Path following with a security margin for mobile robots

This paper addresses the problem of determining a feedback control law, robust with respect to localization errors, allowing a mobile robot to follow a prescribed path. The model that we consider is a dynamic extension of the usual kinematic model of a mobile robot in the sense that the path curvature is defined as a new state variable. The control variables are the linear velocity and the derivative of the curvature. By defining a sliding manifold we determine a stabilizing controller for the nominal system, that is when the exact configuration is supposed to be known. Then, we prove that the system remains stable when the feedback control inputs use estimated values instead of the exact values, and we characterize the control robustness with respect to localization and curvature estimation errors. The control robustness is expressed by determining a bounded attractive domain containing the configuration error as the closed-loop control is performed with the estimated state values. Two control laws are successively proposed. The former is deduced from Lyapunov's direct method, and the latter is based on variable structure control techniques. Using variable structure control we show that the size of the attractive domain can be easily minimized while keeping the balance between short response time, low output oscillation, and large stability domain. Knowledge of this attractive domain allows us to compute easily a security margin to guarantee obstacle avoidance during the path following process. Experimental results are presented at the end of the paper.