Curve Tracking Control Under State Constraints and Uncertainties

We study a class of steering control problems for free-moving particles tracking a curve in the plane and also in a three-dimensional environment, which are central problems in robotics. In the two-dimensional case, we provide adaptive controllers for curve tracking under unknown curvatures and control uncertainty. The system dynamics include a nonlinear dependence on the curvature, and are coupled with an estimator for the unknown curvature to form the augmented error dynamics. This nonlinear dependence puts our curvature identification objective outside the scope of existing adaptive tracking and parameter identification results that were limited to cases where the unknown parameters enter the system in an affine way. We prove input-to-state stability of the augmented error dynamics under polygonal state constraints and under suitable known bounds on the curvature and on the control uncertainty. When the uncertainty is zero, this ensures tracking of the curve and convergence of the curvature estimate to the unknown curvature. In the three-dimensional setting, we provide a new method to achieve curve tracking, identify unknown control gains, and maintain robust forward invariance of compact regions in the state space, under arbitrarily large perturbation bounds. Our new technique entails scaling certain control components