Modeling and Control of Dynamical Systems with Active Singularities and Sensing in a Singular Motion Phase

Dynamical systems with active, or controlled, singularities are characterized by constraints, either naturally present or created through actuation, capable of radically changing the attainability set of the post-impact system state. The latter is achieved through the admission of the impulsive control actions during the system engagement with the constraint. The goal of the present work is: i) to introduce the first description of mechanical systems with controlled singularities and sensing in the singular phase that admits control over observations, and ii) to demonstrate on an example the computation of a sensor-based optimal control law in the singular phase. It is shown that the optimal control in this class of problems gives rise to new concepts: the interlaced singular phase and the multi-impulse control signal.