Impedance Optimization for Uncertain Contact Interactions Through Risk Sensitive Optimal Control

This paper addresses the problem of computing optimal impedance schedules for\nlegged locomotion tasks involving complex contact interactions. We formulate\nthe problem of impedance regulation as a trade-off between disturbance\nrejection and measurement uncertainty. We extend a stochastic optimal control\nalgorithm known as Risk Sensitive Control to take into account measurement\nuncertainty and propose a formal way to include such uncertainty for unknown\ncontact locations. The approach can efficiently generate optimal state and\ncontrol trajectories along with local feedback control gains, i.e. impedance\nschedules. Extensive simulations demonstrate the capabilities of the approach\nin generating meaningful stiffness and damping modulation patterns before and\nafter contact interaction. For example, contact forces are reduced during early\ncontacts, damping increases to anticipate a high impact event and tracking is\nautomatically traded-off for increased stability. In particular, we show a\nsignificant improvement in performance during jumping and trotting tasks with a\nsimulated quadruped robot.\n