The Surprising Effectiveness of Linear Models for Whole-Body Model-Predictive Control

2025-09-22

AI Summary

This study investigates the necessity boundary of nonlinear dynamics modeling in legged robot motion control. Addressing the limitations of conventional approaches—which rely on online nonlinear dynamics computation and complex trajectory planning—we propose a whole-body model predictive control (MPC) framework based on linear time-invariant (LTI) dynamics approximation, eliminating the need for real-time nonlinear equation solving or matrix inversion. Our key contribution is a rigorous demonstration that, across a broad range of operating conditions, a simplified LTI model suffices to achieve high-dynamic locomotion: stable walking, strong disturbance rejection, and goal-directed navigation on a quadrupedal robot; dynamic walking on a hydraulic humanoid; and robust performance despite significant simulation-to-reality gaps. These results challenge the prevailing assumption that precise nonlinear dynamics models are indispensable for legged control, establishing a new paradigm for efficient, lightweight whole-body controller design.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Model-Based Reasoning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

When do locomotion controllers require reasoning about nonlinearities? In this work, we show that a whole-body model-predictive controller using a simple linear time-invariant approximation of the whole-body dynamics is able to execute basic locomotion tasks on complex legged robots. The formulation requires no online nonlinear dynamics evaluations or matrix inversions. We demonstrate walking, disturbance rejection, and even navigation to a goal position without a separate footstep planner on a quadrupedal robot. In addition, we demonstrate dynamic walking on a hydraulic humanoid, a robot with significant limb inertia, complex actuator dynamics, and large sim-to-real gap.

Problem

• Investigating when locomotion controllers need nonlinear dynamics modeling
• Developing linear model-predictive control for complex legged robot locomotion
• Validating controller performance on quadruped and hydraulic humanoid robots

Innovation

• Linear time-invariant model for whole-body dynamics
• No online nonlinear dynamics evaluations required
• No matrix inversions in the formulation