Exponential stabilization of the rolling sphere

In this paper we present a non-smooth controller for exponential stabilization of the sphere. This has remained an open problem despite significant progress in nonholonomic systems. Our control design is based on inputs in a rotating coordinate frame that individually produce primitive motions of the sphere along straight lines and circular arcs. The rotating coordinate frame is chosen in concert with Euler angle description of orientation and placement of the desired configuration at the singularity of the representation. In our paper, we separately establish global stability of the desired configuration and exponential convergence. Our theoretical claims are validated through numerical simulations.

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