Ehsan Taheri

Shape-Based Approximation of Constrained Low-Thrust Space Trajectories Using Fourier Series

Space mission trajectory design using low-thrust capabilities is becoming increasingly popular. However, trajectory optimization is a very challenging and time-consuming task. In this paper, we build upon existing shapebased techniques to present an alternative Fourier series approximation for rapid low-thrust-rendezvous/orbitraising trajectory construction with thrust-acceleration constraint-handling capability. The new flexible representation, along with the constraint-handling capability, makes this method a suitable candidate for feasibility assessment of a whole range of trajectories within the given system propulsive budget. In addition, the solutions present opportunities for direct optimization techniques. A key point in the proposed method is its ability to solve problemswith a greater number of free parameters than in shape-basedmethods. Several case studies are presented: simpleEarth–Mars rendezvous, rendezvous/orbit raising for lowEarth orbit to geostationary orbit, and two phasing problems. Results clearly depict the advantage of the proposed method in handling thrust constraints and its applicability to a wide range of problems.

Enhanced smoothing technique for indirect optimization of minimum-Fuel low-Thrust trajectories

Indirect methods used for solving optimal-control problems, when combined with proper initialization and homotopy approaches, remain attractive for space trajectory optimization, as they are able to achieve fast convergence to a solution of the necessary conditions. In this paper, the extended logarithmic-smoothing technique is revisited and integrated with an indirect method to efficiently generate minimum-fuel time-fixed low-thrust rendezvous trajectories. This approach is considered for three cases, in which equations of motion are expressed in terms of Cartesian, spherical, and modified equinoctial coordinates. In addition, the paper addresses the calculation of the Jacobian matrix of the constraints via an implementation of the state-transition-matrix approach, which avoids the discontinuities of the control along the trajectory. The application of the method to two interplanetary missions from Earth to Mars and to asteroid Dionysus is demonstrated. It is shown that, by exploiting the state transitio...

Aircraft Optimal Terrain/Threat-Based Trajectory Planning and Control

In this paper, single- and multi-objective three-dimensional terrain- and threat-based trajectory planning and control are addressed for optimal time, fuel, and altitude scenarios. To obtain more realistic and feasible trajectories, a high-fidelity, six-degree-of-freedom dynamic model of the aircraft is used that includes accurate aerodynamic and propulsion models in all path-planning scenarios. The paper is composed of two parts. In the first part, optimal trajectories are generated using a global differential-evolution-based optimization algorithm. A comprehensive analysis of the resulting optimal trajectories reveals major characteristics of each scenario, which are generally different. In the second part of the paper, a multi-input, multi-output nonlinear model predictive controller is established to enable the aircraft to track the optimal paths in real time. The controller uses a neurofuzzy predictor model that is trained using the local linear model tree algorithm. A robustness analysis shows that ...

Fast Initial Trajectory Design for Low-Thrust Restricted-Three-Body Problems

This paper presents an approach to generate initial trajectories in a three-body dynamical framework, assuming the use of a low-thrust propulsion system. Finite Fourier series were previously implemented successfully in approximating two-dimensional continuous-thrust trajectories in two-body dynamic models. In this paper, Finite Fourier series are implemented in a dual-level-solver strategy for low-thrust trajectory approximation, in the presence of thrust acceleration constraints, in the three-body dynamic model. This approximation enables the feasibility assessment of low-thrust trajectories, especially in the presence of thrust level constraint. The developed method demonstrates capability in generating trajectories using a fully automated procedure for various levels of thrust acceleration with a moderate to high number of revolutions. The suitability of using the approximated trajectories as initial guesses for high-fidelity solvers is demonstrated.

Co-states initialization of minimum-time low-thrust trajectories using shape-based methods

This paper presents an approach for co-state initialization which is a crucial step in solving minimum-time low-thrust trajectory optimization problems using indirect optimal control numerical methods. Indirect methods used in determining the optimal space trajectories result in two-point boundary value problems which are typically solved by single- or multiple-shooting methods. Accurate initialization of the so-called co-state variables is necessary to achieve numerical convergence of iterative boundary value problem solvers. In this paper, we propose a method which exploits the trajectory generated by a shape-based method to estimate the initial values of the co-states. The performance of the algorithm is compared against two other approaches which respectively exploit random initialization of the co-states and a genetic algorithm. It is shown that by using the proposed approach, numerical convergence is improved especially for trajectories with higher number of revolutions.

Constraint Low-Thrust Trajectory Planning in Three-Body Dynamic Models: Fourier Series Approach

In this paper, a systematic method for constructing the low-thrust trajectories in the restricted three-body dynamical model is introduced using a finite fourier series approximation. The dynamic model complexity requires both computational efficiency and efficient programming implementation in the solution strategy; both have been achieved by a new compact state representation. The thrust-coast-thrust segmenting strategy is assumed in this work. The proposed approximation technique enables the feasibility assessment of low-thrust trajectories, especially in the presence of thrust level constraints within complex dynamics. Several examples of low thrust acceleration levels have been considered and analyzed. The resulting approximated trajectories can be used as initial guess for the high-fidelity optimization solvers.