VFO Path following Control with Guarantees of Positionally Constrained Transients for Unicycle-Like Robots with Constrained Control Input

Abstract

The Vector-Field-Orientation (VFO) method is a control design concept which was originally introduced for the unicycle kinematics to solve two classical control tasks corresponding to the trajectory tracking and set-point control problems. A unified solution to both the tasks was possible by appropriate definitions of the so-called convergence vector field. So far, there has not been a version of the VFO control law for the third classical control task concerning the path following problem, which is particularly meaningful in the context of practical applications. The paper fills this gap by presenting a novel VFO path following controller devised for robots of unicycle-like kinematics with the amplitude-limited control input. Opposite to most path following controllers proposed in the literature, the new control law utilizes the recently introduced level curve approach which does not employ any parametrization of a reference path. In this way, the proposed solution is free of main limitations resulting from the need of unique determination of the shortest distance from a robot to the path. In contrast to other solutions, a formal analysis of the closed-loop dynamics presented in this paper provides sufficient conditions which guarantee constrained transients of robot motion with the position confined to a prescribed subset around a reference path. Theoretical results have been validated by numerical examples and experimentally verified with utilization of a laboratory-scale differentially driven robot.