Analysis of optimization strategies for solving space manoeuvre vehicle trajectory optimization problem

In this paper, two types of optimization strategies are applied to solve the Space Manoeuvre Vehicle (SMV) trajectory optimization problem. The SMV dynamic model is constructed and discretized applying direct multiple shooting method. To solve the resulting Nonlinear Programming (NLP) problem, gradient-based and derivative free optimization techniques are used to calculate the optimal time history with respect to the states and controls. Simulation results indicate that the proposed strategies are effective and can provide feasible solutions for solving the constrained SMV trajectory design problem

A review of optimization techniques in spacecraft flight trajectory design

For most atmospheric or exo-atmospheric spacecraft flight scenarios, a well-designed trajectory is usually a key for stable flight and for improved guidance and control of the vehicle. Although extensive research work has been carried out on the design of spacecraft trajectories for different mission profiles and many effective tools were successfully developed for optimizing the flight path, it is only in the recent five years that there has been a growing interest in planning the flight trajectories with the consideration of multiple mission objectives and various model errors/uncertainties. It is worth noting that in many practical spacecraft guidance, navigation and control systems, multiple performance indices and different types of uncertainties must frequently be considered during the path planning phase. As a result, these requirements bring the development of multi-objective spacecraft trajectory optimization methods as well as stochastic spacecraft trajectory optimization algorithms. This paper aims to broadly review the state-of-the-art development in numerical multi-objective trajectory optimization algorithms and stochastic trajectory planning techniques for spacecraft flight operations. A brief description of the mathematical formulation of the problem is firstly introduced. Following that, various optimization methods that can be effective for solving spacecraft trajectory planning problems are reviewed, including the gradient-based methods, the convexification-based methods, and the evolutionary/metaheuristic methods. The multi-objective spacecraft trajectory optimization formulation, together with different class of multi-objective optimization algorithms, is then overviewed. The key features such as the advantages and disadvantages of these recently-developed multi-objective techniques are summarised. Moreover, attentions are given to extend the original deterministic problem to a stochastic version. Some robust optimization strategies are also outlined to deal with the stochastic trajectory planning formulation. In addition, a special focus will be given on the recent applications of the optimized trajectory. Finally, some conclusions are drawn and future research on the development of multi-objective and stochastic trajectory optimization techniques is discussed

Violation learning differential evolution-based hp-Adaptive pseudospectral method for trajectory optimization of Space Maneuver Vehicle

The sensitivity of the initial guess in terms of optimizer based on hp-adaptive pseudospectral method for solving Space Maneuver Vehicles (SMV) trajectory optimization problem has long been recognised as a difficult problem. Because of the sensitivity with regard to the initial guess, it may cost the solver a large amount of time to do the Newton iteration and get the optimal solution or even the local optimal solution. In this paper, to provide the optimizer a better initial guess and solve the SMV trajectory optimization problem, an initial guess generator using violation learning deferential evolution algorithm is introduced. A new constraint-handling strategy without using penalty function is presented to modify the fitness values so that the performance of each candidate can be generalized. In addition, a learning strategy is designed to add diversity for the population in order to improve the convergency speed and avoid local optima. Several simulation results are conducted by using the combination algorithm; Simulation results indicated that using limited computational efforts, the method proposed to generate initial guess can have better performance in terms of convergency ability and convergency speed compared with other approaches. By using the initial guess, the combinational method can also enhance the quality of the solution and reduce the number of Newton iteration and computational time. Therefore, The method is potentially feasible for solving the SMV trajectory optimization problem

Improved gradient-based algorithm for solving aeroassisted vehicle trajectory optimization problems

Space maneuver vehicles (SMVs) [1,2] will play an increasingly important role in the future exploration of space because their on-orbit maneuverability can greatly increase the operational flexibility, and they are more difficult as a target to be tracked and intercepted. Therefore, a well-designed trajectory, particularly in the skip entry phase, is a key for stable flight and for improved guidance control of the vehicle [3,4]. Trajectory design for space vehicles can be treated as an optimal control problem. Because of the highly nonlinear characteristics and strict path constraints of the problem, direct methods are usually applied to calculate the optimal trajectories, such as the direct multiple shooting method [5], direct collocation method [5,6], or hp hp -adaptive pseudospectral method [7,8]

High-fidelity trajectory optimization for aeroassisted vehicles using variable order pseudospectral method

In this study, the problem of time-optimal reconnaissance trajectory design for the aeroassisted vehicle is considered. Different from most works reported previously, we explore the feasibility of applying a high-order aeroassisted vehicle dynamic model to plan the optimal flight trajectory such that the gap between the simulated model and the real system can be narrowed. A highly-constrained optimal control model containing six-degree-of-freedom vehicle dynamics is established. To solve the formulated high-order trajectory planning model, a pipelined optimization strategy is illustrated. This approach is based on the variable order Radau pseudospectral method, indicating that the mesh grid used for discretizing the continuous system experiences several adaption iterations. Utilization of such a strategy can potentially smooth the flight trajectory and improve the algorithm convergence ability. Numerical simulations are reported to demonstrate some key features of the optimized flight trajectory. A number of comparative studies are also provided to verify the effectiveness of the applied method as well as the high-order trajectory planning model

Trajectory planning for hypersonic reentry vehicle satisfying deterministic and probabilistic constraints

The present work explores the optimal flight of aero-assisted reentry vehicles during the atmospheric entry flight phase with the consideration of both deterministic and control chance constraints. To describe the mission profile, a chance-constrained optimal control model is established. Due to the existence of probabilistic constraints (chance constraints), standard numerical trajectory planning algorithms cannot be directly applied to address the considered problem. Hence, we firstly present an approximation-based strategy to replace the probabilistic constraint by a deterministic version. In this way, the transformed optimal control model becomes solvable for standard trajectory optimization methods. In order to obtain enhanced computational performance, an alternative convex-relaxed optimal control formulation is also given. This is achieved by convexifying the vehicle nonlinear dynamics/constraints and by introducing a convex probabilistic constraint handling strategy. Numerical simulations are provided to demonstrate the effectiveness of these two chance-constrained optimization approaches and the corresponding probabilistic constraint handling strategies

Solving multiobjective constrained trajectory optimization problem by an extended evolutionary algorithm

Highly constrained trajectory optimization problems are usually difficult to solve. Due to some real-world requirements, a typical trajectory optimization model may need to be formulated containing several objectives. Because of the discontinuity or nonlinearity in the vehicle dynamics and mission objectives, it is challenging to generate a compromised trajectory that can satisfy constraints and optimize objectives. To address the multiobjective trajectory planning problem, this paper applies a specific multiple-shooting discretization technique with the newest NSGA-III optimization algorithm and constructs a new evolutionary optimal control solver. In addition, three constraint handling algorithms are incorporated in this evolutionary optimal control framework. The performance of using different constraint handling strategies is detailed and analyzed. The proposed approach is compared with other well-developed multiobjective techniques. Experimental studies demonstrate that the present method can outperform other evolutionary-based solvers investigated in this paper with respect to convergence ability and distribution of the Pareto-optimal solutions. Therefore, the present evolutionary optimal control solver is more attractive and can offer an alternative for optimizing multiobjective continuous-time trajectory optimization problems

Two-stage trajectory optimization for autonomous ground vehicles parking maneuver

This paper proposes a two-stage optimization framework for generating the optimal parking motion trajectory of autonomous ground vehicles. The motivation for the use of this multi-layer optimization strategy relies on its enhanced convergence ability and computational efficiency in terms of finding optimal solutions under the constrained environment. In the first optimization stage, the designed optimizer applies an improved particle swarm optimization technique to produce a near-optimal parking movement. Subsequently, the motion trajectory obtained from the first stage is used to start the second optimization stage, where gradient-based techniques are applied. The established methodology is tested to explore the optimal parking maneuver for a car-like autonomous vehicle with the consideration of irregularly parked obstacles. Simulation results were produced and comparative studies were conducted for different mission cases. The obtained results not only confirm the effectiveness but also reveal the enhanced performance of the proposed optimization framework

Solving constrained trajectory planning problems using biased particle swarm optimization

Constrained trajectory optimization has been a critical component in the development of advanced guidance and control systems. An improperly planned reference trajectory can be a main cause of poor online control performance. Due to the existence of various mission-related constraints, the feasible solution space of a trajectory optimization model may be restricted to a relatively narrow corridor, thereby easily resulting in local minimum or infeasible solution detection. In this work, we are interested in making an attempt to handle the constrained trajectory design problem using a biased particle swarm optimization approach. The proposed approach reformulates the original problem to an unconstrained multi-criterion version by introducing an additional normalized objective reflecting the total amount of constraint violation. Besides, to enhance the progress during the evolutionary process, the algorithm is equipped with a local exploration operation, a novel ε-bias selection method, and an evolution restart strategy. Numerical simulation experiments, obtained from a constrained atmospheric entry trajectory optimization example, are provided to verify the effectiveness of the proposed optimization strategy. Main advantages associated with the proposed method are also highlighted by executing a number of comparative case studies

An interactive fuzzy physical programming for solving multiobjective skip entry problem

The multi-criteria trajectory planning for Space Manoeuvre Vehicle (SMV) is recognised as a challenging problem. Because of the nonlinearity and uncertainty in the dynamic model and even the objectives, it is hard for decision makers to balance all of the preference indices without violating strict path and box constraints. In this paper, to provide the designer an effective method and solve the trajectory hopping problem, an Interactive Fuzzy Physical Programming (IFPP) algorithm is introduced. A new multi-objective SMV optimal control problem is formulated and parameterized using an adaptive technique. By using the density function, the oscillations of the trajectory can be captured effectively. In addition, an interactive decision-making strategy is applied to modify the current designer’s preferences during optimization process. Two realistic decision-making scenarios are conducted by using the proposed algorithm; Simulation results indicated that without driving objective functions out of the tolerable region, the proposed approach can have better performance in terms of the satisfactory degree compared with other approaches like traditional weighted-sum method, Goal Programming (GP) and fuzzy goal programming (FGP). Also, the results can satisfy the current preferences given by the decision makers. Therefore, The method is potentially feasible for solving multi-criteria SMV trajectory planning problems