Singular-perturbation-based sliding mode control with practical slackness prevention for elastic antagonistic...

This paper investigates robust tracking and practical slackness prevention for elastic antagonistic cable-driven joints. A representative elbow joint of a 7-DOF cable-driven manipulator (CDM) is considered because it has a typical motor, cable and joint coupling structure. A coupled dynamic model is established by considering cable elasticity, motor dynamics, joint motion, and the positive cable tension condition. Based on singular perturbation theory, the dynamics are separated into slow joint motion and fast cable tension dynamics. For the slow dynamics, sliding mode control with a tangent barrier gain within the singular perturbation framework (SP-tanBGSMC) is developed to improve tracking robustness and constrain the sliding variable. For the fast dynamics, a fast loop deformation regulator is introduced to restrict cable deformation and support positive cable tension within a prescribed margin. The analysis yields ultimate bounds for the slow loop variables and practical boundedness of the overall closed loop system. Simulations and representative experiments support robust tracking and practical preservation of the cable deformation constraint under the tested conditions; the experiments provide positive model-based tension estimates, while the simulation with a displacement disturbance on the motor side supports practical slackness prevention.