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.