Reentry Trajectory Research Articles

Multitask-constrained reentry trajectory planning for hypersonic gliding vehicle

This paper studies the reentry trajectory planning problems for hypersonic gliding vehicle under multiple tasks. Different from the former achievements, this paper takes into account the practical tasks involved in the reentry phase, including penetration of interceptors, evasion of the no-fly zones, and the arrival of the waypoints. Firstly, the constraints during the reentry phase are analyzed in detail, and the original trajectory planning problem is formulated. Secondly, the hp-adaptive pseudospectral discretization method is proposed to effectively reduce the discretization error. Relevant variables are introduced to relax and transform severe intractable constraints of multiple nonconvex forms, thus enhancing the robustness of the planning process. Thirdly, the improved sequential convex programming with decision variables algorithm is proposed to ensure the converged trajectory satisfies complicated tasks. The theoretical analysis is also presented to demonstrate that the converged trajectory is the approximate stationary solution of the discrete form of the original problem. Finally, the effectiveness of the proposed algorithms is validated through numerical simulation.

A novel constrained skew-Gaussian filter and its application to maneuverable reentry vehicle tracking

The state of the system generally satisfies specific constraints imposed by material properties or physical laws, so the application of these constraints can improve the accuracy of state estimation. In this paper, a novel recursive filter referred as constrained high-degree cubature skew-Gaussian filter (CHCSGF) is proposed, which achieves soft-constrained state estimation by compressing the probability density of unconstrained states with constraint information. First, the probability density of the state under inequality soft constraints is modeled as a skew-Gaussian (SG) distribution, rather than truncated or single Gaussian distributions. Then, a recursive constrained SG filter is developed to handle inequality soft constraints in linear systems. Addressing nonlinear challenges, a 5th-degree spherical-radial cubature approximation method is presented to numerically calculate SG-weighted integrals for the nonlinear transformation of SG distribution. Finally, the CHCSGF algorithm is proposed using this method to tackle nonlinear filtering problems. The CHCSGF is applied to reentry trajectory tracking to improve estimation accuracy by dealing with heat flow, dynamic pressure and overload constraints during reentry flight. Simulation results demonstrate that the CHCSGF achieves higher estimation accuracy than unconstrained methods under nonlinear inequality soft constraints, and is robust to the constraints with a prior error. Compared to particle filter and moving horizon estimation, the computational complexity of CHCSGF is significantly reduced.

Sequential Convex Programming for Reentry Trajectory Optimization Utilizing Modified hp-Adaptive Mesh Refinement and Variable Quadratic Penalty

Due to the strong nonlinearity in the reentry trajectory planning problem for reusable launch vehicles (RLVs), the scale of the problem after high-precision discretization can become significantly large, and the non-convex path constraints are prone to exceed limits. Meanwhile, the objective function oscillation phenomenon may occur due to successive convexification, which results in poor convergence. To address these issues, a novel sequential convex programming (SCP) method utilizing modified hp-adaptive mesh refinement and variable quadratic penalty is proposed in this paper. Firstly, a local mesh refinement algorithm based on constraint violation is proposed. Additional mesh intervals and mesh points are added in the vicinity of the constraint violation points, which improves the satisfaction of non-convex path constraints. Secondly, a sliding window-based mesh reduction algorithm is designed and introduced into the hp-adaptive pseudospectral (PS) method. Unnecessary mesh intervals are merged to reduce the scale of the problem. Thirdly, a variable quadratic penalty-based SCP method is proposed. The quadratic penalty term related to the iteration direction and the weight coefficient updating strategy is designed to eliminate the oscillation. Numerical simulation results show that the proposed method can strictly satisfy path constraints while the computational efficiency and convergence of SCP are improved.

Sequential convex programming without penalty function for reentry trajectory optimization problem

Sequential convex programming (SCP) has been extensively utilized in reentry trajectory optimization due to its high computational efficiency. However, the current SCP approaches primarily rely on penalty function, where the selection of the penalty function weight presents a significant challenge. In this paper, an improved trust region shrinking SCP algorithm is proposed that separates the treatment of the objective function and constraint violation without the need for selecting penalty function weight and introduction of slack variables. Firstly, from the perspective of multi-objective optimization, the filter and acceptance condition are introduced to ensure that the proposed algorithm converges to feasible solutions and then to the optimal solution based on switching condition and sufficient condition. Then an effective feasibility restoration phase is proposed to address infeasibility of subproblems without introducing slack variables, while ensuring the robustness of the proposed algorithm. Additionally, a theoretical analysis is provided to guarantee the convergence of the algorithm. Finally, simulations are conducted to verify that the proposed algorithm demonstrates a 69.54% improvement in average solution time and stronger robustness compared to basic trust region shrinking SCP algorithm. Simultaneously, the proposed algorithm also demonstrates an advantage in solving speed compared to a particular advanced penalty function-based SCP algorithm.

Design of Entire-Flight Pinpoint Return Trajectory for Lunar DRO via Deep Neural Network

Lunar DRO pinpoint return is the final stage of manned deep space exploration via a lunar DRO station. A re-entry capsule suffers from complicated dynamic and thermal effects during an entire flight. The optimization of the lunar DRO return trajectory exhibits strong non-linearity. To obtain a global optimal return trajectory, an entire-flight lunar DRO pinpoint return model including a Moon–Earth transfer stage and an Earth atmosphere re-entry stage is constructed. A re-entry point on the atmosphere boundary is introduced to connect these two stages. Then, an entire-flight global optimization framework for lunar DRO pinpoint return is developed. The design of the entire-flight return trajectory is simplified as the optimization of the re-entry point. Moreover, to further improve the design efficiency, a rapid landing point prediction method for the Earth re-entry is developed based on a deep neural network. This predicting network maps the re-entry point in the atmosphere and the landing point on Earth with respect to optimal control re-entry trajectories. Numerical simulations validate the optimization accuracy and efficiency of the proposed methods. The entire-flight return trajectory achieves a high accuracy of the landing point and low fuel consumption.

Transient Plasma Wind Tunnel Testing Under Thermomechanical Loads for Reentry Break-Up Analysis

This paper introduces a novel approach for transient plasma wind tunnel testing in an arcjet facility, enabling the experimental simulation of the aerothermal loads along reentry trajectory segments. Such experiments newly allow for the investigation of the causes of break-up events. The trajectory segment is simulated by duplicating the time-resolved profiles of the characteristic flow parameters, namely, heat flux and stagnation pressure as well as the mechanical load, which represents the aerodynamic forces. In arcjet facilities, the parameters that govern the plasma condition are split into variable and constant parameters, which define the available altitude range that can be replicated. The variable conditions arc current and ambient pressure were determined with steady-state trajectory points and traces determined between these conditions resulting in a full trajectory segment. The test time then relates directly to an altitude on the trajectory segment, which allows for an experimental determination of the main break-up altitude. The methodology is applied to a trajectory segment of the transport vehicle CYGNUS OA6, covering an altitude range from 85 to 70 km. A transient break-up experiment on an aluminum bar yielded a failure at an altitude corresponding to 77.6 km, showing a thermomechanical characteristic. These results align well with the observed break-up altitude of CYGNUS OA6, showing the potential of the proposed method.

Global sensitivity analysis of stochastic re-entry trajectory using explainable surrogate models

The assessment of casualty risks associated with re-entry necessitates a comprehensive analysis of trajectories and the examination of pertinent safety-related quantities such as the ground impact area and ground reaching velocity. In practical scenarios, the presence of uncertainty in input conditions introduces variability in safety-related quantities. Consequently, employing stochastic re-entry trajectory analysis becomes crucial in overcoming the limitations of conventional deterministic analyses. Conducting sensitivity assessments during the break-up phase is imperative to gain more insights into how to manage the variability of safety-related measures. Therefore, this paper conducted a surrogate-based global sensitivity analysis and employed explainability machine learning techniques to unveil the complexities of the relationship between input uncertainty conditions and three key measures: ground-reaching velocity, falling range, and falling time, with the object of interest being the Apollo-type capsule. A three-step polynomial chaos expansion-based strategy was devised to efficiently approximate the discontinuous relationships. The results show that the relationship is characterized by severe discontinuity that separates two modes: low- and high-ground reaching velocity caused by the presence of two distinct trim points, with precautionary measures that should be taken to prevent the occurrence of the latter. From this set of procedures, three key input conditions that significantly affect the safety-related measures were identified, namely, the altitude, pitch rate, and path angle of the capsule during the breakup. Subsequently, explainability techniques were utilized to give suggestions on how to control the input variability and avoid the high ground reaching velocity mode, aiming to achieve more dependable predictions for the three safety parameters mentioned earlier.

Reentry trajectory optimization of hypersonic glide vehicle based on improved particle swarm algorithm

The reentry process of hypersonic glide vehicle presents a host of intricate constraint issues. A method for optimizing the reentry trajectory of hypersonic glide vehicle is presented to achieve the shortest possible reentry time. The approach utilizes the improved particle swarm optimization (IPSO) algorithm. Firstly, population initialization is performed using the quasi-oppositional differential evolution (QODE) strategy to promote diversity within the population. Then an adaptive adjustment algorithm is designed for the inertia weight coefficient and learning factor to achieve a balance between global and local search capabilities. Finally, utilizing the IPSO algorithm for optimizing the flight parameters of the reentry trajectory, the reentry time is reduced from 338 seconds to 335 seconds. The simulations results indicate that the IPSO algorithm outperforms both the standard PSO algorithm and genetic algorithm (GA) in terms of optimization performance index.

A decision fusion-based method for global sensitivity analysis of complicated experiments

In real world, the relationship between experimental input and output has become more and more complex, which brings great challenges to the sensitivity analysis. This paper proposes a decision fusion based global sensitivity analysis method for complicated experiments, which not only provides quantitative evluation of the input factor influence on experimental results, but also mines the correlation and form the explicit criteria in IF-THEN fomation for further guidance. The theory of decision information system and continuous attribute discretization is presented first for transforming the experimental input and output into a decision table. In order to calculate the sensitivity of the factors and extract valid correlation criterions between conditional attributes and decision attributes simultaneously, the discrimination matrx is utilized for attribute reduction. Then a sensitivity analysis method based on decision fusion is proposed by organically assembling experiment design, attribute discretization, the discrimization matrix, and attribute reduction. Finally, the effectiveness and practicality of the proposed method were verified by the application of sensitivity analysis in hypersonic vehicle re-entry trajectory experiment.

A composite planning method considering avoidance of multiple no-fly zones

Aiming at the problem that multiple no-fly zones need to be avoided in the reentry process of aircraft, a composite programming method combining conjugate gradient and dynamic programming is proposed. The method divides the reentry flight trajectory into two parts: the longitudinal plane and the transverse plane. The longitudinal plane uses the conjugate gradient method to guide the aircraft to meet the minimum mass of the thermal protection system during the whole flight. The horizontal plane mainly uses the dynamic programming method to obtain a reasonable obstacle avoidance route and inversely calculates the change law of the heading angle. The simulation results show that the three-dimensional reentry trajectory can reasonably solve the problem of avoiding multiple no-fly zones and meeting the aerodynamic constraints of the flight process.

A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm.

Reentry trajectory planning for hypersonic vehicles via an improved sequential convex programming method

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem. The solution efficiency and convergence properties of the planning algorithm become an essential point when considering the practical application scenarios. In this paper, an augmented-Lagrange-based improved sequential convex programming algorithm is proposed to solve it and achieve superior solutions with higher accuracy and efficiency. Firstly, the mapped Chebyshev pseudo-spectral method is utilized to convert the continuous optimal control problem into a highly approximately discretized one. In this framework, the discretization technique is employed to discretize the states and control variables at the time interval, which leads to the improvement of ill-conditioned differential matrix and better approximation properties of the variables. Moreover, by introducing slack variables, automatically updated penalty parameters and Lagrange multipliers during the convexification processing, the original nonconvex problem is transformed into an augmented-Lagrange-function-formed relaxed convex one. Then, the arrived convex subproblem can be solved iteratively by the matured interior-point method until the predetermined precision is satisfied. Based on this transformation, it can effectively alleviate the numerical difficulty and improve the convergence property of the proposed improved sequential convex programming algorithm. Finally, Rigorous theoretical analysis is conducted to prove that the solution sequence generated by the proposed algorithm could converge to an approximate global solution of the original problem. Numerical simulations are also presented, and it is demonstrated that the solution time of the proposed algorithm is more than 95% less than that of the traditional nonlinear programming methods without losing the merits of high precision.

A three-stage sequential convex programming approach for trajectory optimization

Recently, sequential convex programming (SCP) has become a potential approach in trajectory optimization because of its high efficiency. To improve stability and discretization accuracy, a three-stage SCP approach based on the hp-adaptive Radau pseudospectral discretization is proposed in this paper. In most instances, the initial subproblem may risk infeasibility due to the undesignated initial guess. Therefore, we design a constraint relaxation stage for the SCP to enhance the feasibility of the subproblem as much as possible. Once the subproblem can be directly solved, the iteration enters the second stage, during which a mesh refinement algorithm based on discretization error analysis is utilized to decrease the discretization error to the tolerance. In the final stage, the damping term is introduced into the objective of the subproblem to suppress the oscillation of the solution and accelerate the convergence. A dual-channel control reentry trajectory optimization and an ascent trajectory optimization are taken as examples, and the simulation results show that the proposed approach outperforms conventional SCP approaches in terms of accuracy and efficiency.

Impact Analysis of Different Trajectory Shapes on Optimization Based on Original Natural Algorithm

In this paper, the reentry phase of the Aerospaceplane is taken as the research object, and the performance parameters of the reusable rocket of a private company are analyzed. Aiming at the guidance and control scheme of the spacecraft returning to the reentry trajectory in the real environment, the original natural algorithm is optimized by considering various reentry flight constraints, and the improved original natural algorithm is used to optimize the reentry trajectory of the Aerospaceplane. We obtained two types of reentry trajectories in the presence of large flight-restricted areas, the “S-type” trajectory and the “spiral-type” trajectory, and obtained data on various influencing factors. The results showed that the basic state parameters of the spiral trajectory optimized using the improved original natural algorithm after adding constraints met the constraint conditions. The aerodynamic heating rate and overload of the spiral reentry trajectory were to some extent greater than those of the S-type trajectory. Under the increasingly stringent requirements of the aerospace environment, new requirements were put forward for the thermal protection system to meet the wider environmental situation. This paper uses the improved original natural algorithm for the first time and applies it to the field of aerospace reentry and entry and adds more constraints to this algorithm for computation. Besides, for the first time, the macroscopic nature of trajectory types is used as a comparative element for parameter comparison, providing a reference basis for selecting trajectory optimization directions from the macroscopic perspective of trajectory types.

Hybrid-order soft trust region-based sequential convex programming for reentry trajectory optimization

Due to the complex aerodynamic effects, the reentry trajectory optimization problem is highly nonlinear. When using sequential convex programming (SCP) methods to solve it, the iteration solution is difficult to converge. To improve this, we propose a hybrid-order soft trust region-based SCP method. We analyze the penalty effect of typical trust regions. Based on the analysis, we develop a hybrid-order soft trust region combining a small-weight first-order component and a higher-order components. To solve the subproblem reliably and effectively, we equivalently reformulate it as a second-order cone programming (SOCP) form through the relaxation technique. Combined with the line search method, we further design an SCP algorithm with guaranteed convergence under some assumptions. In the numerical simulations, the effectiveness and robustness of the proposed method have been verified using a nominal case and 200 Monte Carlo cases.

“I Feel like I Have ‘Prison’ Tattooed on my Forehead”: Women’s Trajectories after Release from Incarceration

Although reentry has been well explored, less is known about women’s reentry trajectories and whether reentry experiences change over time. The current study explored women’s experiences from prison release to 15-months post-release using interviews with 29 women across four states. Themes from early reentry (2 weeks–4 months) underscored women’s struggle for survival. Women were dependent on informal support, struggling to readjust to mothering, and experiencing stigma from potential employers. Themes from later reentry (8–15 months) mostly portrayed the complexities of social support as mothering remained challenging, family support became a double-edged sword, and formal support services were difficult to access.

A novel re-entry trajectory design strategy enforcing inequality and terminal constraints in height-velocity plane

A novel re-entry trajectory design approach for a winged reusable launch vehicle that satisfies path and terminal state constraints in the height velocity plane is proposed in this paper. A two-phase re-entry trajectory is proposed. A height-velocity plane entry corridor is designed using all path and quasi-equilibrium glide constraints. The proposed method creates the reference trajectory inside the re-entry corridor using three piecewise polynomials, such as linear and logarithmic. A two-parameter search optimization problem minimizes terminal range-to-go error for this reference trajectory generation problem. Improved Search Space Reduction solves this optimization problem. The Improved Search Space Reduction algorithm is compared to the Grey Wolf Optimizer and Particle Swarm Optimisation algorithms to prove its efficacy and superiority. The reference bank angle is modified using feedback linearization and bank reversal logic to create an entry trajectory that meets all path and terminal constraints. The effectiveness of the proposed method has been validated through Monte Carlo simulations that incorporate uncertainties such as variations in initial state, uncertainties in aerodynamics, and atmospheric perturbations. The controller OPAL-RT OP4510 provides bank angle command at every instant based on the current state of the vehicle parameters associated with real-time simulator OP4510. The real-time hardware-in-loop simulation results show that the obtained re-entry trajectory satisfies all path and terminal constraints.

Reentry trajectory design of a hypersonic vehicle based on reinforcement learning

In this research, we investigate control of a hypersonic vehicle (HV) following its reentry into the Earth’s atmosphere, using deep reinforcement learning (DRL) in a continuous space. Here, we incorporate the basic kinematic and force equations of motion for a vehicle in an atmospheric flight to formulate the reentry trajectory satisfying the boundary constraints and multiple mission related process constraints. The aerodynamic model of the vehicle emulates the properties of a common aero vehicle (CAV-H), while the atmospheric model of the Earth represents a standard model based on US Standard Atmosphere 1976, with significant simplification to the planetary model. In an unpowered flight, we then control the vehicle’s trajectory by perturbing its angle of attack and bank angle to achieve the desired objective, where the control problem is based on different actor-critic frameworks that utilize neural networks (NNs) as function approximators to select and evaluate the control actions in continuous state and action spaces. First, we train the model following each of the methods, that include on-policy proximal policy approximation (PPO) and off-policy twin delayed deterministic policy gradient (TD3). From the trajectory generated, we select a nominal trajectory for each algorithm that satisfies our mission requirements based on the reward model.

Gaussian Distribution–Based Control Vector Parameterization Method for Constrained Hypersonic Vehicle Reentry Trajectory Optimization

Gaussian Distribution–Based Control Vector Parameterization Method for Constrained Hypersonic Vehicle Reentry Trajectory Optimization

Descent Property in Sequential Second-Order Cone Programming for Nonlinear Trajectory Optimization

Sequential second-order cone programming (SSOCP) is commonly used in aerospace applications for solving nonlinear trajectory optimization problems. The SSOCP possesses good real-time performance. However, one long-standing challenge is its unguaranteed convergence. In this paper, we theoretically analyze the descent property of the penalty function in the SSOCP. Using Karush–Kuhn–Tucker conditions, we obtain two important theoretical results: 1) the penalty function of the original nonlinear problem always descends along the iteration direction; 2) a sufficiently small trust region can decrease the penalty function. Based on these two results, we design an improved trust region shrinking algorithm with theoretically guaranteed convergence. In numerical simulations, we verify the proposed algorithm using a reentry trajectory optimization problem.