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This paper shows how to define quantitative measures of a robot’s ability to balance itself actively on a single point of support. These measures are expressed as ratios of velocities, and are called velocity gains. This paper builds on earlier work in this area by showing how these gains can be defined and calculated for the case of a general planar robot balancing on a general rolling-contact point in the plane, and the case of a general spatial robot balancing on a general rolling-contact point in 3D space. The case of balancing on a contact area with compliance is also considered. The paper concludes with two examples showing how to use velocity gains in the design of a triple pendulum and the analysis of a hydraulic quadruped.

Quantitative Measures of a Robot's Ability to Balance