Recent Advances in the Time-Freezing Reformulation for Numerical Optimal Control of Dynamic Systems with State Jumps

Armin Nurkanović

University of Freiburg

Tuesday, December 21, 2021, 11:00 - 12:00


This talk gives an overview of some of the recent advances within the time-freezing reformulation. The main idea of time-freezing is to introduce a clock state and an auxiliary dynamic system whose trajectory endpoints satisfy the state jump law. When the auxiliary system is active, the clock state is not evolving, hence by taking only the parts of the trajectory when the clock state was active, we can recover the original solution.

In particular, we present a novel approach to derive auxiliary dynamics where multiple state jumps, triggered by nonlinear constraints, can be treated. Thereby we improve our previous work, where only linear constraints and special cases of multiple sate jumps could be treated. Moreover, we introduce extension of the time-freezing reformulation for complementarity Lagrangian systems with state jumps (most widely used to model rigid bodies with impact, e.g., robotic systems). We cover not only the easier case of elastic impacts, but also the difficult case, when after the state jump the system evolves on the boundary of the dynamic's feasible set. In nonsmooth mechanics this corresponds to inelastic impacts. We discuss how to resolve contact breaking and frictional impacts without slipping. The theoretical findings will be illustrated on tutorial examples.
Meeting-ID: 627 9173 7415
Password: syscop2021