A System for Collaborative Design, Analysis, and Optimization of Spacecraft Trajectories

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.

In the present research, optimal control problem for low thrust spacecraft orbital transfer is investigated by combination of analytical method and Artificial Bee Colony (ABC) algorithm, which is a population-based method. Spacecraft trajectory optimization is defined for orbital transfer from Low Earth Orbit (LEO) to Geosynchronous Earth Orbit (GEO). In the proposed analytical method co-state variables are simplified by employing concepts of optimal control and specific conditions which are considered for the problem, consequently, an adjoint differential equation is added to set of differential equations and these equations are solved simultaneously that result in optimum transfer trajectory. Dynamic modeling of the problem is represented based on Edelbaum equations and trajectory design is carried out considering circular orbits. Optimization problem is defined for different kinds of objective functions such as minimum time, minimum control effort, minimum time with minimum control effort as well as both minimum time and minimum control effort considering different optimal weighted coefficients. These coefficients are searched by means of artificial bee colony algorithm in weighted minimum time minimum effort scheme. Initial values of control variable and terminal time for all defined objective functions are foraged through artificial bee colony algorithm. The rate of changes of the states and control variables are obtained and depicted during orbit transfer. The obtained results demonstrate considerable convergence as well as sufficient accuracy.

Low-thrust interplanetary spacecraft trajectory optimization poses a uniquely difficult problem to solve because of the inherent nonlinearities of the dynamics and constraints as well as the large size of the search space of possible solutions. Tools currently exist that optimize low-thrust interplanetary trajectories, but these tools are rarely openly available to the public, and when they are available they require multiple interfaces between multiple different packages. The goal of this work is to present a new piece of low-thrust interplanetary spacecraft trajectory optimization software that is open-source and entirely self-contained so that more people can have access to the ability to design interplanetary trajectories. To achieve this goal, a gradient-descent based nonlinear programming method, called the interior point method, was used. The nonlinear programming method was chosen so that results from this work could be compared and contrasted with results from Spacecraft Trajectory Optimization Suite (STOpS), which uses heuristics to iterate towards a solution. Interior point methods are popular because of their ability to handle large amounts of equality and inequality constraints, which is a characteristic that is valuable for low-thrust interplanetary spacecraft trajectories. The software developed, Interior Point Optimizer (IP Optimizer), was then validated against test cases with known solutions to ensure that the software delivered the intended results. Lastly, a constraint satisfaction, a minimum-time, and a maximum-final-mass optimization problem were solved and compared with literature to illustrate the advantages of IP Optimizer and the methods it employs. For the constraint satisfaction problem, IP Optimizer was able to find a solution that exactly satisfied the desired terminal constraints whereas STOpS had an error of 2.29 percent. In this case, IP Optimizer had a reduced runtime of 15 percent compared to STOpS as well. When minimizing time for a spacecraft transfer, IP Optimizer improved upon the solution found by STOpS by 5.3 percent. The speed of convergence for IP Optimizer was almost twice as fast as STOpS for this case. These results show that IP Optimizer is faster than STOpS at converging on a solution and the solution it converges to has a better objective value and more accurately satisfies the terminal constraints than STOpS. Lastly, the maximum-final-mass problem resulted in an objective value that was only 0.5 percent lower than the value found in literature.

As an increasing number of asteroids are being discovered, detecting them using limited propulsion resources and time has become an urgent problem in the aerospace field. However, there is no universal fast asteroid sequence selection method that finds the trajectories for multiple low-thrust spacecraft for detecting a large number of asteroids. Furthermore, the calculation efficiency of the traditional trajectory optimization method is low, and it requires a large number of iterations. Therefore, this study combines Monte Carlo tree search (MCTS) with spacecraft trajectory optimization. A fast MCTS pruning algorithm is proposed, which can quickly complete asteroid sequence selection and trajectory generation for multispacecraft exploration of multiple asteroids. By combining the Bezier shape-based (SB) method and MCTS, this study realizes the fast search of the exploration sequence and the efficient optimization of the continuous transfer trajectories. In the simulation example, compared with the traversal algorithm, the MCTS pruning algorithm obtained the global optimal detection sequence of the search tree in a very short time. Under the same conditions, the Bezier SB method obtained the transfer trajectory with a better performance index faster than the finite Fourier series SB method. Performances of the proposed method are illustrated through a complex asteroid multiflyby mission design.

According to the disadvantages of indirect method for trajectory optimization, that initial value the for conjugate variables are highly sensitive and can not obtain the global optimal solution, this paper introduced hybrid genetic algorithm to search initial value of conjugate variables, solved equations to obtain the track of Near Spacecraft at unpowered gliding phase. In the optimization process, the author takes the constraints of heating rate, dynamic pressure and overload into consideration, and optimizes the trajectory of under different initial factors. Numerical simulations confirm the applicability of the presented algorithm. Considering practical applications, some typical spacecraft gliding trajectory are optimized. The discussion of the numerical simulations gives some valuable opinions in practical applications.

This paper gives an overview of a collaborative design system (CDS) for electromechanical products. To reduce design costs and to manufacture high-quality products, it is well known that concurrent engineering (CE) is a very efficient approach. Three-dimensional (3D) CAD system and engineering database system are essential components of CE. The CDS is an environment to realize CE. By creating 3D models in a computer and performing some simulations such as mechanical, electronic, software simulation and integrated simulations, it is possible to estimate functions, assemblability, manufacturability and so on, before making prototype models. In this paper, we outline the CDS and mainly discuss the total information management system (TIMS) which makes an important role of the CDS. This paper describes the implementation experience of some functions of the TIMS.

The Trajectory Analysis and Optimization System (TAOS) is software that simulates point--mass trajectories for multiple vehicles. It expands upon the capabilities of the Trajectory Simulation and Analysis program (TAP) developed previously at Sandia National Laboratories. TAOS is designed to be a comprehensive analysis tool capable of analyzing nearly any type of three degree-of-freedom, point-mass trajectory. Trajectories are broken into segments, and within each segment, guidance rules provided by the user control how the trajectory is computed. Parametric optimization provides a powerful method for satisfying mission-planning constraints. Althrough TAOS is not interactive, its input and output files have been designed for ease of use. When compared to TAP, the capability to analyze trajectories for more than one vehicle is the primary enhancement, although numerous other small improvements have been made. This report documents the methods used in TAOS as well as the input and output file formats.

The team design becomes increasingly important to future manufacturing industry. This paper focus on the key issues of collaborative 3D design system through Internet or Intranet in CSCW(Computer Support for Cooperative Work). In the paper, we propose our solutions of concurrency control tactics, collaboration aware, multi-mode communications network management, synchronous real-time protection in a collaborative 3D design system. Based on open source projects-open CASCADE and Adaptive Communication Environment (ACE), we implement our collaborative 3D design system, and experiments show our system can meet the requirements of some 3D cooperative modeling design applications.

The increasing number and variety of spacecraft that are expected to operate within cislunar space and other multi-body gravitational environments throughout the solar system necessitates the continued development of strategies for rapid trajectory design and design space exploration. In the field of robotics, similar needs have been addressed using motion primitives that capture the fundamental building blocks of motion and are used to rapidly construct complex paths. Inspired by this concept, this paper leverages motion primitives to construct a framework for rapid and informed spacecraft trajectory design in a multi-body gravitational system. First, motion primitives of fundamental solutions, e.g., selected periodic orbits and their stable and unstable manifolds, are generated via clustering to form a discrete summary of segments of the phase space. Graphs of motion primitives are then constructed and searched to produce primitive sequences that form candidate initial guesses for transfers of distinct geometries. Continuous transfers are computed from each initial guess using multi-objective constrained optimization and collocation. This approach is demonstrated by constructing an array of geometrically distinct transfers between libration point orbits in the Earth-Moon circular restricted three-body problem with impulsive maneuvers.

Celestial chaos: The new logics of theory-testing in orbital dynamics

This paper presents an approach for multi-spacecraft trajectory planning, optimization and control. Maneuver planning as a global optimization problem is solved using genetic algorithms (GA). Methods were devised to reduce the dimensionality of the decision space, yet retain adequate generality of maneuver possibilities. A compact formulation based on thruster switching-times was used for generic point-to-point spacecraft maneuvers. Optimal control is implicitly satisfied by "bang-coast-bang" actuation schemes. Maneuver profiles, including line-of-sight and orthogonal collision avoidance, were developed. A GA optimizer selects the optimal parameter set for each scenario. Simulation case studies were performed for 2, 3 and 5-spacecraft formation initialization tasks. Objective criteria used in the evaluation function included: endpoint errors; collision avoidance; path lengths; maneuvering times; fuel usage and equalization. In all cases, a nominal GA computed feasible trajectories. Objective criteria trade-offs were demonstrated by selective weighting. Ongoing work includes multi-objective optimization of multiple spacecraft trajectories using niched-Pareto genetic algorithms.

Uncertainties in multidisciplinary design optimization (MDO) have a significant influence on the whole design process of engineering systems. The most probable point (MPP) based reliability analysis is an approach that utilizes the safety index β to measure the effect of uncertainties. Collaborative optimization (CO) is a two-level optimization method specially created for large-scale distributed-analysis applications. Simulated annealing-based collaborative optimization (SA—CO) is one of the improved forms of CO that overcomes the difficulty of convergence given the existing of highly nonlinear consistency constraints. By combining the MPP-based reliability analysis method with SA—CO, we present a new collaborative reliability analysis method under the environment of MDO to deal with uncertainties existing in MDO, that is, MPP—SA—CO. Demonstrated by two typical examples, the proposed method inherits the advantages of CO. Also, accurate and efficient results are obtained by employing simulated annealing algorithmic as the system level optimizer and it features response surface instead of disciplinary optimization.

During the early phases of engineering design, the costs committed are high, costs incurred are low, and the design freedom is high. It is well documented that decisions made in these early design phases drive the entire design's life cycle cost. In a traditional paradigm, key design decisions are made when little is known about the design. As the design matures, design changes become more difficult in both cost and schedule to enact. The current capability-based paradigm, which has emerged because of the constrained economic environment, calls for the infusion of knowledge usually acquired during later design phases into earlier design phases, i.e. bringing knowledge acquired during preliminary and detailed design into pre-conceptual and conceptual design. An area of critical importance to launch vehicle design is the optimization of its ascent trajectory, as the optimal trajectory will be able to take full advantage of the launch vehicle's capability to deliver a maximum amount of payload into orbit. Hence, the optimal ascent trajectory plays an important role in the vehicle's affordability posture yet little of the information required to successfully optimize a trajectory is known early in the design phase. Thus, the current paradigm of optimizing ascent trajectories involves generating point solutions for every change in a vehicle's design parameters. This is often a very tedious, manual, and time-consuming task for the analysts. Moreover, the trajectory design space is highly non-linear and multi-modal due to the interaction of various constraints. When these obstacles are coupled with the Program to Optimize Simulated Trajectories (POST), an industry standard program to optimize ascent trajectories that is difficult to use, expert trajectory analysts are required to effectively optimize a vehicle's ascent trajectory. Over the course of this paper, the authors discuss a methodology developed at NASA Marshall's Advanced Concepts Office to address these issues. The methodology is two-fold: first, capture the heuristics developed by human analysts over their many years of experience; and secondly, leverage the power of modern computing to evaluate multiple trajectories simultaneously and therefore enable the exploration of the trajectory's design space early during the pre- conceptual and conceptual phases of design. This methodology is coupled with design of experiments in order to train surrogate models, which enables trajectory design space visualization and parametric optimal ascent trajectory information to be available when early design decisions are being made.

In this paper I describe the utility of, and present an accessible derivation of, the classic Leitmann equation. This is an analytic,approximate equation which relates propulsion system requirements to space mission requirements for a power-limited orvariable-specific-impulse rocket. It is valid in the limiting case that the rocket thrust acceleration is much larger than that ofgravity, which is true for certain categories of interplanetary transfers. This equation has been known since at least 1959, but its utility to early-stage mission design and scoping studies may no longer be universally appreciated. The accessible derivation is an elementary application of the Calculus of Variations and does not require detailed knowledge of that field, making it suitable for application by students and for building understanding and physical insight. I show that this equationcan be used to produce approximate designs and scoping studies for crewed missions to Mars and the outer planets, and torobotic flybys of other star systems. Finally I summarize a few other scenarios approximately susceptible to this accessibleapproach: Ascending to orbit from a circular, airless world; starting and ending an interplanetary transfer in a low orbit; and accomplishing higher-energy missions by jettisoning (staging) propulsion units. Keywords: Spacecraft Trajectory Optimization, Variable Specific Impulse, Mars

Mars entry trajectory planning using robust optimization and uncertainty quantification