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This paper presents the design and validation of controlling hopping on the3D bipedal robot Cassie. A spring-mass model is identified from the kinematicsand compliance of the robot. The spring stiffness and damping are encapsulatedby the leg length, thus actuating the leg length can create and control hoppingbehaviors. Trajectory optimization via direct collocation is performed on thespring-mass model to plan jumping and landing motions. The leg lengthtrajectories are utilized as desired outputs to synthesize a control Lyapunovfunction based quadratic program (CLF-QP). Centroidal angular momentum, takingas an addition output in the CLF-QP, is also stabilized in the jumping phase toprevent whole body rotation in the underactuated flight phase. The solution tothe CLF-QP is a nonlinear feedback control law that achieves dynamic jumpingbehaviors on bipedal robots with compliance. The framework presented in thispaper is verified experimentally on the bipedal robot Cassie.

Bipedal Hopping: Reduced-order Model Embedding via Optimization-based Control