Flachheitsbasierte Trajektorienoptimierung entlang von Wegpunkten für ein lineares Ballbot-System

In this article we formulate a flatness-based trajectory generation procedure along waypoints for a new mobile robot (Ballbot). Therefore, we derive and interpret the flat output of the linearized Ballbot system. Based on a piecewise polynomial trajectory design we formulate an optimization problem for minimizing the transition time such that a stationary movement (movement without acceleration) is obtained at the waypoints. State and input constraints are considered. A proper initialization of the optimization parameters leads to a performant initial trajectory and enables a real-time application. An exemplary trajectory design shows the effectivity of the approach.