We study Monge’s optimal transportation problem, where the cost is given by optimal control cost. We prove the existence and uniqueness of an optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures with respect to Lebesgue, and most importantly the absence of sharp abnormal minimizers. In particular, this result is applicable in the case of subriem...

The purpose of this article is to illustrate the role of connections and symmetries in the Wheeled Inverted Pendulum (WIP) mechanism an underactuated system with rolling constraints popularized commercially as the Segway, and thereby arrive at a set of simpler dynamical equations that could serve as the starting point for more complex feedback control designs. The first part of the article view...

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

The theory of mechanical systems with nonholonomic constraints has a long history in classical mechanics; see e.g. the books by Neimark & Fufaev [14], Edelen [6], Rosenberg [16], Arnold [l] and the references quoted in there. In this literature, nonholonomic mechanical systems are described within the variational framework by Euler-Lagrange equations with extra terms corresponding to the constr...

Lagrangian systems with ideal nonholonomic constraints can be expressed as implicit index 2 differential-algebraic equations (DAEs) and can be derived from the Lagrange-d’Alembert principle. We define a new nonholonomically constrained discrete Lagrange-d’Alembert principle based on a discrete Lagrange-d’Alembert principle for forced Lagrangian systems. Nonholonomic constraints are considered a...

In this paper, we generalize the Boltzmann–Hamel equations for nonholonomic mechanics to a form suited for the kinematic or dynamic optimal control of mechanical systems subject to nonholonomic constraints. In solving these equations one is able to eliminate the controls and compute the optimal trajectory from a set of coupled first-order differential equations with boundary values. By using an...

This paper presents several classical mechanical systems with nonholonomic constraints from the point of view of sub-Riemannian geometry. For those systems that satisfy the bracket generating condition the system can move continuously between any two given states. However, the paper provides a counterexample to show that the bracket generating condition is not also a sufficient condition for co...

This paper investigates the problem of adaptive stabilization of nonholonomic mobile robots with nonholonomic constraints under the condition that the kinematic parameters are unknown and no known constants can (lower and upper) bound them. By defining a new unknown parameter which need dynamic updating, and also by using input-state-scaling transformation and backstepping technique, an adaptiv...

In this paper, we consider a hybrid control strategy for stabilization of nonholonomic systems. In particular, we deal with a typical nonholonomic system, namely a two-wheeled vehicle. We first rewrite the system in a chained form, and then transform it into a nonholonomic integrator (NHI) system. Finally, we apply and modify the hybrid control method for the NHI system, so that the entire syst...

We consider kinematic chains evolving on a nite{ dimensional Lie group G under nonholonomic constraints, where snake{like global motion is induced by shape variations of the system. In particular, we consider the case when the evolution of the system is restricted to a subspace h of the corresponding Lie algebra G; where h is not a subalgebra of G and it generates the whole algebra under Lie br...