Non-linear phase different control for precise output force of bi-articularly actuated manipulators

Bi-articular actuators – actuator spanning two joints – play fundamental role in robot arms designed under the human musculoskeletal actuation paradigm. Unlike kinematic redundancy, actuator redundancy resulting from bi-articular actuation brings advantages such as increasing stability, reducing link's inertia, and decreasing non-linearity of the end-effector force with respect to the force direction. The traditional phase different control (PDC) resolves actuator redundancy on the basis of a linearized model derived from measured human muscle activity. Such linear model produces a non-zero error in calculation between a desired output force and necessary inputs. In this paper, the non-linear phase different control (NLPDC) is proposed to resolve actuator redundancy with no error. The maximum end-effector force of BiWi, bi-articularly actuated, and wire-driven arm, is measured using both PDC and NLPDC. When the robot arm moves towards singular configurations, the measured error in output force remains within the modeling error if using NLPDC, while such error increases significantly for PDC. Furthermore, unlike PDC, the proposed NLPDC allows design of joint stiffness and torque independently, reduction of necessary total muscle input force, and precise calculation of maximum output force.