Related papers: Lie Group Formulation of Recursive Dynamics Algori…
The discrete gradient structure and the positive definiteness of discrete fractional integrals or derivatives are fundamental to the numerical stability in long-time simulation of nonlinear integro-differential models. We build up a…
The purpose of this article is to analyze several Lie algebras associated to "orbit configuration spaces" obtained from a group G acting freely, and properly discontinuously on the upper 1/2-plane H^2. The Lie algebra obtained from the…
Mobile manipulators are finding use in numerous practical applications. The current issues with mobile manipulation are the large state space owing to the mobile base and the challenge of modeling high degree of freedom systems. It is…
We provide and analyze the high order algorithms for the model describing the functional distributions of particles performing anomalous motion with power-law jump length and tempered power-law waiting time. The model is derived in [Wu,…
We present a novel first order controller for systems evolving on matrix Lie groups, a major use case of which is Cartesian velocity control on robot manipulators. This controller achieves global exponential trajectory tracking on a number…
Achieving stable hopping has been a hallmark challenge in the field of dynamic legged locomotion. Controlled hopping is notably difficult due to extended periods of underactuation combined with very short ground phases wherein ground…
We propose a new method for simulating certain type of time-dependent Hamiltonian $H(t) = \sum_{i=1}^m \gamma_i(t) H_i$ where $\gamma_i(t)$ (and its higher order derivatives) is bounded, computable function of time $t$, and each $H_i$ is…
This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using…
We introduce a general procedure for computing higher-order moments of correlation functions in open quantum systems, extending the scope of our recent work on Memory Kernel Coupling Theory (MKCT) [W. Liu, Y. Su, Y. Wang, and W. Dou,…
Given a Lie group $G$, we elaborate the dynamics on $T^*T^*G$ and $T^*TG$, which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space $TT^*G$, which may be defined by a Lagrangian or a Hamiltonian function.…
The observation and description of collective excitations in solids is a fundamental issue when seeking to understand the physics of a many-body system. Analysis of these excitations is usually carried out by measuring the dynamical…
We propose a Hybrid High-Order (HHO) formulation of the incompressible Navier--Stokes equations, that is well suited to be employed for the simulation of turbulent flows. The spatial discretization relies on hybrid velocity and pressure…
Consider a discrete finite-dimensional, Markovian market model. In this setting, discretely sampled American options can be priced using the so-called ``non-recombining'' tree algorithm. By successively increasing the number of exercise…
Several recently released humanoid robots, inspired by the mechanical design of Cassie, employ actuator configurations in which the motors are displaced from the joints to reduce leg inertia. While studies accounting for the full kinematic…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
The unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic…
The numerical solution of the Stokes equations on an evolving domain with a moving boundary is studied based on the arbitrary Lagrangian-Eulerian finite element method and a second-order projection method along the trajectories of the…
In this paper we construct higher-order variational integrators for a class of degenerate systems described by Lagrangians that are linear in velocities. We analyze the geometry underlying such systems and develop the appropriate theory for…
This letter presents a method to reduce the computational demands of including second-order dynamics sensitivity information into the Differential Dynamic Programming (DDP) trajectory optimization algorithm. An approach to DDP is developed…
In this paper, we present a Newton-Euler formulation of the equations of motion for underwater vehicles with an interntal moving mass actuator. Furthermore, the moving mass dynamics are expressed as an extension to the manoeuvring model for…