횡방향 기동을 하는 위성발사체의 3차원 궤적최적화와 직접식 유도기법

During the early phases of engineering design, the costs committed are high, costs incurred are low, and the design freedom is high. It is well documented that decisions made in these early design phases drive the entire design's life cycle cost. In a traditional paradigm, key design decisions are made when little is known about the design. As the design matures, design changes become more difficult in both cost and schedule to enact. The current capability-based paradigm, which has emerged because of the constrained economic environment, calls for the infusion of knowledge usually acquired during later design phases into earlier design phases, i.e. bringing knowledge acquired during preliminary and detailed design into pre-conceptual and conceptual design. An area of critical importance to launch vehicle design is the optimization of its ascent trajectory, as the optimal trajectory will be able to take full advantage of the launch vehicle's capability to deliver a maximum amount of payload into orbit. Hence, the optimal ascent trajectory plays an important role in the vehicle's affordability posture yet little of the information required to successfully optimize a trajectory is known early in the design phase. Thus, the current paradigm of optimizing ascent trajectories involves generating point solutions for every change in a vehicle's design parameters. This is often a very tedious, manual, and time-consuming task for the analysts. Moreover, the trajectory design space is highly non-linear and multi-modal due to the interaction of various constraints. When these obstacles are coupled with the Program to Optimize Simulated Trajectories (POST), an industry standard program to optimize ascent trajectories that is difficult to use, expert trajectory analysts are required to effectively optimize a vehicle's ascent trajectory. Over the course of this paper, the authors discuss a methodology developed at NASA Marshall's Advanced Concepts Office to address these issues. The methodology is two-fold: first, capture the heuristics developed by human analysts over their many years of experience; and secondly, leverage the power of modern computing to evaluate multiple trajectories simultaneously and therefore enable the exploration of the trajectory's design space early during the pre- conceptual and conceptual phases of design. This methodology is coupled with design of experiments in order to train surrogate models, which enables trajectory design space visualization and parametric optimal ascent trajectory information to be available when early design decisions are being made.

The numerical method to solve simultaneous design and control optimization problems is considered. Firstly, the simultaneous optimization problem dealt with in this paper is defined, and this problem is transformed into a new formulated nonlinear programming problem. Considering that the nonlinear programming problem is solved by using a sequential quadratic programming method, the diagonal form of the Hessian matrix for the Lagrange function is introduced in a new formulation named Block Diagonal Hessian (BDH) method. Secondly, the BDH method is applied to the simultaneous spaceplane design and trajectory optimization problem, where the best size and its optimal trajectory are estimated to realize it. Through the several calculations, it is confirmed that the proposed BDH method is effective for simultaneous design and control optimization problems.

An improved hp adaptive pseudo-spectral method ia scaling parameters designed for the hypersonic vehicle trajectory optimization problem. In this paper, we take hypersonic vehicle as the research object, consider its ascent phase with various constraints, and establish a multi-constrained climbing segment trajectory optimization model with the shortest ascent time as the objective function. Because the nonlinear programming problem (NLP) obtained by applying the hp adaptive pseudo-spectral method to discretize the trajectory optimization model has high dimensionality, which makes the trajectory optimization problem difficult to solve, we propose an improved hp adaptive pseudo-spectral method. The algorithm uses the improved wild horse optimizer (IWHO) algorithm to adjust the distribution of interpolation nodes and the order of interpolation polynomials in the trajectory optimization subinterval, which avoids unnecessary mesh refinement and reduces the dimensionality of the discretized obtained NLP with a given precision, and improves the efficiency of the trajectory optimization solution. Simulation results show that the trajectories solved by the designed hybrid optimization algorithm satisfy all process constraints and terminal constraints.

Trajectory optimization for lunar soft landing with a Hamiltonian-based adaptive mesh refinement strategy

An algorithm for solving aircraft trajectory optimization problems using scalable high fidelity simulation models and pseudospectral discretization methods is presented. The resulting parameter optimization problem is solved with an SQP algorithm. One of the problems that arise when using complex simulation models in combination with gradient based optimization algorithms is the generation of an appropriate initial guess. To address this issue two different simulation models are implemented: a mere point-mass simulation model with three degrees of freedom (DoF) and a full nonlinear six degree of freedom dynamic model of the same aircraft. In contrast to the 6-DoF model, the generation of an initial guess for the point-mass model can be performed by a geometric approach that can easily be handled by the user. The optimal solution of the point-mass model will be used as an initial guess for the high fidelity optimization problem. To enable this, an iterated extended Kalman Filter is implemented to adapt the optimal solution of the point-mass model such that it can be used as an initial guess for the 6-DoF optimization. This way, the convergence rate of the overall trajectory optimization problem can be significantly improved. The benefits of the method are illustrated by an air race example involving two dynamic models of an aerobatic aircraft.

Trajectory optimization for lunar rover performing vertical takeoff vertical landing maneuvers in the presence of terrain

In this work, we propose a trajectory optimization approach for robot navigation in cluttered 3D environments. We represent the robot's geometry as a semialgebraic set defined by polynomial inequalities such that robots with general shapes can be suitably characterized. We exploit the collision-free space directly to construct a graph of free regions, search for the reference path, and allocate each waypoint on the trajectory to a specific region. Then, we incorporate a uniform scaling factor for each free region and formulate a Sums-of-Squares (SOS) optimization problem whose optimal solutions reveal the containment relationship between robots and the free space. The SOS optimization problem is further reformulated to a semidefinite program (SDP), and the collision-free constraints are shown to be equivalent to limiting the scaling factor along the entire trajectory. Next, to solve the trajectory optimization problem with the proposed safety constraints, we derive a guiding direction for updating the robot configuration to decrease the minimum scaling factor by calculating the gradient of the Lagrangian at the primal-dual optimum of the SDP. As a result, this seamlessly facilitates the use of gradient-based methods in efficient solving of the trajectory optimization problem. Through a series of simulations and real-world experiments, the proposed trajectory optimization approach is validated in various challenging scenarios, and the results demonstrate its effectiveness in generating collision-free trajectories in dense and intricate environments.

A general overview of the topic of trajectory optimization is presented. The general trajectory optimization problem is posed, and the two broad classes of indirect and direct methods for solving trajectory optimization problems are discussed. A brief discussion is then given of well‐known software tools to solve trajectory optimization problems. Finally, a brief survey is given of famous trajectory optimization problems that have been solved in aerospace engineering.

The problem of trajectory optimization is important in all space missions. The solution of this problem enables one to specify the optimum thrust steering program which should be followed to achieve a specified mission objective, simultaneously satisfying the constraints.1 It is well known that whether or not the ascent trajectory is optimal can have a significant impact on propellant usage for a given payload, or on payload weight for the same gross vehicle weight.2 Consequently, ascent guidance commands are usually optimized in some fashion. Multi-stage vehicles add complexity to this analysis process as changes in vehicle properties in one stage propagate to the other stages through gear ratios and changes in the optimal trajectory. These effects can cause an increase in analysis time as more variables are added and convergence of the optimizer to system closure requires more analysis iterations. In this paper, an approach to simplifying this multi-stage problem through the creation of an upper stage capability boundary is presented. This work was completed as part of a larger study focused on trade space exploration for the advanced booster system that will eventually form a part of NASA s new Space Launch System.3 The approach developed leverages Design of Experiments and Surrogate Modeling4 techniques to create a predictive model of the SLS upper stage performance. The design of the SLS core stages is considered fixed for the purposes of this study, which results in trajectory parameters such as staging conditions being the only variables relevant to the upper stage. Through the creation of a surrogate model, which takes staging conditions as inputs and predicts the payload mass delivered by the SLS upper stage to a reference orbit as the response, it is possible to identify a of staging conditions which all satisfy the SLS requirement of placing 130 metric tons into low-Earth orbit (LEO).3 This identified surface represents the 130 metric ton capability boundary for the upper stage, such that if the combined first stage and boosters can achieve any one staging point on that surface, then the design is identified as feasible. With the surrogate model created, design and analysis of advanced booster concepts is streamlined, as optimization of the upper stage trajectory is no longer required in every design loop.

This paper proposes a linear programming approach for onboard optimization of rocket trajectories, motivated by the need for reliable and computationally efficient trajectory optimization methods in real-time applications. To reformulate rocket trajectory optimization problems within a linear programming framework, a polytopal approximation method is developed. The polytopal approximation method approximates the thrust magnitude constraint using a set of artificial variables and linear constraints. Compared with a state-of-the-art approximation method, the polytopal approximation method demonstrates a higher accuracy-to-size ratio, enabling rocket trajectory optimization problems to be cast into linear subproblems without significantly increasing problem sizes. As linear subproblems can be readily solved by linear programming solvers, the proposed trajectory optimization approach inherits the solver’s reliability and computational efficiency, making it potentially useful for critical onboard applications. An ascent trajectory optimization problem is provided as an illustrative example to demonstrate the effectiveness of the proposed linear programming approach.

The quad-rotor UAV formation trajectory optimization is the basis of high precision tracking control. Researching the problem of quad-rotor UAV formation trajectory optimization, firstly the nonlinear quad-rotor UAV model is built and simplified, meanwhile the model parameters are obtained; then the collision avoidance, the state variables constraints and the control varibles constraints are considered; finally the hp-adaptive pseudospectral method that select the discrete points adaptively is used to convert the optimal control problem to be a nonlinear programming problem. The smulation results shows, taking six quad-rotor UAV for research objects, the optimal trajectory has a good effect whiling satisfying the engineering requirements.

Wireless rechargeable sensor networks with a charging unmanned aerial vehicle (CUAV) have broad application prospects in the power supply of the rechargeable sensor nodes (SNs). However, how to schedule a CUAV and design the trajectory to improve the charging efficiency of the entire system is still a vital problem. In this article, we formulate a joint-CUAV scheduling and trajectory optimization problem (JSTOP) to simultaneously minimize the hovering points of CUAV, the number of the repeatedly covered SNs, and the flying distance of CUAV for charging all SNs. Due to the complexity of JSTOP, it is decomposed into two optimization subproblems that are CUAV scheduling optimization problem (CSOP) and CUAV trajectory optimization problem (CTOP). CSOP is a hybrid optimization problem that consists of the continuous and discrete solution space, and the solution dimension in CSOP is not fixed since it should be changed with the number of hovering points of CUAV. Moreover, CTOP is a completely discrete optimization problem. Thus, we propose a particle swarm optimization (PSO) with a flexible dimension mechanism, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -means operator, and a punishment-compensation mechanism (PSOFKP) and a PSO with a discretization factor, a 2-opt operator, and a path crossover reduction mechanism (PSOD2P) to solve the converted CSOP and CTOP, respectively. Simulation results evaluate the benefits of PSOFKP and PSOD2P under different scales and settings of the network, and the stability of the proposed algorithms is verified.

Trajectory Optimization for Planetary Multi-Point Powered Landing

Joint resource and trajectory optimization in a UAV-enabled dual-function radar-communication network

This paper investigates a reliability-based trajectory optimization method for the design of soft landing trajectory on an irregular shape asteroid with highly uncertain gravitational field. First, the gravitational field of the irregular asteroid is described by the finite particle model. Second, to avoid the singularity and reduce the sensitivity, the original finite particle model is modified to an “N-body/two-body” switching dynamic model. The trajectory optimization problem in the switching dynamic model is summarized as an optimal control problem and is then transformed into a two-point boundary value problem by Pontryagin’s maximum principle. By solving the two-point boundary value problem with a homotopic continuation procedure, the nominal optimal trajectory is obtained. Third, the uncertainty caused by the nonuniform mass distribution of the asteroid is considered. With high uncertainty, the deterministic optimal control problem becomes a parameter optimization problem with reliability constraints. This problem is then solved by a sequential optimization and reliability assessment, and the parallel computation technique is adopted. Finally, two soft landing trajectories are optimized using the proposed method to demonstrate the effectiveness of the technique.