Performance Aspects of Orbit Propagation Using the Unified State Model

The Unified State Model (USM) is a single model that allowed conveying objects of popular programming languages and databases. The USM model exploits and emphase common properties of all objects. The mapping between popular data models and USM has been already shown. In consequence the Universal Query Language (UQL) has been proposed as a set of base operators. UQL pretends to cover most popular query languages and construction of USM and base operators of the UQL has been performed. Examples of simple SQL queries expressed via UQL has been already demonstrated. In this paper we present how operators of a multi-set extended relational algebra can be expressed by UQL operators.KeywordsRelational ModelComplex ObjectSimple ObjectRelational AlgebraProper StateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The orbital state of a satellite in a central force field can be uniquely described by its velocity hodograph, a circle, rather than the Keplerian conic. Also, its coordinate-frame rotation about the attracting center is definable, without singularity, by the four-parameter set of Euler parameters. A unified state model of orbital trajectory and attitude dynamics has previously been developed by use of state variables of the orbital velocity hodograph and Euler parameters. The dynamical constraint equations of this orbital state model are especially effective in advanced techniques of state estimation, used for orbit determination and prediction.

FORCED drag compensation using continuous low-thrust propulsion has been considered for satellites in low Earth orbit. This simple, but nonoptimal, scheme merely requires that the thrust vector is directed opposite to the drag vector and that the magnitude of the two are equal. In principle, the drag force acting on the spacecraft could be determined onboard using accurate accelerometers. However, for small, low-cost spacecraft such sensors may be unavailable.An alternative strategy would be to Ž x the thrust magnitude equal to the expected air drag that would be experienced by the spacecraft. The thrust levelwould be periodically updated based on ground-based orbit determination. In this Engineering Note, it is shown that such a forced circular orbit with a Ž fixed thrust level is exponentially unstable for all physically reasonable atmosphere models.

Frozen orbits and Sun-synchronous orbits are useful in exploration of terrestrial planets’ surface and atmosphere with a view to future human exploration. This work therefore develops novel orbits around terrestrial planets using continuous low-thrust propulsion to enable one new and unique investigations of the planets. This paper considers the use of continuous acceleration by solar electric propulsion, to achieve artificial frozen orbits and artificial Sun-synchronous orbits around terrestrial planets. These artificial orbits are similar to natural frozen orbits and Sun-synchronous orbits around Mercury, Venus, the Earth, and Mars, and the orbital parameters can be designed arbitrarily with the help of continuous low-thrust control. The control strategies to achieve the artificial orbits take into account $J_{2}$ , $J_{3}$ , and $J_{4}$ perturbations of terrestrial planets. It is proved that the control strategies minimize characteristic velocity. Relevant formulas are derived, and numerical results are presented. For the natural frozen orbits, the arguments of periapsis are about 270° for Mercury, Venus, and Mars, whereas about 90° for the Earth. By exerting both radial and transverse thrusts simulation shows that the control acceleration and characteristic velocity of the artificial frozen orbit around Mercury are the smallest among these plants. The characteristic velocity within one orbital period for Mercury is only 0.0089 m/s. The natural Sun-synchronous orbits exist around the Earth and Mars, but not around Mercury and Venus. By offsetting the perturbation acceleration in norm direction, the control acceleration and characteristic velocity of the artificial Sun-synchronous orbit around Mars are less than those of the others. The characteristic velocity within one orbital period is only 18.0885 m/s for the artificial Sun-synchronous orbit around Mars. The relationships between the control thrusts and the primary orbital parameters of the artificial orbits around other terrestrial planets are always similar to those around the Earth. Finally, one constellation of the artificial frozen orbit and the artificial Sun-synchronous orbit is designed by using the multiobjective evolutionary algorithm based on decomposition (MOEA/D), in which a Gaussian process is used to build a surrogate model in lieu of the expensive problem. Simulation shows that the control scheme effectively extends the orbital parameters’ selection ranges of the two types of artificial orbits around terrestrial planets, compared with the natural frozen orbit and Sun-synchronous orbit. The optimization result of the constellation orbits around Mars shows that the optimization framework is effective.

Improvements in MO programs and computer speeds have dramatically increased the size of molecules that can be optimized by MO methods. This has put a considerable strain on existing geometry optimization techniques. For a given molecular system, the performance of a geometry optimization method can vary significantly depending on the coordinates used. Nonredundant internal coordinates (e.g., Z-matrix coordinates) are easily constructed and behave well for acyclic molecules but can be quite troublesome for cyclic systems. Cartesian coordinates behave well for rigid, cyclic molecules but can be quite poor for flexible, acyclic systems. Mixed cartesian and internal coordinates have been suggested as a means of combining the best of both approaches and are particularly convenient for cyclic systems with flexible substituents. The efficiency of these different approaches is compared for a number of molecules. © 1992 John Wiley & Sons, Inc.

A technique of searching for optimal trajectories with gravity assisted maneuvers (GAMs) for interplanetary transfers of spacecraft (SC) with an electric propulsion system (EPS) is proposed. In this case, the indirect optimization method is used. A distinctive feature of this technique is the combination of optimality conditions at the point of GAMs within a single boundary value problem for two cases, when the height of the flyby hyperbola with the GAM is less than or equal to the maximum one. This approach makes it possible to considerably reduce the volume of necessary calculations in optimizing SC interplanetary trajectories that include GAMs. It considers end-to-end trajectory optimization with an analysis of the full set of optimality conditions at the point of the GAM. The efficiency of the proposed approach is demonstrated by the example of optimization of interplanetary trajectories from Earth to Mercury with a GAM in the vicinity of Venus and from Earth to Jupiter with a GAM near Earth.

This paper deals with the trajectory optimization, through a direct method, for the SIMONE mission study. The mission consists of six identical microsatellites, each targeting a rendezvous with a different type of NEO using low-thrust propulsion both for deep space navigation and for Earth escape phase, departing from an Earth orbit. The direct method used consists of a transcription using polynomial base functions in which trajectory and control laws are reduced to a finite set of unknown states and controls, then a parametric optimization is carried out on these unknowns with an NLP technique. Finally, the optimal trajectory is recovered from these unknown states and controls by a polynomial interpolation. The mission has been conceptually divided in two segments inside the Earth sphere of influence, dealing with the perigee rising and with the escape from Earth gravity field through a Moon gravity assist, and an interplanetary segment, dealing with the transfer to each of the six selected targets. Two different cases were analyzed for each trajectory, one which considers the engine characteristics fixed for the entire mission, and the second which instead considers maximum thrust level and specific impulse dependent on the distance from Sun.

BackgroundThe studies on protein folding/unfolding indicate that the native state topology is an important determinant of protein folding mechanism. The folding/unfolding behaviors of proteins which have similar topologies have been studied under Cartesian space and the results indicate that some proteins share the similar folding/unfolding characters.ResultsWe construct physical property space with twelve different physical properties. By studying the unfolding process of the protein G and protein L under the property space, we find that the two proteins have the similar unfolding pathways that can be divided into three types and the one which with the umbrella-shape represents the preferred pathway. Moreover, the unfolding simulation time of the two proteins is different and protein L unfolding faster than protein G. Additionally, the distributing area of unfolded state ensemble of protein L is larger than that of protein G.ConclusionUnder the physical property space, the protein G and protein L have the similar folding/unfolding behaviors, which agree with the previous results obtained from the studies under Cartesian coordinate space. At the same time, some different unfolding properties can be detected easily, which can not be analyzed under Cartesian coordinate space.

Differential drive robots are widely used in various scenarios thanks to their straightforward principle, from household service robots to disaster response field robots. The nonholonomic dynamics and possible lateral slip of these robots lead to difficulty in getting feasible and high-quality trajectories. Although there are several types of driving mechanisms for real-world applications, they all share a similar driving principle, which involves controlling the relative motion of independently actuated tracks or wheels to achieve both linear and angular movement. Therefore, a comprehensive trajectory optimization to compute trajectories efficiently for various kinds of differential drive robots is highly desirable. In this paper, we propose a universal trajectory optimization framework, enabling the generation of high-quality trajectories within a restricted computational timeframe for these robots. We introduce a novel trajectory representation based on polynomial parameterization of motion states or their integrals, such as angular and linear velocities, which inherently matches the robots’ motion to the control principle. The trajectory optimization problem is formulated to minimize computation complexity while prioritizing safety and operational efficiency. We then build a full-stack autonomous planning and control system to demonstrate its feasibility and robustness. We conduct extensive simulations and real-world testing in crowded environments with three kinds of differential drive robots to validate the effectiveness of our approach.Note to Practitioners—The Differential drive robot, known for its simple mechanics and high maneuverability, is widely used in many applications. However, current methods have limitations in practice when high-performance motion is needed. Due to the state representation in Cartesian space, path planning makes it difficult to consider nonholonomic constraints directly. The existing trajectory optimization cannot effectively constrain the angular velocity and it is difficult to model forward and backward motion into a continuous trajectory. This paper provides a novel trajectory representation that inherently utilizes the motion performance of differential drive robots, which ensures its universality for different platforms, and reduces the time required to generate trajectories to ensure real-time performance. Based on this, we propose a robust planning and control framework to achieve efficient navigation. We release the source code at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://zju-fast-lab.github.io/DDR-opt/</uri> facilitating expansion and deployment for practitioners. We validate this framework through extensive experiments, demonstrating its capability to navigate challenging environments.

Despite the rapid development of computer technology, there is a need to increase the speed of steady state calculations and state estimation. It is connected with the calculation model dimension increasing, which is caused by smart grid concept implementation, distributed generation penetration and energy markets development. There are many papers that considered different approaches for state estimation computation speed increase by optimization mathematical operation with matrix and linear equation system solvers. In particular, some earlier papers tell that rectangular coordinates are significantly more preferable in terms of calculation speed than polar for state vector representation. This fact is necessary to check for modern computers. In this research it was examined for state estimation of three phase power system model.

This short communication considers the calculation of player speed from tracking data. Whereas there are many player tracking systems, all rely on the collection of Cartesian coordinates corresponding to the players on the pitch. From these Cartesian coordinates, there are many ways that one could approximate player speed and acceleration. We introduce some simple principles from exploratory data analysis, which help yield more reliable speed calculations. The general principles are illustrated on various player tracking systems.

This paper describes a recently developed method for the determination of optimal, e g minimum-fuel or minimum-time, trajectories for spacecraft. The method will be introduced after a brief discussion of methods previously used by researchers for trajectory optimization. However, the objective here is not to discuss all such methods or provide a comprehensive description of them but rather to provide sufficient information regarding extant methods that what is novel and beneficial about the solution method we have developed may be recognized. Several example optimal trajectories for spacecraft using lowthrust propulsion will be presented.KeywordsOptimal Control ProblemOptimal TrajectoryPrime VectorAdjoint VariableSystem Differential EquationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The problem of motion trajectory optimization with constraints is considered for robotic system with actuated joints. Constraints concern contacts and path-following in the Cartesian space. These constraints arise in walking patterns. In this study, we are dealing with cases where the same constraints hold during a given motion. The trajectory optimization is performed by defining some state variables as polynomials, and the best parameters of the polynomial functions are obtained from suitable optimization programs. By taking into account motion constraints, it appears that the number of the problem's optimization parameters can be reduced. Subsequently, the structure of the optimization problem is different. A procedure to solve this optimization problem is proposed. A simple case is used to compare the proposed methods with the one that is used for solving the similar problem without parameters reduction

Recent advances in unsteady flow visualization

Coordinated motion of two robots in Cartesian space is considered in the paper. Coordinated trajectory is generated as the sum of two motions: programmed and corrective. The corrective motion aims at limitation of the interaction force between robots. For calculation of the corrective motion speed the idea of mechanical impedance is used. As a measure of force interactions between robots change of distance between robots TCPs is used. Simulation experiments carried out for one dimensional case show that application of impedance based correctors results in the linear growth of change of distance between robots TCPs for constant difference between robots programmed speeds. Thus a modification of impedance based correctors is proposed. The modification consists in introduction of an integrating element in series with impedance corrector. Simulation tests for the modified correctors provide improved results – magnitude of change of distance is decreased. Linear increase of change of distance for impedance corrector is changed into a constant non zero value, whereas constant non zero value is changed into zero value. Simulation results for two dimensional case of coordinated motion are also presented.