Finite-time Guiding Vector Fields for Accelerated Path Following of Nonholonomic Robots

Abstract

Guiding vector fields (GVFs) have been widely applied in robotic path-following control. However, most, if not all, of the existing studies derive control algorithms that only render the path-following error asymptotically converging to zero, while more stringent time constraints on the path-following error convergence have not been fully studied. In this paper, by introducing a signum-based function, we propose a finite-time GVF that enables a nonholonomic robot to follow an arbitrary smooth nD desired path within a finite time. Note that the finite time is dependent on the initial condition and can be computed in advance. In practical applications, we design a controller based on the proposed GVF for the unicycle model. This controller drives a nonholonomic robot’s velocity to align with that of the GVF within a finite time. In addition, we introduce the extension of the proposed GVF to the distributed motion coordination among an arbitrary number of robots. Finally, we conduct two experiments using unmanned ground vehicles to validate the effectiveness of the proposed algorithms.