Synthesis of a stabilizing feedback for a wheeled robot with constrained control resource

Stabilization of motion of a wheeled robot with constrained control resource by means of a continuous feedback linearizing the closed-loop system in a neighborhood of the target path is considered. We pose the problem of finding the feedback coefficients such that the phase portrait of the nonlinear closed-loop system is topologically equivalent to that of a linear system with a stable node, with the asymptotic rate of decrease of the deviation from the target path being as high as possible. On this family, we pose the problem of minimization of “overshooting” for arbitrary initial conditions. The solution of this optimization problem is proved to be a limit discontinuous control law. A hybrid control law is proposed that, on the one hand, ensures the desired properties of the phase portrait and minimal overshooting and, on the other hand, does not result in a chattering inherent in systems with discontinuous feedbacks.