Related papers: Virtual Nonholonomic Constraints: A Geometric Appr…
Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints…
Virtual constraints are relations imposed in a control system that become invariant via feedback, instead of real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the…
In this paper, we give sufficient conditions for and deduce a control law under which a mechanical control system converges exponentially fast to a virtual linear nonholonomic constraint that is control invariant via the same feedback…
Nonholonomic systems are, so to speak, mechanical systems with a prescribed restriction on the velocities. A virtual nonholonomic constraint is a controlled invariant distribution associated with an affine connection mechanical control…
In this paper, we address the problem of stabilizing a system around a desired manifold determined by virtual nonlinear nonholonomic constraints. Virtual constraints are relationships imposed on a control system that are rendered invariant…
We propose a new description of dynamics of autonomous mechanical systems which includes the momentum-velocity relation. This description is formulated as a variational principle of virtual action more complete than the Hamilton Principle.…
In this paper, we provide a geometric characterization of virtual nonlinear nonholonomic constraints from a symplectic perspective. Under a transversality assumption, there is a unique control law making the trajectories of the associated…
The paper is concerned with mechanical systems which are controlled by implementing a number of time-dependent, frictionless holonomic constraints. The main novelty is due to the presence of additional non-holonomic constraints. We develop…
In this article we study virtual nonholonomic constraints, which are relations between the generalized coordinates and momenta of a mechanical system that can be enforced via feedback control. We design a constraint which emulates…
We consider learning nonholonomic dynamical systems while discovering the constraints, and describe in detail the case of the rolling disk. A nonholonomic system is a system subject to nonholonomic constraints. Unlike holonomic constraints,…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
In this paper we use an affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. In particular, we aim at minimizing the norm-squared of the control input to move the…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
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…
This paper presents a coordinate-free formulation of virtual holonomic constraints for underactuated Lagrangian control systems on Riemannian manifolds. It is shown that when a virtual constraint enjoys a regularity property, the…
We approach the analysis of dynamical and geometrical properties of nonholonomic mechanical systems from the discussion of a more general class of auxiliary constrained Hamiltonian systems. The latter is constructed in a manner that it…
In this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz's variational principle, by restricting the variations so that they satisfy the nonholonomic constraints. We prove…
Foot slip is a major source of instability in bipedal locomotion on low-friction or uncertain terrain. Standard control approaches typically assume no-slip contact and therefore degrade when slip occurs. We propose a control framework that…
This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity…
The problem of tracking an arbitrary curve in the state space is considered for underactuated driftless control-affine systems. This problem is formulated as the stabilization of a time-varying family of sets associated with a neighborhood…