Geometric Gait Optimization for Kinodynamic Systems Using a Lie Group Integrator

2025-04-27

AI Summary

This work addresses gait optimization and motion planning for mobile systems with hybrid kinematic–dynamic characteristics—such as nonholonomic wheeled robots and biomimetic swimming robots. We propose a geometric modeling and optimization framework that unifies second-order dynamics with nonholonomic constraints. For the first time, we integrate Lie group numerical integrators with Lagrangian reduction, leveraging manifold symmetries to enable variational gait optimization. The framework supports anisotropic added inertia and fluid drag modeling, overcoming limitations of Euclidean-space-based optimization. Evaluated on roller racer, snakeboard, and Purcell swimmer platforms, our method efficiently generates diverse locomotion behaviors—including acceleration, steady-state cruising, steering, and smooth multi-gait transitions. Both simulation and physical experiments demonstrate high accuracy and strong generalizability across distinct underactuated, nonholonomic systems.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

This paper presents a gait optimization and motion planning framework for a class of locomoting systems with mixed kinematic and dynamic properties. Using Lagrangian reduction and differential geometry, we derive a general dynamic model that incorporates second-order dynamics and nonholonomic constraints, applicable to kinodynamic systems such as wheeled robots with nonholonomic constraints as well as swimming robots with nonisotropic fluid-added inertia and hydrodynamic drag. Building on Lie group integrators and group symmetries, we develop a variational gait optimization method for kinodynamic systems. By integrating multiple gaits and their transitions, we construct comprehensive motion plans that enable a wide range of motions for these systems. We evaluate our framework on three representative examples: roller racer, snakeboard, and swimmer. Simulation and hardware experiments demonstrate diverse motions, including acceleration, steady-state maintenance, gait transitions, and turning. The results highlight the effectiveness of the proposed method and its potential for generalization to other biological and robotic locomoting systems.

Problem

• Optimizing gaits for kinodynamic systems with mixed properties
• Modeling dynamics with nonholonomic constraints and fluid effects
• Planning diverse motions including transitions and turning

Innovation

• Lie group integrator for kinodynamic gait optimization
• Variational method integrating nonholonomic constraints
• Multi-gait motion planning for diverse locomotion