arXiv subjects

Torbjørn Smith

Publications and source records attributed to Torbjørn Smith.

4 recordsLinked to original sources

arXiv2025

Nonparametric adaptive payload tracking for an offshore crane

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.

cs.RO↗

arXiv2024

Learning Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces and Random Features

A method for learning Hamiltonian dynamics from a limited and noisy dataset is proposed. The method learns a Hamiltonian vector field on a reproducing kernel Hilbert space (RKHS) of inherently Hamiltonian vector fields, and in particular, odd Hamiltonian vector fields. This is done with a symplectic kernel, and it is shown how the kernel can be modified to an odd symplectic kernel to impose the odd symmetry. A random feature approximation is developed for the proposed odd kernel to reduce the problem size. The performance of the method is validated in simulations for three Hamiltonian systems. It is demonstrated that the use of an odd symplectic kernel improves prediction accuracy and data efficiency, and that the learned vector fields are Hamiltonian and exhibit the imposed odd symmetry characteristics.

cs.LG↗

arXiv2024

Learning dissipative Hamiltonian dynamics with reproducing kernel Hilbert spaces and random Fourier features

This paper presents a new method for learning dissipative Hamiltonian dynamics from a limited and noisy dataset. The method uses the Helmholtz decomposition to learn a vector field as the sum of a symplectic and a dissipative vector field. The two vector fields are learned using two reproducing kernel Hilbert spaces, defined by a symplectic and a curl-free kernel, where the kernels are specialized to enforce odd symmetry. Random Fourier features are used to approximate the kernels to reduce the dimension of the optimization problem. The performance of the method is validated in simulations for two dissipative Hamiltonian systems, and it is shown that the method improves predictive accuracy significantly compared to a method where a Gaussian separable kernel is used.

cs.LG↗

arXiv2024

Learning of Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces

This paper presents a method for learning Hamiltonian dynamics from a limited set of data points. The Hamiltonian vector field is found by regularized optimization over a reproducing kernel Hilbert space of vector fields that are inherently Hamiltonian, and where the vector field is required to be odd or even. This is done with a symplectic kernel, and it is shown how this symplectic kernel can be modified to be odd or even. The performance of the method is validated in simulations for two Hamiltonian systems. The simulations show that the learned dynamics reflect the energy-preservation of the Hamiltonian dynamics, and that the restriction to symplectic and odd dynamics gives improved accuracy over a large domain of the phase space.

cs.RO↗