Spacecraft Trajectory Optimization: A review of Models, Objectives, Approaches and Solutions

This article is a survey paper on solving spacecraft trajectory optimization problems. The solving process is decomposed into four key steps of mathematical modeling of the problem, defining the objective functions, development of an approach and obtaining the solution of the problem. Several subcategories for each step have been identified and described. Subsequently, important classifications and their characteristics have been discussed for solving the problems. Finally, a discussion on how to choose an element of each step for a given problem is provided.La Caixa, TIN2016-78365-

Advances in Constrained Spacecraft Relative Motion Planning

This dissertation considers Spacecraft Relative Motion Planning (SRMP), where maneuvers are planned for one or more spacecraft to execute in close proximity to obstacles or to each other. The need for this type of maneuver planning has grown in recent years as the space environment becomes more cluttered, and the focus on space situational awareness increases. In SRMP, maneuvers must accommodate non-linear and non-convex constraints, be robust to disturbances, and be implementable on-board spacecraft with limited computational capabilities. Consequently, many standard optimization or path planning techniques cannot be directly applied to SRMP. In this dissertation, three novel SRMP techniques are developed and simulations are presented to illustrate the implementation of each method. Firstly, an invariance-based SRMP technique is proposed. Maneuvers are planned to transition a spacecraft between specified natural motion trajectories, which require no control to follow, while avoiding obstacles and accommodating minimum and maximum actuation limits. The method is based on a graph search applied to a ``virtual net'' with nodes corresponding to natural motion trajectories. Adjacency rules in the virtual net are based on safe positively invariant tubes built around each natural motion trajectory. These rules guarantee safe transitions between adjacent natural motion trajectories, even when set-bounded disturbances are present. Procedures to construct the safe positively invariant tubes and the virtual net are developed. Methods to reduce calculations are proposed and shown to significantly reduce computation time, with tradeoffs related to maneuver planning flexibility. Secondly, a SRMP technique is developed for the specific problem of satellite inspection. In this setting, an inspector spacecraft maneuvers to gather information about a target spacecraft. An information collection model is developed and used to construct a rapidly computable analytical control law based on the local gradient of the information rate. This control law drives the inspector spacecraft on a path along which the rate of information collection is strictly increasing. To ensure constraint satisfaction, the local gradient control law is combined with a state feedback control law, and rules are developed to govern switches between the two controllers. The method is shown to be effective in generating trajectories to gather information about a specified target point while accommodating disturbances. Finally, a control strategy is proposed to generate a formation containing an arbitrary number of vehicles. This strategy is based on an add-on predictive control mechanism known as a parameter governor. Parameter governors work by modifying parameters, such as gains or offsets, in a nominal closed-loop system to enforce constraints and improve performance. The parameter governor is first developed in a general setting, using generic non-linear system dynamics and an arbitrary formation design. Required calculations are minimized, and non-convex constraints are accommodated through use of a parameter update strategy based on graph colorability theory, and by limiting parameter values to a discrete set. A convergence analysis is presented, proving that under reasonable assumptions, the parameter governor is guaranteed to generate the desired formation. Two specific parameter governors, referred to as the Scale Shift Governor and Time Shift Governor, are proposed and applied to generate formations of spacecraft. These parameter governors enforce constraints by modifying either scale- or time-shifts applied to the target trajectory provided to each spacecraft in formation. Simulation case studies show the effectiveness of each method and demonstrate robustness to disturbances.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145795/1/gfrey_1.pd

Optimal and Robust Neural Network Controllers for Proximal Spacecraft Maneuvers

Recent successes in machine learning research, buoyed by advances in computational power, have revitalized interest in neural networks and demonstrated their potential in solving complex controls problems. In this research, the reinforcement learning framework is combined with traditional direct shooting methods to generate optimal proximal spacecraft maneuvers. Open-loop and closed-loop feedback controllers, parameterized by multi-layer feed-forward artificial neural networks, are developed with evolutionary and gradient-based optimization algorithms. Utilizing Clohessy- Wiltshire relative motion dynamics, terminally constrained fixed-time, fuel-optimal trajectories are solved for intercept, rendezvous, and natural motion circumnavigation transfer maneuvers using three different thrust models: impulsive, finite, and continuous. In addition to optimality, the neurocontroller performance robustness to parametric uncertainty and bounded initial conditions is assessed. By bridging the gap between existing optimal and nonlinear control techniques, this research demonstrates that neurocontrollers offer a flexible and robust alternative approach to the solution of complex controls problems in the space domain and present a promising path forward to more capable, autonomous spacecraft

Mercury/Gemini program design survey. NASA/ERC design criteria program stability, guidance and control

Mercury/Gemini stability, guidance, and control equipment design criteri

Spacecraft Trajectory Planning for Optimal Observability using Angles-Only Navigation

This work leverages existing techniques in angles-only navigation to develop optimal range observability maneuvers and trajectory planning methods for spacecraft under constrained relative motion. The resulting contribution is a guidance method for impulsive rendezvous and proximity operations valid for elliptic orbits of arbitrary eccentricity. The system dynamics describe the relative motion of an arbitrary number of maneuvering (chaser) spacecraft about a single non-cooperative resident-space-object (RSO). The chaser spacecraft motion is constrained in terms of the 1) collision bounds of the RSO, 2) maximum fuel usage, 3) eclipse avoidance, and 4) optical sensor field of view restrictions. When more than one chaser is present, additional constraints include 1) collision avoidance between formation members, and 2) formation longevity via fuel usage balancing. Depending on the type of planetary orbit, quasi-circular or elliptic, the relative motion dynamics are approximated using a linear time-invariant or a linear time-varying system, respectively. The proposed method uses two distinct parameterizations corresponding to each system type to reduce the optimization problem from 12 to 2 variables in Cartesian space, thus simplifying an otherwise intractable optimization problem

Cross Entropy-based Analysis of Spacecraft Control Systems

Space missions increasingly require sophisticated guidance, navigation and control algorithms, the development of which is reliant on verification and validation (V&V) techniques to ensure mission safety and success. A crucial element of V&V is the assessment of control system robust performance in the presence of uncertainty. In addition to estimating average performance under uncertainty, it is critical to determine the worst case performance. Industrial V&V approaches typically employ mu-analysis in the early control design stages, and Monte Carlo simulations on high-fidelity full engineering simulators at advanced stages of the design cycle. While highly capable, such techniques present a critical gap between pessimistic worst case estimates found using analytical methods, and the optimistic outlook often presented by Monte Carlo runs. Conservative worst case estimates are problematic because they can demand a controller redesign procedure, which is not justified if the poor performance is unlikely to occur. Gaining insight into the probability associated with the worst case performance is valuable in bridging this gap. It should be noted that due to the complexity of industrial-scale systems, V&V techniques are required to be capable of efficiently analysing non-linear models in the presence of significant uncertainty. As well, they must be computationally tractable. It is desirable that such techniques demand little engineering effort before each analysis, to be applied widely in industrial systems. Motivated by these factors, this thesis proposes and develops an efficient algorithm, based on the cross entropy simulation method. The proposed algorithm efficiently estimates the probabilities associated with various performance levels, from nominal performance up to degraded performance values, resulting in a curve of probabilities associated with various performance values. Such a curve is termed the probability profile of performance (PPoP), and is introduced as a tool that offers insight into a control system's performance, principally the probability associated with the worst case performance. The cross entropy-based robust performance analysis is implemented here on various industrial systems in European Space Agency-funded research projects. The implementation on autonomous rendezvous and docking models for the Mars Sample Return mission constitutes the core of the thesis. The proposed technique is implemented on high-fidelity models of the Vega launcher, as well as on a generic long coasting launcher upper stage. In summary, this thesis (a) develops an algorithm based on the cross entropy simulation method to estimate the probability associated with the worst case, (b) proposes the cross entropy-based PPoP tool to gain insight into system performance, (c) presents results of the robust performance analysis of three space industry systems using the proposed technique in conjunction with existing methods, and (d) proposes an integrated template for conducting robust performance analysis of linearised aerospace systems

Publications of the Jet Propulsion Laboratory, July 1961 through June 1962

Jpl bibliography on space science, 1961-196