Landing Trajectory Research Articles

Seismic petrophysics workflow applied to Delaware Basin

Petrophysical analysis of unconventional plays that are comprised of organic mudrock needs detailed data QC and preparation to optimize the results of quantitative interpretation. This includes accurate computation of mineral volumes, total organic carbon (TOC), porosity, and saturations. We used TOC estimation to aid the process of determining the best pay zones for development of such reservoirs. TOC was calculated as a weighted average of Passey’s (empirical) and the bulk density-based (theoretical) methods. In organic mudrock reservoirs, the computed TOC log was used as an input to compute porosity and calibrate rock-physics models (RPMs), which are needed for understanding the potential of source rocks or finding sweet spots and their contribution to the amplitude variation with offset (AVO) changes in the seismic data. Using calibrated RPM templates, we found that TOC is driving the elastic property variations in the Avalon Formation. We determined the layering and rock fabric anisotropy using empirical relationships or modeled in the rock property characterization process because reflectivity effects are often seen in the observed seismic used for well tie and wavelet estimation. A Class IV AVO response was seen at the top of the Avalon Formation, which is typical of an unconventional reservoir. We then performed solid organic matter (TOC) substitution to account for variability of elastic properties and their contrasts as expressed in seismic amplitudes. To complete the characterization of the intervals of interest, we used conventional seismic petrophysical methods in the workflow and found that the main driver modifying the elastic properties for the Avalon shales was TOC; this conclusion serves as a foundation in integrated seismic inversion that may target lithofacies, TOC, and geomechanical properties. Seismic reservoir characterization results are critical in constraining landing zones and trajectories of the horizontal wells. The final interpretation may be used to rank targets, optimize drilling campaigns, and ultimately improve production.

Helicopter Safe Landing Trajectory after Main Rotor Actuator Failures

Main rotor actuator failure leads to catastrophic accidents for single main rotor helicopters. This paper focuses on safe landing trajectories after an actuator is locked in place by the remaining actuators, without introducing other control inputs. A general swashplate geometry is described, and new reconfiguration solutions for the control mixer are presented. The safe landing trajectories are obtained by formulating a nonlinear optimal control problem based on a nonlinear helicopter dynamic model and geometry constraints due to actuator failure. Safe landing trajectory results are shown with various initial forward velocities of all actuator failure cases. The safe initial speed boundaries are also explored by employing speed sweeps.

A Convex Programming Method for Rocket Powered Landing With Angle of Attack Constraint

Real time trajectory planning is vital in rocket precision powered landing guidance. Due to the nonconvex angle of attack (AOA) constraint and other constraints, including nonlinear dynamics and thrust constraint, the powered landing trajectory planning problem is highly nonconvex, which makes it difficult to be solved in real time via existing nonconvex optimization algorithms. As the main contribution of this paper, the AOA constraint is taken into account in the problem. A convex feasible set method is presented to handle it, in which a quadratic concave function is introduced to find a convex feasible subset in the original AOA constraint and the second order term of this function is estimated by Gersgorin disc theorem. For the remaining nonconvexities, the lossless convexification is employed to address the thrust constraint, and the successive linearization is performed to handle the nonlinear dynamics. Thus, a convex optimization problem with AOA constraint for landing trajectory planning is built. The optimal solution to the original problem is obtained by iteratively solving convex problems. Numerical simulations show that the proposed method can find a feasible landing trajectory where the AOA constraint is satisfied and has a better convergence performance compared with the traditional linearization method.

Reachability as a Unifying Framework for Computing Helicopter Safe Operating Conditions and Autonomous Emergency Landing

We present a numeric method to compute the safe operating flight conditions for a helicopter such that we can ensure a safe landing in the event of a partial or total engine failure. The unsafe operating region is the complement of the backwards reachable tube, which can be found as the sub-zero level set of the viscosity solution of a Hamilton-Jacobi (HJ) equation. Traditionally, numerical methods used to solve the HJ equation rely on a discrete grid of the solution space and exhibit exponential scaling with dimension, which is problematic for the high-fidelity dynamics models required for accurate helicopter modeling. We avoid the use of spatial grids by formulating a trajectory optimization problem, where the solution at each initial condition can be computed in a computationally efficient manner. The proposed method is shown to compute an autonomous landing trajectory from any operating condition, even in non-cruise flight conditions.

Active Disturbance Rejection Attitude Control for a Bird-Like Flapping Wing Micro Air Vehicle During Automatic Landing

To solve the attitude control problem of bird-like flapping wing micro air vehicles (FWMAVs) during automatic landing, an active disturbance rejection control (ADRC) architecture is proposed in this paper. This control scheme takes into account the attitude control of flapping, transition and gliding modes in the process of automatic landing. To verify the control effect, the aerodynamic estimation method of the flapping wing based on quasi-steady theory and the dynamics of an FWMAV in Lagrangian form are applied in the simulation. The proposed control architecture consists of two independent ADRC controllers to stabilize the attitude of the pitch and roll channels. The system disturbance and the coupling effects between channels are estimated by an extended state observer (ESO) and compensated in real time in the control output. The convergence of the ESO and ADRC is proven. Simulation results show that even if the aircraft is in different flight modes, the ADRC controller can track the target trajectory quickly and accurately. Then, to realize automatic landing in a real environment, a simplified two-stage landing trajectory is designed. A landing test is carried out on this basis. The test results show that ADRC can not only stabilize the flight attitude in flapping mode but also obtain a satisfactory control accuracy and convergence speed when the aircraft is in the transition and gliding modes, confirming its usefulness in automatic landing.

Receding Horizon Longitudinal Control Technology for Automatic Carrier Landing With Variable Reference Trajectory Based on Sliding Rate Information

In this paper, the longitudinal control of automatic carrier landing is studied. First, the carrier landing control problem is transformed into an optimal control problem of trajectory tracking. Considering the constraints of the control variables and the rate of change of control variables in the realistic landing process, the original linear small disturbance model is expanded. Based on the symplectic pseudospectral method and the adaptive regression prediction technology, a fast receding horizon carrier landing control technology with a variable reference trajectory is developed. Finally, the effectiveness of the control algorithm is verified by simulations at different sea states, initial deviations, and reference trajectory selection strategies. The simulation results demonstrate that the introduction of deck motion prediction can greatly reduce the phase delay of the control system and enhance the tracking ability of the carrier-based aircraft and improve the control effectiveness significantly. The proposed algorithm can precisely control the carrier landing trajectory under initial deviations, the external continuous wind disturbances, and random error of the state variables. Additionally, the calculation efficiency of the present control algorithm is sufficient for real-time online tracking.

Helicopter Landing Trajectory Optimization after Tail Rotor Control Failure in Different Collective Pitch

This paper studies helicopter optimal landing and control procedure after tail rotor control failure (TRCF) in different collective pitch. The optimal control problem of landing after tail rotor control failure was solved numerically by direct multiple shooting method and sequential quadratic programming. A sample helicopter optimal landing procedures after tail rotor control failure in large collective pitch and small collective pitch were investigated respectively. As can be seen from the results, when the tail rotor is stuck at large collective pitch, the tail rotor provides a large lateral force, which facilitates landing with small forward speed and descent rate in a large power state. The pilot can maintain stability of heading by side slipping. When the tail rotor is stuck at small collective pitch, the tail rotor provides a small lateral force, which is favorable for flying near economic speed, but difficult for a safe landing. A normal landing maneuver will cause a high yaw rate at touchdown, which is dangerous. Therefore, autorotation is preferred during touchdown because the landing is more secure with small yaw rate. The trajectory optimization method of helicopter safe landing after tail rotor control failure can provide a reference for flight test.

Fast Generation of Optimal Asteroid Landing Trajectories Using Deep Neural Networks

To improve the autonomy and reliability of asteroid landings, an intelligent approach to fast and reliable generation of optimal landing trajectories is proposed. Unfortunately, the indirect methods require good initial guesses for shootings. To address this issue, deep neural networks (DNNs) are developed to approximate the costates of the indirect methods and supply good initial solutions to achieve high success rate of shootings. This article focuses on the following three contributions. First, the original asteroid landing problems are connected with two-dimensional (2-D) asteroid-free transfer problems using model continuation and state transformation techniques. Second, DNNs are developed and optimized to approximate the costates of the 2-D transfers with high accuracy. Third, a systematical solution for asteroid landing trajectory optimization is developed, wherein the DNNs provide good initial solutions, and the accurate solutions for landings are obtained through a solution continuation process. Additionally, an alternative solution supplying strategy based on error statistics of DNN approximation is presented to take over the solution supplying when the predictions of DNNs fail to converge to the optima. Evaluations of the DNNs for solution supplying and simulations of landings on 433 Eros and 101955 Bennu are given to substantiate the effectiveness of the proposed techniques and demonstrate the performance of the developed algorithm.

Fast solution continuation of time-optimal asteroid landing trajectories using deep neural networks

To improve the autonomy and reliability of asteroid landing control, a fast solution continuation approach for time-optimal asteroid landing trajectories is presented in this study. The contributions of this study are threefold. First, a deep neural network (DNN) is developed to approximate the gravitational field of asteroids, and the corresponding time consumption of gravity calculation in trajectory propagation is significantly reduced. Second, the original 3-dimensional (3D) landing control problem is connected to a simplified 2D one according to the continuation relationship between these model dynamics. Third, the 2D control problem is further transformed into a multi-variable root-finding problem with analytical shooting equations with the help of a Gauss-Legendre integral method and could be quickly solved by shooting methods. Taking the solution of this root-finding problem as an initial guess, the accurate solution of the original time-optimal landing problem can be quickly obtained through a backward solution continuation process. Finally, numerical simulations of landings on 443 Eros are given to verify the effectiveness of the proposed techniques and thus to illustrate the excellent performance on rapidity, convergence and solution accuracy of the developed algorithm for the generation of time-optimal landing trajectories.

Pseudo-spectral 방법 및 무차원 운동방정식 기반 최적 달 착륙 경로 생성

In this paper, the optimal landing trajectory from lunar parking orbit to moon surface is generated by pseudo-spectral method, robust Sequential Quadratic Programming(rSQP) method and Non-dimensional motion equation. This research focuses on analyzing the fuel consumption of spacecraft. Therefore, the objective function is defined as minimizing fuel consumption. The pseudo-spectral method is firstly explained and then the equation of motion for spacecraft is defined in polar coordinate system. The equation of motion is derived by point mass model because the space and moon do not have the atmosphere such as air. So, the 6 Degree of freedom (6DOF) is not required to define the equation of motion. The equation of motion is changed to non-dimensional equation of motion to enhance the accuracy of lunar landing trajectory. By generating optimal landing trajectory from lunar parking orbit to moon surface, which use the non-dimensional equation of motion, the required fuel, thrust vector direction and its norm would be checked. It is judged that this research is very useful for developing spacecraft and computing the required fuel mass. Furthermore, the research can be utilized for aircraft and car trajectory generation.

Adaptive trajectory generation based on real-time estimated parameters for impaired aircraft landing

ABSTRACTThis paper is motivated by a need to address the challenge of securing a safe landing after suffering from inflight impairment. In this paper, a new adaptive generalised model predictive static programming (G-MPSP) is developed to generate a safe emergency landing trajectory for impaired aircraft. Utilising the computationally efficient G-MPSP framework, the proposed algorithm enables adaptation of model parameters based on the prediction errors to ensure reasonable guidance performance. Based on the estimated parameters, a feasible landing trajectory is then generated by the flexible finite-horizon G-MPSP with input constraints. The integrated approach features explicit closed-form solutions for both parameter estimation and trajectory generation. Its effectiveness is demonstrated by simulations in the presence of parameter uncertainties and noises and by comparison studies with the non-adaptive G-MPSP.

Autonomous Landing Control of Highly Flexible Aircraft Based on Lidar Preview in the Presence of Wind Turbulence

This paper investigates preview-based autonomous landing control of a highly flexible flying wing model using short-range light detection and ranging (Lidar) wind measurements in the presence of wind turbulence. The preview control system is developed based on a reduced-order linear aeroelastic model and employs a two-loop control scheme. The outer loop employs the linear active disturbance rejection control and PI algorithms to track the reference landing trajectory and vertical speed, respectively, and to generate the attitude angle command. This is then used by the inner loop using H $_{\infty }$ preview control to compute the control inputs to the actuators (control flaps and thrust). A landing trajectory navigation system is designed to generate real-time reference commands for the landing control system. A Lidar simulator is developed to measure the wind disturbances at a distance in front of the aircraft, which is provided to the inner-loop H $_{\infty }$ preview controller as prior knowledge to improve control performance. Simulation results based on the full-order nonlinear flexible aircraft dynamic model show that the preview-based landing control system is able to land the flying wing effectively and safely, showing better control performance than the baseline landing control system (without preview) with respect to landing effectiveness and disturbance rejection. The control system's robustness to measurement error in the Lidar system is also demonstrated.

Analysis of emerging disturbing factors on the descent vehicle with inflatable mechanical devices during the descent stage

The movement of asymmetric descent vehicles, in contrast to the movement of symmetrical landing vehicles, has a number of features. The main of them consist in the emergence of such dynamic phenomena as progressive self-rotation, vibrational-rotational resonances, nutation-precession instability, auto-oscillations, and others. In this paper, the entire landing trajectory is divided into main stages of movement, and then an analysis of some of the most unfavourable variants of movement at each stage is given. The conclusion is about the worst options. This must be taken into account when designing such descent vehicles with inflatable structures.

Characterization of the Agilkia region through discrete-element simulation of Philae’s rebound

Context. The cold gas system and anchoring harpoons that were designed to hold Philae down after it landed on the Agilkia region of comet 67P/Churyumov-Gerasimenko (67P) failed. This caused the lander to move on a complex trajectory that comprised multiple impacts and rebounds. The motion of Philae was mainly dominated by the gravitational environment and the physical properties of the surface on Agilkia. This allows us to determine the physical properties of the surface layer by high-fidelity discrete-element simulations of Philae’s rebounds. Aims. We explore the surface physical properties of the Agilkia region on comet 67P by minimizing the difference in Philae’s rebound status between observational data and simulations based on the assumption of a granular-boulder hybrid surface material. Methods. We first developed an efficient gravity model to accurately approximate the high-resolution polyhedral shape of the comet. This allowed us to run many simulations for the landing trajectory. We developed a complete dynamical model of the motion of Philae, including a mechanical model of the lander and the hybrid surface model. This focused in particular on the interaction of discrete elements in Philae and the granular regolith layer with a boulder added on top of it. We used mixed discrete optimization to determine the input physical variables on Agilkia to fit the rebound observational data (Philae’s rebound velocity). Results. The discrete-element simulation constrained by Philae’s rebound velocity implies that Philae first impacted on a boulder and scratched it with the landing gear. After this, its three soles interacted with the granular regolith, which consists of particles with a mean diameter of 0.014 ± 0.004 cm. The thickness of the region interaction is estimated to be 0.272 ± 0.062 m with a corresponding density of 1443 ± 231 kg m−3. The Young modulus for each particle is estimated to be 108 Pa. Based on a porosity of 0.75, the friction of the surface of particles is derived to be moderate, with a friction coefficient of about 0.6.

Research on Optimal Landing Trajectory Planning Method between an UAV and a Moving Vessel

The location, velocity, and flight path angle of an autonomous unmanned aerial vehicle (UAV) landing on a moving vessel are key factors for an optimal landing trajectory. To tackle this challenge, this paper proposes a method for calculating the optimal approach landing trajectory between an UAV and a small vessel. A numerical approach (iterative method) is used to calculate the optimal approach landing trajectory, and the initial lead is introduced in the calculation process of the UAV trajectory for the inclination and heading angle for accuracy improvement, so that the UAV can track and calculate the optimal landing trajectory with high precision. Compared with the variational method, the proposed method can calculate an optimal turning direction angle for the UAV during the landing. Simulation experiments verify the effectiveness of the proposed algorithm and give optimal initialization values.

DESCENT TRAJECTORY RECOVERY OF CHANG’E-4 LANDER BASED ON DESCENT IMAGES

Abstract. Chang’e-4 lander, carrying Yutu-2 rover, was successfully landed on the far side of lunar surface in Von Kármán crater inside the South Pole-Aitken basin on January 3rd, 2019. The descent images, captured by the descent camera mounted on the lander, captured the sequential descent images and recorded the scene changes during the entry, descent and landing (EDL) process. This paper proposed a bundle adjustment based geometric processing method for descent and landing trajectory recovery using descent images. A frame camera based self-calibration model was introduced for high precision estimation of interior and exterior parameters of descent images simultaneously in a least squares manners. Evenly distributed GCPs were selected from the landing area in a digital orthophoto map generated from LROC NAC images and SLDEM2015. The experimental results demonstrated the effectiveness of the proposed method in Chang’e-4 descent trajectory recovery.

Autonomous Landing of a Micro Aerial Vehicle on a Moving Platform Using a Composite Landmark

In the existing vision-based autonomous landing systems for micro aerial vehicles (MAVs) on moving platforms, the limited range of landmark localization, the unknown measurement bias of the moving platform (such as wheel-slip or inaccurate calibration of encoders), and landing trajectory knotting seriously affect system performance. To overcome the above shortcomings, an autonomous landing system using a composite landmark is proposed in this paper. In the proposed system, a notched ring landmark and two-dimensional landmark are combined as an R2D landmark to provide visual localization over a wide range. In addition, the wheel-slip and imprecise calibration of encoders are modeled as the unknown measurement bias of the encoders and estimated online via an extended Kalman filter. The landing trajectory is planned by a solver as a convex quadratic programming problem in each control cycle. Meanwhile, an iterative algorithm for adding equality constraints is proposed and used to verify whether the planned trajectory is feasible or not. The simulation and actual landing experiment results verify the following: the visual localization with the R2D landmark has the advantages of wide localization range and high localization accuracy, the pose estimation result of the moving platform with unknown encoder measurement bias is continuous and accurate, and the proposed landing trajectory planning algorithm provides a continuous trajectory for reliable landing.

Numerical study of the rotational direction effect on aerodynamic loading characteristics of shipborne helicopter rotor

ABSTRACTNumerical simulations of ship/rotor-coupled flowfield have been performed to investigate the rotational direction effects on a shipborne single-rotor helicopter in different deck landing trajectories (i.e., lateral and longitudinal translation) based on Reynolds-averaged Navier-Stokes (RANS) solver. Both the momentum source model and moving overset mesh model are employed to simulate the effect of the rotor on the ship airwake for different levels of fidelity requirement. The aerodynamic loading characteristics in terms of time-averaged and root-mean-square (RMS) thrust and pitch and roll moments are compared for two helicopter rotors with opposite rotation directions in a starboard 30 degrees wind condition. The time-averaged results show that the mean thrust of a counterclockwise rotor is greater than that of a clockwise rotor, particularly in the lateral translation phase. This suggests that a helicopter with a counterclockwise rotor could provide more collective control margin under this condition. Furthermore, a more significant reduction in pitch moment is experienced by the counterclockwise rotor during the two landing trajectories, and thus the effect of the aircraft being pulled towards the hangar tends to be more severe on the helicopter with the counterclockwise rotor. RMS loading results indicate that the unsteady loading levels on the clockwise rotor are much higher than that of the counterclockwise rotor in all three axes for most of the lateral and longitudinal translation phases. As a result, the pilot is likely to experience a higher workload when operating a helicopter with a clockwise rotor in the case of a deck landing in this wind condition.

Robust planning the landing process of unmanned aerial vehicles

Currently, the study of unmanned aerial vehicle (UAV) in complex environments is relatively well developed and has many achievements. However, the fact that the landing process of UAVs in complex or unknown environments is a significant challenge for scientists. In this paper, the problem on how to determine the desired landing orbit will be solved. The approach and landing process might be constructed from the straight lines and orbit curves. This study indicates that the UAV has four landing trajectories because the UAV can turn left or right to reach the left or right circle in the landing process. The calculation is based on solving aircraft equations of motion and analytical method. This paper also shows the methodologies to determine the landing routes that the UAV can be landing in any direction or given direction. The simulation results utilising MATLAB software show that the calculated landing orbit is the shortest.

Navigation-Optimal-Guidance for Precision Planetary Landing by Convexification of Estimated-Error-Variance of Navigation

This paper presents a navigation optimal powered descent landing guidance for autonomous precision planetary landing. High precision navigation is required for precision landing and use of terrain relative navigation (TRN) is being studied. Since the navigation accuracy of the TRN depends on the landing trajectory, we propose the navigation optimal trajectory to improve landing accuracy. This paper defines the optimal control problem which minimizes the navigation error at landing by using the estimated error covariance of the Kalman filter of the navigation algorithm. By assumption and approximation, around reference trajectory, trace of covariance matrix is linearized with respect to the landing trajectory, and the trajectory is discrete linearized with respect to the dynamics and non-convex constraints. The problem is convexified by these discrete-linearizations and formulated to sub-problem of Second-order cone programming (SOCP). Therefore, this problem is solved by iterative convexification and convex-optimization. The effectiveness of the algorithm is confirmed by Monte Carlo simulation on Mars landing problem. In this simulation, the accuracy of TRN depends on the line of sight distance of the image sensor. The proposed guidance algorithm by using convex programming can potentially be implemented in spacecraft as onboard real-time applications.