Desired Trajectory Generation for Balancing with Respect to Periodic External Force

This paper presents a desired trajectory generation of the biped base joint that keeps the CoP position at the constant position when periodic external forces are exerted. For a single sinusoidal external force, the desired trajectory is set based on the frequency transfer function that relates the desired angle and the external force to the ankle torque. For generic periodic external forces, Fourier expansion is introduced, and the Fourier coefficients are estimated based on the framework of an adaptive control. Simulations will demonstrate the effectiveness of this method.