VFO feedback control using positively-invariant funnels for mobile robots travelling in polygonal worlds with bounded curvature of motion

Abstract

Feedback control of mobile robots guaranteeing preservation of state constraints resulting from obstacles in the environment and input constraints imposed by robot mechanical construction is essential in practical applications of robotic systems. The safety of motion execution is often ensured by a strategy of driving the robot through a sequence of funnels representing safe, positively invariant subsets of robot configuration space for utilized feedback control laws. In this paper, the VFO (Vector Field Orientation) control law is leveraged to develop such a feedback control strategy for a unicycle robot with bounded curvature of motion. The proposed definition of funnels arises naturally from analysis of the VFO control law under curvature constraints. Obstacles in the environment are handled by shrinking the funnels using additional artificial curvature constraints. An exact analytic method for computation of funnels is presented. To make the funnels positively-invariant and guarantee motion safety, the original VFO control law has been modified. In contrast to numerous methods available in the literature, proposed feedback control strategy ensures at least C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> continuity of the control signals during transitions between funnels. Effectiveness of our approach has been verified by simulations, during which the robot was driven through a sequence of funnels planned in the cluttered environment using the RRT* algorithm.