Near Time-Optimal Real-Time Path Following Under Error Tolerance and System Constraints

Abstract

An online fast path following control algorithm subject to contouring error tolerance and other prototypical constraints, analogous to a racing car within track boundaries, is presented. A receding horizon quadratic programming (QP) for real-time implementation on electromechanical systems is proposed. A key feature of the algorithm is that the challenging constrained minimal-time optimization is approximated by minimizing the distance between an unattainable target and actual location when moving along the contour, mimicking pursuing rabbit lures in greyhound racing. Modeling errors and other uncertainties in implementation are compensated for by observer state feedback, which provides real-time updates of initial states for every receding horizon optimization. Applying the proposed online method, the requirement of an accurate model from conventional offline trajectory planning methods is relaxed. The proposed method is demonstrated by experimental results from a 1 kHz sampling rate implementation on a multi-axis nanolithographic position system.