Trajectory Planning for a Segway Model exploiting Inherent Feedforward Structure

Abstract

Time/energy optimal trajectory planning for a Segway model (inverted pendulum on two independently actuated wheels) is addressed. Basis for this planning is the dynamical model for this under-actuated, non-holonomic multibody system. In order to reduce the calculation effort for the optimization, an input/output transformation is applied, which leads to a control system in strict feedforward form. The full system state can thus be described by two outputs, which are parameterized by two B-splines. The system is required to move on the ground within a predefined area. For the optimization the control points of the B-Splines serve as optimization variables and the cost functional is comprised of the overall energy of the robot and the terminal time. Additionally to the maximum motor velocities and torques, the maximum ground reaction forces give rise to the constraints. The latter are crucial to ensure that the wheels do not slip.