In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the controlled dynamics are given by a nonholonomic mechanical system. In our paper, the controlled equations are derived using a basis of vector fields adapted to t...

The long term goals of the project are: (1) To establish systems and algorithms for controlled Lagrangian particle tracking that will be used to improve the accuracy of model based prediction of trajectories of controlled underwater vehicles subjected to ocean current. (2) To achieve a mission planning system for robotic underwater sensor networks that are able to perform automatic or semiautom...

The long term goals of the project are: (1) To establish systems and algorithms for controlled Lagrangian particle tracking that will be used to improve the accuracy of model based prediction of trajectories of controlled underwater vehicles subjected to ocean current. (2) To achieve a mission planning system for robotic underwater sensor networks that are able to perform automatic or semiautom...

Formations that contain a small number of robots are modeled as controlled Lagrangian systems on Jacobi shape space. This allows a block-structured control of position, orientation and shape of the formation. Feedback control laws are derived using control Lyapunov functions. The controlled dynamics converges to the invariant set where desired shape is achieved. Controllers are implemented in a...

AbsIruct-Formations that contain a small number of robots are modeled as controlled Lagrangian systems on Jacobi shape space. This allows a blocked decoupled control for position, orientation and shape of the formation. Feedback control laws are derived using control Lyapunov functions. The controlled dynamics converges to the invariant set where desired shape is achieved. Controllers are imple...

We propose an efficient semi-Lagrangian method for solving the two-dimensional incompressible Euler equations with high precision on a coarse grid. The new approach evolves flow map using gradient-augmented level set (GALSM). Since can be decomposed into submaps (each over finite time interval), error controlled by choosing remapping times appropriately. This leads to numerical scheme that has ...

This paper is an outgrowth of the work of Bloch, Krishnaprasad, Marsden and Sánchez de Alvarez [1992], where a feedback control that stabilizes intermediate axis rigid body rotation using an internal rotor was found. Stabilization is determined by use of the energy-Casimir (Arnold) method. In the present paper we show that this feedback controlled system can be written as the Euler-Lagrange equ...