Optimal Design of Nonlinear Series Elastic Actuator for Minimization of Actuator Power

In this paper, we propose a methodology to optimize the nonlinear stiffness of nonlinear Series Elastic Actuators (SEAs). The nonlinear restoring forces of the springs are optimized in order to minimize the mechanical power of the actuators of the SEAs. We define the cost function as the time average of the square of the actuator power, and use a 3 order Hermite interpolation to parameterize the restoring force of the nonlinear springs. The cost function is optimized using a Sequential Quadratic Programming (SQP) algorithm. We detail the bounds on the design parameters and the nonlinear optimization constraints. We show an example of optimal design in the case of a 3 Degree Of Freedom (DOF) manipulator, and in the last section we show that the optimal nonlinear springs calculated for this manipulator can be realized using a non-circular cable-spool mechanism.