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

TL;DR

The paper tackles collision-free locomotion for dynamic bipeds in unstructured environments by presenting a real-time MPC framework that jointly handles body and foot avoidance. It introduces two key innovations: an adaptive stepping-time mechanism that speeds body avoidance and a 3D foot-avoidance formulation via MIQP that can select swing-foot trajectories to either step over or navigate around ground obstacles, guided by COM dynamics. The method integrates an ellipse-based collision region to account for obstacle velocity, employs a soft minimum-travel-distance constraint to avoid local minima, and leverages an OSC for robust tracking at high frequencies. Validation includes simulations on Cassie and Digit, with hardware experiments on Digit demonstrating practical viability and improved dodging performance, suggesting significant potential for real-world humanoid navigation in dynamic environments.

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.

Figures (7)

• Figure 1: (A) Bipedal robots must avoid dynamic and foot-level obstacles in their environment. (B) A Digit humanoid using model-predictive control (MPC) to step over foot-level obstacles.
• Figure 2: Block diagram for the presented controller. (1) MPC computes a collision-free CoM and Feet trajectory at 50-200Hz. (2) The Operational Space Controller computes the torques necessary to track the MPC reference at 1kHz. (3) An EKF is implemented to estimate base states.
• Figure 3: (A) A LIPM-based MPC is implemented to generate collision-free trajectories. (B) The approximation is improved by linearizing constraints around a trajectory from the previous MPC solution. (C) We used a half-space relaxation with slack variables to model the collision-free regions 10341951.
• Figure 4: (A) The avoidance direction computed based on the ellipse-based method is more effective by considering obstacle's velocity. (B) The step timing of the next step can be adjusted based on the MPC foothold tracking error.
• Figure 5: Illustration of our swing foot 3D obstacle avoidance: (1) We use Mixed Integer Quadratic Programming to select foothold from the decomposed safe region represented by a quadrant. (2) Height constraints is imposed along the swing foot trajectory to achieve collision avoidance in 3D.