Related papers: Learning Nonholonomic Dynamics with Constraint Dis…
Incorporating the Hamiltonian structure of physical dynamics into deep learning models provides a powerful way to improve the interpretability and prediction accuracy. While previous works are mostly limited to the Euclidean spaces, their…
Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonholonomic equations of motion for an arbitrary rigid body…
This paper presents a method that learns a regionally stable recurrent neural network model from a set of input-output data generated by an unknown dynamical system. Relying on generalized sector conditions on the deadzone activation…
We extend the learning from demonstration paradigm by providing a method for learning unknown constraints shared across tasks, using demonstrations of the tasks, their cost functions, and knowledge of the system dynamics and control…
We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…
In the comparison of nonholonomic mechanics and constrained variational mechanics, invariant affine subbundles arise in the determination of the initial conditions where the two methods yield the same trajectories. Motivated by this,…
We study the dynamics of pairs of connected masses in the plane, when nonholonomic (knife-edge) constraints are realized by forces of viscous friction, in particular its relation to constrained dynamics, and its approximation by the method…
This paper presents a combined strategy for tracking a non-holonomic mobile robot which works under certain operating conditions for system parameters and disturbances. The strategy includes kinematic steering and velocity dynamics learning…
To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…
We explore a new type of discretizations of lattice dynamical models of the Klein-Gordon type relevant to the existence and long-term mobility of nonlinear waves. The discretization is based on non-holonomic constraints and is shown to…
We propose a class of nonlocal diffusion systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. The kernel is not necessarily symmetric or compactly…
The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the Hamiltonian structure in the reduced model, certain…
Data-driven approaches are increasingly popular for identifying dynamical systems due to improved accuracy and availability of sensor data. However, relying solely on data for identification does not guarantee that the identified systems…
We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if…
Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics. Recent works improve generalization for predicting trajectories by learning the Hamiltonian or Lagrangian…
We introduce a method which allows one to recover the equations of motion of a class of nonholonomic systems by finding instead an unconstrained Hamiltonian system on the full phase space, and to restrict the resulting canonical equations…
We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is defined as the motion of a rigid body with a vanishing projection…
Non-conservative loads of the follower type are usually believed to be the source of dynamic instabilities such as flutter and divergence. It is shown that these instabilities (including Hopf bifurcation, flutter, divergence, and…
We consider a simple motivating example of a non-Hamiltonian dynamical system with time-dependent constraints obtained by imposing rheonomic non-integrable Bilimovich's constraint on a freely rotating rigid body. Dynamics of this…
The aim of this paper is to show that the Lagrange-d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them, here we consider the…