Fast Side-Stepping of the Triple Inverted Pendulum via Constrained Nonlinear Feedforward Control Design

The side-stepping of the triple inverted pendulum serves as a benchmark problem for the presentation of a new feedforward control design technique for finite-time transition problems under consideration of output constraints. The inversion-based design treats the transition task as a two-point boundary value problem (BVP) defined in the input-output coordinates of the pendulum. As a necessary condition for its solvability, a sufficient number of free parameters is provided in a set-up function for the cart acceleration. The new approach allows to directly incorporate output constraints of the pendulum within the BVP, which is solved by a standard MATLAB function. A linear LQR controller is used to stabilize the pendulum along the feedforward side-stepping trajectories. Experimental results for the triple inverted pendulum illustrate the accuracy and robustness of the proposed feedforward/feedback control scheme.

I. INTRODUCTION

Inverted pendulums are often used in nonlinear control education and research due to challenging features like unstable and nonlinear dynamics as well as nonminimum—phase and nonholonomic behavior. A vast range of contributions exists for the stabilization of different types of inverted pendulums, see e.g. [14], [5], [1]. In the recent past, also the tracking problem has been studied especially for single inverted pendulums [2], [16], [10], [12].