Time-Efficient Path Planning for Semi-Rigid Multi-Robot Formations

In this paper, we propose a novel approach for execution and planning-time efficient path planning for a formation of robots moving in complex indoor environments. Our approach combines the Voronoi Diagram (VD) with spline-based path planning to create smooth paths with limited curvature. We also incorporate free spaces into the VD to reduce the maximum curvature of the paths. Due to the high obstacle clearance enabled by VDs and the reduced curvature, we can reach higher velocities, given a permissible control error. Our simulation evaluation uses 200 randomly generated paths and compares the results with a splined Relaxed A* path planner. Our method saves several seconds for a 70-meter-long path with significantly reduced tracking error. These results demonstrate the potential of our approach for time-efficient path planning in complex indoor environments.

I. Introduction

Robot formations consisting of multiple mobile robots are often employed to extend the capabilities of a single robot or to break down complex tasks into simpler subtasks [1]. These formations can be used to transport objects that would otherwise be too heavy, big, or delicate for a single mobile robot. In many cooperative object transport scenarios, it is necessary to maintain a rigid or semi-rigid formation, which requires the relative pose of the individual robots to stay constant. Any violation of the formation can introduce unwanted forces into the carried object. However, maintaining fixed distances in a multi-robot formation is practically impossible due to measurement errors, latency and hardware limitations. This is especially true for nonholonomic robots, as their relative pose can only be maintained in parallel formation or on straight lines [2]. One possible solution to the difficulty in maintaining fixed distances is to equip the robots with bearings or manipulators that decouple the platform from the object. But even with this decoupling, the permissible deviations are limited by the distance to obstacles or the decoupling system's range. Therefore, the permissible control error becomes a limiting factor when trying to increase the formation's velocity along the path (path velocity).