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Coupling Reduced Order Models via Feedback Control for 3D Underactuated Bipedal Robotic Walking

This paper presents a feedback control methodology for 3D dynamic underactuated bipedal walking, that couples an actuated spring-loaded-inverted-pendulum (aSLIP)for forward walking and the passive Linear Inverted Pendulum (LIP)for lateral balancing. The applications of the reduced order models are twofold. First, we utilize aSLIP optimization to design optimal leg length and angle trajectories, and use the LIP dynamics to find desired boundary condition for lateral roll. Second, we present two feedback stabilization laws which are based on the reduced order models and applied on the full robot to stabilize the sagittal walking and lateral balancing separately. The ultimate feedback controller on the full order 3D walking robot is implemented via control Lyapunov function based Quadratic Programs (CLF-QPs). In particular, the reduced order models are used to approximate the underactuated dynamics and plan desired trajectories that are tracked via CLF-QPs. The end result is 3D underactuated walking, demonstrated in simulation on the bipedal robot Cassie.