Accurate and efficient spin integration for particle accelerators

Accurate spin tracking is a valuable tool for understanding spin dynamics in particle accelerators and can help improve the performance of an accelerator. In this paper, we present a detailed discussion of the integrators in the spin tracking code gpuSpinTrack. We have implemented orbital integrators based on drift-kick, bend-kick, and matrix-kick splits. On top of the orbital integrators, we have implemented various integrators for the spin motion. These integrators use quaternions and Romberg quadratures to accelerate both the computation and the convergence of spin rotations. We evaluate their performance and accuracy in quantitative detail for individual elements as well as for the entire RHIC lattice. We exploit the inherently data-parallel nature of spin tracking to accelerate our algorithms on graphics processing units.Comment: 43 pages, 17 figure

A nonlinear modal-based framework for low computational cost optimal control of 3D very flexible structures

A nonlinear modal-based reduced-order model, equipped with an efficient adjoint-sensitivity analysis, is presented as a low computational cost framework for optimal control of very flexible structures, with particular focus on efficiently computing finite rotations. Multiple shooting is shown to improve convergence of a highly nonlinear problem when compared to the single shooting case, with optimisation further accelerated via parallelisation, which suggests the presented approach may be employed for real-time control of very flexible structures

Physical human-robot collaboration for object co-manipulation based on adaptable compliant control

Au cours des dernières décennies, l'industrie a évolué afin d'augmenter la productivité, d'améliorer la qualité et de réduire les dangers auxquels sont exposés les opérateurs. En ce sens, l'utilisation des robots a évolué au fil du temps, tout en acquérant toujours plus d'importance, grâce à leur précision, leur force accrue et leur possibilité de répéter des mouvements d'une grande précision. Au vu de l’évolution constante des technologies actuelles, il est également possible d'imaginer de nouveaux défis et des tâches plus complexes qui pourraient être accomplis par les robots. Par exemple, ces derniers pourraient travailler dans un environnement beaucoup plus varié, sans avoir besoin d'être isolés dans des zones sécurisées. Pour que ce scénario soit possible et réaliste, les interactions entre une personne et un robot doivent être traitées rigoureusement, en particulier dans le cas de l'interaction physique Homme-robot (pHRI). L'avantage de cette association est de combiner l'expérience et les capacités de décision d'une personne avec la force et la précision d'un robot. Dans le cadre de cette thèse, l'interaction entre une personne et le robot est plus ambitieuse, car le concept de collaboration physique homme-robot (pHRC) est utilisé. La personne et le robot (en particulier un robot manipulateur) doivent être capables de travailler en contact physique continu, pour effectuer une tâche, mais aussi pour faciliter le travail de l’opérateur ou les opérations de manutentions. Un des éléments clés de cette étude est d’aider l’opérateur dans son travail quotidien en réduisant les efforts qu’il devrait fournir si le robot n'était pas présent. Cette thèse vise donc à améliorer les performances des contrôleurs lorsque la charge utile n'est pas connue ou qu'elle évolue (même pendant la tâche) afin d’obtenir une meilleure collaboration pour le déplacement d'un objet. L'amélioration des capacités de partage de charge en robotique pour les tâches collaboratives pourrait engendrer une évolution certaine sur la façon de concevoir les tâches fréquentes dans l'industrie telles que les tâches d'assemblage, de déplacement de chargés lourdes dans un entrepôt, ou encore des opérations de perçage ou de sciage. En vue de la variété de tâches possibles, le contrôleur doit avoir un comportement adaptable selon le niveau d’interaction avec la personne et la compliance souhaitée. Dans cette thèse, le robot collaboratif KUKA LBR iiwa 14 R820 est utilisé pour étudier et évaluer par des simulations et des expériences le cas d'une charge inconnue portée à la fois par un individu et le robot. Un scénario de pHRC est tout d’abord proposé pour les simulations afin d'étudier l'influence des contrôleurs (tels que la commande par impédance ou par admittance). Des améliorations relatives aux lois de commande classiques sont proposées pour le déplacement des charges de poids inconnu. Ces modifications permettent également d’adapter le comportement du robot, le tout sous une même loi de commande. En effet, soit il aide l’opérateur en devenant un collaborateur compliant et adaptable soit il exécute lui-même sa propre tâche de manière indépendante. Par ailleurs, des expériences sont réalisées pour valider l'approche proposée tout en montrant les avantages de cette méthode qui permet le partage de charge. De plus, une application possible pour effectuer une tâche collaborative entre des personnes et un robot transportant des objets d'un endroit à l'autre est présentée dans cette étude. Enfin, des critères quantitatifs de collaboration sont mis en évidence afin d'évaluer les méthodes proposées. Des problématiques liées notamment aux questions de sécurité concernant la passivité du système sont également discutées

From expressive gesture to sound: the development of an embodied mapping trajectory inside a musical interface

This paper contributes to the development of a multimodal, musical tool that extends the natural action range of the human body to communicate expressiveness into the virtual music domain. The core of this musical tool consists of a low cost, highly functional computational model developed upon the Max/MSP platform that (1) captures real-time movement of the human body into a 3D coordinate system on the basis of the orientation output of any type of inertial sensor system that is OSC-compatible, (2) extract low-level movement features that specify the amount of contraction/expansion as a measure of how a subject uses the surrounding space, (3) recognizes these movement features as being expressive gestures, and (4) creates a mapping trajectory between these expressive gestures and the sound synthesis process of adding harmonic related voices on an in origin monophonic voice. The concern for a user-oriented and intuitive mapping strategy was thereby of central importance. This was achieved by conducting an empirical experiment based on theoretical concepts from the embodied music cognition paradigm. Based on empirical evidence, this paper proposes a mapping trajectory that facilitates the interaction between a musician and his instrument, the artistic collaboration between (multimedia) artists and the communication of expressiveness in a social, musical context

Decentralized Adaptive Control for Collaborative Manipulation of Rigid Bodies

In this work, we consider a group of robots working together to manipulate a rigid object to track a desired trajectory in $SE(3)$. The robots do not know the mass or friction properties of the object, or where they are attached to the object. They can, however, access a common state measurement, either from one robot broadcasting its measurements to the team, or by all robots communicating and averaging their state measurements to estimate the state of their centroid. To solve this problem, we propose a decentralized adaptive control scheme wherein each agent maintains and adapts its own estimate of the object parameters in order to track a reference trajectory. We present an analysis of the controller's behavior, and show that all closed-loop signals remain bounded, and that the system trajectory will almost always (except for initial conditions on a set of measure zero) converge to the desired trajectory. We study the proposed controller's performance using numerical simulations of a manipulation task in 3D, as well as hardware experiments which demonstrate our algorithm on a planar manipulation task. These studies, taken together, demonstrate the effectiveness of the proposed controller even in the presence of numerous unmodeled effects, such as discretization errors and complex frictional interactions

Optimal control of a helicopter unmanned aerial vehicle (UAV)

This thesis addresses optimal control of a helicopter unmanned aerial vehicle (UAV). Helicopter UAVs may be widely used for both military and civilian operations. Because these helicopters are underactuated nonlinear mechanical systems, high-performance controller design for them presents a challenge. This thesis presents an optimal controller design via both state and output feedback for trajectory tracking of a helicopter UAV using a neural network (NN). The state and output-feedback control system utilizes the backstepping methodology, employing kinematic and dynamic controllers while the output feedback approach uses an observer in addition to these controllers. The online approximator-based dynamic controller learns the Hamilton-Jacobi-Bellman (HJB) equation in continuous time and calculates the corresponding optimal control input to minimize the HJB equation forward-in-time. Optimal tracking is accomplished with a single NN utilized for cost function approximation. The overall closed-loop system stability is demonstrated using Lyapunov analysis. Simulation results are provided to demonstrate the effectiveness of the proposed control design for trajectory tracking. A description of the hardware for confirming the theoretical approach, and a discussion of material pertaining to the algorithms used and methods employed specific to the hardware implementation is also included. Additional attention is devoted to challenges in implementation as well as to opportunities for further research in this field. This thesis is presented in the form of two papers --Abstract, page iv

ATTITUDE CONTROL ON SO(3) WITH PIECEWISE SINUSOIDS

This dissertation addresses rigid body attitude control with piecewise sinusoidal signals. We consider rigid-body attitude kinematics on SO(3) with a class of sinusoidal inputs. We present a new closed-form solution of the rotation matrix kinematics. The solution is analyzed and used to prove controllability. We then present kinematic-level orientation-feedback controllers for setpoint tracking and command following. Next, we extend the sinusoidal kinematic-level control to the dynamic level. As a representative dynamic system, we consider a CubeSat with vibrating momentum actuators that are driven by small $\epsilon$-amplitude piecewise sinusoidal internal torques. The CubeSat kinetics are derived using Newton-Euler\u27s equations of motion. We assume there is no external forcing and the system conserves zero angular momentum. A second-order approximation of the CubeSat rotational motion on SO(3) is derived and used to derive a setpoint tracking controller that yields order O(ε2) closed-loop error. Numerical simulations are presented to demonstrate the performance of the controls. We also examine the effect of the external damping on the CubeSat kinetics. In addition, we investigate the feasibility of the piecewise sinusoidal control techniques using an experimental CubeSat system. We present the design of the CubeSat mechanical system, the control system hardware, and the attitude control software. Then, we present and discuss the experiment results of yaw motion control. Furthermore, we experimentally validate the analysis of the external damping effect on the CubeSat kinetics

Simulation Testbed for Entry Analysis and Design (STEAD)

The simulation of a spacecraft in an accurately modeled environment gives engineers and researchers important data on the feasibility of designs. The Simulation Testbed for Entry Analysis and Design (STEAD) is a modular simulation analysis tool for entry vehicles, capable of testing any spacecraft on any planetary body. Although there are existing software packages in use to perform these simulations, STEAD is structured to reduce the workload for the user to generate new environments for each simulation and provide a starting point from which to build, test, and analyze systems. STEAD is built on the SpaceCRAFT platform, allowing the user to connect new models and simulate engineering designs in a virtual reality (VR) environment. Although SpaceCRAFT can be used for many different space mission scenarios, this thesis focuses on the simulation and analysis of a lifting body entry vehicle. The integration of existing environmental models, such as NASA GRAMs and JPL SPICE, provide an accurate simulation environment for STEAD. Additionally, the first iteration of a generic atmospheric model was developed to accurately simulate the physical processes on any planetary body. The thesis adds functionality to the core SpaceCRAFT platform through the implementation of a dynamics propagation system and creation of interfaces for MATLAB and FORTRAN mathematical models. To demonstrate a use case for the software, STEAD was used to simulated the trajectory of a test vehicle using guidance commands provided by both an open-loop and closed-loop algorithm based on the Theory of Connections. The simulation tool was used to analyse the performance of the real-time guidance algorithm in an accurately modeled environment that provided realistic perturbations, such as density variation and wind speeds

Near Real-Time Closed-Loop Optimal Control Feedback for Spacecraft Attitude Maneuvers

Optimization of spacecraft attitude maneuvers can significantly reduce attitude control system size and mass, and extend satellite end-of-life. Optimal control theory has been applied to solve a variety of open-loop optimal control problems for terrestrial, air, and space applications. However, general application of real-time optimal controllers on spacecraft for large slew maneuvers has been limited because open-loop control systems are inherently vulnerable to error and the computation necessary to solve for an optimized control solution is resource intensive. This research effort is focused on developing a near real-time optimal control (RTOC) system for spacecraft attitude maneuvers on the Air Force Institute of Technology\u27s 2nd generation simulated satellite, SimSat II. To meet the end goal of developing a RTOC controller, necessary preliminary steps were completed to accurately characterize SimSAT II\u27s mass properties and attitude control system. Using DIDO, a pseudospectral-based optimal control solver package, to continuously solve and execute a sequence of optimized open-loop control solutions in near real-time, the RTOC controller can optimally control the state of the satellite over the course of a large angle slew maneuver. In this research, simulation and experimental results clearly demonstrate the benefit of RTOC versus other non-optimal control methods for the same maneuver

AAS/GSFC 13th International Symposium on Space Flight Dynamics

This conference proceedings preprint includes papers and abstracts presented at the 13th International Symposium on Space Flight Dynamics. Cosponsored by American Astronautical Society and the Guidance, Navigation and Control Center of the Goddard Space Flight Center, this symposium featured technical papers on a wide range of issues related to orbit-attitude prediction, determination, and control; attitude sensor calibration; attitude dynamics; and mission design