A method is presented to solve a stochastic, nonlinear optimal control problem representative of ... more A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a distribution steering problem. Typical distribution steering problems rely on the underlying uncertainties to be Gaussian distributions. This work expands on previous developments by embedding Gaussian mixture distributions into the formulation to better handle the uncertainty propagation and chance constraints involved. The method is applied to a finite-thrust Earth-to-Mars transfer problem. Evaluation via Monte Carlo analysis shows a greater satisfaction of constraints under non-Gaussian distributions of the state and a statistically lower cost.
A method is presented to solve a stochastic, nonlinear optimal control problem representative of ... more A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a distribution steering problem. Typical distribution steering problems rely on the underlying uncertainties to be Gaussian distributions. This work expands on previous developments by embedding Gaussian mixture distributions into the formulation to better handle the uncertainty propagation and chance constraints involved. The method is applied to a finite-thrust Earth-to-Mars transfer problem. Evaluation via Monte Carlo analysis shows a greater satisfaction of constraints under non-Gaussian distributions of the state and a statistically lower cost.
Soil is a material with unique features and behavior at the interface between the biologic, hydro... more Soil is a material with unique features and behavior at the interface between the biologic, hydrologic, lithologic, and atmospheric spheres of our planet that plays a vital role in human welfare. The history of soil has been in step with the history of the use of soils to grow plants, a history of agriculture from earlier civilizations to our days. Until the 19 th century, no experimentation and testing of theories were conducted and there was no real science. Soil science was born about 150 years ago with the works of English, German, Danish and, above all, Russian scientists. In mid-20 th century, under pressure of human activities upon the environment, soil science out grew its base knowledge applied to agriculture and agronomy to play an ever-increased role of land and environmental issues. It was born the concept of soil security and soil was understood in its role of delivering ecosystem services and used to quantify the soil resource aggregating contributions of soil scientists, economists, social scientists and policy makers for decisionmaking process about soil.
Feedback control of constrained non-linear dynamical systems satisfying a certain optimality crit... more Feedback control of constrained non-linear dynamical systems satisfying a certain optimality criterion and meeting a specified transfer objective in the state space is recognized as one of the most challenging problems in control theory. One approach to computing optimal feedback policies is the dynamic programming route of numerically solving the Hamilton-Jacobi-Bellman (HJB) partial differential equation directly. In this paper an alternate and more tractable dynamic programming approach, the optimal feedback synthesis method, is utilized. The effectiveness of this method is demonstrated through an explicit guidance scheme for the heating-rate-constrained maneuver of an Aeroassisted Transfer Vehicle (AOTV). In optimal feedback synthesis, a feedback chart is constructed from a family of open-loop extremals, thus ensuring optimality with respect to any initial condition in the family. This paper presents a solution to the AOTV optimal feedback synthesis problem using the Gaussian process spatial prediction method of universal kriging. A closed-form expression for a near-optimal guidance law is derived. Its performance is found to be very promising; initial atmospheric entry errors due to simulated thruster misfiring are seen to be accurately corrected while the algebraic stateinequality constraint is closely respected.
This paper presents a new extremal-field approach for synthesizing nearly-optimal feedback contro... more This paper presents a new extremal-field approach for synthesizing nearly-optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general non-linear differential equations. The proposed method utilizes a spatial statistical technique called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. The kriging framework estimates an unknown function by observing its input-output behavior at a number of neighboring “training” sites. In universal kriging, a feedback map is considered to be the linear combination of a deterministic regression polynomial model and Gaussian random function. The parameters of the kriging model are computed based on data from offline-computed open-loop extremals, generated by a direct or indirect method. Numerical examples involving both autonomous and nonautonomous systems are presented to evaluate the effectiveness of this methodology. For each solved problem, the performance of the feedback controller is ascertained by comparing the feedback solutions with open-loop ones. The numerical accuracy of the feedback solutions is very encouraging, and the low computational overhead of this approach makes it a suitable candidate for real-time applications.
Particle swarm optimization is an evolutionary optimization method that relies on a group of pote... more Particle swarm optimization is an evolutionary optimization method that relies on a group of potential solutions to explore the search space. Conceptually, each particle in the swarm uses its own memory, as well as the knowledge accumulated by the entire swarm, to iteratively converge on the optimal solution. It is relatively easy to implement and, unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, has been little explored. In this work, particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems, including thrust programming for minimum fuel, multiburn spacecraft orbit transfer, and computing minimumtime rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of nonlinear mixed-integer programming problems with the swarming technique. A dynamic multistage-assignment penalty function is incorporated to enforce the associated constraints. For each test case, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy.
This paper presents a new extremal-field approach for synthesizing nearly optimal feedback contro... more This paper presents a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit–evasion games described by general nonlinear differential equations. The proposed method uses a spatial statistical technique called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. The kriging framework estimates an unknown function by observing its input–output behavior at a number of neighboring “training" sites. In universal kriging, a feedback map is considered to be the linear combination of a deterministic regression polynomial model and Gaussian random function. The parameters of the kriging model are computed based on data from offline-computed open-loop extremals, generated by a direct or indirect method. Numerical examples involving both autonomous and nonautonomous systems are presented to evaluate the effectiv...
The particle swarm algorithm is a population-based heuristic method successfully applied in sever... more The particle swarm algorithm is a population-based heuristic method successfully applied in several fields of research, only recently to aerospace trajectories. It represents a very intuitivemethodology for optimization, inspired by the behavior of bird flocks while searching for food. In this work, the method is applied to (impulsive and finitethrust) multiple-burn rendezvous trajectories. First, the technique is employed to determine the globally optimal four-impulse rendezvous trajectories for two challenging test cases. Second, the same problems are solved under the assumption of using finite thrust. In this context, the control function is assumed to be a linear combination of B-splines. Themethod at hand is relatively straightforward to implement anddoes not require an initial guess, unlike gradient-based solvers. Despite its simplicity and intuitiveness, the particle swarm methodology proves to be quite effective in finding the optimal solution to orbital rendezvous optimization problems with considerable numerical accuracy.
Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS) is a mission concept be... more Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS) is a mission concept being developed in preparation for the 2021 MidEX Announcement of Opportunity. This paper describes the key features of the OASIS architecture as they are currently understood. OASIS’s choice of a large inflatable primary reflector results in large collection areas at very high mass efficiency enabling the science mission. We describe the spacecraft bus, based on Northrop Grumman’s LEOstar-2, and the receiver, a heritage design based on the GUSTO balloon heterodyne system. We also discuss the observing strategy and pointing requirements from its planned L1 location. Particular emphasis is placed on challenges to the design, such as momentum management, balancing consumable mass allocations, thermal management, and testing.
The mission use of electric propulsion (EP) systems providing continuous, low thrust has steadily... more The mission use of electric propulsion (EP) systems providing continuous, low thrust has steadily increased over the past several years. As EP technology continues to mature, the upward trend in its efficient utilization is expected to persist. A particularly challenging and long-studied low-thrust trajectory design problem is Electric Orbit Raising, i.e. the design of many-revolution, long duration transfers in the planetocentric space. Numerous methods, both analytical and numerical, optimal and sub-optimal, open-and-closed-loop, and involving models of various degrees of complexity, have been proposed. This paper attempts to characterize and classify the more popular of these methods and their variants.
The ability to detect sudden and unexpected changes in the ephemerides of tracked space objects i... more The ability to detect sudden and unexpected changes in the ephemerides of tracked space objects is a crucial feature of space event monitoring systems. These changes may arise from actual space events such as satellite maneuvers or collisions, from cross-tagging of space objects as might occur during a fly-by, or even from inadvertently introduced defects in the orbit determination (OD) workflow. Utilizing robust time series forecasting techniques, this paper introduces a new method for detecting sudden changes in the ephemeris of a tracked object. Test cases drawn from known space events demonstrate that the software implementation of this method is able to flag each sequentially supplied orbitdetermined state as in-or out-of-family depending on whether the state is statistically typical relative to a configurable look-back interval.
The effect of launch injection errors on the deployment time and deployed mass of all-electric sa... more The effect of launch injection errors on the deployment time and deployed mass of all-electric satellites is investigated in this paper. A stochastic formulation is presented to capture the effect of uncertainties in the initial conditions of the electric orbit-raising problem. Specifically the errors in perigee, apogee and inclination of the injection orbit obtained from launch vehicle user manuals are considered. The stochastic framework is integrated with a fast and robust automated optimizer of low-thrust trajectories in order to propagate the initial condition uncertainties. Monte Carlo simulations are conducted to compute the statistics of transfer time and final deployed mass, by assuming Gaussian distribution for the initial states. The framework is also applicable to large-scale injection errors resulting from a launch vehicle anomaly or failure. Numerical simulations are presented to demonstrate efficacy of the developed concepts.
The ability to detect sudden and unexpected changes in the ephemerides of tracked space objects i... more The ability to detect sudden and unexpected changes in the ephemerides of tracked space objects is a crucial feature of space event monitoring systems. These changes may arise from actual space events such as satellite maneuvers or collisions, from cross-tagging of space objects as might occur during a fly-by, or even from inadvertently introduced defects in the orbit determination (OD) workflow. Utilizing robust time series forecasting techniques, this paper introduces a new method for detecting sudden changes in the ephemeris of a tracked object. Test cases drawn from known space events demonstrate that the software implementation of this method is able to flag each sequentially supplied orbitdetermined state as in-or out-of-family depending on whether the state is statistically typical relative to a configurable look-back interval.
A method is presented to solve a stochastic, nonlinear optimal control problem representative of ... more A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a distribution steering problem. Typical distribution steering problems rely on the underlying uncertainties to be Gaussian distributions. This work expands on previous developments by embedding Gaussian mixture distributions into the formulation to better handle the uncertainty propagation and chance constraints involved. The method is applied to a finite-thrust Earth-to-Mars transfer problem. Evaluation via Monte Carlo analysis shows a greater satisfaction of constraints under non-Gaussian distributions of the state and a statistically lower cost.
A method is presented to solve a stochastic, nonlinear optimal control problem representative of ... more A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a distribution steering problem. Typical distribution steering problems rely on the underlying uncertainties to be Gaussian distributions. This work expands on previous developments by embedding Gaussian mixture distributions into the formulation to better handle the uncertainty propagation and chance constraints involved. The method is applied to a finite-thrust Earth-to-Mars transfer problem. Evaluation via Monte Carlo analysis shows a greater satisfaction of constraints under non-Gaussian distributions of the state and a statistically lower cost.
Soil is a material with unique features and behavior at the interface between the biologic, hydro... more Soil is a material with unique features and behavior at the interface between the biologic, hydrologic, lithologic, and atmospheric spheres of our planet that plays a vital role in human welfare. The history of soil has been in step with the history of the use of soils to grow plants, a history of agriculture from earlier civilizations to our days. Until the 19 th century, no experimentation and testing of theories were conducted and there was no real science. Soil science was born about 150 years ago with the works of English, German, Danish and, above all, Russian scientists. In mid-20 th century, under pressure of human activities upon the environment, soil science out grew its base knowledge applied to agriculture and agronomy to play an ever-increased role of land and environmental issues. It was born the concept of soil security and soil was understood in its role of delivering ecosystem services and used to quantify the soil resource aggregating contributions of soil scientists, economists, social scientists and policy makers for decisionmaking process about soil.
Feedback control of constrained non-linear dynamical systems satisfying a certain optimality crit... more Feedback control of constrained non-linear dynamical systems satisfying a certain optimality criterion and meeting a specified transfer objective in the state space is recognized as one of the most challenging problems in control theory. One approach to computing optimal feedback policies is the dynamic programming route of numerically solving the Hamilton-Jacobi-Bellman (HJB) partial differential equation directly. In this paper an alternate and more tractable dynamic programming approach, the optimal feedback synthesis method, is utilized. The effectiveness of this method is demonstrated through an explicit guidance scheme for the heating-rate-constrained maneuver of an Aeroassisted Transfer Vehicle (AOTV). In optimal feedback synthesis, a feedback chart is constructed from a family of open-loop extremals, thus ensuring optimality with respect to any initial condition in the family. This paper presents a solution to the AOTV optimal feedback synthesis problem using the Gaussian process spatial prediction method of universal kriging. A closed-form expression for a near-optimal guidance law is derived. Its performance is found to be very promising; initial atmospheric entry errors due to simulated thruster misfiring are seen to be accurately corrected while the algebraic stateinequality constraint is closely respected.
This paper presents a new extremal-field approach for synthesizing nearly-optimal feedback contro... more This paper presents a new extremal-field approach for synthesizing nearly-optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general non-linear differential equations. The proposed method utilizes a spatial statistical technique called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. The kriging framework estimates an unknown function by observing its input-output behavior at a number of neighboring “training” sites. In universal kriging, a feedback map is considered to be the linear combination of a deterministic regression polynomial model and Gaussian random function. The parameters of the kriging model are computed based on data from offline-computed open-loop extremals, generated by a direct or indirect method. Numerical examples involving both autonomous and nonautonomous systems are presented to evaluate the effectiveness of this methodology. For each solved problem, the performance of the feedback controller is ascertained by comparing the feedback solutions with open-loop ones. The numerical accuracy of the feedback solutions is very encouraging, and the low computational overhead of this approach makes it a suitable candidate for real-time applications.
Particle swarm optimization is an evolutionary optimization method that relies on a group of pote... more Particle swarm optimization is an evolutionary optimization method that relies on a group of potential solutions to explore the search space. Conceptually, each particle in the swarm uses its own memory, as well as the knowledge accumulated by the entire swarm, to iteratively converge on the optimal solution. It is relatively easy to implement and, unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, has been little explored. In this work, particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems, including thrust programming for minimum fuel, multiburn spacecraft orbit transfer, and computing minimumtime rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of nonlinear mixed-integer programming problems with the swarming technique. A dynamic multistage-assignment penalty function is incorporated to enforce the associated constraints. For each test case, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy.
This paper presents a new extremal-field approach for synthesizing nearly optimal feedback contro... more This paper presents a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit–evasion games described by general nonlinear differential equations. The proposed method uses a spatial statistical technique called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. The kriging framework estimates an unknown function by observing its input–output behavior at a number of neighboring “training" sites. In universal kriging, a feedback map is considered to be the linear combination of a deterministic regression polynomial model and Gaussian random function. The parameters of the kriging model are computed based on data from offline-computed open-loop extremals, generated by a direct or indirect method. Numerical examples involving both autonomous and nonautonomous systems are presented to evaluate the effectiv...
The particle swarm algorithm is a population-based heuristic method successfully applied in sever... more The particle swarm algorithm is a population-based heuristic method successfully applied in several fields of research, only recently to aerospace trajectories. It represents a very intuitivemethodology for optimization, inspired by the behavior of bird flocks while searching for food. In this work, the method is applied to (impulsive and finitethrust) multiple-burn rendezvous trajectories. First, the technique is employed to determine the globally optimal four-impulse rendezvous trajectories for two challenging test cases. Second, the same problems are solved under the assumption of using finite thrust. In this context, the control function is assumed to be a linear combination of B-splines. Themethod at hand is relatively straightforward to implement anddoes not require an initial guess, unlike gradient-based solvers. Despite its simplicity and intuitiveness, the particle swarm methodology proves to be quite effective in finding the optimal solution to orbital rendezvous optimization problems with considerable numerical accuracy.
Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS) is a mission concept be... more Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS) is a mission concept being developed in preparation for the 2021 MidEX Announcement of Opportunity. This paper describes the key features of the OASIS architecture as they are currently understood. OASIS’s choice of a large inflatable primary reflector results in large collection areas at very high mass efficiency enabling the science mission. We describe the spacecraft bus, based on Northrop Grumman’s LEOstar-2, and the receiver, a heritage design based on the GUSTO balloon heterodyne system. We also discuss the observing strategy and pointing requirements from its planned L1 location. Particular emphasis is placed on challenges to the design, such as momentum management, balancing consumable mass allocations, thermal management, and testing.
The mission use of electric propulsion (EP) systems providing continuous, low thrust has steadily... more The mission use of electric propulsion (EP) systems providing continuous, low thrust has steadily increased over the past several years. As EP technology continues to mature, the upward trend in its efficient utilization is expected to persist. A particularly challenging and long-studied low-thrust trajectory design problem is Electric Orbit Raising, i.e. the design of many-revolution, long duration transfers in the planetocentric space. Numerous methods, both analytical and numerical, optimal and sub-optimal, open-and-closed-loop, and involving models of various degrees of complexity, have been proposed. This paper attempts to characterize and classify the more popular of these methods and their variants.
The ability to detect sudden and unexpected changes in the ephemerides of tracked space objects i... more The ability to detect sudden and unexpected changes in the ephemerides of tracked space objects is a crucial feature of space event monitoring systems. These changes may arise from actual space events such as satellite maneuvers or collisions, from cross-tagging of space objects as might occur during a fly-by, or even from inadvertently introduced defects in the orbit determination (OD) workflow. Utilizing robust time series forecasting techniques, this paper introduces a new method for detecting sudden changes in the ephemeris of a tracked object. Test cases drawn from known space events demonstrate that the software implementation of this method is able to flag each sequentially supplied orbitdetermined state as in-or out-of-family depending on whether the state is statistically typical relative to a configurable look-back interval.
The effect of launch injection errors on the deployment time and deployed mass of all-electric sa... more The effect of launch injection errors on the deployment time and deployed mass of all-electric satellites is investigated in this paper. A stochastic formulation is presented to capture the effect of uncertainties in the initial conditions of the electric orbit-raising problem. Specifically the errors in perigee, apogee and inclination of the injection orbit obtained from launch vehicle user manuals are considered. The stochastic framework is integrated with a fast and robust automated optimizer of low-thrust trajectories in order to propagate the initial condition uncertainties. Monte Carlo simulations are conducted to compute the statistics of transfer time and final deployed mass, by assuming Gaussian distribution for the initial states. The framework is also applicable to large-scale injection errors resulting from a launch vehicle anomaly or failure. Numerical simulations are presented to demonstrate efficacy of the developed concepts.
The ability to detect sudden and unexpected changes in the ephemerides of tracked space objects i... more The ability to detect sudden and unexpected changes in the ephemerides of tracked space objects is a crucial feature of space event monitoring systems. These changes may arise from actual space events such as satellite maneuvers or collisions, from cross-tagging of space objects as might occur during a fly-by, or even from inadvertently introduced defects in the orbit determination (OD) workflow. Utilizing robust time series forecasting techniques, this paper introduces a new method for detecting sudden changes in the ephemeris of a tracked object. Test cases drawn from known space events demonstrate that the software implementation of this method is able to flag each sequentially supplied orbitdetermined state as in-or out-of-family depending on whether the state is statistically typical relative to a configurable look-back interval.
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Papers by Pradipto Ghosh