An online asymmetric trajectory generation method for biped robots is proposed to maintain dynamical postural stability and increase energy autonomy, based on the running stability criterion defined in phases. In a support phase, an asymmetric trajectories for the hip and swing leg of the biped robots is obtained from an approximated running model with two springless legs and a spring-loaded inverted pendulum model so that the zero moment point should exist inside the safety boundary of a supporting foot, and the supporting leg should absorb large reaction forces, take off and fly through the air. The biped robot is under-actuated with six degrees of under-actuation during flight. The trajectory generation strategies for the hip and both legs in a flight phase use the approximated running model and non-holonomic constraints based on the linear and angular momenta at the mass center. Next, we present an impedance control with a force modulation strategy to guarantee a stable landing on the ground and simultaneously track the desired trajectories where the desired impedance at the hip link and both legs is specified. A series of computer simulations for two different types of biped robots show that the proposed running trajectory and impedance control method satisfy the two conditions for running stability and make the biped robot more robust to variations in the desired running speed, gait transitions between walking and running, and parametric modeling errors. We have examined the feasibility of this method with running experiments on a 12-DOF biped robot without arms. The biped robot could run successfully with average forward speed of about 0.3359 [m/s].
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