A paper about trajectory optimization in hybrid systems. Interesting, as it relaxes would be naively been consider a core constraint of hybrid systems - the order at which vector fields are switched through. While specific for a rigid body, it provides a scablable numerical tool to optimizie over the ‘aggregate’ dynamics, rather than find optimal solutions in each vector field with a known ordering.
Link to Paper
Authors : Michael Posa, Cecilia Cantu, and Russ Tedrake
Journal : International Journal of Robotics Research.
Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Most state-of-the-art techniques treat the discontinuous dynamics of contact as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning through contact that eliminates the requirement for an a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem (LCP) for forward simulation, the proposed algorithm leverages Sequential Quadratic Programming (SQP) to naturally resolve contact constraint forces while simultaneously optimizing a trajectory and satisfying nonlinear complementarity constraints. The method scales well to high dimensional systems with large numbers of possible modes.We demonstrate the approach using three increasingly complex systems: rotating a pinned object with a finger, planar walking with the Spring Flamingo robot, and high speed bipedal running on the FastRunner platform.