Abstract
The multi-robot path planning aims to explore a set of non-colliding paths with the shortest sum of lengths for multiple robots. The most popular approach is to artificially decompose the map into discrete small grids before applying heuristic algorithms. To solve the path planning in continuous environments, we propose a decentralized two-stage algorithm to solve the path-planning problem, where the obstacle and inter-robot collisions are both considered. In the first stage, an obstacle- avoidance path-planning problem is mathematically developed by minimizing the travel length of each robot. Specifically, the obstacle-avoidance trajectories are generated by approximating the obstacles as convex-concave constraints. In the second stage, with the given trajectories, we formulate a quadratic programming (QP) problem for velocity control using the control barrier and Lyapunov function (CBF-CLF). In this way, the multi-robot collision avoidance as well as time efficiency are satisfied by adapting the velocities of robots. In sharp contrast to the conventional heuristic methods, path length, smoothness and safety are fully considered by mathematically formulating the optimization problems in continuous environments. Extensive experiments as well as computer simulations are conducted to validate the effectiveness of the proposed path-planning algorithm.
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