Monique Chyba

An Almost Global Tracking Control Scheme for Maneuverable Autonomous Vehicles and its Discretization

This technical note treats the challenging control problem of tracking a desired continuous trajectory for a maneuverable autonomous vehicle in the presence of gravity, buoyancy and fluid dynamic forces and moments. A realistic dynamics model that applies to maneuverable vehicles moving in 3-D Euclidean space is used for obtaining this control scheme. While applications of this control scheme include autonomous aerial and underwater vehicles, we focus on an autonomous underwater vehicle (AUV) application because of its richer, more nonlinearly coupled, dynamics. The desired trajectory and trajectory tracking errors are globally characterized in the nonlinear state space. Almost global asymptotic stability to the desired trajectory in the nonlinear state space is demonstrated both analytically and through numerical simulations.

Time-Minimal Control of Dissipative Two-Level Quantum Systems: The Generic Case

The objective of this article is to complete preliminary results from the work of Bonnard and Sugny (2009) and Sugny et al. (2007), concerning the time-minimal control of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation. The extremal system is described by a 3D-Hamiltonian depending upon three parameters. We combine geometric techniques with numerical simulations to deduce the optimal solutions.

Underwater vehicles: the minimum time problem

We consider the minimum time problem for a class of underwater vehicles. We focus on the situation of initial and final configurations at rest satisfying x/sub 0/ /spl ne/ x/sub f/, z/sub 0/ = z/sub f/, /spl Theta//sub 0/ /spl Theta//sub f/ = 0. We supplement our theory with a numerical study of optimal bang-bang and singular solutions and include a discussion on a possible Fuller-like phenomenon.

Autonomous Underwater Vehicles: Singular Extremals and Chattering

In this paper, we consider the time minimal problem for an Autonomous Underwater Vehicle. We investigate, on a simplified model, the existence of singular extremals and discuss their optimality status. Moreover, we prove that singular extremals corresponding to the angular acceleration are of order 2. We produce in this case a semi-canonical form of our Hamiltonian system and we can conclude the existence of chattering extremals..

Designing Efficient Trajectories for Underwater Vehicles Using Geometric Control Theory

In this paper, we consider the minimum time problem for underwater vehicles. Using Lagrangian mechanics, we write the equations of motion for marine vehicles with 6 degrees of freedom as a controlled mechanical system. We then apply the necessary conditions from the maximum principle for a trajectory to be time optimal. Using techniques from differential geometry we analyze the resuls. Finally we supplement the theoretical study with numerical simulations.

Detecting Earth’s temporarily-captured natural satellites—Minimoons

Abstract We present a study on the discoverability of temporarily captured orbiters (TCOs) by present day or near-term anticipated ground-based and space-based facilities. TCOs (Granvik, M., Vaubaillon, J., Jedicke, R. [2012]. Icarus 218, 262–277) are potential targets for spacecraft rendezvous or human exploration (Chyba, M., Patterson, G., Picot, G., Granvik, M., Jedicke, R., Vaubaillon, J. [2014]. J. Indust. Manage. Optim. 10, 477–501) and provide an opportunity to study the population of the smallest asteroids in the Solar System. We find that present day ground-based optical surveys such as Pan-STARRS and ATLAS can discover the largest TCOs over years of operation. A targeted survey conducted with the Subaru telescope can discover TCOs in the 0.5–1.0xa0m diameter size range in about 5 nights of observing. Furthermore, we discuss the application of space-based infrared surveys, such as NEOWISE, and ground-based meteor detection systems such as CAMS, CAMO and ASGARD in discovering TCOs. These systems can detect TCOs but at a uninteresting rate. Finally, we discuss the application of bi-static radar at Arecibo and Green Bank to discover TCOs. Our radar simulations are strongly dependent on the rotation rate distribution of the smallest asteroids but with an optimistic distribution we find that these systems have >80% chance of detecting a >10xa0cm diameter TCO in about 40xa0h of operation.

Underwater vehicles: a surprising non time-optimal path

This paper deals with the time-optimal problem for a class of underwater vehicles. We prove that if two configurations at rest can be joined by a horizontal or a vertical translation in the body frame coordinates, then there exists a shorter path. Our computations are based on the maximum principle and use that translations in the body frame coordinates are time-equivalent to paths formed by concatenations of 2-singular extremals that are proved to be non time-optimal.

Earth’s Temporarily-Captured Natural Satellites – The First Step towards Utilization of Asteroid Resources

Granvik et al. (2012) predict that the Earth is surrounded by a cloud of small temporarily-captured asteroids. These temporarily-captured orbiters (TCOs) originate in the near-Earth-object (NEO) population and are temporarily captured in the potential well of the Earth-Moon system (EMS). Granvik et al. (2012) predict that the largest object in orbit around Earth at any given moment (other than the Moon) has a diameter D ~1 m (Sect. 6.2). The number of TCOs is inversely proportional to their size such that there are on the order of 103 0.1-meter-diameter TCOs in orbit around Earth at any given time.

Two Applications of Geometric Optimal Control to the Dynamics of Spin Particles

The purpose of this article is to present the application of methods from geometric optimal control to two problems in the dynamics of spin particles. First, we consider the saturation problem for a single spin system and second, the control of a linear chain of spin particles with Ising couplings. For both problems the minimizers are parameterized using Pontryagin Maximum Principle and the optimal solution is found by a careful analysis of the corresponding equations.

TOWARDS PRACTICAL IMPLEMENTATION OF TIME OPTIMAL TRAJECTORIES FOR UNDERWATER VEHICLES

In this paper, we are concerned with the practical implementation of time optimal numerical techniques on underwater vehicles. We briefly introduce the model of underwater vehicle we consider and present the parameters for the test bed ODIN (Omni-Directional Intelligent Navigator). Then we explain the numerical method used to obtain time optimal trajectories with a structure suitable for the implementation. We follow this with a discussion on the modifications to be made considering the characteristics of ODIN. Finally, we illustrate our computations with some experimental results.