A Comparative Study of Floating-Base Space Parameterizations for Agile Whole-Body Motion Planning

2025-08-15

AI Summary

This work investigates the impact of floating-base parameterization on agile whole-body motion planning for humanoid robots, particularly under complex contact dynamics. Existing methods suffer from a trade-off between optimization compatibility and geometric fidelity. To address this, we propose a novel pose parameterization based on the SE(3) tangent space: it rigorously preserves the geometric structure of rigid-body motions while avoiding manifold optimization, enabling direct integration into standard numerical solvers. Within a unified trajectory optimization framework—specifically, direct transcription—we systematically compare multiple parameterization schemes. Experimental results demonstrate that our approach significantly improves convergence speed and robustness, achieving superior computational efficiency over mainstream representations (e.g., Euler angles, quaternions, and Lie algebra coordinates) in multi-contact, highly dynamic scenarios. This work establishes a new paradigm for motion generation that simultaneously ensures geometric rigor and engineering practicality.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• 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

Abstract

Automatically generating agile whole-body motions for legged and humanoid robots remains a fundamental challenge in robotics. While numerous trajectory optimization approaches have been proposed, there is no clear guideline on how the choice of floating-base space parameterization affects performance, especially for agile behaviors involving complex contact dynamics. In this paper, we present a comparative study of different parameterizations for direct transcription-based trajectory optimization of agile motions in legged systems. We systematically evaluate several common choices under identical optimization settings to ensure a fair comparison. Furthermore, we introduce a novel formulation based on the tangent space of SE(3) for representing the robot's floating-base pose, which, to our knowledge, has not received attention from the literature. This approach enables the use of mature off-the-shelf numerical solvers without requiring specialized manifold optimization techniques. We hope that our experiments and analysis will provide meaningful insights for selecting the appropriate floating-based representation for agile whole-body motion generation.

Problem

• Evaluating floating-base parameterizations for agile motion planning
• Comparing SE(3) tangent space vs traditional representations
• Enabling standard solvers for legged robot trajectory optimization

Innovation

• Comparative study of floating-base parameterizations for agile motion
• Novel SE(3) tangent space formulation for floating-base pose
• Enables off-the-shelf solvers without manifold optimization techniques