Traversing from point-to-point along a straight line with a ballbot

The planar motion to traverse from point to point with a ballbot is discussed. Our aim is to propose an analytical method to plan motions that can be robustly executed by feedback control. The approach is based on defining geometric virtual relations among the generalized coordinates. These relations form the basis of a reparametrization of the system dynamics for motion planning, and an introduction of coordinates transverse to the desired trajectories useful for controller design. Results of numerical simulation are presented to illustrate the performance and robustness of the closed-loop system.