Reduction and Identification for Hybrid Dynamical Models of Terrestrial Locomotion

Dynamic interaction between an agent and an environment inevitably involves intermittent contact, for instance between limbs and terrain, hands and objects, or multiple coordinating agents. The hybrid dynamical system that models this interaction is complex, generally comprised of combinatorial numbers of discrete operating modes corresponding to the nonlinear dynamics of distinct contact configurations. Drawing inspiration from biological locomotion, we focus on rhythmic interactions that may be encoded as periodic orbits in this hybrid system, and find simple and robust criteria for model order reduction of such behaviors. In particular, we show that the dynamics near a hybrid periodic orbit are generically approximated by an invariant subsystem that is equivalent to a classical dynamical system. The appearance of this reduced-order model enables the translation of identification tools from classical dynamical systems theory to the hybrid setting, providing a computational bridge between the efforts of biologists and engineers studying terrestrial locomotion.

Sam Burden is a PhD candidate in EECS at UC Berkeley advised by Prof. Shankar Sastry. He studies locomotion and manipulation in robotics and biomechanics using novel tools from hybrid systems theory.