningful problem sizes. The work advances persistent multi-agent coverage by enabling coordinated, time-bounded, collision-free operation and offering a concrete induction-heating application that highlights the method's potential for flexible, low-cost domestic systems. Mathematically, the solution hinges on solving a QC-LP to satisfy $\ abla P$-driven coverage with constraints like $\\sum_{i \\in \\mathcal{I}_{\\mathbf{q}}} \\rho_{i,j} \\theta_{i,j} = P^*(\\mathbf{q})$ and formulating a MILP to minimize simultaneous motion via $f_{schedule}$, all while preserving a consistent timeline through $A_{i,j}$, $D_{i,j}$, and modular timing variables.

Abstract

In this paper we propose a periodic solution to the problem of persistently covering a finite set of interest points with a group of autonomous mobile agents. These agents visit periodically the points and spend some time carrying out the coverage task, which we call coverage time. Since this periodic persistent coverage problem is NP-hard, we split it into three subproblems to counteract its complexity. In the first place, we plan individual closed paths for the agents to cover all the points. Second, we formulate a quadratically constrained linear program to find the optimal coverage times and actions that satisfy the coverage objective. Finally, we join together the individual plans of the agents in a periodic team plan by obtaining a schedule that guarantees collision avoidance. To this end, we solve a mixed integer linear program that minimizes the time in which two or more agents move at the same time. Eventually, we apply the proposed solution to an induction hob with mobile inductors for a domestic heating application and show its performance with experiments on a real prototype.

Figures (9)

• Figure 1: Example of scheduling. (a)-(b) Each row represents the plan of an agent. The points $\mathbf{q}_i$ that each agent covers are represented in different colors. The coverage times are depicted by the width of the colored rectangles and the gray rectangles represent the time needed to move between points. (c) Paths followed by the agents $i_1, i_2$ and $i_3$ in blue, red and green, respectively. The radius of the agents is $r_i=5$ units.
• Figure 2: Number of solutions found for the times and productions (dark blue) and for the scheduling (yellow).
• Figure 3: Mean calculation time of the coverage times and productions solving problem \ref{['Eq:QuadProgram']}. Each figure represents the results with a different cost function and different colors represent different number of agents.
• Figure 4: Mean calculation time of the scheduling solving Problem \ref{['Prob:Sched']}.
• Figure 5: Prototype of induction hob with mobile inductors.