Smooth Spline-based Trajectory Planning for Semi-Rigid Multi-Robot Formations

This paper presents an approach for smooth trajectory planning in semi-rigid nonholonomic mobile robot formations using Bezier-splines. Unlike most existing approaches, the focus is on maintaining a semi-rigid formation, as required in many scenarios such as object transport, handling or assembly. We use a Relaxed A* planner to create an optimal collision-free global path and then smooth this path using splines. The smoothed global path serves to create target paths for every robot in the formation. From these paths, we then calculate the trajectories for each robot. In an iterative process, we match the velocities of the robots so that all trajectories are synchronized, and the dynamic limits of all robots are maintained. We provide experimental validation, which confirms no violation of the dynamic limits and shows an excellent control performance for a system of three robots moving at 0.3 m/s.