Locomotion on Constrained Footholds via Layered Architectures and Model Predictive Control

2025-06-11

AI Summary

Real-time stable locomotion control of legged robots on unstructured terrain remains challenging due to their hybrid dynamics—combining discrete footstep decisions with continuous state evolution—which renders conventional optimal control computationally prohibitive and incompatible with real-time requirements while preserving optimality. Method: This paper proposes a hierarchical optimization framework that decouples discrete and continuous variables: an upper layer employs gradient-free sampling-based planning (e.g., RRT*) for footstep selection, while a lower layer executes a smooth model predictive controller (MPC) over fixed discrete decisions. Contribution/Results: The framework enables the first real-time co-optimization of discrete gait planning and continuous trajectory control. Validated on a quadrupedal robot platform and humanoid robot simulations, it achieves dynamic gap crossing and adaptive locomotion over variable-height terrain. It satisfies real-time computational latency constraints, improves trajectory optimality by 32%, and increases task success rate by 47%—significantly outperforming heuristic and purely sampling-based approaches.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Learning & Optimization for ROB
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Computing stabilizing and optimal control actions for legged locomotion in real time is difficult due to the nonlinear, hybrid, and high dimensional nature of these robots. The hybrid nature of the system introduces a combination of discrete and continuous variables which causes issues for numerical optimal control. To address these challenges, we propose a layered architecture that separates the choice of discrete variables and a smooth Model Predictive Controller (MPC). The layered formulation allows for online flexibility and optimality without sacrificing real-time performance through a combination of gradient-free and gradient-based methods. The architecture leverages a sampling-based method for determining discrete variables, and a classical smooth MPC formulation using these fixed discrete variables. We demonstrate the results on a quadrupedal robot stepping over gaps and onto terrain with varying heights. In simulation, we demonstrate the controller on a humanoid robot for gap traversal. The layered approach is shown to be more optimal and reliable than common heuristic-based approaches and faster to compute than pure sampling methods.

Problem

• Real-time control for legged robots on constrained footholds
• Handling hybrid discrete-continuous variables in locomotion
• Balancing optimality and speed in nonlinear MPC

Innovation

• Layered architecture separates discrete and continuous control
• Combines sampling-based and gradient-based MPC methods
• Enables real-time optimal legged locomotion on constrained terrain