A Fixed–Time Positional Path–Following Control System for Unicycle–Like Mobile Robots with Constrained Inputs: Design and Robustness

This paper presents a fixed-time solution to the positional path-following control task for unicycle-like mobile robots with constraints imposed on the control inputs. The proposed control system, designed for a guidance point located out of the robot wheels’ axle, guarantees local convergence of a positional error for a guidance point in finite time which is upper bounded by a constant (independent of an initial robot configuration). Apart from control derivation and a stability proof conducted for closed-loop dynamics, the paper includes also a robustness analysis which reveals how the fixed-time control function improves robustness of the closed-loop system to external perturbations affecting the control input channels of a robot. Numerical simulations and experimental results validate the concept, and also highlight some computational and implementation issues important in practical applications.