## Robotics Laboratory

The group has a long tradition in robotics research and runs a Robotics Lab. While initial research focused on trajectory optimization of industrial robots in production, but also in space, the attention now has shifted to the generation of efficient and open-loop stable motions for biologically inspired walking robots and to the study of biological gaits.

Problems investigated range from one-and two-legged hopping, walking and running robots to anthropomorphic models of track running and platform diving. The resulting mathematical models are hybrid periodic dynamic systems with multiple ODE or DAE phases and state variable discontinuities.

Since the stability of the resulting motion is of particular interest in this context, we develop methods to determine solutions of periodic optimal control problems that are open-loop stable. The criteria used in this context such as the spectral radius of the monodromy matrix of the periodic solution lead to non-differentiable functions involving first order derivatives of the non-smooth trajectories.