We formulate an approach to the geometry of Riemann–Cartan spaces provided with nonholonomic distributions defined by generic off–diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart–Moffat and Finsler–Lag...

We consider nonholonomic geodesic flows of left-invariant metrics and left-invariant nonintegrable distributions on compact connected Lie groups. The equations of geodesic flows are reduced to the Euler–Poincaré–Suslov equations on the corresponding Lie algebras. The Poisson and symplectic structures give raise to various algebraic constructions of the integrable Hamiltonian systems. On the oth...

we design a two-stage scheme to consider trajectory planning problem of two mobile manipulators for cooperative transportation of a rigid body in presence of static obstacles. within the first stage, regarding the static obstacles we develop a method that searches the workspace for the shortest possible path between start and goal configurations by constructing a graph on a portion of the confi...

We study stationary configurations mimicking nonholonomic locally anisotropic black rings (for instance, with ellipsoidal polarizations and/or imbedded into solitonic backgrounds) in three/six dimensional pseudo–Finsler/ Riemannian spacetimes. In the asymptotically flat limit, for holonomic configurations, a subclass of such spacetimes contains the set of five dimensional black ring solutions w...

We model pseudo–Finsler geometries, with pseudo–Euclidean signatures of metrics, for two classes of four dimensional nonholonomic manifolds: a) tangent bundles with two dimensional base manifolds and b) pseudo–Riemannian/ Einstein manifolds. Such spacetimes are enabled with nonholonomic distributions and associated nonlinear connection structures and theirs metrics are solutions of the field eq...

in this paper, the important formation control problem of nonholonomic wheeled mobile robots is investigated via a leader-follower strategy. to this end, the dynamics model of the considered wheeled mobile robot is derived using lagrange equations of motion. then, using adams multi-body simulation software, the obtained dynamics of the wheeled system in matlab software is verified. after that, ...

A geometrically exact model of a Cosserat rod with nonholonomic constraints is outlined. The constraint forces are derived from the framework of nonholonomic mechanics by using arguments from Cauchy analysis, and a thorough discussion is given concerning the nature of these constraints. By making an additional assumption on the magnitude of the deflections, a simplified model similar to the Eul...