Geometric Motion Planning for Inertial Systems

The locomotion of many systems is a cyclic pattern which is achieved by internal joint motions to move through the environment. The main goal of this research is to develop an effective tool for motion planning for robots with multiple links in which they balance the benefit of pushing against their environment with the cost of doing so, where the cost of motion is inertial. Standard numerical optimizers can find efficient gaits for given systems, but do not capture the energy landscape that shapes these gaits. Therefore, we wish to understand the inertial geometry of the system in terms of the curves and accelerations that produce the most efficient gaits. This is achieved using two tools: constructing metric fields and constructing geodesics. The metric field in mechanical systems is obtained from the system's inertia which illustrates where it is easier to move in parameterized space. The geodesic illustrates the natural dynamic path of the system which is defined as the straightest path on the manifold. Using these tools, this research develops a variational principle for generating optimal gaits for inertia-based locomoting systems that provides visual insights on the optimal gait.