Langevin Thermostat for Rigid Body Dynamics

We present a new method for isothermal rigid body simulations using the quaternion representation and Langevin dynamics. It can be combined with the traditional Langevin or gradient (Brownian) dynamics for the translational degrees of freedom to correctly sample the NVT distribution in a simulation of rigid molecules. We propose simple, quasi-symplectic second-order numerical integrators and test their performance on the TIP4P model of water. We also investigate the optimal choice of thermostat parameters.Comment: 15 pages, 13 figures, 1 tabl

Symmetry-preserving Observers

This paper presents three non-linear observers on three examples of engineering interest: a chemical reactor, a non-holonomic car, and an inertial navigation system. For each example, the design is based on physical symmetries. This motivates the theoretical development of invariant observers, i.e, symmetry-preserving observers. We consider an observer to consist in a copy of the system equation and a correction term, and we give a constructive method (based on the Cartan moving-frame method) to find all the symmetry-preserving correction terms. They rely on an invariant frame (a classical notion) and on an invariant output-error, a less standard notion precisely defined here. For each example, the convergence analysis relies also on symmetries consideration with a key use of invariant state-errors. For the non-holonomic car and the inertial navigation system, the invariant state-errors are shown to obey an autonomous differential equation independent of the system trajectory. This allows us to prove convergence, with almost global stability for the non-holonomic car and with semi-global stability for the inertial navigation system. Simulations including noise and bias show the practical interest of such invariant asymptotic observers for the inertial navigation system.Comment: To be published in IEEE Automatic Contro

On-orbit assembly using superquadric potential fields

The autonomous on-orbit assembly of a large space structure is presented using a method based on superquadric artificial potential fields. The final configuration of the elements which form the structure is represented as the minimum of some attractive potential field. Each element of the structure is then considered as presenting an obstacle to the others using a superquadric potential field attached to the body axes of the element. A controller is developed which ensures that the global potential field decreases monotonically during the assembly process. An error quaternion representation is used to define both the attractive and superquadric obstacle potentials allowing the final configuration of the elements to be defined through both relative position and orientation. Through the use of superquadric potentials, a wide range of geometric objects can be represented using a common formalism, while collision avoidance can make use of both translational and rotation maneuvers to reduce total maneuver cost for the assembly process

Optimal Reconfiguration of Formation Flying Spacecraft--a Decentralized Approach

This paper introduces a hierarchical, decentralized, and parallelizable method for dealing with optimization problems with many agents. It is theoretically based on a hierarchical optimization theorem that establishes the equivalence of two forms of the problem, and this idea is implemented using DMOC (Discrete Mechanics and Optimal Control). The result is a method that is scalable to certain optimization problems for large numbers of agents, whereas the usual “monolithic” approach can only deal with systems with a rather small number of degrees of freedom. The method is illustrated with the example of deployment of spacecraft, motivated by the Darwin (ESA) and Terrestrial Planet Finder (NASA) missions

Deterministic and Recursive Approach in Attitude Determination for InnoSAT

Attitude determination system (ADS) was indispensable in attitude control of satellite. Especially for InnoSAT due to the limitation of budget, weight, and power, the attitude was determined using onboard position sensors. Previous research has successfully implemented the attitude determination using only Earth's magnetic field sensors for small attitude angle, but the approach produced quite big error for large attitude angle. This paper presents attitude determination for InnoSAT using combination of sun sensors and earth's magnetic field for large attitude angle. The attitude was determined using a deterministic (QUEST) and recursive (EKF) approach. A problem arises when using the sun sensors while the satellite experiencing eclipse. Consequently, the accuracy of both approaches was analyzed at eclipse and no eclipse conditions. The result shows that deterministic approach produced better accuracy at no eclipse but recursive approach produced better accuracy at eclipse. The strategy to apply the both approaches and eclipse conditions also discussed in this paper