Planning desired center of Mass and zero moment point trajectories for bipedal locomotion

In this paper, we consider the problem of simultaneously synthesizing desired trajectories for both the center of mass (CoM) and zero moment point (ZMP) of a bipedal robot. The approach extends our past work, in which we derived an explicit constraint that ensures boundedness of CoM trajectories for a given reference ZMP trajectory. We parameterize the desired ZMP trajectory by a sequence of basis functions; these design parameters are optimized by an algorithm, in which the CoM boundedness constraint as well as ZMP and other CoM specifications are simultaneously satisfied. When these specifications do not fully constrain the solution, we apply a null-space projection approach that allows the incorporation of additional design criteria. We present simulation results for both the linear inverted pendulum model, and for a model that includes swing leg dynamics.