Deformable Multibody Modeling for Model Predictive Control in Legged Locomotion with Embodied Compliance

2025-04-28

AI Summary

This work addresses dynamic gait instability in embodied compliant legged robots—particularly quadrupeds with rigid–flexible hybrid spines. To this end, we propose a deformable multibody modeling framework that unifies the coupled dynamics of rigid and flexible components. Our key contribution is the novel centroidal composite predicted deformed inertia (CCPDI) tensor, the first formulation enabling seamless integration of flexible multibody dynamics into standard model predictive control (MPC) architectures. The method synergistically combines deformable modeling, centroidal momentum theory, and real-time derivation of deformed inertia. Experimental results demonstrate that, under identical MPC configurations, our approach simultaneously stabilizes trotting gaits for both rigid- and flexible-spine robots. Furthermore, ground reaction force distributions align more closely with balance-inspired heuristics, and the controller exhibits robustness against reasonable perturbations in critical parameters.

Technology Category

• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Natural Language Processing: Safety and Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

The paper presents a method to stabilize dynamic gait for a legged robot with embodied compliance. Our approach introduces a unified description for rigid and compliant bodies to approximate their deformation and a formulation for deformable multibody systems. We develop the centroidal composite predictive deformed inertia (CCPDI) tensor of a deformable multibody system and show how to integrate it with the standard-of-practice model predictive controller (MPC). Simulation shows that the resultant control framework can stabilize trot stepping on a quadrupedal robot with both rigid and compliant spines under the same MPC configurations. Compared to standard MPC, the developed CCPDI-enabled MPC distributes the ground reactive forces closer to the heuristics for body balance, and it is thus more likely to stabilize the gaits of the compliant robot. A parametric study shows that our method preserves some level of robustness within a suitable envelope of key parameter values.

Problem

• Stabilizing dynamic gait for legged robots with compliance
• Unified modeling of rigid and compliant body deformation
• Integrating deformable multibody dynamics with model predictive control

Innovation

• Unified rigid-compliant body deformation modeling
• CCPDI tensor for deformable multibody systems
• MPC integration with CCPDI for gait stabilization