Ehsan Taheri

Auburn University | AU · Department of Aerospace Engineering

Low-thrust trajectories can be designed with efficient solar electric propulsion (SEP) systems. One class of electric propulsion systems allows for modulation of specific impulse and thrust magnitude (i.e., variable-specific-impulse variable-thrust (VIVT) engines). In this paper, we present both an indirect-and a direct-based approach for optimizin...

Low-thrust trajectories with more realistic thruster and power models improve the practicality and fidelity of the solutions in terms of reflecting the real mission and for mass budget calculations. Solar-powered electric ion and Hall-effect thrusters can operate at many discrete modes corresponding to various power levels. However, the selection o...

Solutions to general nonlinear optimal control problems (OCPs) exhibit dispersions under model uncertainties and it is desirable to generate optimal solutions that exhibit less sensitivity to model uncertainties. We propose a novel solution desensitization method dubbed "Reduced Desensitization Formulation (RDF)" by leveraging homogeneity of the co...

Spacecraft trajectory optimization is an essential task in space mission design. The propulsion system of the spacecraft can affect the type of trajectories that can be realized by a spacecraft. In the past few decades, electric propulsion systems (with their characteristic high specific impulse values, but low thrust magnitudes) have revolutionize...

Rendezvous maneuvers are designed to match the position and velocity vectors of a target body (e.g., planet, comet, satellite) whereas transfer maneuvers are designed to match the orbital elements of the target body, except for the true anomaly under a two-body dynamical model. The question of how many impulsive maneuvers are necessary to minimize...

In space mission design, an important operational constraint is planned periodic coast arcs, during which various mission-critical tasks such as navigation or ground communications are performed. These constraints, typically implemented as thruster duty cycles, can be described as discrete coasting events enforced periodically during intervals of d...

The question of how many impulses is necessary to optimize a transfer-type maneuver has remained open for decades. Recently, the introduction of optimal switching surfaces revealed the existence of iso-impulse trajectories with differing numbers of impulses for fixed-time rendezvous maneuvers. In this paper, the multiplicity of minimum-Δv impulsive...

Impulsive trajectories provide time-and Δ-reachability insights. Two novel homotopy-based methods are proposed for generating optimal many-impulse, multi-revolution maneuvers. The first method is based on the continuation over the specific impulse value, which is shown to enhance convergence performance of the resulting two-point boundary-value pro...

Spacecraft path-planning approaches that are capable of producing not only autonomous but also generalized solutions promise to open new modalities for robotic exploration and servicing in orbit environments characterized by epistemic uncertainty. Our hypothesis is that, in face of large systemic uncertainties, learning control policies from human...

We study the multiplicity of minimum-∆v impulsive trajectories for long-time-horizon problems. One notable feature of these extremal impulsive trajectories is that many of the impulses are applied at a specific position, highlighting the significance of what we coin as "impulse anchor positions." We demonstrate that for long-time-horizon maneuvers...

Solutions to practical optimal control problems (OCPs) may consist of control profiles that switch between control limits or assume values interior to its admissible set, either due to activation of inequality state path constraints or existence of singular control arcs. Moreover, abrupt switches in the control (i.e., bang-bang control) jeopardizes...

The fields of trajectory optimization and optimal control are closely connected. Practical trajectory optimization techniques are built on the indirect and direct methods for solving optimal control problems. Indirect methods seek to satisfy the first-order necessary conditions of optimality, while direct methods discretize the problem and transcri...

We introduce an optimization tool for solving impulsive trajectory optimization problems within the nonlinear restricted three-body dynamical models. The proposed tool uses acceleration-based switching surfaces to generate high-quality, near-impulsive trajectories. High-acceleration trajectories are found by sweeping through the acceleration value...

This work presents a comparison between fixed-time, low-thrust, minimum-fuel trajectories obtained using an enhanced indirect method and a successive convexification method. Convex optimization guarantees convergence in polynomial time. However, trajectory optimization problems are often non-convex and must be transformed into convex sub-problems a...

We propose an alternative derivation of extremal control inputs for optimal control problems with mixed regular and singular control arcs and in the presence of state path constraints. As an application, we consider the classical Goddard rocket vertical ascent problem with bounded control and a state path constraint on the dynamic pressure value. F...

This study investigates a complicated reentry trajectory optimization problem for a reusable launch vehicle (RLV) in the presence of two control constraints and three state path constraints. Upon using traditional indirect methods, the considered RLV reentry trajectory optimization problem is converted into a complicated 12-point boundary-value pro...

Indirect formalism of optimal control theory is used to generate minimum-time and minimum-fuel trajectories for formation of two spacecraft (deputies) relative to a chief satellite. For minimum-fuel problems, a hyperbolic tangent smoothing method is used to facilitate numerical solution of the resulting boundary-value problems by constructing a one...

In this study, a supervised machine learning approach called Gaussian process regression (GPR) was applied to approximate optimal bi-impulse rendezvous maneuvers in the cis-lunar space. We demonstrate the use of the GPR approximation of the optimal bi-impulse transfer to patch points associated with various invariant manifolds in the cis-lunar spac...

Variational approach to optimal control theory converts trajectory optimization problems into two- or multiple-point boundary-value problems, which consist of costates (i.e., Lagrange multipliers associated with the states). Estimating missing values of the non-intuitive costates is an important step in solving the resulting boundary-value problems...

Motion-planning (or guidance) algorithms play an important role in the overall mission design of aerospace vehicles, and in particular, unmanned aerial vehicles. We propose a novel method for generating smooth reference trajectories using the Finite Fourier Series (FFS) method. Trajectories generated using the FFS method are compared against the tr...

This paper presents an efficient indirect optimization method to solve time-and fuel-optimal asteroid landing trajectory design problems. The gravitational field of the target asteroid is approximated with two methods: 1) a simple two-body (point-mass) model, and 2) a high-fidelity polyhedral model. A homotopy approach, at the level of the gravity-...

In this paper, we investigate the problem of optimal coordination of connected vehicles under automated driving (CVAD) at intersections. More specifically, we propose the intersection trajectory optimal control problem (ITOP), in which an intersection is a space without movement-related horizontal markings or structural restrictions, except for the...

In this paper, we investigate the manifolds of three Near-Rectilinear Halo Orbits (NRHOs) and optimal low-thrust transfer trajectories using a high-fidelity dynamical model. Time- and fuel-optimal low-thrust transfers to (and from) these NRHOs are generated leveraging their ‘invariant’ manifolds, which serve as long terminal coast arcs. Analyses ar...

Numerical solutions of optimal control problems are influenced by the appropriate choice of coordinates. The proposed method based on the variational approach to map costates between sets of coordinates and/or elements is suitable for solving optimal control problems using the indirect formalism of optimal control theory. The Jacobian of the nonlin...

A supervised machine learning approach called the Gaussian Process Regression (GPR) is applied to approximate the optimal bi-impulse rendezvous maneuvers in cis-lunar space. The use of GPR approximation of the optimal bi-impulse transfer to patch-points associated with various invariant manifolds in the cis-lunar space is demonstrated. The proposed...

A novel indirect-based trajectory optimization framework is proposed that leverages ephemeris-driven, "invariant manifold analogues" as long-duration asymptotic terminal coast arcs while incorporating eclipses and perturbations during the optimization process in an ephemeris model; a feature lacking in state of the art software like MYSTIC and Cope...

Low-thrust trajectory design can be converted into boundary-value problems, which are typically challenging to solve because of a small domain of convergence and lack of knowledge about the initial costates when indirect formalism of optimal control is adopted. Many techniques have been developed to overcome the problem of guessing the initial cost...

A novel methodology is proposed for designing low-thrust trajectories to quasi-periodic, near rectilinear Halo orbits that leverages ephemeris-driven, "invariant manifold analogues" as long-duration asymptotic terminal coast arcs. The proposed methodology generates end-to-end, eclipse-conscious, fuel-optimal transfers in an ephemeris model using an...

This paper proposes an overarching trajectory-power-propulsion co-optimization framework by incorporating actual discrete operation modes of electric thrusters within the optimal control formulation of spacecraft trajectory design. An interplanetary trajectory from Earth to comet 67P/Churyumov-Gerasimenko is formulated and solved using a spacecraft...

Application of idealized constant-specific-impulse, constant-thrust electric thruster performance models or curve-fitted polynomials is quite common for spacecraft trajectory design. However, incorporation of realistic performance models of multi-mode electric thrusters leads to notable challenges, and at the same time, offers unprecedented system-...

The complexities in using indirect optimization methods get compounded for practical co-optimization problems in the presence of continuous and discrete design variables. In this paper, realistic multimode electric propulsion systems are incorporated within the formulation of gravity-assist, low-thrust trajectory design problems. Electric thrusters...

In this work, end-to-end low-thrust transfers from a GTO orbit to a low-altitude lunar orbit by exploiting the manifolds of a chosen Earth-Moon L1 halo orbit was studied. The practicality of piece-wise, minimum-time transfers that exploit halo orbit manifolds is demonstrated, which offers more flexibility to meet mission objectives. It is known tha...

A novel acceleration-based formulation is proposed to construct minimum-∆v bang-off-bang thrust profiles and impulsive maneuvers in a rapid manner. The proposed methodology leads to substantial simplifications by removing mass state, thrust magnitude and specific impulse values from the ensuing boundary-value problems. Standard acceleration-based m...

A method is proposed to map costates between two sets of coordinates. The proposed method is suitable for solving optimal control problems using indirect methods and with different sets of coordinates or elements. The Jacobian of the non-linear map between any two sets of coordinates/elements plays a pivotal role in the costate vector transformatio...

In this paper, two methodologies are investigated for generating the missing initial costate values of the Hamiltonian boundary-value problems associated with minimum-fuel low-thrust trajectories. Specifically, the set of Cartesian coordinates and Modified Equinoctial Elements (MEEs) are used for modeling dynamics. The initial costates are obtained...

In this work, an enhanced indirect optimization method is implemented as the inner-level solver within a hybrid evolutionary-indirect dual-level algorithm. The input to the algorithm is a user-defined sequence of planets. The outer-level optimization algorithm, a particle swarm algorithm, optimizes over boundary conditions , time of phases, and gra...

This study investigates the application of a recently developed construct, the Uniform Trigonometrization Method (UTM), to the singular control problems in chemical engineering. The UTM involves minimal modifications to the original problem, thereby generating near‐singular control solutions that can be used for conceptual design and serve as an al...

Application of idealized constant-specific-impulse, constant-thrust electric thruster performance models or curve-fitted polynomials is quite common for spacecraft trajectory design. However, the incorporation of realistic performance models of multi-mode electric thrusters leads to notable challenges, and at the same time, offers unprecedented sys...

Indirect optimization methods convert optimal control problems (OCPs) into two-or multi-point boundary-value problems. A highly desirable feature of indirect methods, specifically for space applications, is that high-resolution trajectories can be generated, which satisfy the first-order necessary conditions of optimality. A recently developed Comp...

Minimum-time planet-centric transfer maneuvers are investigated for spacecraft equipped with solar-powered, low-thrust electric thrusters. Many orbital revolutions in the presence of perturbations make the task of trajectory design quite challenging. To enhance the numerical convergence properties of the standard single-shooting solution methods, t...

This study investigates the use of trigonometric functions to resolve two major issues encountered when solving practical optimal control problems (OCPs) that are characterized by non-linear controls. First, OCPs with constraints on non-linear controls require the solution to a multi-point boundary value problem, which poses additional computationa...

Near-Rectilinear Halo Orbits (NRHOs) are deemed to be favorable candidates for establishing a near-future crewed space station in the cis-lunar space. Although the 9:2 resonant southern $L_2$ NRHO has been earmarked as the working orbit for the Lunar Gateway Mission, a plethora of other neighboring resonant NRHOs are also viable options. The invari...

A trigonometric-based regularization technique is proposed for generating fuel-optimal low-thrust trajectories. For a spacecraft equipped with a constant specific impulse and constant maximum-thrust engine, thrust magnitude profile exhibits non-smooth, bang-off-bang structures. The number (and time instant) of switches between thrust and coast arcs...

A trigonometric-based regularization method is applied to the entry phase where the vehicle is subject to three state path constraints: dynamic pressure, stagnation point heat-rate, and g-load. The vehicle trajectory is controlled through modulating the angle of attack and bank angle. Presence of state and control path constraints is a challenging...

In this paper, we propose a framework for generating low-thrust trajectories with multiple gravity-assist maneuvers using a finite Fourier series shape-based (FFS-SB) method. The FFS-SB method is capable of handling thrust and state constraints and can produce three-dimensional approximate fuel-and time-optimal trajectories. These features make the...

This study investigates the application of a recently developed construct, the Uniform Trigonometrization Method (UTM), to the singular control problems in chemical engineering. The UTM involves minimal modifications to the original problem, thereby generating near-singular control solutions that can be used for conceptual design and serve as an al...

Application of indirect optimization methods to solve constrained optimal control problems is not a straightforward task. This study presents a new construct --- the Uniform Trigonometrization Method (UTM) --- that enables handling problems with control bounds and state path constraints within the indirect formalism. First, three different classes...

In trajectory planning and control design for unmanned air vehicles, highly simplified models are typically used to represent the vehicle dynamics and the operating environment. The goal of this work is to perform real-time, but realistic, flight simulations and trajectory planning for quad-copters in low-altitude (<500 m) atmospheric conditions. T...

Designing optimal spacecraft trajectories is a critical task for any mission design. In particular, mission designers seek to exploit from the combined effects of planetary gravity-assist maneuvers and electric propulsions systems to reduce both the flight time and propellant consumption. In order to obtain more realistic results, disturbances such...

Lyapunov methods are well established as a versatile approach for generating feasible and robustly converging spiral-type low-thrust trajectories. The present study introduces Lya-punov optimal methods for low-thrust guidance. The approach makes use of the regularized modified equinoctial orbit elements in such a way that a nominal trajectory can b...

A renewed interest in revisiting the Moon has blown wide open the previously ajar door to research avenues in the field of Earth-Moon transfer trajectories. While the advent of low-thrust propulsion systems has opened up possibilities to undertake more complicated missions, designing optimal transfer trajectories in this domain is no easy feat. His...

Indirect optimization methods convert optimal control problems (OCPs) into two-or multi-point boundary-value problems. A highly desirable feature of indirect methods, specifically for space applications, is that high-resolution trajectories can be generated, which satisfy the first-order necessary conditions of optimality. We utilize the features o...

Equipping a spacecraft with multiple solar-powered electric engines (of the same or different types) compounds the task of optimal trajectory design due to presence of both real-valued inputs (power input to each engine in addition to the direction of thrust vector) and discrete variables (number of active engines). Each engine can be switched on/o...

Efficient performance of a number of engineering systems is achieved through different modes of operation - yielding systems described as “hybrid”, containing both real-valued and discrete decision variables. Prominent examples of such systems, in space applications, could be spacecraft equipped with 1) a variable-Isp, variable-thrust engine or 2)...

Design of low-thrust trajectories with realistic solar electric propulsion (SEP) models is challenging since 1) engine's thrust depends on the available power, which itself depends on both the distance from the Sun and efficiency degradation of the solar arrays, and 2) in practice, engines operate at only a finite number of throttle settings. Missi...

Application of indirect optimization methods to solve constrained optimal control problems (OCPs) is a challenging task. This study demonstrates the utility of a new construct, the Unified Trigonometrization Method (UTM), which alleviates some of the issues associated with OCPs that consist of control bounds and state path constraints. Three differ...

Spacecraft equipped with variable specific impulse, variable-thrust (VIVT) engines may exhibit multiple switches between high- and low-thrust operation modes during their interplanetary trajectories. A new framework, composite smooth control (CSC), is recently developed to alleviate a number of challenges that arise when optimal control problems as...

A central problem in orbit transfer optimization is to determine the number, time, direction, and magnitude of velocity impulses that minimize the total impulse. This problem was posed in 1967 by T. N. Edelbaum, and while notable advances have been made, a rigorous means to answer Edelbaum’s question for multiple-revolution maneuvers has remained e...

It is not surprising that the idea of efficient maintenance algorithms (originally motivated by strict emission regulations, and now driven by safety issues, logistics and customer satisfaction) has culminated in the so-called condition-based maintenance program. Condition-based program/monitoring consists of two major tasks, i.e., \textit{diagnost...

Designing long-duration lunar orbiter missions is challenging due to the Moon’s highly nonlinear gravity field and the third-body perturbations induced by the Earth, Sun and other large bodies. The absence of a Lunar atmosphere has offered the possibility for mission designers to search for extremely low-altitude, quasi-stable lunar orbits. In additi...

The presence of extremely low-altitude, lunar quasi-frozen orbits (QFOs) has given rise to interesting mission opportunities. These QFOs are ideal for close-range, high-resolution mapping of the lunar south pole, and their inherent stability translates into minimal station-keeping efforts. Despite the aforementioned desirable characteristics, desig...

Equipping a spacecraft with multiple solar-powered electric engines (of the same or different types) compounds the task of optimal trajectory design due to presence of both real-valued inputs (power input to each engine in addition to the direction of thrust vector) and discrete variables (number of active engines). Each engine can be switched on/o...

Application of traditional indirect optimization methods to optimal control problems (OCPs) with control and state path constraints is not a straightforward task. However, recent advances in regularization techniques and numerical continuation methods have enabled application of indirect methods to very complex OCPs. This study demonstrates the uti...

Efficient performance of a number of engineering systems is achieved through different modes of operation-yielding systems described as "hybrid", containing both real-valued and discrete decision variables. Prominent examples of such systems, in space applications, could be spacecraft equipped with 1) a variable-Isp , variable-thrust engine or 2) m...

Equipping a spacecraft with multiple solar-powered electric engines (of the same or different types) compounds the task of optimal trajectory design due to presence of both real-valued inputs (power input to each engine in addition to the direction of thrust vector) and discrete variables (number of active engines). Each engine can be switched on/o...

Application of traditional indirect optimization methods to optimal control problems (OCPs) with control and state path constraints is not a straightforward task. However, recent advances in regularization techniques and numerical continuation methods have enabled application of indirect methods to very complex OCPs. This study demonstrates the uti...

Low-thrust propulsion technology and planetary gravity-assist maneuvers make a promising combination for deep space explorations. Hybrid optimal control methods have proven to be an excellent solution framework which exploits the advantages of both direct and indirect optimization methods, while alleviating their drawbacks. We employ a recently int...

The wave energy converter (WEC) devices provide access to a renewable energy source. Developing control strategies to harvest maximum wave energy requires solving a constrained optimal control problem. It is shown that singular control arcs may constitute part (or the entire) of extremal trajectories. Characterizing the optimal control structure, e...

The wave energy converter (WEC) devices provide access to a renewable energy source. Developing control strategies to harvest maximum wave energy requires solving a constrained optimal control problem. It is shown that singular control arcs may constitute part (or the entire) of extremal trajectories. Characterizing the optimal control structure, e...

We present a new methodology to incorporate shadow-and time-triggered constraints within the indirect optimization methods to solve low-thrust fuel-optimal orbit transfer problems. Such constraints could represent, for instance, zero thrusting during an eclipse or a time interval during which the thruster has to be shut down during a mission scienc...

One of the fundamental tasks in space mission design is to choose a set of inter-disciplinary mission-critical parameters that are used for both sizing spacecraft sub-systems and designing optimal trajectories. Trajectory design and sub-system sizing are tightly coupled tasks and mission designers are interested in algorithms that not only improve...