Dynamic manipulability of the center of mass: A tool to study, analyse and measure physical ability of robots

This paper introduces dynamic manipulability of the center of mass (CoM) as a metric to measure robots' physical abilities to accelerate their CoMs in different directions. By decomposing the effects of velocity dependent constraints, such as unilateral contacts and friction cones, CoM dynamic manipulability is defined as a velocity independent metric which depends only on robot's configuration and inertial parameters. Thus, this metric is independent of any choice of controller and expresses only physical abilities of robots. This important property makes the proposed metric a proper tool to study, analyse and design current and future robots. The outcome of the CoM dynamic manipulability analysis in this paper is an ellipsoid in the CoM acceleration space which graphically shows accessible points due to the unit weighted norm of joint torques. Physical meanings and concepts of two reasonable choices for the weighting matrix, which is used in the weighted norm of joint torques, are discussed and illustrative examples are presented. Since the proposed metric measures physical ability to accelerate the CoM, it is claimed to be a suitable tool to study balance ability of legged robots.