Reentry Trajectory Research Articles

Reentry Trajectory Design with Pigeon Inspired Optimization Using Derived Angle of Attack Profile

AbstractThis paper proposes two strategies that generate the entry trajectories using pigeon inspired optimization (PIO) for a lifting type reentry vehicle. The obtained entry trajectory should be ...

Dynamical uncertainty and demisability occurrence for the atmospheric re-entry of SOHO

Re-entry trajectories to the Earth have been recently considered as a valuable end-of-life option also for Sun–Earth Libration Point Orbits (LPO) missions. In this work, we investigate in detail the case corresponding to SOHO. On the one hand, we show how the main uncertainties associated with the problem affect the probability of re-entry and the corresponding point at the interface with the atmosphere. Monte Carlo propagations are applied to different cases of uncertainties. They correspond to the orbit determination, the efficiency of the maneuver required to target the Earth, and the characteristics of the spacecraft determining the solar radiation pressure effect. On the other hand, we provide a comparison between a classical re-entry from a LEO and a hypervelocity re-entry from a LPO, in terms of area affected by the re-entry and demise percentage.

Re-entry trajectory optimization using pigeon inspired optimization based control profiles

In this paper, the entry trajectory optimization problem of lifting type re-entry vehicle with path constraints is solved using Pigeon Inspired Optimization (PIO). Entry trajectory optimization problem involves finding the control profiles, bank angle, and angle of attack to guide the vehicle safely to the destination. The proposed approach parametrizes the bank angle to be a linear function of energy while the angle of attack is considered to be a monotonic function of Mach number. Thus, the problem of finding control profiles is transformed into three parameter search problem. The PIO algorithm is used to find the values of these parameters that minimizes the objective function. The terminal heading angle offset is minimized using traditional bank reversal logic. A new approach is proposed in which the bank angle is modulated to eliminate the oscillations observed in the altitude profile of an entry vehicle with a high lift to drag ratio (L/D). A methodology to satisfy the given load factor constraint is also proposed, as an alternative to traditional penalty factor approach used for incorporating path constraints in PIO algorithm. The proposed approach is further validated by considering sub-cases with different load factor limits and bank angle as the only control variable. The angle of attack profile obtained from the previous case is considered as the nominal profile. The proposed trajectory optimization strategy using PIO algorithm is simulated for Common Aero Vehicle with high L/D ratio (CAV-H) with different load factor constraint limits. The results show that the obtained angle of attack profile minimizes the peak heat rate experienced by the vehicle and bank angle modulation eliminates the oscillations in the altitude profile as well as makes the entry trajectory satisfy the load factor constraint.

Preliminary Analysis of the Hexafly-International Vehicle

Airbreathing hypersonic flight is an ongoing challenge with the potential to cut air travel time and provide cheaper access to space. Waveriders are potential candidates for achieving hypersonic cruise speed or proper acceleration within the atmosphere. Current research tends to focus on key issues like flight mechanics, thermal loading, aero-elasticity, aerodynamic and aerothermodynamics at hypersonic speeds. Design problems in each of these areas must be solved if the design of a hypersonic waverider-like vehicle is to be viable. In this framework, the HEXAFLY-INT project aims at testing in free-flight conditions an innovative gliding vehicle with several breakthrough on-board technologies to be launched along a suborbital trajectory. Its preliminary conceptual design has been carried out by means of tools suitable to design vehicles to fly in hypersonic conditions. Aerodynamic and trajectory analyses have been carried out to assess mission capability as well. Once the aeroshape and the reference mission have been identified, system and sub-system analysis have been performed to close the system loop. The main results of the design analysis carried out during the preliminary phase of the study (such as vehicle aerodynamics and aerothermodynamics, re-entry trajectories, structures and mechanisms, and on the overall system, as well), are presented in this work.

Toward an understanding of supersonic modes in boundary-layer transition for hypersonic flow over blunt cones

Realistic flight vehicles for reentry into the Earth’s atmosphere are commonly similar to blunted cones. The main reason for blunting a cone is to mitigate high heat loads at the nose. Another reason for blunting the cone is to delay boundary-layer transition. It is commonly understood that the second mode is damped in flow over a cone as the nose radius is increased. This is thought to lead to the delay in transition. Here, a blunted cone at a realistic reentry trajectory point with significant real-gas effects is studied. It is shown, using linear stability theory and direct numerical simulation, that there exist multiple unstable modal instabilities in the boundary layer. One of these modal instabilities is called the supersonic mode, as its phase velocity is supersonic relative to the flow velocity at the edge of the boundary layer. Its growth rate is found to increase with increasing nose radius until a certain nose radius is reached. After this radius, any further increase in nose radius decreases its growth rate. There is adequate agreement between theory and direct numerical simulation for the growth rate, phase velocity and eigenfunction of the supersonic mode. At the reentry conditions tested, the supersonic mode is more likely the cause of boundary-layer transition than the second mode for blunted cones with a small wall-temperature ratio. Initial parametric studies confirm that a decrease in wall temperature amplifies the supersonic mode. Also, the supersonic mode’s growth rate is shown to be a maximum when its phase velocity is aligned with the flow velocity.

Reentry Trajectory Optimization for a Hypersonic Vehicle Based on an Improved Adaptive Fireworks Algorithm

Generation of optimal reentry trajectory for a hypersonic vehicle (HV) satisfying both boundary conditions and path constraints is a challenging task. As a relatively new swarm intelligent algorithm, an adaptive fireworks algorithm (AFWA) has exhibited promising performance on some optimization problems. However, with respect to the optimal reentry trajectory generation under constraints, the AFWA may fall into local optimum, since the individuals including fireworks and sparks are not well informed by the whole swarm. In this paper, we propose an improved AFWA to generate the optimal reentry trajectory under constraints. First, via the Chebyshev polynomial interpolation, the trajectory optimization problem with infinite dimensions is transformed to a nonlinear programming problem (NLP) with finite dimension, and the scope of angle of attack (AOA) is obtained by path constraints to reduce the difficulty of the optimization. To solve the problem, an improved AFWA with a new mutation strategy is developed, where the fireworks can learn from more individuals by the new mutation operator. This strategy significantly enhances the interactions between the fireworks and sparks and thus increases the diversity of population and improves the global search capability. Besides, a constraint-handling technique based on an adaptive penalty function and distance measure is developed to deal with multiple constraints. The numerical simulations of two reentry scenarios for HV demonstrate the validity and effectiveness of the proposed improved AFWA optimization method, when compared with other optimization methods.

Improved Chicken Swarm Optimization Method for Reentry Trajectory Optimization

Reentry trajectory optimization has been researched as a popular topic because of its wide applications in both military and civilian use. It is a challenging problem owing to its strong nonlinearity in motion equations and constraints. Besides, it is a high-dimensional optimization problem. In this paper, an improved chicken swarm optimization (ICSO) method is proposed considering that the chicken swarm optimization (CSO) method is easy to fall into local optimum when solving high-dimensional optimization problem. Firstly, the model used in this study is described, including its characteristic, the nonlinear constraints, and cost function. Then, by introducing the crossover operator, the principles and the advantages of the ICSO algorithm are explained. Finally, the ICSO method solving the reentry trajectory optimization problem is proposed. The control variables are discretized at a set of Chebyshev collocation points, and the angle of attack is set to fit with the flight velocity to make the optimization efficient. Based on those operations, the process of ICSO method is depicted. Experiments are conducted using five algorithms under different indexes, and the superiority of the proposed ICSO algorithm is demonstrated. Another group of experiments are carried out to investigate the influence of hen percentage on the algorithm’s performance.

Reentry Trajectory Optimization using Gradient Free Algorithms

In this work, a study on atmospheric reentry trajectory optimization using gradient free optimization techniques is presented. Genetic Algorithm (GA), Pattern Search (PS) and Simulated Annealing (SA) approaches are explored for the considered nonlinear constrained trajectory optimization problem. Aerodynamic performance indicator, (L/D), is used as a control variable to minimize the objective function subject to various terminal and in-flight path constraints. Results and findings on the performance comparison of the considered methods are discussed.

A Study on Re-entry Predictions of Uncontrolled Space Objects for Space Situational Awareness

The key risk analysis technologies for the re-entry of space objects into Earth’s atmosphere are divided into four categories: cataloguing and databases of the re-entry of space objects, lifetime and re-entry trajectory predictions, break-up models after re-entry and multiple debris distribution predictions, and ground impact probability models. In this study, we focused on reentry prediction, including orbital lifetime assessments, for space situational awareness systems. Re-entry predictions are very difficult and are affected by various sources of uncertainty. In particular, during uncontrolled re-entry, large spacecraft may break into several pieces of debris, and the surviving fragments can be a significant hazard for persons and properties on the ground. In recent years, specific methods and procedures have been developed to provide clear information for predicting and analyzing the re-entry of space objects and for ground-risk assessments. Representative tools include object reentry survival analysis tool (ORSAT) and debris assessment software (DAS) developed by National Aeronautics and Space Administration (NASA), spacecraft atmospheric re-entry and aerothermal break-up (SCARAB) and debris risk assessment and mitigation analysis (DRAMA) developed by European Space Agency (ESA), and semi-analytic tool for end of life analysis (STELA) developed by Centre National d’Etudes Spatiales (CNES). In this study, various surveys of existing re-entry space objects are reviewed, and an efficient re-entry prediction technique is suggested based on STELA, the life-cycle analysis tool for satellites, and DRAMA, a re-entry analysis tool. To verify the proposed method, the re-entry of the Tiangong-1 Space Lab, which is expected to re-enter Earth’s atmosphere shortly, was simulated. Eventually, these results will provide a basis for space situational awareness risk analyses of the re-entry of space objects.

An adaptive reentry guidance method considering the influence of blackout zone

Reentry guidance has been researched as a popular topic because it is critical for a successful flight. In view that the existing guidance methods do not take into account the accumulated navigation error of Inertial Navigation System (INS) in the blackout zone, in this paper, an adaptive reentry guidance method is proposed to obtain the optimal reentry trajectory quickly with the target of minimum aerodynamic heating rate. The terminal error in position and attitude can be also reduced with the proposed method. In this method, the whole reentry guidance task is divided into two phases, i.e., the trajectory updating phase and the trajectory planning phase. In the first phase, the idea of model predictive control (MPC) is used, and the receding optimization procedure ensures the optimal trajectory in the next few seconds. In the trajectory planning phase, after the vehicle has flown out of the blackout zone, the optimal reentry trajectory is obtained by online planning to adapt to the navigation information. An effective swarm intelligence algorithm, i.e. pigeon inspired optimization (PIO) algorithm, is applied to obtain the optimal reentry trajectory in both of the two phases. Compared to the trajectory updating method, the proposed method can reduce the terminal error by about 30% considering both the position and attitude, especially, the terminal error of height has almost been eliminated. Besides, the PIO algorithm performs better than the particle swarm optimization (PSO) algorithm both in the trajectory updating phase and the trajectory planning phases.

Drag derived altitude aided navigation method

The navigation problem of the lifting reentry vehicles has attracted much research interest in the past decade. This paper researches the navigation in the blackout zone during the reentry phase of the aircraft, when the communication signals are attenuated and even interrupted by the blackout zone. However, when calculating altitude, a pure classic inertial navigation algorithm appears imprecise and divergent. In order to obtain a more precise aircraft altitude, this paper applies an integrated navigation method based on inertial navigation algorithms, which uses drag derived altitude to aid the inertial navigation during the blackout zone. This method can overcome the shortcomings of the inertial navigation system and improve the navigation accuracy. To further improve the navigation accuracy, the applicable condition and the main error factors, such as the atmospheric coefficient error and drag coefficient error are analyzed in detail. Then the damping circuit design of the navigation control system and the damping coefficients determination is introduced. The feasibility of the method is verified by the typical reentry trajectory simulation, and the influence of the iterative times on the accuracy is analyzed. Simulation results show that iterative three times achieves the best effect.

Rarefied aerodynamics of a deployable re-entry capsule

Several research activities have been already carried out in the field of low-ballistic coefficient re-entry capsules based on deployable umbrella-like aero-shield. The flexible aero-shield, made of ceramic fabrics, acts both as an aero-brake and a Thermal Protection System (TPS), making possible to perform a re-entry from orbital or suborbital conditions with relatively low values of the aero-thermo-dynamic loads.Previous studies have already analyzed Aerodynamics of similar systems, identifying self-stabilizing configurations and creating a preliminary database of force and moment coefficients in different flight regimes.This work is intended to provide a systematic overview of the aerodynamic behavior of a deployable capsule in the rarefied regime, where the differences between the re-entry trajectories from Low-Earth-Orbit and suborbital flight conditions are more evident. Particular focus is given to the longitudinal stability analysis, which demonstrates that, as the continuum hypersonic regime approaches, the capsule could show a stable equilibrium condition in the unfavorable reverse attitude. This unwanted equilibrium condition could be counteracted by moving the center of gravity out of the symmetry axis.

Approximate analytical solutions for heat fluxes in three-dimensional hypersonic flow over blunt bodies

Analytical expressions for the heat flux divided by its value at the stagnation point which depend on the geometric parameters invariant with respect to the choice of the coordinate system, as well as expressions depending on the geometry and the pressure on the surface which have a wider applicability range are obtained in the problem of three-dimensional hypersonic flow over blunt bodies at large and moderate Reynolds numbers. These formulas are derived by solving the thin viscous shock layer equations for a perfect gas using the integral method of successive approximations developed by the author. The accuracy and the range of applicability of the analytical solutions are estimated by comparing them with numerical solutions. On the basis of comparisons with numerical solutions for multicomponent chemically nonequilibrium air at altitudes from 90 to 50 km of the spacecraft reentry trajectory in the Earth’s atmosphere it is shown that the formulas obtained can be used for calculations of the heat flux on an ideal catalytic surface of bodies in hypersonic chemically reacting gas flow.

Reentry trajectory and survivability estimation of small space debris with catalytic recombination

A code has been developed to analyze reentry trajectories and survivability of space debris. In particular, an attention was given to small sizes. Based on simple shapes such as a sphere, a cylinder, and a box with sizes of 12.5–50cm, reentry trajectories were calculated. Materials considered were graphite epoxy, aluminum, and titanium. In total, 120 different cases were examined. The results were compared and validated with various existing codes. Good agreement was found. In the heat transfer calculation, all of the existing codes used the well known Lees’ and Fay and Riddell’s formulae which assume an equilibrium boundary layer flow with a super-catalytic wall where the surface recombination efficiency is regarded infinity. In the case of small space debris having sizes of 2.5–10cm, however, the flow residence time behind a shock wave is far too short, so that the super-catalytic assumption leads to over-estimation of surface heat transfer rates. Assuming a frozen boundary layer, a finite catalytic recombination can be considered and the results were compared with that of the super-catalytic cases. Both hollow and solid spheres were considered with different sizes and materials. In total, 24 different cases were examined. The results showed that, 16 out of 24 cases survived, while only 8 cases for the super-catalytic and 19 cases for the non-catalytic walls survived, implying the importance of catalytic wall effects for the study of small space debris.

Reentry Trajectory Optimization for Hypersonic Glide Vehicle with Flexible Initial Conditions

In the reentry trajectory optimization for unpowered hypersonic glide vehicles (HGVs), the initial reentry conditions (IRCs), which are crucial for flight performance, are partly flexible instead of being specified. Aiming at simultaneously determining the optimal IRCs and optimal control policy, a hybrid optimization strategy with an evaluate-during-optimize framework is proposed in this paper. The IRCs are considered as additional independent design variables, and an evaluation process with multiple performance indicators is established to determine the best IRCs. With the analytic hierarchy process (AHP)-based multicriteria decision-making (MCDM) method, a synthesized scalar objective function is set up. Adopting this objective function, feedback information from the evaluation process can be fully included in the optimization process, resulting in a unified optimization framework. The Chebyshev pseudospectral method (CPM) is then introduced as a direct method for solving the resulting trajectory optimization problem. Numerical simulation results for a generic HGV show that the proposed technique is efficient and straightforward. Moreover, this strategy has strong universality for solving optimal control problems with flexible initial conditions.

Reentry trajectory optimization with waypoint and no-fly zone constraints using multiphase convex programming

This study proposes a multiphase convex programming approach for rapid reentry trajectory generation that satisfies path, waypoint and no-fly zone (NFZ) constraints on Common Aerial Vehicles (CAVs). Because the time when the vehicle reaches the waypoint is unknown, the trajectory of the vehicle is divided into several phases according to the prescribed waypoints, rendering a multiphase optimization problem with free final time. Due to the requirement of rapidity, the minimum flight time of each phase index is preferred over other indices in this research. The sequential linearization is used to approximate the nonlinear dynamics of the vehicle as well as the nonlinear concave path constraints on the heat rate, dynamic pressure, and normal load; meanwhile, the convexification techniques are proposed to relax the concave constraints on control variables. Next, the original multiphase optimization problem is reformulated as a standard second-order convex programming problem. Theoretical analysis is conducted to show that the original problem and the converted problem have the same solution. Numerical results are presented to demonstrate that the proposed approach is efficient and effective.

Why a future commercial spacecraft must be able to SWIM

Regarding current as well as future commercial space transportation (CST) projects, new re-entry trajectory profiles, differing from capsule and shuttle-like approaches, have to be taken into account. These characteristics are mainly ruled by the principle of “landing like an aircraft at an airport”. This directly generates the need to be taken in a system wide information management (SWIM) consideration because of the fact, that all the future air traffic participants are requested to act as SWIM communicating sub-systems by the future Single European Sky Air Traffic Management Research (SESAR) SWIM “Intranet for ATM” concept. Against the background of the global character of future CST operations and the associated SWIM harmonization need referring the U.S. Next Generation Air Transportation System (NextGen) and SESAR, the presented solution addresses near real-time information sharing for normal air traffic protection purposes in the event of a future space vehicle breakup and bases on the already harmonized data format standards Aeronautical Information Exchange Model (AIXM) and Flight Information Exchange Model (FIXM).

Influence of Ablation on Vacuum-Ultraviolet Radiation in a Plasma Wind Tunnel Flow

Plasma wind tunnel experiments have been performed simulating a Hayabusa reentry trajectory point at 78.8 km altitude with a velocity of corresponding to a local mass–specific enthalpy of and a stagnation pressure of 2.44 kPa. Ablation–radiation coupling is investigated using a carbon preform sample, a lightweight carbon phenolic ablator sample, and cooled copper. Optical emission spectroscopic measurements in the vacuum ultraviolet (VUV) regime (116–197 nm) have been conducted through a bore hole in the stagnation point of the different samples. Optical emission spectroscopic measurements in the UV/VIS spectral range (320–810 nm) have been conducted viewing the plasma from the side. The stagnation point VUV radiation to the carbon preform sample is strongest, whereas it is weakest for the carbon phenolic sample. In the UV/VIS both carbon-based material samples lead to stronger plasma radiation than copper. Atomic number densities in front of the samples are largest for the carbon preform sample and lowest for the carbon phenolic sample. Rotational and vibrational temperatures are lower for both the carbon-based materials compared with copper. The measurements show for the first time experimentally the radiative heat flux mitigation by carbon phenolic materials.

Multi-objective reentry trajectory optimization method via GVD for hypersonic vehicles

In the constrained reentry trajectory design of hypersonic vehicles, multiple objectives with priorities bring about more difficulties to find the optimal solution. Therefore, a multi-objective reentry trajectory optimization (MORTO) approach via generalized varying domain (GVD) is proposed. Using the direct collocation approach, the trajectory optimization problem involving multiple objectives is discretized into a nonlinear multi-objective programming with priorities. In terms of fuzzy sets, the objectives are fuzzified into three types of fuzzy goals, and their constant tolerances are substituted by the varying domains. According to the principle that the objective with higher priority has higher satisfactory degree, the priority requirement is modeled as the order constraints of the varying domains. The corresponding two-side, single-side, and hybrid-side varying domain models are formulated for three fuzzy relations respectively. By regulating the parameter, the optimal reentry trajectory satisfying priorities can be achieved. Moreover, the performance about the parameter is analyzed, and the algorithm to find its specific value for maximum priority difference is proposed. The simulations demonstrate the effectiveness of the proposed method for hypersonic vehicles, and the comparisons with the traditional methods and sensitivity analysis are presented.

The Uncontrolled Reentry of Progress-M 27M

ABSTRACT Uncontrolled reentries of sizable space objects are becoming of growing concern due to the increase of space activities around the Earth and population on the ground. After providing an updated review of various aspects of the problem, this paper presents the exemplar case of Progress-M 27M, whose control was lost immediately after launch, on April 28, 2015, and which reentered on May 8. As in similar previous occurrences, the Space Flight Dynamics Laboratory of ISTI/CNR, in Pisa, was in charge of reentry predictions for the Italian civil protection authorities and space agency. The first prediction was issued in the morning of April 30, in the morning of May 7 the only potentially risky reentry trajectory over central Italy was identified, and in the afternoon of May 7, about 12hours before the actual reentry, any residual risk for Europe and Italy was finally excluded.