Geometric Gait Optimization for Kinodynamic Systems Using a Lie Group Integrator
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909595620868096 |
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| author | Yang, Yanhao Hatton, Ross L. |
| author_facet | Yang, Yanhao Hatton, Ross L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19072 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Gait Optimization for Kinodynamic Systems Using a Lie Group Integrator Yang, Yanhao Hatton, Ross L. Robotics 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. |
| title | Geometric Gait Optimization for Kinodynamic Systems Using a Lie Group Integrator |
| topic | Robotics |
| url | https://arxiv.org/abs/2504.19072 |