arXiv subjects

Ehsan Taheri

Publications and source records attributed to Ehsan Taheri.

At least 19 recordsLinked to original sources

arXiv2026

Diffusion-Based Multiple-Shooting Indirect Optimal Control for Fuel-Optimal Spacecraft Trajectory Generation

Diffusion-based generative models (DMs) have found applications in control problems, and in particular robotics, where the DMs enable exploration of possible control solutions. A critical shortcoming of these applications is that they have lacked optimality guarantees. This is a problem for their potential use in fuel-optimal spacecraft trajectories that are characterized with long time-horizons and bang-bang profiles. Alternatively, indirect optimal control methods ensure explicit satisfaction of necessary conditions, but are highly sensitive to the initial costate estimation needed to solve the resulting Hamiltonian boundary-value problems (HBVPs). To alleviate this sensitivity and enlarge the convergence domain of HBVPs, advanced indirect methods have been developed that use smoothing approaches and continuation. We propose a diffusion-based multiple shooting indirect control method that combines the exploration capability of DMs with indirect method to generate fuel-optimal spacecraft trajectories. We benchmark our method against an advanced indirect method on a fuel-optimal Earth-Mars low-thrust transfer problem, showing higher convergence robustness than the advanced indirect method that is based on random costate initialization. Code and visualizations are available at https://saeidtafazzol.github.io/Diffusion_Indirect_Control/.

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arXiv2026

Robust Spacecraft Low-Thrust Trajectory Design: A Chance-Constrained Covariance-Steering Approach

This paper proposes a systematic method for generating practical and robust low-thrust spacecraft trajectories. One contribution is to consider the change in mass of the spacecraft at two levels: a) the propulsive acceleration and b) the intensity of the stochastic disturbances. A covariance variable formulation is considered, which is computationally more efficient than the factorized covariance implementation. The proposed approach is applied to two- (i.e., planar) and three-dimensional heliocentric phases of spacecraft flight from Earth to Mars under the restricted two-body dynamics. The results highlight the importance of keeping track of mass change to generate more realistic, robust trajectories for interplanetary space missions to avoid underestimation of mission risks.

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arXiv2025

Incorporating the nonlinearity index into adaptive-mesh sequential convex optimization for minimum-fuel low-thrust trajectory design

Successive convex programming (SCP) is a powerful class of direct optimization methods, known for its polynomial complexity and computational efficiency, making it particularly suitable for autonomous applications. Direct methods are also referred to as ``discretize-then-optimize'' with discretization being a fundamental solution step. A key step in all practical direct methods is mesh refinement, which aims to refine the solution resolution by enhancing the precision and quality of discretization techniques through strategic distribution and placement of mesh/grid points. We propose a novel method to enhance adaptive mesh refinement stability by integrating it with a nonlinearity-index-based trust-region strategy within the SCP framework for spacecraft trajectory design. The effectiveness of the proposed method is demonstrated through solving minimum-fuel, low-thrust missions, including a benchmark Earth-to-Asteroid rendezvous and an Earth-Moon L2 Halo-to-Halo transfer using the Circular Restricted Three-Body (CR3BP) model.

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arXiv2025

Eigendecomposition Parameterization of Penalty Matrices for Enhanced Control Design: Aerospace Applications

Modern control algorithms require tuning of square weight/penalty matrices appearing in quadratic functions/costs to improve performance and/or stability output. Due to simplicity in gain-tuning and enforcing positive-definiteness, diagonal penalty matrices are used extensively in control methods such as linear quadratic regulator (LQR), model predictive control, and Lyapunov-based control. In this paper, we propose an eigendecomposition approach to parameterize penalty matrices, allowing positive-definiteness with non-zero off-diagonal entries to be implicitly satisfied, which not only offers notable computational and implementation advantages, but broadens the class of achievable controls. We solve three control problems: 1) a variation of Zermelo's navigation problem, 2) minimum-energy spacecraft attitude control using both LQR and Lyapunov-based methods, and 3) minimum-fuel and minimum-time Lyapunov-based low-thrust trajectory design. Particle swarm optimization is used to optimize the decision variables, which will parameterize the penalty matrices. The results demonstrate improvements of up to 65% in the performance objective in the example problems utilizing the proposed method.

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arXiv2025

Constrained Fuel and Time Optimal 6DOF Powered Descent Guidance Using Indirect Optimization

Powered descent guidance (PDG) problems subject to six-degrees-of-freedom (6DOF) dynamics allow for enforcement of practical attitude constraints. However, numerical solutions to 6DOF PDG problems are challenging due to fast rotational dynamics coupled with translational dynamics, and the presence of highly nonlinear state/control path inequality constraints. In this work, constrained fuel- and time-optimal 6DOF PDG problems are solved leveraging a regularized indirect method, subject to inequality constraints on the thrust magnitude, thruster gimbal angle, rocket tilt angle, glideslope angle, and angular velocity magnitude. To overcome the challenges associated with solving the resulting multipoint boundary-value problems (MPBVPs), the state-only path inequality constraints (SOPICs) are enforced through an interior penalty function method, which embeds the resulting MPBVPs into a multi-parameter smooth neighboring families of two-point BVPs. Extremal solutions are obtained using an indirect multiple-shooting solution method with numerical continuation. Moreover, an empirical relation is derived for the directly-adjoined Lagrange multipliers associated with SOPICs. The fuel- and time-optimal trajectories are compared against solutions of DIDO -- a capable pseudospectral-based software for solving practical constrained optimal control problems.

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arXiv2025

Classification and Feasibility Assessment of Infinitely Many Iso-Impulse Three-Dimensional Trajectories

In two-body dynamics, it is proven that for a sufficiently long flight time, generating infinitely many iso-impulse solutions is possible by solving a number of $Δv$-allocation problems analytically. A distinct feature of these solutions is the existence of two impulse anchor positions (APs) that correspond to the locations of the impulses on time-free, phase-free, base solutions. In this paper, the existence and utility of three-impulse base solutions are investigated and their complete solution spaces are characterized and analyzed. Since two- and three-impulse base solutions exist, a question arises: How many APs should base solutions have? A strategy is developed for choosing base solutions, which offers a certificate for $Δv$ optimality of general three-dimensional time-fixed rendezvous solutions. Simultaneous allocation of $Δv$ at two and three APs is formulated, which allows for generating $Δv$-optimal solutions while satisfying a constraint on individual impulses such that $Δv \leq Δv_\text{max}$. All iso-impulse solutions are classified in four layers: 1) base solutions, 2) feasible solution spaces, 3) solution families, and 4) solution envelopes. The method enables us to characterize the complete solution space of minimum-$Δv$, iso-impulse, three-dimensional trajectories under the nonlinear two-body dynamics. To illustrate the utility of the method, interplanetary and geocentric problems are considered.

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arXiv2024

End-to-End Lyapunov-Based Eclipse-Feasible Low-Thrust Transfer Trajectories to NRHO

Generating low-thrust transfer trajectories between Earth and the Near Rectilinear Halo Orbit (NRHO), that is selected for NASA's Gateway, can be challenging due to the low control authority available from the propulsion system and the important operational constraint that the duration of all eclipses has to be less than a prescribed 90-minute threshold. We present a method for generating eclipse-feasible, minimum-time solutions to the aforementioned trajectory design problem using a Lyapunov control law. Coasting is enforced during solar eclipses due to both the Earth and Moon. We used particle swarm optimization to optimize the NRHO insertion date, time of flight, and control law parameters according to a cost function that prioritizes 1) convergence to the target orbit, 2) satisfaction of eclipse-duration constraints, and 3) minimization of time of flight. Trajectories can serve as initial guesses for NASA's high-fidelity trajectory design tools such as Copernicus and GMAT.

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arXiv2024

Time-Triggered Reduced Desensitization Formulation For Solving Optimal Control Problems

Fuel-optimal trajectories are inherently sensitive to variations in model parameters, such as propulsion system thrust magnitude. This inherent sensitivity can lead to dispersions in cost-functional values, when model parameters have uncertainties. Desensitized optimal control aims at generating robust optimal solutions while taking into account uncertainties in the model parameters. While desensitization techniques typically apply along the entire flight time, this paper introduces a novel time-triggered desensitization mechanism by modifying a recently developed desensitization method -- the Reduced Desensitization Formulation (RDF). By selectively desensitizing over specific time intervals of trajectories, we demonstrate the improved optimality of desensitized trajectories. We investigate the effects of temporal desensitization on the final cost and trajectory by considering thrust magnitude uncertainty for two classes of low-thrust trajectory optimization problems: 1) minimum-fuel rendezvous maneuvers and 2) orbit-raising maneuvers. Results show that temporal desensitization can achieve similar dispersion levels to full mission desensitization with an improved final cost functional.

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arXiv2024

Comparison of control regularization techniques for minimum-fuel low-thrust trajectory design using indirect methods

Minimum-fuel low-thrust trajectories typically consist of a finite, yet unknown number of switches in the thrust magnitude profile. This optimality-driven characteristic of minimum-fuel trajectories poses a challenge to the numerical methods that are typically used for solving the resulting Hamiltonian boundary-value problems (BVPs). In this paper, we compare the impact of the popular hyperbolic-tangent-based smoothing with a novel L2-norm-based smoothing on the convergence performance of quasi-Newton gradient-based methods. Both smoothing methods are applied directly at the level of control, which offer a significant implementation simplicity. We also investigate the application of each method in scenarios where the State Transition Matrix (STM) is used for accurate calculation of the sensitivities of the residual vector of the resulting BVPs with respect to the unknown initial costate values. The effectiveness of each control smoothing method is assessed across several benchmark minimum-fuel low-thrust trajectory optimization problems.

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arXiv2024

Expanding the Class of Quadratic Control-Lyapunov Functions for Low-Thrust Trajectory Optimization

Control laws derived from Control-Lyapunov Functions (CLFs) offer an efficient way for generating near-optimal many-revolution low-thrust trajectories. A common approach to constructing CLFs is to consider the family of quadratic functions using a diagonal weighting matrix. In this paper, we explore the advantages of using a larger family of quadratic functions. More specifically, we consider positive-definite weighting matrices with non-zero off-diagonal elements (hereafter referred to as "full" matrices). We propose a novel eigendecomposition method for parameterizing $N$-dimensional weighting matrices that is easy to implement and guarantees positive-definiteness of the weighting matrices. We use particle swarm optimization, which is a stochastic optimization algorithm, to optimize the parameters and generate near-optimal minimum-time low-thrust trajectories. Solutions obtained using a full positive-definite matrix are compared to the results from the (standard) diagonal weighting matrix for a number of benchmark problems. Results demonstrate that improvements in optimality are achieved, especially for maneuvers with large changes in orbital elements.

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arXiv2024

Co-optimization of spacecraft and low-thrust trajectory with direct methods

Solar-powered electric propulsion systems can operate in multiple modes and their operation is coupled to the power generated by solar arrays. However, the power produced by the solar arrays is a function of the solar array size and heliocentric distance to the Sun, which also depends on the to-be-optimized trajectory. The optimization of spacecraft solar array size, thruster modes, and trajectory can be performed simultaneously, capitalizing on the inherent couplings. In this work, we co-optimize the spacecraft's solar array size, thruster modes, and trajectory using a direct optimization, which allows for maximizing the net delivered mass. A particular challenge arises due to the existence of discrete operating modes. We proposed a method for smoothly selecting optimal operation modes among a set of finite possible modes. The utility of the proposed method is demonstrated successfully by solving a benchmark problem, i.e., the Earth to Comet 67P fixed-time rendezvous problem. The results indicate that utilizing multiple modes increases the net useful mass compared to a single mode and leads to a smaller solar array size for the spacecraft.

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arXiv2023

Rapid Determination of Low-Thrust Spacecraft Reachable Sets in Two-Body and Cislunar Problems

The reachable set of controlled dynamical systems consist of the set of all possible reachable states from an initial condition, over a certain period of time under various control and operation constraints and exogenous disturbances. For space applications, determination of reachable sets is invaluable for trajectory planning, collision avoidance, ensuring safe and optimal performance in complex, real-world scenarios. Leveraging the connection between minimum-time and reachable sets, we propose a method for rapid determination of reachable sets for finite- and low-thrust spacecraft using an indirect minimum-time multi-stage formulation and the primer vector theory. Reachable set analyses are presented for a minimum-time low-thrust Earth-Mars rendezvous problem and for several cislunar applications under circular restricted three-body dynamics. For the Earth-Mars problem and thruster parameters, results indicate that the minimum-time solution lies within the feasible set of position vectors, but on the boundary of the reachable set of velocity vectors. For the cislunar problems, L2 Halo orbit and Lunar Gateway 9:2 NRHO are considered. Our results indicate that the reachable set of low-thrust spacecraft coincides with invariant manifolds existing in the multi-body dynamical environments.

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arXiv2023

Minimum-Time Trajectory Optimization With Data-Based Models: A Linear Programming Approach

In this paper, we develop a computationally-efficient approach to minimum-time trajectory optimization using input-output data-based models, to produce an end-to-end data-to-control solution to time-optimal planning/control of dynamic systems and hence facilitate their autonomous operation. The approach integrates a non-parametric data-based model for trajectory prediction and a continuous optimization formulation based on an exponential weighting scheme for minimum-time trajectory planning. The optimization problem in its final form is a linear program and is easy to solve. We validate the approach and illustrate its application with a spacecraft relative motion planning problem.

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arXiv2019

Survey of prognostics methods for condition-based maintenance in engineering systems

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{diagnostics} and \textit{prognostics} each of which has provided the impetus and technical challenges to the scientists and engineers in various fields of engineering. Prognostics deals with the prediction of the remaining useful life, future condition, or probability of reliable operation of an equipment based on the acquired condition monitoring data. This approach to modern maintenance practice promises to reduce the downtime, spares inventory, maintenance costs, and safety hazards. Given the significance of prognostics capabilities and the maturity of condition monitoring technology, there have been an increasing number of publications on machinery prognostics in the past few years. These publications cover a wide range of issues important to prognostics. Fortunately, improvement in computational resources technology has come to the aid of engineers by presenting more powerful onboard computational resources to make some aspects of these new problems tractable. In addition, it is possible to even leverage connected vehicle information through cloud-computing. Our goal is to review the state of the art and to summarize some of the recent advances in prognostics with the emphasis on models, algorithms and technologies used for data processing and decision making.

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arXiv2019

A Novel Approach for Optimal Trajectory Design with Multiple Operation Modes of Propulsion System, Part 1

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-$I_{\text{sp}}$, variable-thrust engine or 2) multiple engines each capable of switching on/off independently. To alleviate the challenges that arise when an indirect optimization method is used, a new framework --- Composite Smooth Control (CSC) --- is proposed that seeks smoothness over the entire spectrum of distinct control inputs. A salient aftermath of the application of the CSC framework is that the original multi-point boundary-value problem can be treated as a two-point boundary-value problem with smooth, differentiable control inputs; the latter is notably easier to solve, yet can be made to accurately approximate the former hybrid problem. The utility of the CSC framework is demonstrated through a multi-year, multi-revolution heliocentric fuel-optimal trajectory for a spacecraft equipped with a variable-$I_{\text{sp}}$, variable-thrust engine.

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arXiv2019

Entry Trajectory Optimization for Mars Science Laboratory Class Missions Using Indirect Unified Trigonometrization Method

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 utility and application of an advanced indirect method, the Unified Trigonometrization Method (UTM), to a Mars Science Laboratory type entry problem. The objective is to maximize the parachute deployment altitude for a free-time, fixed-final-velocity entry trajectory. For entry vehicles, in addition to the bank angle that is characterized by bang-bang control profiles, there are typically three state path constraints that have to be considered, namely, the dynamic pressure, heat rate and g-load. This study shows that the UTM enables simultaneous regularization of the bang-bang control and satisfaction of the state path constraints. Two scenarios with and without state path constraints are considered. The results obtained using the UTM for both of these cases are found to be in excellent agreement with a direct optimization method. Furthermore, an interesting feature emerges in the optimal control profile of the UTM during the initial high-altitude part of the resulting optimal trajectory for the scenario with state path constraints, which has an appealing practical implication.

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arXiv2019

A Novel Approach for Optimal Trajectory Design with Multiple Operation Modes of Propulsion System, Part 2

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/off independently and "optimal" operating power of each engine depends on the available solar power, which depends on the distance from the Sun. Application of the Composite Smooth Control (CSC) framework to a heliocentric fuel-optimal trajectory optimization from the Earth to the comet 67P/Churyumov-Gerasimenko is demonstrated, which presents a new approach to deal with multiple-engine problems. Operation of engine clusters with 4, 6, 10 and even 20 engines of the same type can be optimized. Moreover, engine clusters with different/mixed electric engines are considered with either 2, 3 or 4 different types of engines. Remarkably, the CSC framework allows us 1) to reduce the original multi-point boundary-value problem to a two-point boundary-value problem (TPBVP), and 2) to solve the resulting TPBVPs using a single-shooting solution scheme and with a random initialization of the missing costates. While the approach we present is a continuous neighbor of the discontinuous extremals, we show that the discontinuous necessary conditions are satisfied in the asymptotic limit. We believe this is the first indirect method to accommodate a multi-mode control of this level of complexity with realistic engine performance curves. The results are interesting and promising for dealing with a large family of such challenging multi-mode optimal control problems.

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arXiv2019

Optimal Control of Wave Energy Converters Using Epsilon-Trig Regularization Method

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, especially with the possibility of many switches between regular and singular control arcs, is challenging due to lack of \textit{a priori} information about: 1) optimal sequence as well as number of the regular and singular control arcs, and 2) the corresponding optimal switch times (from a regular to a singular arc and vice versa). This investigation demonstrates the application of a recently developed construct, the Epsilon-Trig Regularization Method (ETRM), to the problem of maximizing energy harvesting for a point-absorber WEC model in the presence of control constraints. Utility of the ETRM for the WEC problem is demonstrated by comparing its high-quality results against those in the literature for a number of test cases.

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