Dual-MPC Footstep Planning for Robust Quadruped Locomotion

TL;DR

This work tackles robust quadruped locomotion by addressing angular momentum control missing from GRF-centric approaches. It introduces a dual-model predictive control framework that couples a footstep MPC with a GRF MPC in a mutual feedback loop, enabling coordinated optimization of footstep placement and ground reaction forces. The key contributions are the dual-input, coupled formulation for angular momentum tracking, iterative convergence between the two MPCs, and demonstrated robustness across asymmetric friction, wrench disturbances, and deformable grass terrain on a Unitree GO1, with real-time computability. The approach reduces body-state oscillations and extends stance and swing phases, yielding practical improvements for real-world, on-board quadruped locomotion under varied conditions.

Abstract

In this paper, we propose a footstep planning strategy based on model predictive control (MPC) that enables robust regulation of body orientation against undesired body rotations by optimizing footstep placement. Model-based locomotion approaches typically adopt heuristic methods or planning based on the linear inverted pendulum model. These methods account for linear velocity in footstep planning, while excluding angular velocity, which leads to angular momentum being handled exclusively via ground reaction force (GRF). Footstep planning based on MPC that takes angular velocity into account recasts the angular momentum control problem as a dual-input approach that coordinates GRFs and footstep placement, instead of optimizing GRFs alone, thereby improving tracking performance. A mutual-feedback loop couples the footstep planner and the GRF MPC, with each using the other's solution to iteratively update footsteps and GRFs. The use of optimal solutions reduces body oscillation and enables extended stance and swing phases. The method is validated on a quadruped robot, demonstrating robust locomotion with reduced oscillations, longer stance and swing phases across various terrains.

Figures (9)

• Figure 1: Illustration of the proposed method. The GRF and predicted GRF correspond to the solutions of the GRF MPC. The friction pyramid represents the GRF inequality constraint. The footstep denotes the swing-leg solution obtained from the footstep MPC, where the equality constraint is the current footstep of the stance leg, and the inequality constraint corresponds to the footstep inequality constraint.
• Figure 2: Overall locomotion architecture.
• Figure 3: Experimental setup. (a) Asymmetric friction terrain composed of high and low friction surfaces. The left side is the low-friction surface, while the right side is the high-friction surface. (b) The F/T sensor is mounted at a location offset along the x-axis from the CoM.
• Figure 4: Experimental results of locomotion on asymmetric friction terrain, showing desired values and states. (a) Velocity in body frame. (b) Roll, pitch, and yaw. (c) Angular velocity.
• Figure 5: Boxplots of GRFs for each leg during locomotion, comparing the proposed method with the baseline.