Related papers: Virtual Affine Nonholonomic Constraints
Virtual knots are defined diagrammatically as a collection of figures, called virtual knot diagrams, that are considered equivalent up to finite sequences of extended Reidemeister moves. By contrast, knots in $\mathbb{R}^3$ can be defined…
This paper proposes a funnel control method under time-varying hard and soft output constraints. First, an online funnel planning scheme is designed that generates a constraint consistent funnel, which always respects hard (safety)…
We introduce new topological quantum invariants of compact oriented 3-manifolds with boundary where the boundary is a disjoint union of two identical surfaces. The invariants are constructed via surgery on manifolds of the form $F \times I$…
Planning trajectories for nonholonomic systems is difficult and computationally expensive. When facing unexpected events, it may therefore be preferable to deform in some way the initially planned trajectory rather than to re-plan entirely…
This paper deals with the stabilization problem for nonlinear control-affine systems with the use of oscillating feedback controls. We assume that the local controllability around the origin is guaranteed by the rank condition with Lie…
It is known that if a nonlinear control affine system without drift is bracket generating, then its associated sub-Laplacian is invertible under some conditions on the domain. In this note, we investigate the converse. We show how…
In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically…
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains to be an outstanding problem. We develop an experimentally feasible control framework for nonlinear…
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…
By designing tailor-made resonance modes with structured atoms, metamaterials allow us to obtain constitutive parameters outside their limited range from natural or composite materials. Nonetheless, tuning the constitutive parameters relies…
This text presents an introduction to an emerging paradigm in control of dynamical systems and differentiable reinforcement learning called online nonstochastic control. The new approach applies techniques from online convex optimization…
One of the founders of the mechanics of nonoholonomic systems is Voronec who published in 1901 a significant generalization of the Caplygin's equations, by removing some restrictive assumptions. In the frame of nonholonomic systems, the…
Vector fields are advantageous in handling nonholonomic motion planning as they provide reference orientation for robots. However, additionally incorporating curvature constraints becomes challenging, due to the interconnection between the…
We define new notions of groups of virtual and welded knots (or links) and we study their relations with other invariants, in particular the Kauffman group of a virtual knot.
The controllability of networks comprising homogeneous multi-input multi-output linear subsystems with linear couplings among them is examined, from a modal perspective. The eigenvalues of the network model are classified into two groups:…
Nonlinear interactions between phonon modes govern the behavior of vibrationally highly excited solids and molecules. Here, we demonstrate theoretically that optical cavities can be used to control the redistribution of energy from a highly…
This paper considers a class of nonlinear time harmonic Maxwell systems at fixed frequency, with nonlinear terms taking the form $\mathscr{X}(x,|\vec E(x)|^2)\vec E(x)$, $\mathscr{Y}(x,|\vec H(x)|^2)\vec H(x)$, such that $\mathscr{X}(x,s)$,…
This paper investigates the problem of controlling a linear system under possibly unbounded stochastic noise with unknown convex cost functions, known as an online control problem. In contrast to the existing work, which assumes the…
We study relations between vakonomically and nonholonomically constrained Lagrangian dynamics for the same set of linear constraints. The basic idea is to compare both situations at the level of variational principles, not equations of…
A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…