Quasi-equilibrium Glide Condition Research Articles

Analytic Time Reentry Cooperative Guidance for Multi-Hypersonic Glide Vehicles

Aiming at the cooperative guidance problem of multi-hypersonic glide vehicles, a cooperative guidance method based on a parametric design and an analytical solution of time-to-go is proposed. First, the hypersonic reentry trajectory optimization problem was transformed into a parameter optimization problem. The parameters were optimized to determine the angle of attack profile and the time to enter the altitude velocity reentry corridor. Then, using the quasi-equilibrium glide condition, the estimation form of the remaining flight time was analytically derived to satisfy accurately the cooperative time constraint. Using the remaining time-to-go and range-to-go, combined with the heading angle deviation corridor, the bank angle command was further calculated. Finally, the swarm intelligence optimization algorithm was used to optimize the design parameters to obtain the cooperative guidance trajectory satisfying the time constraint. Simulations showed that the analytical time reentry cooperative guidance algorithm proposed in this paper can accurately meet the time constraints and cooperative flight accuracy. Monte Carlo simulation experiments verified that the proposed algorithm demonstrates a robust performance.

A Real-Time Reentry Guidance Method for Hypersonic Vehicles Based on a Time2vec and Transformer Network

In this paper, a real-time reentry guidance law for hypersonic vehicles is presented to accomplish rapid, high-precision, robust, and reliable reentry flights by leveraging the Time to Vector (Time2vec) and transformer networks. First, referring to the traditional predictor–corrector algorithm and quasi-equilibrium glide condition (QEGC), the reentry guidance issue is described as a univariate root-finding problem based on bank angle. Second, considering that reentry guidance is a sequential decision-making process, and its data has inherent characteristics in time series, so the Time2vec and transformer networks are trained to obtain the mapping relation between the flight states and bank angles, and the inputs and outputs are specially designed to guarantee that the constraints can be well satisfied. Based on the Time2vec and transformer-based bank angle predictor, an efficient and precise reentry guidance approach is proposed to realize on-line trajectory planning. Simulations and analysis are carried out through comparison with the traditional predictor-corrector algorithm, and the results manifest that the developed Time2vec and transformer-based reentry guidance algorithm has remarkable improvements in accuracy and efficiency under initial state errors and aerodynamic parameter perturbations.

Adaptive Entry Guidance for Hypersonic Gliding Vehicles Using Analytic Feedback Control

This paper presents an adaptive, simple, and effective guidance approach for hypersonic entry vehicles with high lift-to-drag (L/D) ratios (e.g., hypersonic gliding vehicles). The core of the constrained guidance approach is a closed-form, easily obtained, and computationally efficient feedback control law that yields the analytic bank command based on the well-known quasi-equilibrium glide condition (QEGC). The magnitude of the bank angle command consists of two parts, i.e., the baseline part and the augmented part, which are calculated analytically and successively. The baseline command is derived from the analytic relation between the range-to-go and the velocity to guarantee the range requirement. Then, the bank angle is augmented with the predictive altitude-rate feedback compensations that are represented by an analytic set of flight path angle needed for the terminal constraints. The inequality path constraints in the velocity-altitude space are translated into the velocity-dependent bounds for the magnitude of the bank angle based on the QEGC. The sign of the bank command is also analytically determined using an automated bank-reversal logic based on the dynamic adjustment criteria. Finally, a feasible three-degree-of-freedom (3DOF) entry flight trajectory is simultaneously generated by integrating with the real-time updated command. Because no iterations and no or few off-line parameter adjustments are required using almost all analytic processing, the algorithm provides remarkable simplicity, rapidity, and adaptability. A considerable range of entry flights using the vehicle data of the CAV-H is tested. Simulation results demonstrate the effectiveness and performance of the presented approach.

Entry Guidance With Terminal Time Control Based on Quasi-Equilibrium Glide Condition

The terminal constraints in entry guidance design are generally position and velocity constraints. In this study, the terminal time constraint is also taken into account. The estimates of time-to-go and range-to-go are discussed based on the quasi-equilibrium glide condition. Further analysis reveals that only two among the time-to-go, range-to-go, and terminal velocity are independent. Based on this observation, a guidance method is designed, which provides a new aspect to exploit the potential of entry guidance.

Glide guidance for reusable launch vehicles using analytical dynamics

This paper proposes a novel glide guidance law for the reusable launch vehicle (RLV), in which longitudinal and lateral paths are separately designed to quickly derive guidance commands. First, an altitude profile is designed in the longitudinal plane. Using this profile, the terminal altitude, flight path angle, and position are naturally met and the quasi-equilibrium glide condition (QEGC) is easily satisfied. Second, analytical solutions of altitude, velocity, and flight path angle are deduced in the glide phase; so the values of path constraints and performance index can also be analytical calculated. Third, a new concept of virtual target is proposed to design the lateral motion. By analytically determining the virtual target with the solutions in the glide phase, the cross-range is online adjusted to control the dissipation in velocity. Finally, the guidance law is proposed based on these analytical solutions. In the guidance law, longitudinal and lateral motions are controlled by online updating the profile and revising the virtual target, respectively. Integration-based predictors are unnecessary in comparison with conventional guidance laws, so a short guidance period can be used to improve the robustness. The effectiveness and the robustness of the proposed method are demonstrated with various scenarios and Monte Carlo simulation, respectively.

Rapid entry trajectory planning without segmentation

A new rapid entry trajectory planning algorithm for hypersonic glide vehicles is presented in this paper. Firstly, build a new technique to calculate the boundary of the control variable that satisfy the path and control constraints without using quasi-equilibrium glide condition (QEGC). Secondly the optimal control variable is expressed as function of current state. Then combine two of them by control coordination. Finally, introduce one or two constant parameters to satisfy the final state condition. The approach is tested using the CAV model. This algorithm is efficient and will provide feasible trajectory without reversal of bank angle. It can apply for entire entry process, segmentation and the QEGC is unnecessary.

A Novel Reentry Trajectory Generation Method Using Improved Particle Swarm Optimization

This paper proposes a new reentry trajectory generation method, which mainly comprises two parts: reentry profile design and trajectory optimization. Different from conventional methods that design angle-of-attack (AOA) and bank-angle profiles, a height-range profile is proposed in this paper. Using this profile, the AOA can be directly derived and the quasi-equilibrium glide condition is easily satisfied. In addition, the bank angle is analytically derived with the heading error, with only one reversal. Finally, the original problem is transformed into a parameter optimization problem and solved by an improved particle swarm optimization (PSO) method. In PSO, a comparison principle is proposed to tackle constraints and three modifications are applied to the swarm evolution to enhance the searching capacity. To conquer disturbances, an online profile updating strategy is developed based on the nominal profile, so complicated work of designing a trajectory tracker is avoided. Simulation validates the effectiveness of the proposed method and demonstrates that the improved PSO is comparable to the pseudospectral method and is better than the basic PSO.

Rapid trajectory planning of a reusable launch vehicle for airdrop with geographic constraints

Online feasible trajectory generation for an airdrop unpowered reusable launch vehicle is addressed in this article. A rapid trajectory planning algorithm is proposed to satisfy not only the multiple path and terminal constraints but also the complex geographic constraints of waypoints and no-fly zones. Firstly, the lower and upper boundaries of the bank angle that implement all the path constraints are obtained based on the quasi-equilibrium glide condition. To determine the bank angle directly, a weighted interpolation of the boundaries is then developed, which provides an effective approach to simplify the planning process as a one-parameter search problem. Subsequently, three types of lateral planning algorithms are designed to determine the sign of the bank angle according to the requirements of waypoints passage, no-fly-zones avoidance, and terminal constraints in the airdrop process, and the convergence of these methods for passing over the waypoints and meeting the terminal conditions has been clarified and formally demonstrated. Considering the constraints in the actual airdrop flight missions, the planning trajectory is divided into several subphases to facilitate the application of corresponding algorithms. Finally, the performance of the proposed algorithm is assessed through three airdrop missions of reusable launch vehicle with different geographic constraints. Besides, the effectiveness of the algorithm is demonstrated by the Monte Carlo simulation results.

Entry trajectory generation without reversal of bank angle

A rapid entry trajectory planning algorithm for hypersonic glide vehicles is presented in this paper, and the avoidance of no-fly zones with large cross-range is achieved. The highly-constrained entry trajectory generation mission is accomplished using an adjustable angle of attack and bank, instead of a nominal angle of attack and reversal logic of bank angle. In this way, the maneuvering capability of the vehicle is greatly improved. Moreover, as no reversal of bank angle exists in the whole flight, the control command is easier to follow. Firstly, longitudinal entry corridor with an adjustable angle of attack is built up. The drag acceleration profile is represented as five piecewise affine functions of the energy, which are adjusted to meet the requirements of the trajectory length and lateral maneuvering capability. Secondly, based on the quasi-equilibrium glide condition (QEGC), the maximum and minimum boundary of the lateral lift-to-drag corridor corresponding to the current drag acceleration profile is approximated, and the lateral profile is represented as an interpolation result of the boundaries. Finally, the parameters of longitudinal and lateral profile are found by the Newton iteration scheme with the help of a reduced order system. A combined proportional integral derivative (PID) tracker is also designed to follow the drag and heading angle profile. The approach is tested using the Common Aero Vehicle model. Simulation results demonstrate that the generated entry trajectories can avoid no-fly zone with a large cross-range and achieve the terminal conditions while satisfying all the complex path constraints.

Feasible footprint generation with uncertainty effects

Landing footprint is critical in generating feasible entry trajectories for hypersonic glide vehicles. In this paper, a new landing footprint generation algorithm that considers multiple uncertainty effects is proposed, based on the improved 3D acceleration profile planning method. First, a new entry corridor with uncertainty effects is derived, in which the angle of attack profile is adjustable at any time during the entire flight. Second, the longitudinal drag profile is designed as the interpolation results of the upper and lower fitting safe boundaries. The corresponding lateral lift-to-drag corridor is obtained using the quasi-equilibrium glide condition. A combined Proportion Integration Differentiation (PID) tracker is used to follow the planned profiles in the longitudinal and lateral corridors, and the feasible entry trajectories are completed. Finally, feasible footprint is generated by repeatedly computing the reachable boundaries for all the profiles in the new safe corridor, as well as the analytical calculation of the maximum range point. The approach is tested using the Common Aero Vehicle-H model. Simulation results demonstrate that the proposed algorithm can rapidly generate a feasible footprint of entry for vehicles while satisfying all the path and terminal constraints.

Fault-tolerant guidance for hypersonic vehicle based on predictor-corrector strategy

A fault-tolerant guidance law using the predictor-corrector theory for a hypersonic vehicle (HSV) is designed to solve the problem of online trajectory planning under faults in reentry phase. Once the fault occurs, based on the quasi equilibrium glide condition (QEGC), the new limitations of reentry corridor are transformed into the constraints of attack angle, which are used to obtain the prediction of attack angle with Newton iterative method. Then, with the attack angle obtained, the roll angle is predicted based on the range-to-go by iteration. Eventually, the attitude guidance of HSV is achieved to meet the demands of reentry corridor constraints combined with limits of fault. By continuous iteration, the predictor-corrector possesses a strong ability of fault-tolerant. Besides, it also does not need the stand trajectory, which makes it suitable to on-line trajectory planning, especially under fault situations. In this paper, compared with the stand model of attack angle, the simulation results show that the guidance provided in this paper is real-time and effective.

Rapid generation of entry trajectory with multiple no-fly zone constraints

An entry trajectory planning algorithm that generates flyable trajectories satisfying multiple no-fly zones and other path and terminal constraints is presented. The algorithm divides the entry trajectory into initial and glide phases. In the initial phase, the maximum value of heating rate is controlled accurately as the altitude of the quasi-equilibrium glide condition (QEGC) transition point is adjusted with a nominal angle of attack and a parameterized bank angle. In the glide phase, a geometry based planning algorithm that relies on the center positions and radius of the multiple no-fly zones, is proposed to calculate the waypoints of the virtual flight path. The magnitude and reversal point of the bank angle in each sub-phase are searched based on a reduced-order lateral system with the predictor-corrector method. The altitude is designed as an analytical function of energy, and the QEGC is employed to analytically solve the remaining state variables. Finally, a linear quadratic regulator is used to test the realization of the 3D trajectory. The algorithm is tested using the common aero vehicle-H model. The results demonstrate that the algorithm can rapidly generate the entry trajectory with multiple no-fly zone constraints and achieve complex flight missions satisfying all flight constraints.

Approach and Landing Range Guidance for an Unpowered Reusable Launch Vehicle

A new method has been developed for predicting and controlling the ground range of an unpowered reusable launch vehicle. The key feature is the use of the quasi-equilibrium glide condition to create a database of range-to-go versus energy for different values of the glide-efficiency factor. Downtrack range to runway touchdown is predicted by performing a two-dimensional table lookup of the range-to-go database. Unlike most predictor–corrector guidance methods, the proposed ground-range guidance scheme does not require onboard numerical integration of the governing equations of motion. Another key element is the coupling between the latter stages of the traditional terminal area energy management phase and the entire approach and landing phase, where the flare-to-touchdown maneuver is concisely parameterized by an exponential altitude profile. Numerical simulations demonstrate that this new method can accurately and reliably guide the vehicle to the desired touchdown conditions despite large errors in the initial states, large errors in the initial downtrack distance to the runway, and aerodynamic drag dispersions.

Highly constrained optimal gliding guidance

A novel highly constrained optimal gliding guidance algorithm, which can satisfy multiple path and terminal constraints in the presence of no-fly zones for hypersonic vehicle, is investigated in this paper. It employs line-of-sight angle to describe the relative location relationship between flight path and no-fly zones, and proposes boundaries selection algorithm for each no-fly zone, which is called avoidance strategy, with minimum energy consumption. The boundaries determined by avoidance strategy divide the flight process and guidance task into several stages. In each stage, it constructs guidance models based on quasi-equilibrium glide condition in longitudinal and lateral directions respectively, and employs optimal control to generate guidance law to satisfy terminal location, altitude, and flight path angle constraints. In addition, all the path constraints, including heating rate, dynamic pressure, and overload, are converted into the angle-of-attack constraint to ensure the guidance mission can be accomplished successfully. This algorithm is independent of standard trajectory, and all the guidance commands, including the bank angle and the angle of attack, can be calculated analytically in real time and adaptively. Finally, the simulation results of CAV-H indicate that the proposed strategy can guide the vehicle to satisfy multiple different constraints with high precision and avoid no-fly zones effectively.

Hybrid Re-entry Guidance for Reusable Launch Vehicle

A hybrid re-entry guidance approach, based on the nominal trajectory guidance method and predictor-corrector guidance, is proposed for the reusable launch vehicle (RLV). This approach generates a feasible re-entry trajectory which consists ofpre-entry phase, optimized bank angle phase and predictor-corrector phase. With the help of quasi-equilibrium glide condition (QEGC), the angle's constraints are transformed from re-entry constraints in optimized bank angle phase, and then guidance command is optimized using sequential quadratic program (SQP).In predictor-corrector phase, downrange errors are repeatedly calculated to updateconstant bank angle profiles.A bank reversal strategy based upon an azimuth error deadbandis designed to control crossrange. Simulationswith nominal and dispersion conditions demonstrategood performance of the guidance method.

Footprint Problem with Angle of Attack Optimization for High Lifting Reentry Vehicle

A formal analysis to footprint problem with effects of angle of attack (AOA) is presented. First a flexible and rapid standardized method for footprint generation is developed. Zero bank angle control strategy and the maximum crossrange method are used to obtain virtual target set; afterward, closed-loop bank angle guidance law is used to find footprint by solving closest approach problem for each element in virtual target set. Then based on quasi-equilibrium glide condition, the typical inequality reentry trajectory constraints are converted to angle of attack lower boundary constraint. Constrained by the lower boundary, an original and practical angle of attack parametric method is proposed. By using parametric angle of attack profile, optimization algorithm for angle of attack is designed and the impact of angle of attack to footprint is discussed. Simulations with different angle of attack profiles are presented to demonstrate the performance of the proposed footprint solution method and validity of optimal algorithm.

Quasi-equilibrium glide adaptive guidance for hypersonic vehicles

The entry-glide guidance strategy for hypersonic vehicles that can satisfy both terminal and path constraints is investigated in this paper. We propose a quasi-equilibrium glide adaptive guidance methodology based on the quasi-equilibrium glide condition (QEGC), which innovatively utilizes the quasi-equilibrium glide phenomenon in lifting entry. With the aid of QEGC, both range and terminal velocity can be predicted analytically with high precision. The path constraints are converted into angle of attack constraints, which has been difficult to realize by using traditional predictive guidance methods. The algorithm is independent of the standard trajectory. All the guidance commands, including the bank angle and the angle of attack, are calculated analytically in real time, which endows the algorithm with sufficient adapbility. The results of a CAV-H vehicle guidance test show that the algorithm leads the vehicle along a quasi-equilibrium glide trajectory satisfying both the terminal and path constraints and has sufficient flexibility for occasional mission changes. Furthermore, the robustness of the guidance algorithm under disturbances is validated through a Monte Carlo simulation.

Constrained Predictor-Corrector Entry Guidance

In this paper we develop a numerical predictor-corrector entry guidance algorithm for vehicles with medium to higher lifting capability. A major dierence between the current algorithm and existing predictor-corrector algorithms is that the current algorithm has the ability to enforce all inequality trajectory constraints commonly seen in entry ight. The enabling mechanism is the so-called quasi-equilibrium glide condition (QEGC). The QEGC allows convenient translation of the path constraints in the velocity-altitude space into the energy-dependent upper and lower bounds for the magnitude of the bank angle. As such, the algorithm is able to enforce the path constraints without suering the usual side eects of increasing complexity and degraded robustness. Another unique feature of the current algorithm is on-line adaptation of a parameter in the lateral guidance logic so that the nal heading alignment oset is tightly regulated. Extensive dispersion simulation results are presented to demonstrate the eectiveness and precision of the algorithm.

Rapid Generation of Accurate Entry Landing Footprints

Rapid and reliable generation of the landing footprint of an entry vehicle is the key capability required for on-board determination of landing options. Under the conventional formulation of the maximum crossrange problem at specified downranges, the footprint problem is difficult to numerically solve. When inequality trajectory constraints are imposed, accurate determination of footprints becomes even more challenging. Using the quasi-equilibrium glide condition (QEGC) in entry flight, a near-optimal, closed-form bank angle control law is first developed for the class of problems including maximum-crossrange problem. Then it is shown that the footprint problem is equivalent to seeking the solutions of a series of much simpler problems of closest approach to a moving virtual target. The closest-approach problem is a univariate root-finding problem using the near-optimal control law. Common inequality entry trajectory constraints are enforced without any additional difficulty with appropriate velocity-dependent bounds of the bank angle by using the QEGC. As a result, an accurate and fully constrained landing footprint from any feasible initial condition can be obtained rapidly and very reliably. The validity of the method is verified with independent trajectory optimization software. Footprints for an entry vehicle in several different mission scenarios and constraint settings are generated to demonstrate the method.

Asymptotic Analysis of Quasi-Equilibrium Glide in Lifting Entry Flight

The physical phenomenon of near equilibrium glide in entry flight of a lifting vehicle has long been a very useful utility in flight mechanics analysis and entry guidance designs. But no rigorous mathematical characterization of this quasi-equilibrium flight condition exists that can help provide a deeper understanding of when and how such a flight condition takes place and what is the precise relationship between exact and quasi-equilibrium glide. We present a formal analysis to quasi-equilibrium entry flight in this paper. We embed the quasi-equilibrium gliding flight problem in a class of regular perturbation problems and obtain solutions in asymptotic expansions. We show that the zeroth-order solution is an exact equilibrium glide solution. We provide the complete solution structure and convergence analysis. Our analysis yields quantitative accuracy estimates to the quasi-equilibrium glide condition that can guide how this approximation can be best used. The solution structure we obtain naturally leads to what can be done to improve the accuracy of the quasi-equilibrium glide condition.