Stiffness Control of a Continuum Manipulator in Contact with a Soft Environment

Stiffness control of a continuum robot can prevent excessive contact forces during robot navigation inside delicate, uncertain and confined environments. Furthermore, it enables the selection of tip stiffnesses that match varying task requirements. This paper introduces a computationally-efficient approach to continuum-robot stiffness control that is based on writing the forward kinematic model as the product of two transformations. The first transformation calculates the non-contact kinematics of the robot and can be formulated based on the specific type of continuum robot under consideration. The second transformation calculates the tip deflection due to applied forces and is efficiently computed using the special Cosserat rod model. To implement a desired tip stiffness, the two transformations are used to solve for the actuator positions that deform the manipulator so as to generate the required tip force at the measured tip position. The efficacy of the proposed controller is demonstrated experimentally on a concentric-tube continuum robot.