CoM control for underactuated 2D hopping robots with series-elastic actuation via higher order Partial Feedback Linearization

In this work we introduce a method for enforcing stance phase trajectories on the center of mass (CoM) for a series-elastic actuated 2D hopping robot with realistic actuator dynamics and underactuation. Building on earlier work, we generate CoM trajectories by abstracting the system to a single point mass moving along a 4th order asymmetric trajectory and analytically solve for the effective ground reaction force vector to indirectly enforce stable trajectories on the body angular acceleration, while maintaining precise ballistic take-off conditions on the CoM. By controlling the CoM directly, we provide solutions that account for the real impact dynamics of the system in order to accurately regulate stride length, and provide a framework that allows for future work in the construction of trajectories to achieve desired results such as stride switching, operation on rough terrain, and disturbance rejection. We utilize Partial Feedback Linearization (PFL) control directly on the CoM position, however due to the series-elastic actuation and compliance in the leg, a classical acceleration-based PFL construction is impossible because of the spring force instantaneously determining the acceleration of the leg of the robot. Therefore we present a solution that constructs PFL control laws about the 4th derivative of the CoM position variables.