Path following with a security margin for mobile robots

This paper addresses the problem of determining a feedback control law, rob ust 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 curvatu re is defined as a new state variable. The control variables are the linear velocity and the derivative of the curvature. By defining a sliding manifo ld we determine a stabilizing controller for the nominal system, that is wh en the exact configuration is supposed to be known. Then, we prove that the system remains stable when the feedback control inputs use estimated value s instead of the exact values, and we characterize the control robustness w ith respect to localization and curvature estimation errors. The control ro bustness is expressed by determining a bounded attractive domain containing the configuration error as the closed-loop control is performed with the e stimated state values. Two control laws are successively proposed. The form er is deduced from Lyapunov's direct method, and the latter is based on var iable structure control techniques. Using variable structure control we sho w that the size of the attractive domain can be easily minimized while keep ing the balance between short response time, low output oscillation, and la rge stability domain. Knowledge of this attractive domain allows us to comp ute easily a security margin to guarantee obstacle avoidance during the pat h following process. Experimental results are presented at the end of the p aper.