Optimized energy addition for a planar slip model with redundant joints

The planar and energetically conservative Spring-Loaded Inverted Pendulum (SLIP) model with a linear spring has been modified in recent years to include an articulated knee, friction and contact losses, and energy thrusts during stance to stabilize forward velocity and hopping height. The work presented here advances the SLIP template toward a biological anchor by adding a third parallel articulating joint, which provides redundancy in the inverse kinematics solution space. Instead of one actuator into which an energy thrust can be added, the total thrust can be distributed between two actuators operating on the lower two leg joints (the hip joint remains passive during stance as in the original SLIP model). It is shown that a careless distribution of the thrust can lead to significant energy loss, so an offline search protocol is presented as a general approach for resolving the optimal thrust distribution ratio between these joints. The results of the offline search are then approximated for rapid computation of this ratio during hopping tests in a high-fidelity simulation engine.