On the design of stable periodic orbits of a triple pendulum on a cart with experimental validation

In this paper, we enhance an inversion-based control approach towards the stabilization of a periodic orbit of a multi-link triple pendulum on a cart. To this end, a nominal trajectory is obtained by formulating the considered transition problem as a two-point boundary value problem (BVP) in input-output representation. For solvability of the resulting BVP, a setup function is introduced such that additional parameters are provided in the differential equation of the internal dynamics. Based on the linearized dynamics about the nominal trajectory, a linear-quadratic-Gaussian (LQG) controller is implemented to compensate for measurement noise, model uncertainties, and external disturbances. This way we achieve to force a triple pendulum to move along a non-trivial periodic orbit and render it attractive. The high performance and accuracy of our approach is illustrated on an experimental setup. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper focuses on enhancing an inversion-based control approach for stabilizing a periodic orbit of a multi-link triple pendulum on a cart. By introducing a nominal trajectory and a linear-quadratic-Gaussian controller, the high performance and accuracy of the method are successfully demonstrated on an experimental setup.