In this paper we derive variational integrators for optimal control problems of nonholonomic mechanical systems. We rewrite the system as a constrained second-order variational problem, that is, as a problem where the Lagrangian and constraints are defined in terms of the position, velocity and the acceleration of the system. Instead of discretizing directly the equations of motion, we discreti...

This paper is concerned with iterative learning control of Hamiltonian systems with nonholonomic constraints. The author has proposed a novel iterative learning control method based on the symmetric property of Hamiltonian control systems. Unfortunately, however, it is not applicable to nonholonomic systems. The present paper proposes a set of feedback and coordinate transformations converting ...

The geometry of constrained Lagrangian systems is developed using the Lagrange-d’Alembert principle, extending the variational approach of Marsden, Shkoller, and Patrick, Comm. Math. Phys. 199:351–395 from holonomic to nonholonomic systems. It emerges that the instrinsic geometry of nonholonomic systems corresponds to the geometry of the distributional Hamiltonian systems of Sniatycki, Rep. Mat...

Several schemes have been proposed in the path planning-literature to plan collision-free and feasible trajectories for non-holonomic mobile robots. A classical scheme is the two-step approach proposed in 4, 8, 5] which consists in rst computing a collision-free holonomic path, and then in transforming this path by a sequence of feasible ones. The quality of the solution and the computational c...

In this paper; we are interested principally in dynamic modelling of quadrotor while taking into account the high-order nonholonomic constraints in order to develop a new control scheme as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new state-space representation. After, the use of Backstepping approach for the s...

We propose a framework for synthesizing real-time trajectories for a wide class of coordinating multi-agent systems. The class of problems considered is characterized by the ability to decompose a given formation objective into an equivalent set of lower dimensional problems. These include the so called radar deception problem and the formation control problems that fall under formation keeping...

We argue that the Einstein gravity theory can be reformulated in almost Kähler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of nonsymmetric theories of gravitation (NGT) on manifolds enabled with nonholonomic distributions is analyzed. There are considered some conditions when the fundamental g...

In this paper, a new controller is proposed by using backstepping method for the trajectory tracking problem of nonholonomic dynamic mobile robots with nonholonomic constraints under the condition that there is a distance between the mass center and the geometrical center and the distance is unknown. And an adaptive feedback controller is also proposed for the case that some kinematic parameter...

This papers studies discrete nonholonomic mechanical systems whose configuration space is a Lie group G Assuming that the discrete Lagrangian and constraints are left-invariant, the discrete Euler–Lagrange equations are reduced to the discrete Euler–Poincaré–Suslov equations. The dynamics associated with the discrete Euler–Poincaré–Suslov equations is shown to evolve on a subvariety of the Lie ...

This paper develops the notion of implicit Lagrangian systems and presents some of their basic properties in the context of Dirac structures. This setting includes degenerate Lagrangian systems and systems with both holonomic and nonholonomic constraints, as well as networks of Lagrangian mechanical systems. The definition of implicit Lagrangian systems with a configuration space Q makes use of...