Closed-loop inverse kinematics under inequality constraints: Application to concentric-tube manipulators

In this paper, a novel closed-loop inverse kinematics scheme that is capable of handling inequality constraints is proposed. By a proper adoption of slack variables and using the task priority concept, the proposed method allows for the accommodation of inequality constraints in a closed-form inverse kinematics solution for robotic manipulators. Unlike other formulations, the proposed scheme does not require solving a sequence of constrained optimization problems in real time and in this sense is faster. The performance of the proposed scheme is investigated through an implementation for real-time control of a concentric-tube robot with a restricted operational space. The experimental results demonstrate the efficacy of the scheme in handling inequality constraints in real-time closed-loop inverse kinematics.