Impedance Optimization for Uncertain Contact Interactions Through Risk Sensitive Optimal Control

TL;DR

This paper develops a risk-sensitive optimal control method to compute impedance schedules for legged robots, improving contact interaction handling under uncertainty by balancing disturbance rejection and measurement noise.

Contribution

It extends stochastic optimal control to include measurement uncertainty in contact location estimation, enabling more robust impedance modulation for legged locomotion.

Findings

Enhanced contact force regulation during early contact phases

Improved stability and performance in jumping and trotting tasks

Adaptive impedance modulation based on contact state and impact anticipation

Abstract

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