Clarke Transform: A Lingua Franca for Continuum Robotics

Robotics can be viewed as the art of transformations between spaces. Therefore, the roboticist's knowledge and intuition about these spaces and their interconnections are essential for avoiding inefficient and opaque ad hoc solutions, which hinder reproducibility and progress within the community. It is argued that limitations in reproducibility and benchmarking in continuum robotics stem from the absence of principled transformations, which leads to inconsistent and incompatible representations across different approaches. In this article, the role of transformations is revisited, and common pitfalls arising from inadequate abstractions and parameterizations are identified. The recently introduced Clarke transform and the associated Clarke coordinates demonstrate how such challenges can be systematically addressed. In particular, they enable a linear, low‐dimensional parameterization for a broad class of robot morphologies, referred to as displacement‐actuated continuum robots. Furthermore, this parameterization facilitates standardization, enables benchmarking, improves reuse, and enhances interpretability. More broadly, principled transformations are positioned as a prerequisite for systematic benchmarking and as a key enabler of reproducibility and sustainable progress in continuum robotics.