Maximilian Raff successfully defended his Ph.D. with the title "Optimization and Continuation of Gaits and Other Non-Smooth Orbits".
Examination committee:
- Prof. Dr. C. David Remy
- Prof. Dr.-Ing. Christian Ebenbauer
- Assoc. Prof. Ludovic Righetti.
Abstract:
This dissertation develops mathematical tools to analyze and generate energy-economic locomotion patterns (gaits) in legged systems by exploiting their natural, unactuated dynamics. These unactuated periodic motions are considered energy-optimal behaviors and are framed as solutions to an inverse optimal control problem, where no actuation corresponds to minimal energy cost.
The work focuses on two main approaches. First, continuation methods are used to compute families of periodic motions in conservative hybrid systems that preserve quantities such as energy. In the absence of dissipation, these motions form continuous families parameterized by energy level, often emerging from simple motions such as equilibria.
Second, trajectory optimization is extended to include these passive motions through a parameterized approach that connects conservative and dissipative systems via a homotopy parameter. The resulting optimality conditions enable the use of continuation techniques to compute families of locally optimal gaits. Both direct and indirect solution methods are used, supported by a shooting approach.
Together, these tools provide a systematic framework for exploring how natural dynamics shape economic gaits in legged systems