Compliance computation for continuum types of robots

This paper presents a mathematical formulation for calculation of the compliance of continuum type of robots. The mathematical model of the continuum robot is built following the Cosserat rod theory and focuses on a single section Cosserat rod under arbitrary loading. The compliance of the robot is described as a set of ordinary differential equations with split boundary conditions. This new set of compliance equations is directly coupled to the solution of the forward kinematics of the robot. After solving the forward kinematics problem, these solutions can be directly used to compute the compliance. A particular class of continuum robots in which the compliance of the robot can be formulated as an initial value problem and solved in a single numerical integration is discussed. The paper provides experimental validation of the proposed method.