Using Clarke Transform to Create a Framework on the Manifold: From Sampling via Trajectory Generation to Control

TL;DR

This paper introduces a Clarke coordinate-based framework for continuum robots, enabling efficient planning, trajectory generation, and control on the manifold, demonstrated through simulation of a four-segment robot.

Contribution

It develops a modular, computationally efficient framework on the manifold for continuum robots using Clarke coordinates, linking joint space constraints to smooth trajectories.

Findings

Framework is modular, efficient, and branchless.

Smooth trajectories can be generated respecting kinematic constraints.

Simulation confirms the framework's effectiveness for a four-segment robot.

Abstract

We present a framework based on Clarke coordinates for spatial displacement-actuated continuum robots with an arbitrary number of joints. This framework consists of three modular components, i.e., a planner, trajectory generator, and controller defined on the manifold. All components are computationally efficient, compact, and branchless, and an encoder can be used to interface existing framework components that are not based on Clarke coordinates. We derive the relationship between the kinematic constraints in the joint space and on the manifold to generate smooth trajectories on the manifold. Furthermore, we establish the connection between the displacement constraint and parallel curves. To demonstrate its effectiveness, a demonstration in simulation for a displacement-actuated continuum robot with four segments is presented.