This paper investigates the optimization and control of biped walking motion on a rolling cylinder. We design a balance controller for a simplified linear model of a biped robot, which comprises a foot connected to a lump mass through an ankle joint and a translational spring and damper. We also derive a collision model for the system consisting of the cylinder, supporting leg, and swing leg. With the balance controller and collision model, the robot motion is uniquely determined by the initial state. We can, therefore, optimize the initial state so that the robot achieves a cyclic gait with a constraint on the desired average rolling velocity. Once an optimal initial state is obtained, we further discuss how to maintain the cyclic motion under disturbances. More specifically, we present a method for computing the joint angles and velocities of the swing leg before it collides with the cylinder. The optimization and control results are demonstrated in simulation.
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