Abstract
The area of continuum robotics is showing potential in a variety of applications including surgical robotics, search and rescue operations, manufacturing, and assembly. Shape-changing mechanisms provide the theoretical tools for the synthesis of spatial chains of rigid bodies that position themselves along curves of any complexity. This article introduces a method for generating the backbone of a continuum robot that closely approximates a given spatial curve. The approach combines the kinematic model of the continuum robot, which operates under the constant curvature assumption, with the design profile and target profile concepts from established spatial shape-changing mechanism theory. This approach involves an analysis of the accessibility of the terminal orientation of the spatial curve, which subsequently identifies a rapid synthesis method. This method facilitates the creation of a backbone with a predetermined number of segments that closely aligns with the tangential direction of the reference points of the target profile while simultaneously approximating the target profile itself. Optimization techniques demonstrate the efficacy of using the generated backbone of the rapid approximation method as the initial design for the optimization. In a situation where a close approximation is not needed at interim steps, optimization is not needed to provide a displacement sequence to move the robot.
