Dynamic Bipedal MPC with Foot-level Obstacle Avoidance and Adjustable Step Timing

TL;DR

This paper introduces a real-time MPC framework for bipedal robots that enhances obstacle avoidance by dynamically adjusting step timing and planning foot trajectories around obstacles, improving navigation in unstructured environments.

Contribution

It presents novel formulations for adaptive step timing and 3D foot-avoidance that implicitly select swing trajectories, advancing obstacle avoidance capabilities in bipedal robotics.

Findings

Effective obstacle avoidance demonstrated on Cassie and Digit robots.

Improved body and foot safety through convex decomposition and mixed-integer programming.

Successful hardware implementation on Digit robot.

Abstract

Collision-free planning is essential for bipedal robots operating within unstructured environments. This paper presents a real-time Model Predictive Control (MPC) framework that addresses both body and foot avoidance for dynamic bipedal robots. Our contribution is two-fold: we introduce (1) a novel formulation for adjusting step timing to facilitate faster body avoidance and (2) a novel 3D foot-avoidance formulation that implicitly selects swing trajectories and footholds that either steps over or navigate around obstacles with awareness of Center of Mass (COM) dynamics. We achieve body avoidance by applying a half-space relaxation of the safe region but introduce a switching heuristic based on tracking error to detect a need to change foot-timing schedules. To enable foot avoidance and viable landing footholds on all sides of foot-level obstacles, we decompose the non-convex safe region on the ground into several convex polygons and use Mixed-Integer Quadratic Programming to determine the optimal candidate. We found that introducing a soft minimum-travel-distance constraint is effective in preventing the MPC from being trapped in local minima that can stall half-space relaxation methods behind obstacles. We demonstrated the proposed algorithms on multibody simulations on the bipedal robot platforms, Cassie and Digit, as well as hardware experiments on Digit.