Multigoal output regulation via supervisory control: Application to stabilization of a unicycle

We consider the problem of robust output regulation for nonlinear systems in the following sense: given a system with input disturbances, we are interested in steering one output to zero while tolerating an steady-state error on the second output. In other words, we are interested in input-output (asymptotic) stability for one output and practical (asymptotic) stability for the second. Upon the assumption that we dispose of two controllers each of which achieves separately a control objective (for either output) we propose a switching rule to commute between the two controllers appropriately i.e., conserving the input-output stability, to some extent. The problem studied is reminiscent of different concrete situations such as simultaneaous synchronization and tracking control of mechanical systems; in this article we revisit the problem of stabilizing a unicycle (regulation of the first output) towards a point while ensuring obstacle-collision avoidance (practical stabilization of the second output).