Optimal Gait Design for Systems with Drift on SO(3)

Abstract

Geckos that jump, cats that fall, and satellites that are inertially controlled fundamentally locomote in the same way. These systems are bodies in free flight that actively reorientate under the influence of conservation of angular momentum. We refer to such bodies as inertial systems. This work presents a novel control method for inertial systems with drift that combines geometric methods and computational control. In previous work, which focused on inertial systems starting from rest, a set of visual tools was developed that readily allowed on to design gaits. A key insight of this work was deriving coordinates, called minimum perturbation coordinates, which allowed the visual tools to be applied to the design of a wide range of motions. This paper draws upon the same insight to show that it is possible to approximately analyze the kinematic and dynamic contributions to net motion independently. This approach is novel because it uses geometric tools to support computational reduction in automatic gait generation on three-dimensional spaces.