Quantitative measures of a robot’s physical ability to balance

This paper presents quantitative measures of a robot’s physical ability to balance itself actively on a single point, line or area of support. These measures express the ratio of a change in the state of motion of the robot’s center of mass to the amount of action required at the actuated joints in order to produce that change. They therefore represent measures of the gain of the robot mechanism as seen from the point of view of the balance control system. This paper is concerned mainly with ratios of velocities, called velocity gains, and it builds on earlier work by showing how these ratios can be defined and calculated for the case of a general planar or spatial robot balancing on a point, line or general rolling contact, or an area contact with a compliant surface. The paper concludes with three examples of use—design of a triple pendulum, analysis of a hydraulic quadruped, and expressing the physics of planar balancing—followed by a short discussion of gyroscopic balancing.