Enlarging the region of stability using the torque-enhanced active SLIP model

One of the most significant outcomes of bio-inspired robotics research studies is that simple spring-mass models can accurately represent legged locomotion with various sizes and morphologies and hence the legged robots. Specifically, the Spring-Loaded Inverted Pendulum (SLIP) model became a well-known tool among the biologists and robotics researchers due to its simplicity and explanatory nature. Nevertheless, SLIP model has non-integrable system dynamics, which prevents derivation of exact analytical solutions to its dynamics despite its simple nature. In this paper, we propose a torque-enhanced active SLIP (TA-SLIP) model to support partial feedback linearization on nonlinear dynamics of the SLIP model. A linear and rotary actuator is used in TA-SLIP model to inject or remove energy from the system both to support analytic solution of the system dynamics and to control the locomotion. We also investigate the stability of the TA-SLIP model and show that the proposed model increases the region of stability with respect to original SLIP model.