In this paper, we consider an arbitrary number of joints and their arbitrary joint locations along the center line of a displacement-actuated continuum robot. To achieve this, we revisit the derivation of the Clarke transform leading to a formulation capable of considering arbitrary joint locations. The proposed modified Clarke transform opens new opportunities in mechanical design and algorithmic approaches beyond the current limiting dependency on symmetric arranged joint locations. By presenting an encoder-decoder architecture based on the Clarke transform, joint values between different robot designs can be transformed enabling the use of an analogous robot design and direct knowledge transfer. To demonstrate its versatility, applications of control and trajectory generation in simulation are presented, which can be easily integrated into an existing framework designed, for instance, for three symmetric arranged joints.

翻译：本文研究位移驱动连续体机器人中心线上任意数量关节及其任意位置分布的问题。为此，我们重新推导克拉克变换，提出能够处理任意关节位置的新型表述形式。所改进的克拉克变换突破了当前对对称关节排布方式的局限性依赖，为机械设计与算法研究开辟了新途径。通过构建基于克拉克变换的编码器-解码器架构，可实现不同机器人构型间关节参数的相互转换，从而支持类比机器人设计并促进知识直接迁移。为验证其普适性，本文展示了仿真环境中的控制与轨迹生成应用案例，该方案可便捷地集成至现有框架（例如专为三个对称关节设计的系统）中。