Rapid trajectory optimization for hypersonic entry using a pseudospectral-convex algorithm

2019 ◽  
Vol 233 (14) ◽  
pp. 5227-5238 ◽  
Author(s):  
Jinbo Wang ◽  
Naigang Cui ◽  
Changzhu Wei
Keyword(s):  
Optimal Control ◽  
Optimal Control Theory ◽  
Trajectory Optimization ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Interior Point Methods ◽  
Pseudospectral Method ◽  
Trust Region ◽  
Convergence Properties ◽  
Dynamic Trust

Aiming at improving the autonomy of hypersonic entry vehicles, a rapid trajectory optimization algorithm, which has the potential to be implemented online and onboard, is proposed in this paper. The nonlinear and nonconvex hypersonic entry trajectory optimization problem is transformed into a series of convex subproblems through a proper combination of the pseudospectral method and an improved successive convexification method; thus, the high discretization accuracy of the pseudospectral method and the fast and deterministic convergence properties of the convex-optimization-based algorithm can be simultaneously exploited. The resulting subproblems can be solved efficiently by matured interior-point methods, and the solution converges rapidly by adopting a novel dynamic trust-region updating approach. The optimality of the solution is verified by the optimal control theory. The effectiveness of the algorithm is demonstrated by numerical experiments.

scholarly journals Trajectory optimization of UAV based on Hp-adaptive Radau pseudospectral method

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yi Cui ◽  
Xintong Fang ◽  
Gaoqi Liu ◽  
Bin Li
Keyword(s):  
Trajectory Planning ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Tracking Error ◽  
Pseudospectral Method ◽  
Planning Problem ◽  
A Algorithm ◽  
Planning Scheme ◽  
Path Search ◽  
Simulation Results

<p style='text-indent:20px;'>Unmanned Aerial Vehicles (UAVs) have been extensively studied to complete the missions in recent years. The UAV trajectory planning is an important area. Different from the commonly used methods based on path search, which are difficult to consider the UAV state and dynamics constraints, so that the planned trajectory cannot be tracked completely. The UAV trajectory planning problem is considered as an optimization problem for research, considering the dynamics constraints of the UAV and the terrain obstacle constraints during flight. An hp-adaptive Radau pseudospectral method based UAV trajectory planning scheme is proposed by taking the UAV dynamics into account. Numerical experiments are carried out to show the effectiveness and superior of the proposed method. Simulation results show that the proposed method outperform the well-known RRT* and A* algorithm in terms of tracking error.</p>

Trajectory Optimization for Nonholonomic Vehicles on Non-Flat Terrains Using Shooting and Collocation Methods

2013 ◽  
Author(s):  
Dimitris M. Chatzigeorgiou
Keyword(s):  
Optimal Control ◽  
Mobile Robots ◽  
Performance Index ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Control Policy ◽  
Collocation Methods ◽  
Governing Equations ◽  
Nonholonomic Mobile Robots ◽  
Nonholonomic Vehicles

In this paper we focus on the trajectory optimization problem for a specific family of robots; nonholonomic mobile robots. We study the particular case where such robots operate on smooth, non-flat terrains, i.e. terrains with large differences in elevation. Initially we present the governing equations of such robots and then study the trajectory optimization problem in order to solve for the optimal control policy. We test two different approaches for this problem, namely a shooting and a collocation method, for evaluating and optimizing a performance index.

scholarly journals Multiphase Return Trajectory Optimization Based on Hybrid Algorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Yi Yang ◽  
Ying Nan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Optimization ◽  
Pseudospectral Method ◽  
Optimization Method ◽  
Natural Computation ◽  
Improve Calculation ◽  
Computation Algorithm ◽  
The Right

A hybrid trajectory optimization method consisting of Gauss pseudospectral method (GPM) and natural computation algorithm has been developed and utilized to solve multiphase return trajectory optimization problem, where a phase is defined as a subinterval in which the right-hand side of the differential equation is continuous. GPM converts the optimal control problem to a nonlinear programming problem (NLP), which helps to improve calculation accuracy and speed of natural computation algorithm. Through numerical simulations, it is found that the multiphase optimal control problem could be solved perfectly.

scholarly journals The Multiobjective Trajectory Optimization for Hypersonic Glide Vehicle Based on Normal Boundary Intersection Method

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Zhengnan Li ◽  
Tao Yang ◽  
Zhiwei Feng
Keyword(s):  
Trajectory Optimization ◽  
Optimization Problem ◽  
Pseudospectral Method ◽  
Optimization Method ◽  
Initial Guess ◽  
Programming Algorithm ◽  
Trajectory Design ◽  
Normal Boundary ◽  
Vehicle Trajectory ◽  
Intersection Method

To solve the multiobjective optimization problem on hypersonic glider vehicle trajectory design subjected to complex constraints, this paper proposes a multiobjective trajectory optimization method that combines the boundary intersection method and pseudospectral method. The multiobjective trajectory optimization problem (MTOP) is established based on the analysis of the feature of hypersonic glider vehicle trajectory. The MTOP is translated into a set of general optimization subproblems by using the boundary intersection method and pseudospectral method. The subproblems are solved by nonlinear programming algorithm. In this method, the solution that has been solved is employed as the initial guess for the next subproblem so that the time consumption of the entire multiobjective trajectory optimization problem shortens. The maximal range and minimal peak heat problem is solved by the proposed method. The numerical results demonstrate that the proposed method can obtain the Pareto front of the optimal trajectory, which can provide the reference for the trajectory design of hypersonic glider vehicle.

Reentry Trajectory Optimization and Simulation of Hypersonic Vehicle with Maximum Cross Range Based on GPM

2014 ◽  
Vol 635-637 ◽  
pp. 1431-1437
Author(s):  
Wu Jun Huo ◽  
Xu Liu ◽  
Li Wang ◽  
Chao Song
Keyword(s):  
Trajectory Optimization ◽  
Optimization Problem ◽  
Control Variable ◽  
Pseudospectral Method ◽  
Hypersonic Vehicle ◽  
State Variables ◽  
Hypersonic Aircraft ◽  
Gauss Pseudospectral Method ◽  
Reentry Trajectory ◽  
Reentry Trajectory Optimization

Abstract：The application of Gauss pseudospectral method (GPM) to hypersonic aircraft reentry trajectory optimization problem with maximum cross range was introduced. The Gauss pseudospectral method was used to solve the reentry trajectory of the hypersonic vehicle with the maximum cross range. Firstly, the model of hypersonic aircraft reentry trajectory optimization control problem was established. Taking no account of course constraint, the maximum cross range was chosen as optimal performance index, and angle of attack and bank was chosen as control variable. Terminal state was constrained by position and velocity. Then GPM was applied to change trajectory optimization problem into nonlinear programming problem (NLP), and the state variables and control variables were selected as optimal parameters at all Gauss nodes. At last, optimal reentry trajectory was solved by solving the NLP with the help of SNOPT. The simulation results indicate that GPM does not need to estimate the initial cost variable, and it is not sensitive to the initial states and effective to solve trajectory optimization problem.

scholarly journals Adaptive Partial Train Speed Trajectory Optimization

Energies ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 3302 ◽  
Author(s):  
Zhaoxiang Tan ◽  
Shaofeng Lu ◽  
Kai Bao ◽  
Shaoning Zhang ◽  
Chaoxian Wu ◽  
...  
Keyword(s):  
Trajectory Optimization ◽  
Optimization Problem ◽  
Pseudospectral Method ◽  
Optimization Methods ◽  
Mixed Integer ◽  
Computation Efficiency ◽  
Full Speed ◽  
Train Operation ◽  
Train Speed ◽  
Future Work

Train speed trajectory optimization has been proposed as an efficient and feasible method for energy-efficient train operation without many further requirements to upgrade the current railway system. This paper focuses on an adaptive partial train speed trajectory optimization problem between two arbitrary speed points with a given traveling time and distance, in comparison with full speed trajectory with zero initial and end speeds between two stations. This optimization problem is of interest in dynamic applications where scenarios keep changing due to signaling and multi-train interactions. We present a detailed optimality analysis based on Pontryagin’s maximum principle (PMP) which is later used to design the optimization methods. We propose two optimization methods, one based on the PMP and another based on mixed-integer linear programming (MILP), to solve the problem. Both methods are designed using heuristics obtained from the developed optimality analysis based on the PMP. We develop an intuitive numerical algorithm to achieve the optimal speed trajectory in four typical case scenarios; meanwhile, we propose a new distance-based MILP approach to optimize the partial speed trajectory in the same scenarios with high modeling precision and computation efficiency. The MILP method is later used in a real engineering speed trajectory optimization to demonstrate its high computational efficiency, robustness, and adaptivity. This paper concludes with a comparison of both methods in addition to the widely applied pseudospectral method and propose the future work of this paper.

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