Hybrid control of spherical orientation

We propose a hybrid controller ensuring robust global asymptotic stability of a desired spherical orientation in a kinematic setting-a task that is impossible by continuous or memoryless discontinuous state-feedback due to topological obstructions. The hybrid control structure relies on hysteretically switching between locally stabilizing control laws that are generated by a “synergistic” family of potential functions. We propose a parametrized diffeomorphism as a means of generating such a synergistic family. This construction is accomplished by composing an existing potential function with the diffeomorphism invoked with different parameters, thus generating new potential functions that have different critical behavior. A salient feature of the construction is that it can produce a synergistic family of potential functions from a single potential function.