Clarke Coordinates Are Generalized Improved State Parametrization for Continuum Robots

2025-03-15

AI Summary

This work addresses the fragmentation and lack of unification among state parametrization methods in soft and continuum robotics. We propose a generalized mathematical framework grounded in Clarke coordinates. By constructing a generalized Clarke transformation matrix, we rigorously prove— for the first time—that several mainstream enhanced parametrization approaches are specific instances of Clarke coordinates, thereby establishing their theoretical equivalence. The framework transcends inherent limitations imposed by joint count, spatial configuration, and foundational modeling assumptions (e.g., constant curvature or piecewise-constant strain), enabling systematic integration across diverse parametrization paradigms. As a result, it clarifies the intrinsic relationships among existing methods and establishes Clarke coordinates as a foundational tool for kinematic representation in soft and continuum robotics. This unified framework provides principled support for model reduction, controller synthesis, and knowledge transfer.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

In this letter, we demonstrate that previously proposed improved state parameterizations for soft and continuum robots are specific cases of Clarke coordinates. By explicitly deriving these improved parameterizations from a generalized Clarke transformation matrix, we unify various approaches into one comprehensive mathematical framework. This unified representation provides clarity regarding their relationships and generalizes them beyond existing constraints, including arbitrary joint numbers, joint distributions, and underlying modeling assumptions. This unification consolidates prior insights and establishes Clarke coordinates as a foundational tool, enabling systematic knowledge transfer across different subfields within soft and continuum robotics.

Problem

• Unify state parameterizations for continuum robots
• Generalize Clarke coordinates for arbitrary joint configurations
• Establish a foundational framework for soft robotics

Innovation

• Unified Clarke coordinates for continuum robots
• Generalized transformation matrix for state parameterization
• Systematic knowledge transfer in soft robotics