Optimal control of compliant planar robot for safe impact using steepest descent technique

This study introduces a detailed mathematical modeling of a suggested compliant three-link planar robot. The modeling method is based on state-space representation, which allows a standard access to the interconnection of links with Variable Stiffness Actuator (VSA) by means of first-order differential equations. In these differential equations, the expression of the stiffness is derived in the time domain. In addition, the stiffness of VSA as control input exists in a dependent manner with state variables. An iterative numerical method is proposed, in which, the optimal trajectory of VSA is generated using steepest descent method. Besides this, the optimal feedback controller is designed to minimize the velocities of joints to avoid unsafe contact with the environment. Thus, the performance function was to minimize the velocities of joints and stiffness of VSA. The stabilization of joint velocities is achieved within the optimal feedback control system. A computer program is written to test the model and the proposed control method.