Parallel spring simplifies actuator output torque and improves feed-forward learning

In robotics, particularly legged locomotion, there are situations where high gain feedback is not applicable. It is dangerous and may conduce to instability of the robot. In such situations, presence of a feed-forward controller helps the tracking problem while maintaining stability. However, these controllers usually require the system dynamics which may not be available. Furthermore, There are also situations where the frequency response of the actuator output torque is limited and may not be able to produce torques with high variations. In cases of unknown system dynamics, learning feed-forward scheme has been proposed which requires high number of basis functions according to system and trajectory. In this paper we propose a method that employs parallel spring in order to reduce higher frequency components of the actuator output torque. Moreover, the added spring will simplify the process of learning by reducing number of basis functions. Adaptive parallel spring is proposed for the case where different periodic motions are given to the system. Our simulations results on a two-link manipulator show that the adaptive spring will gradually simplify actuator output torque and improve feed-forward learning.