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

Abstract

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.