Optimal control strategies for maximizing the performance of Variable Stiffness Joints with nonlinear springs

A very young robotics research topic is the use of elastic elements in joints to increase their performance. The idea of attaching the robot link to the motor via elastic elements is especially motivated by the possibility to store potential energy in the springs, which enables movement types that could not be implemented with rigid joints. After our recent results on the relation between the spring's potential energy and the optimal control strategy for realising explosive motions using adjustable linear springs with a velocity-controlled motor, we extend in this paper these results to elastic joints with adjustable nonlinear springs. In particular, we build up on the method we first introduced for analysing Variable Stiffness Actuators with fixed motor positions and consider now additionally the control from the motor side. The application of the method is illustrated by investigating serial elastic joints as well as variable stiffness joints with nonlinear springs and it is shown how optimal control strategies for linear systems such as periodic bang-bang excitations with the system's resonant frequency, change in this more general setting to energy-dependent excitations.