Impedance control of a non-linearly coupled tendon driven thumb

A large workspace and proper force capabilities of a robotic thumb can be obtained using a tensegrity structure for the actuation, similar to the human thumb base muscles. Using nonlinear stiffness elements and an antagonistic architecture, the joint stiffness can be adjusted by variation of the tendon pre-tension. However, the highly nonlinear actuation creates new control challenges and in particular the nonlinear tendon kinematics must be accounted for. Despite the challenges, the nonlinear structure is required to achieve the desired torques. In this paper, the dynamic equations of a tendon driven thumb are established. An efficient formulation is proposed to generate the pretension forces in order to preserve the torques and approximate the stiffness matrix. A cascaded structure is used for the controller. The equations for the inner tendon force control loop and the outer impedance control loop are presented. Because of the absence of link side position sensors, an iterative estimation algorithm is proposed and implemented in real-time. It is shown that, using the mechanical joint flexibility, the controller impedance gain can be adjusted to improve the steady-state effective impedance. The search algorithm robustness is evaluated through a set of simulations. Finally, experimental results and equivalent simulations demonstrate the effectiveness of our controller.