📝 SummarXiv

Abstract

A nonparametric adaptive controller is proposed for crane control where the payload tracks a desired trajectory with feedback from the payload position. The controller is based on a novel version of partial feedback linearization where the unactuated crane load dynamics are controlled with the position of the actuated crane dynamics instead of the acceleration. This is made possible by taking advantage of the gravity terms in a new Cartesian model that we propose for the load dynamics. This Cartesian model structure makes it possible to implement a nonparametric adaptive controller which cancels disturbances on the crane load by approximating the effects of unknown disturbance forces and structurally unknown dynamics in a reproducing kernel Hilbert space (RKHS). It is shown that the nonparametric adaptive controller leads to uniformly ultimately bounded errors in the presence of unknown forces and unmodeled dynamics. In addition, it is shown that the proposed partial feedback linearization based on the Cartesian model has certain advantages in payload tracking control also in the non-adaptive case. The performance of the nonparametric adaptive controller is validated in simulation and experiments with good results.