Designing ballistic flipping gait for a one-legged robot

A type of planar one-legged robot is proposed which, unlike a previous one-legged robot with springy legs, consists of three revolute joints, two links and two feet. In Geng et al. (2001), a cyclic jumping gait has been designed for this robot, which required that angular rate of the knee joint be zero at the instant of takeoff and that the knee joint be locked during flight phases. To eliminate these two requirements that were difficult to implement; a different ballistic flipping gait is designed for the robot in this paper. A complete flipping gait cycle is composed of four phases: two stance phases and two flight phases. During flight phases, torque of the knee joint is zero, the total angular momentum with respect to the center of mass of the system is conserved, rotational motion and translational motion is decoupled from each other. Trajectory planning of the four phases is formulated as a problem of numerical optimization subject to nonlinear constraints such as positive reaction force of ground and finite torque of the joints. Energy injected into the robot in a gait cycle is chosen as a criterion of optimization in the simulation