Multi-Rate Nonlinear Model Predictive Control for Wall-Supported Bipedal Locomotion of Quadrupedal Robots

2026-07-01

AI Summary

This work addresses the challenges of bipedal locomotion against walls for quadrupedal robots in constrained environments, where coordinated contact planning and center-of-mass trajectory generation are hindered by nonlinear dynamics and unilateral contact constraints. To overcome these issues, the authors propose a multi-rate nonlinear model predictive control (MR-NMPC) framework with a hierarchical structure: a high-level planner jointly optimizes discrete foot contacts and continuous center-of-mass and orientation trajectories using a single rigid-body model, while a low-level nonlinear whole-body controller tracks the generated references via virtual constraints. By embedding contact planning directly within the optimal control formulation and eliminating heuristic foothold selection, the approach significantly enhances dynamic stability and terrain adaptability. Experiments on the Unitree A1 platform demonstrate a 2.9-fold increase in success rate compared to conventional MPC under rough terrain and external disturbances.

Abstract

This paper presents a novel layered planning and control framework based on multi-rate nonlinear model predictive control (MR-NMPC) that enables quadrupedal robots to perform hybrid bipedal locomotion with wall-assisted support in constrained environments. Real-time trajectory optimization for this locomotion presents significant challenges, as the controller must simultaneously plan for both the contact points and the continuous trajectories of the robot's center of mass (CoM) and orientation within the robot's nonlinear dynamics while accounting for unilateral contact constraints, underactuation, and the switching nature of the robot's dynamics. At the high level of the control framework, an MR-NMPC is proposed, which dynamically plans both the discrete-time trajectories of the contact points and the continuous-time trajectories of the CoM and orientation, using a single rigid body (SRB) dynamics model. By incorporating contact-point planning within the multi-rate optimal control framework, this approach enhances dynamic stability compared to heuristic foot placement strategies. At the low level of the control framework, a nonlinear whole-body controller (WBC) based on virtual constraints and a quadratic program enforces full-order dynamics and tracks the MR-NMPC references. The proposed approach is validated through extensive numerical simulations demonstrating the robust wall-assisted bipedal locomotion of a Unitree A1 quadrupedal robot on rough terrains and under external disturbances in a constrained environment. Comparative analysis shows that the proposed MR-NMPC achieves a 2.9 times higher success rate compared to conventional MPC with heuristic-based foot placement strategies in negotiating irregular terrain at high speeds.

Problem

• bipedal locomotion
• wall-supported
• quadrupedal robots
• trajectory optimization
• nonlinear dynamics

Innovation

• multi-rate NMPC
• wall-supported bipedal locomotion
• contact-point planning
• nonlinear whole-body control
• quadrupedal robot