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Feasible Center of Mass Dynamic Manipulability of humanoid robots

Locomotion stability of a humanoid robot is closely related to the capacity to regulate its Center of Mass (CoM) motion. In this paper, the Feasible Center of Mass Dynamic Manipulability (FCDM) is introduced and analyzed as a measure of this capacity. The effects of posture, joint velocities and gravity on the torque-bounded dynamic manipulability ellipsoid are first analyzed on an n-DOF planar humanoid robot with single-foot support. The ellipse orientation has a linear relationship with the ankle angle, and its shape is independent on the ankle angle. Furthermore, three common and important ground-contact constraints - the unilateral contact-force constraint, the friction constraint, and the Center of Pressure constraint - are incorporated in the derivation of FCDM. It shows geometrically how each of the three constraints shrinks the original torque-bounded manipulability polytope and affects the maximum achievable CoM acceleration in different directions. Finally, a push recovery task was simulated to show that a robot's posture affects the feasible range of the CoM acceleration in a specific direction.