Singularity-Free Guiding Vector Field Over Bézier's Curves Applied to Rovers Path Planning and Path Following

This paper presents a guidance algorithm for solving the problem of following parametric paths, as well as a curvature-varying speed setpoint for land-based car-type wheeled mobile robots (WMRs). The guidance algorithm relies on singularity-free guiding vector fields (SF-GVFs). This novel guiding vector field (GVF) approach expands the desired robot path and the GVF to a higher dimensional space, in which an angular control function can be found to ensure global asymptotic convergence to the desired parametric path while avoiding field singularities. In SF-GVF, paths should follow a parametric definition. This feature makes using Bezier's curves attractive to define the robot's desired path. The curvature-varying speed setpoint, combined with the guidance algorithm, eases the convergence to the path when physical restrictions exist, such as minimal turning radius or maximal lateral acceleration. We provide theoretical results, simulations, and outdoor experiments using a WMR platform assembled with off-the-shelf components. The small rover (WMR) selected provides an easy-to-use nonholonomic platform for the experiments. The results could be extrapolated to full-scale or more complex vehicles, providing the necessary vehicle control system adaptations, while the GVF algorithm would remain the same.