Olav Egeland

Torbjørn Smith, Olav Egeland

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.

Torbjørn Smith, Olav Egeland

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.

Sigmund Hennum Høeg, Aksel Vaaler, Chaoqi Liu et al.

Constructing robots to accomplish long-horizon tasks is a long-standing challenge within artificial intelligence. Approaches using generative methods, particularly Diffusion Models, have gained attention due to their ability to model continuous robotic trajectories for planning and control. However, we show that these models struggle with long-horizon tasks that involve complex decision-making and, in general, are prone to confusing different modes of behavior, leading to failure. To remedy this, we propose to augment continuous trajectory generation by simultaneously generating a high-level symbolic plan. We show that this requires a novel mix of discrete variable diffusion and continuous diffusion, which dramatically outperforms the baselines. In addition, we illustrate how this hybrid diffusion process enables flexible trajectory synthesis, allowing us to condition synthesized actions on partial and complete symbolic conditions.

Torbjørn Smith, Olav Egeland

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.

Sigmund H. Høeg, Yilun Du, Olav Egeland

Diffusion models have seen rapid adoption in robotic imitation learning, enabling autonomous execution of complex dexterous tasks. However, action synthesis is often slow, requiring many steps of iterative denoising, limiting the extent to which models can be used in tasks that require fast reactive policies. To sidestep this, recent works have explored how the distillation of the diffusion process can be used to accelerate policy synthesis. However, distillation is computationally expensive and can hurt both the accuracy and diversity of synthesized actions. We propose SDP (Streaming Diffusion Policy), an alternative method to accelerate policy synthesis, leveraging the insight that generating a partially denoised action trajectory is substantially faster than a full output action trajectory. At each observation, our approach outputs a partially denoised action trajectory with variable levels of noise corruption, where the immediate action to execute is noise-free, with subsequent actions having increasing levels of noise and uncertainty. The partially denoised action trajectory for a new observation can then be quickly generated by applying a few steps of denoising to the previously predicted noisy action trajectory (rolled over by one timestep). We illustrate the efficacy of this approach, dramatically speeding up policy synthesis while preserving performance across both simulated and real-world settings.

Geir Ole Tysse, Andrej Cibicik, Olav Egeland

A vision-based controller for a knuckle boom crane is presented. The controller is used to control the motion of the crane tip and at the same time compensate for payload oscillations. The oscillations of the payload are measured with three cameras that are fixed to the crane king and are used to track two spherical markers fixed to the payload cable. Based on color and size information, each camera identifies the image points corresponding to the markers. The payload angles are then determined using linear triangulation of the image points. An extended Kalman filter is used for estimation of payload angles and angular velocity. The length of the payload cable is also estimated using a least squares technique with projection. The crane is controlled by a linear cascade controller where the inner control loop is designed to damp out the pendulum oscillation, and the crane tip is controlled by the outer loop. The control variable of the controller is the commanded crane tip acceleration, which is converted to a velocity command using a velocity loop. The performance of the control system is studied experimentally using a scaled laboratory version of a knuckle boom crane.

Alexander Meyer Sjøberg, Olav Egeland

An unscented Kalman filter for matrix Lie groups is proposed where the time propagation of the state is formulated on the Lie algebra. This is done with the kinematic differential equation of the logarithm, where the inverse of the right Jacobian is used. The sigma points can then be expressed as logarithms in vector form, and time propagation of the sigma points and the computation of the mean and the covariance can be done on the Lie algebra. The resulting formulation is to a large extent based on logarithms in vector form, and is therefore closer to the UKF for systems in $\mathbb{R}^n$. This gives an elegant and well-structured formulation which provides additional insight into the problem, and which is computationally efficient. The proposed method is in particular formulated and investigated on the matrix Lie group $SE(3)$. A discussion on right and left Jacobians is included, and a novel closed form solution for the inverse of the right Jacobian on $SE(3)$ is derived, which gives a compact representation involving fewer matrix operations. The proposed method is validated in simulations.