Spline-based Path Planning and Reconfiguration for Rigid Multi-Robot Formations

Abstract

This paper presents an approach for continuous path planning in rigid formations containing nonholonomic mobile robots using Beziér-splines. Unlike most existing approaches, the focus is on maintaining a rigid formation, as required in many scenarios such as object transport, handling or assembly. In these scenarios, a constant distance between the individual robots must be kept to avoid damaging the transported object. Also, limitations regarding the velocity and acceleration of each robot have to be taken into account, as every robot traverses in a slightly different path. Especially the distance from the center of the formation to an individual robot has a big impact on the path a mobile robot has to move on to comply with the formation constraints during an orientation change of the formation. Therefore, we use splines to control and optimize the curvature of the formation’s path and limit the velocity and acceleration. The usage of splines requires the calculation of specific support points that can be interpolated. To achieve this, we calculate the formation’s diameter, including the transported object and adjust the inflation radius of the global costmap. To guarantee a collision-free movement from the start to the target position, we use an existing path planner to generate an initial path. The employed Relaxed-A*-Algorithm provides fast computation and an almost optimal initial path, although this path is not continuous. From this path, we extract a number of support points based on the size of the formation. We then fit a fifth-degree Beziér-spline through these points to smooth the discontinuous path. The final result is a computationally efficient, smooth and jerk-limited path that induces minimal disturbances to the formation control. Also, this approach allows us to continuously transition from one formation to another, which can be used to pass narrow passages. To valid the path planning approach presented in this study we showcase simulative and experimental results.