TRAJECTORY DESIGN FOR RANGER AND MARINER MISSIONS
Trajectory optimization for lunar and inter- planetary missions - ranger project
OPTIMIZATION↗
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An Integrated Software Architecture for Solar Cruiser Mission Design and Navigation
Solar Cruiser is a solar sailing mission, riding as a secondary payload to the Interstellar Mapping and Acceleration Probe (IMAP) mission, slated to launch in February of 2025. The Solar Cruiser vehicle will generate thrust via a complex, low-thrust solar sail. The extreme low-thrust nature of the solar sail will leave Solar Cruiser highly sensitive to external environmental effects (such as solar radiation pressure and high-order gravitational perturbations) throughout the entirety of flight. Because of this, preliminary operational optimization routines must be intricately tied to high-order predictive propagation models to ensure the greatest possible confidence in mission success. The Solar Cruiser Mission Design and Navigation (MDNav) team has designed a software tool suite, employing the latest in software containerization technology, to accomplish this task; allowing for seamless development across several users and operating systems. Combining JPL’s Monte toolkit with high-performance optimizers written by the University of Alabama, the proposed architecture allows for instant verification of optimized trajectories within the same development environment that the optimization takes place, removing the need for mission designers and navigators to switch between tools. The MDNav suite image deployment process is separated from the development and operational scripts to be used in flight, which allows for maintaining a low-footprint version control profile without unnecessary file bloating. This paper discusses the historical differences between previous iterations of the Solar Cruiser MDNav tool suite and the current iteration, planned operational interfaces of the tool with other software and subsystems, and the planned path forward in maintaining containerization services for the software throughout the lifetime of Solar Cruiser.
optimization↗
An Integrated Software Architecture for Solar Cruiser Mission Design and Navigation
Solar Cruiser is a solar sailing mission, riding as a secondary payload to the Interstellar Mapping and Acceleration Probe (IMAP) mission, expected to launch in February of 2025. The Solar Cruiser vehicle will generate thrust via a complex, low-thrust solar sail. The extreme low-thrust nature of the solar sail will leave Solar Cruiser highly sensitive to external environmental effects (such as solar radiation pressure and high-order gravitational perturbations) throughout the entirety of flight. Because of this, preliminary & operational optimization routines must be intricately tied to high-order predictive propagation models to ensure the greatest possible confidence in mission success. The Solar Cruiser Mission Design and Navigation (MDNav) team has designed a software tool suite, employing the latest in software containerization technology, to accomplish this task, allowing for seamless development across several users and operating systems. Combining JPL’s Monte toolkit with high-performance optimizers written by researchers at the University of Alabama, the proposed architecture allows for instant verification of optimized trajectories within the same development environment that the optimization takes place, removing the need for mission designers and navigators to switch between tools. The MDNav software suite itself is separated from the development and operational scripts to be used in flight, which allows for maintaining a low-footprint version control profile – thus avoiding unnecessary file bloating. This paper discusses the historical differences between previous iterations of the Solar Cruiser MDNav tool suite and the current iteration, planned operational interfaces of the tool with other software and subsystems, and the planned path forward in maintaining containerization services for the software throughout the lifetime of Solar Cruiser.
Containerization↗
An Integrated Software Architecture for Solar Cruiser Mission Design and Navigation
Solar Cruiser is a solar sailing mission, riding as a secondary payload to the Interstellar Mapping and Acceleration Probe (IMAP) mission, expected to launch in February of 2025. The Solar Cruiser vehicle will generate thrust via a complex, low-thrust solar sail. The extreme low-thrust nature of the solar sail will leave Solar Cruiser highly sensitive to external environmental effects (such as solar radiation pressure and high-order gravitational perturbations) throughout the entirety of flight. Because of this, preliminary & operational optimization routines must be intricately tied to high-order predictive propagation models to ensure the greatest possible confidence in mission success. The Solar Cruiser Mission Design and Navigation (MDNav) team has designed a software tool suite, employing the latest in software containerization technology, to accomplish this task, allowing for seamless development across several users and operating systems. Combining JPL’s Monte toolkit with University of Alabama’s high-performance optimizer, ASSET, the proposed architecture allows for instant verification of optimized trajectories within the same development environment that the optimization takes place, removing the need for mission designers and navigators to switch between tools. The MDNav software suite itself is separated from the development and operational scripts to be used in flight, which allows for maintaining a low-footprint version control profile – thus avoiding unnecessary file bloating. This paper discusses the historical differences between previous iterations of the Solar Cruiser MDNav tool suite and the current iteration, planned operational interfaces of the tool with other software and subsystems, and the planned path forward in maintaining containerization services for the software throughout the lifetime of Solar Cruiser.
solar cruiser↗
Optimized space shuttle trajectory simulation
A computer program for simulating optimized space shuttle trajectories is presented. The program considers the ascent, return, and synergetic maneuvers of lifting boosters and spacecraft. Other constraints on optimum trajectory such as maximum heating, acceleration, angle of attack, and excluded or included overflight or impact regions are examined. Mathematical models are included to support the theoretical aspects of the discussion.
Tramonti, L.↗
Real-time optimal guidance for orbital maneuvering.
A new formulation for soft-constraint trajectory optimization is presented as a real-time optimal feedback guidance method for multiburn orbital maneuvers. Control is always chosen to minimize burn time plus a quadratic penalty for end condition errors, weighted so that early in the mission (when controllability is greatest) terminal errors are held negligible. Eventually, as controllability diminishes, the method partially relaxes but effectively still compensates perturbations in whatever subspace remains controllable. Although the soft-constraint concept is well-known in optimal control, the present formulation is novel in addressing the loss of controllability inherent in multiple burn orbital maneuvers. Moreover the necessary conditions usually obtained from a Bolza formulation are modified in this case so that the fully hard constraint formulation is a numerically well behaved subcase. As a result convergence properties have been greatly improved.
Cohen, A. O.↗
Automated Sensitivity Analysis of Interplanetary Trajectories
This work describes a suite of Python tools known as the Python EMTG Automated Trade Study Application (PEATSA). PEATSA was written to automate the operation of trajectory optimization software, simplify the process of performing sensitivity analysis, and was ultimately found to out-perform a human trajectory designer in unexpected ways. These benefits will be discussed and demonstrated on sample mission designs.
trajectory design↗
A Physics-Based Work-Energy Formulation for Real-Time Trajectory Guidance of A Lunar Lander
Throughout the years, many researchers have calculated and optimized trajectory solutions for lunar landing systems by employing sophisticated mathematical methods, that include: Hamilton’s Principle of Variation, Pontryagin’s maximum principle, and well known convex-optimization techniques among others. Many of these approaches typically require expensive computational resources to achieve convergence in the solution. In an effort to reduce complexity and the computational load required to obtain real-time guidance commands, a simple physics-based work-energy approach has been formulated. This approach is based on the dissipation of the mechanical energy of the vehicle to its final desired energy state required to achieve a safe landing. The rocket engine(s) employed during landing (among other maneuvers) dissipates mechanical energy by both doing work against the velocity vector of the vehicle (thus defining the trajectory path), and by jettisoning mass. Therefore, by solving the energy dissipation problem at every step of the maneuver, a much simpler formulation that naturally and quickly attains convergence is obtained. This formulation is not limited to approach, landing, and divert maneuvers, but in principle it can be employed during de-orbiting, braking burn, ascent, as well as orbit insertion.
Guidance↗
A Physics-Based Work-Energy Formulation for Real-Time Trajectory Guidance of a Lunar Lander
Throughout the years, many researchers have calculated and optimized trajectory solutions for lunar landing systems by employing sophisticated mathematical methods, that include: Hamilton’s Principle of Variation, Pontryagin’s maximum principle, and well known convex-optimization techniques among others. Many of these approaches typically require expensive computational resources to achieve convergence in the solution. In an effort to reduce complexity and the computational load required to obtain real-time guidance commands, a simple physics-based work-energy approach has been formulated. This approach is based on the dissipation of the mechanical energy of the vehicle to its final desired energy state required to achieve a safe landing. The rocket engine(s) employed during landing (among other maneuvers) dissipates mechanical energy by both doing work against the velocity vector of the vehicle (thus defining the trajectory path), and by jettisoning mass. Therefore, by solving the energy dissipation problem at every step of the maneuver, a much simpler formulation that naturally and quickly attains convergence is obtained. This formulation is not limited to approach, landing, and divert maneuvers, but in principle it can be employed during de-orbiting, braking burn, ascent, as well as orbit insertion.
Guidance↗
Application of the steepest ascent optimization method to a reentry trajectory problem
The direct optimization method is presented in detail. Nominal values of the control variables are input parameters. Perturbations are introduced into the control variables and the resulting first order predictions of changes in the payoff, and constraint functions are then determined. Through a sequence of prescribed cycles, a trajectory is eventually obtained which is reasonably close to the optimum. The method is successfully applied to an Apollo three-dimensional reentry problem. The study of this Apollo application problem has resulted in the development of a highly flexible computer program that can be modified to consider other trajectory optimization problems.
Junkin, B. G.↗
Algorithms for Maneuvering Spacecraft Around Small Bodies
A document describes mathematical derivations and applications of autonomous guidance algorithms for maneuvering spacecraft in the vicinities of small astronomical bodies like comets or asteroids. These algorithms compute fuel- or energy-optimal trajectories for typical maneuvers by solving the associated optimal-control problems with relevant control and state constraints. In the derivations, these problems are converted from their original continuous (infinite-dimensional) forms to finite-dimensional forms through (1) discretization of the time axis and (2) spectral discretization of control inputs via a finite number of Chebyshev basis functions. In these doubly discretized problems, the Chebyshev coefficients are the variables. These problems are, variously, either convex programming problems or programming problems that can be convexified. The resulting discrete problems are convex parameter-optimization problems; this is desirable because one can take advantage of very efficient and robust algorithms that have been developed previously and are well established for solving such problems. These algorithms are fast, do not require initial guesses, and always converge to global optima. Following the derivations, the algorithms are demonstrated by applying them to numerical examples of flyby, descent-to-hover, and ascent-from-hover maneuvers.
Acikmese, A. Bechet↗
Optimum Three Impulse Trajectory Generator with Patched Conic Trajectory Model
Optimal multi-impulse trajectories were investigated as a nominal about which asymptotic expansion was used to obtain approximations of optimal low thrust trajectories. The work consisted of the analysis and description of an optimal 3-impulse trajectory program. A patched-conic trajectory model was specifically designed for compatibility with the subsequent addition of the low thrust expansion approximation.
Payne, M. H.↗
Hybrid Differential Dynamic Programming with Stochastic Search
Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.
Aziz, Jonathan↗
Safe microburst penetration techniques: A deterministic, nonlinear, optimal control approach
A relatively large amount of computer time was used for the calculation of a optimal trajectory, but it is subject to reduction with moderate effort. The Deterministic, Nonlinear, Optimal Control algorithm yielded excellent aircraft performance in trajectory tracking for the given microburst. It did so by varying the angle of attack to counteract the lift effects of microburst induced airspeed variations. Throttle saturation and aerodynamic stall limits were not a problem for the case considered, proving that the aircraft's performance capabilities were not violated by the given wind field. All closed loop control laws previously considered performed very poorly in comparison, and therefore do not come near to taking full advantage of aircraft performance.
Psiaki, Mark L.↗
End-to-End Performance Optimization of a Crewed Lunar Landing Mission Staged from a Near Rectilinear Halo Orbit
A crewed lunar landing mission staged from a Near Rectilinear Halo Orbit (NRHO) presents a unique set of challenges not considered before for the Apollo-type direct missions. The NRHO does not have a fixed orbital plane and its period also changes with time, due to which the mission performance is very sensitive to the timing and location of the NRHO departure and arrival burns for a near-polar surface landing site. For such type of mission staged from the NRHO, an end-to-end optimization approach for the entire mission, from the NRHO departure to surface landing and from surface lift-off to the NRHO insertion, is well-suited for extracting the maximum performance out of this design. In this paper, an integrated approach for performing end-to-end optimization of a NRHO-staged crewed lunar landing mission is proposed that optimizes the in-space and powered flight segments simultaneously using Copernicus trajectory optimization tool. Copernicus is augmented with analytical approximations for the in-space, powered descent, and powered ascent segments in this work to improve the convergence of its multiple-shooting based direct optimization method. New analytical solutions are derived for the different phases of the powered flight segments by solving associated guidance problems. These analytical solutions act as initial guesses for starting the numerical optimization of the integrated mission in Copernicus. An example lunar landing mission is simulated to validate the proposed end-to-end optimization approach and the results are compared with the conventional patched trajectory approach.
Bharat Mahajan↗
Hybrid Differential Dynamic Programming with Stochastic Search
Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.
Aziz, Jonathan↗
Optimal abort landing trajectories in the presence of windshear
The abort landing problem is considered with reference to flight in a vertical plane. It is assumed that, upon sensing that the aircraft is in a windshear, the pilot increases the power setting at a constant time rate until maximum power setting is reached; afterward, the power setting is held constant. The performance index being minimized is the peak value of the altitude drop; the resulting optimization problem is a minimax or Chebyshev problem of optimal control. It is found that, for strong-to-severe windshears, the optimal trajectory includes three branches: a descending flight branch followed by a nearly horizontal flight branch, followed by an ascending flight branch after the aircraft has passed through the shear region. The peak altitude drop depends on the windshear intensity, the initial altitude, and the power setting rate; it increases as the windshear intensity increases and the initial altitude increases, and it decreases as the power setting rate increases.
Miele, A.↗
ROBOT. Apollo and AAP preliminary mission profile optimization program. Part 1 - Mathematical formulation
Logic and mathematical model for Saturn launch vehicle trajectory optimization program
Gottlieb, R. G.↗