Lunar Soft Landing Research Articles

A New Blind Selection Approach for Lunar Landing Zones Based on Engineering Constraints Using Sliding Window

Deep space exploration has risen in interest among scientists in recent years, with soft landings being one of the most straightforward ways to acquire knowledge about the Moon. In general, landing mission success depends on the selection of landing zones, and there are currently few effective quantitative models that can be used to select suitable landing zones. When automatic landing zones are selected, the grid method used for data partitioning tends to miss potentially suitable landing sites between grids. Therefore, this study proposes a new engineering-constrained approach for landing zone selection using LRO LOLA-based slope data as original data based on the sliding window method, which solves the spatial omission problem of the grid method. Using the threshold ratio, mean, coefficient of variation, Moran’s I, and overall rating, this method quantifies the suitability of each sliding window. The k-means clustering algorithm is adopted to determine the suitability threshold for the overall rating. The results show that 20 of 22 lunar soft landing sites are suitable for landing. Additionally, 43 of 50 landing sites preselected by the experts (suitable landing sites considering a combination of conditions) are suitable for landing, accounting for 90.9% and 86% of the total number, respectively, for a window size of 0.5° × 0.5°. Among them, there are four soft landing sites: Surveyor 3, 6, 7, and Apollo 15, which are not suitable for landing in the evaluation results of the grid method. However, they are suitable for landing in the overall evaluation results of the sliding window method, which significantly reduces the spatial omission problem of the grid method. In addition, four candidate landing regions, including Aristarchus Crater, Marius Hills, Moscoviense Basin, and Orientale Basin, were evaluated for landing suitability using the sliding window method. The suitability of the landing area within the candidate range of small window sizes was 0.90, 0.97, 0.49, and 0.55. This indicates the capacity of the method to analyze an arbitrary range during blind landing zone selection. The results can quantify the slope suitability of the landing zones from an engineering perspective and provide different landing window options. The proposed method for selecting lunar landing zones is clearly superior to the gridding method. It enhances data processing for automatic lunar landing zone selection and progresses the selection process from qualitative to quantitative.

Braking and attitude control of lunar lander in active descent stage

Abstract China officially launched the lunar exploration project, named “Chang’e Project,” in 2004. Then, in 2013, Chang’e-3 completed the soft landing on the lunar surface, starting a series of studies on the soft landing of spacecraft. This study aims to optimize the dynamic flight guidance and attitude control of the lunar landing module represented by Chang’e-3 in the soft landing stage. After analyzing the attitude control requirements of the soft landing stage of the lunar landing module, this study designs the lunar soft landing process under a variable structure sliding mode (VSSM) control. The study also analyzes the influence of the pulse width modulator (PWM) on the soft landing process. The simulation model of the lunar soft landing guidance and control system is established by MATLAB/Simulink, and the traditional proportional–integral–derivative (PID) control mode is compared with the interference condition. Results show that VSSM + PWM is superior to PID in robustness and accuracy and has a theoretical reference value for future lunar landing exploration and even Mars landing exploration.

Hybrid Approach Named HUAPO Technique to Guide the Lander Based on the Landing Trajectory Generation for Unmanned Lunar Mission.

This manuscript proposes a hybrid method for landing trajectory generation of unmanned lunar mission. The proposed hybrid control scheme is the joint execution of the human urbanization algorithm (HUA) and political optimizer (PO) with radial basis functional neural network (RBFNN); hence it is named as HUA-PORFNN method. The HUA is a metaheuristic method, and it is used to solve several optimization issues and several nature-inspired methods to enhance the convergence speed with quality. On the other hand, multiple-phased political processes inspire the PO. The work aims to guide the lander with minimal fuel consumption from the initial to the final stage, thus minimizing the lunar soft landing issues based on the given cost of operation. Here, the HUAPO method is implemented to overcome thrust discontinuities, checkpoint constraints are suggested for connecting multi-landing phases, angular attitude rate is modeled to obtain radical change rid, and safeguards are enforced to deflect collision along with obstacles. Moreover, first, the issues have been resolved according to the proposed HUAPO method. Here, energy trajectories with 3 terminal processes are deemed. Additionally, the proposed HUAPO method is executed on MATLAB/Simulink site, and the performance of the proposed method is compared with other methods.

Iterative Guidance Algorithm for Lunar Soft Landing

A closed-form explicit guidance algorithm for the deceleration, attitude adjustment and final landing phases before lunar probe soft landing is presented in this paper. Guidance with a variable-thrust engine is extended from the iterative guidance mode (IGM) to satisfy the terminal velocity, position, and attitude constraints. The closed form expression, obtained by integrating the acceleration and shutdown time, is analysed to obtain an explicit ex-pression for the velocity and position requirements and vertical touchdown of the spacecraft toward a designated landing site with high terminal accuracy. The influence of the attitude constraint on the motion equation is analysed to calculate the attitude, which is the physical control variable for the guidance loop. The variable thrust IGM formulation ensures the least switch of the thrust magnitude profile based on the analysis result of the residual flight altitude. The simulation results demonstrate that the proposed multi-constrained iterative guidance method can help accomplish an accurate lunar soft landing and that employed the algorithm is simple and easy to implement in engineering practice.

On flexibility of constraints system under approximation of optimal control problems

For finite-dimensional mathematical programming problems (approximating problems) being obtained by a parametric approximation of control functions in lumped optimal control problems with functional equality constraints, we introduce concepts of rigidity and flexibility for a system of constraints. The rigidity in a given admissible point is treated in the sense that this point is isolated for the admissible set; otherwise, we call a system of constraints as flexible in this point. Under using a parametric approximation for a control function with the help of quadratic exponentials (Gaussian functions) and subject to some natural hypotheses, we establish that in order to guarantee the flexibility of constraints system in a given admissible point it suffices to increase the dimension of parameter space in the approximating problem. A test of our hypotheses is illustrated by an example of the soft lunar landing problem.

Optimal guidance for lunar soft landing with dynamic low-resolution image sequences

To relieve the burden of obtaining high-precision lunar surface information during lunar soft landing, a new guidance algorithm based on dynamic low-resolution image sequences is proposed. The integrated procedure of dynamic descent stage considering obstacle-avoiding requirement without the hover measurement is designed, which enables the spacecraft to optimize the final landing site by rolling in orbit. A small number of points are used to obtain the variance, slope and roughness of the field of vision subarea, and the shortest distance spiral search algorithm is used to determine the safest landing point. In order to reduce unnecessary control, an acceptance domain algorithm of alternative landing sites is designed to judge whether or not to accept the change of landing sites in dynamic low-precision image sequences. Assuming that the control acceleration is adjustable, the non-singular fast terminal sliding mode (NFTSM) controller based on terminal attractor is adopted and improved, and the stability of the closed-loop system is also proved. The validity, reliability and effectiveness of the proposed guidance algorithm are verified by numerical simulation on the case with disturbance and large sample data. The results demonstrate that the image information required for stable lunar soft landing is far less than that of the traditional methods, which can greatly reduce the burden of the onboard computer.

A Novel Indirect Scheme for Optimal Lunar Soft Landing at a Target Site

A Novel Indirect Scheme for Optimal Lunar Soft Landing at a Target Site

PSO-Based Soft Lunar Landing with Hazard Avoidance: Analysis and Experimentation

The problem of real-time optimal guidance is extremely important for successful autonomous missions. In this paper, the last phases of autonomous lunar landing trajectories are addressed. The proposed guidance is based on the Particle Swarm Optimization, and the differential flatness approach, which is a subclass of the inverse dynamics technique. The trajectory is approximated by polynomials and the control policy is obtained in an analytical closed form solution, where boundary and dynamical constraints are a priori satisfied. Although this procedure leads to sub-optimal solutions, it results in beng fast and thus potentially suitable to be used for real-time purposes. Moreover, the presence of craters on the lunar terrain is considered; therefore, hazard detection and avoidance are also carried out. The proposed guidance is tested by Monte Carlo simulations to evaluate its performances and a robust procedure, made up of safe additional maneuvers, is introduced to counteract optimization failures and achieve soft landing. Finally, the whole procedure is tested through an experimental facility, consisting of a robotic manipulator, equipped with a camera, and a simulated lunar terrain. The results show the efficiency and reliability of the proposed guidance and its possible use for real-time sub-optimal trajectory generation within laboratory applications.

Fuel-optimal and Energy-optimal guidance schemes for lunar soft landing at a desired location

Two guidance schemes (i) fuel-optimal (ii) energy-optimal to realize soft landing at a desired location on the moon are developed using the optimal control laws. The optimal control laws are obtained by solving a two-point boundary value problem formulated based on Pontryagin’s principle. The guidance laws, adapted from the optimal control laws, are obtained as a function of unknown co-state variables. Differential Transformation (DT) technique is employed to determine the unknown co-states at each time instant of landing trajectory using the information on the current vehicle state, target landing site (loaded on-board apriori) and the time-to-go. The numerical integration of co-state dynamics is avoided due to the DT based approach. The time-to-go, a critical parameter for any guidance scheme, is computed and updated real time using a simple strategy which uses the current and end states. The simple strategy for time-to-go works well even when the shape of the trajectory is nonlinear. Extensive analysis is carried out to evaluate and compare the proposed guidance schemes. Further, the proposed schemes are compared with other popular guidance schemes. The DT based proposed schemes help quantify the landing masses for fuel-optimal and energy-optimal objectives. Other features of the proposed schemes are that they do not assume constant gravity field and independent of reference trajectory.

Guidance Navigation and Control for Chang’E-5 Powered Descent

To achieve the goal of collecting lunar samples and return to the Earth for the Chang’E-5 spacecraft, the lander and ascender module (LAM) of the Chang’E-5 spacecraft successfully landed on the lunar surface on 1 Dec., 2020. The guidance, navigation, and control (GNC) system is one of the critical systems to perform this task. The GNC system of previous missions, Chang’E-3 and Chang’E-4, provides the baseline design for the Chang’E-5 LAM, and the new characteristics of the LAM, like larger mass and liquid sloshing, also bring new challenges for the GNC design. The GNC design for the descent and landing is presented in this paper. The guidance methods implemented in the powered descent are presented in detail for each phase. Propellant consumption and hazard avoidance should be particularly considered in the design. A reconfigurable attitude control is adopted which consists of the quaternion partition control, phase and gain stabilization filter, and dual observer. This controller could provide fast attitude maneuver and better system robustness. For the navigation, an intelligent heterogeneous sensor data fusion method is presented, and it is applied for the inertial measurement unit and velocimeter data. Finally, the flight results of the LAM are shown. Navigation sensors were able to provide valid measurement data during descent, and the thrusters and the main engine operated well as expected. Therefore, a successful soft lunar landing was achieved by the LAM.

Method for solving chance constrained optimal control problems using biased kernel density estimators

SummaryA method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation transforms the chance constrained optimal control problem into a deterministic optimal control problem that can be solved numerically. The new method developed in this paper approximates the chance constraints using Markov Chain Monte Carlo sampling and kernel density estimators whose kernels have integral functions that bound the indicator function. The nonlinear constraints resulting from the application of kernel density estimators are designed with bounds that do not violate the bounds of the original chance constraint. The method is tested on a nontrivial chance constrained modification of a soft lunar landing optimal control problem and the results are compared with results obtained using a conservative deterministic formulation of the optimal control problem. Additionally, the method is tested on a complex chance constrained unmanned aerial vehicle problem. The results show that this new method can be used to reliably solve chance constrained optimal control problems.

Multi-phase MPSP Guidance for Lunar Soft Landing

In this paper, an autonomous optimal guidance algorithm for multi-phase lunar soft landing is presented. Various stringent requirements of a typical multi-phase soft landing are incorporated in guidance formulation. The proposed guidance law is formulated using the model predictive static programming (MPSP), which is an emerging computational guidance algorithm. High accuracy on the terminal position and velocity at the end of each phase is ensured, as the formulation of the MPSP inherently poses terminal output as a set of hard constraints. The spacecraft terminal orientation requirement is embedded in the guidance formulation in a soft constrained manner. Moreover, to facilitate a smooth transition between successive segments, an initial continuity of the guidance command is also attempted in an approximate manner. The effectiveness of the proposed method is demonstrated with simulation results. A processor-in-loop simulation study has been presented to demonstrate the feasibility of the proposed guidance law for possible on-board implementation.

Smooth Interpolation-Based Fixed-Final-Time Command Generation

This paper proposes a command generation approach based on the smooth interpolation without twist constraints and the input–output relation developed by the generalized model predictive static programming. Commands are efficiently generated to achieve the desired terminal condition at a specified final time in an interpolative manner featuring a noniterative nature. The effectiveness of this approach is demonstrated through three different simulation studies including a double integrator benchmark, a soft lunar landing problem, and a cluster missile guidance problem.

On Application of Gaussian Functions for Numerical Solution of Optimal Control Problems

It is proved that the linear combinations of shifts and contractions of the Gaussian function can be used for an arbitrarily accurate approximation in the space of continuous functions of one variable on any fixed intervals. On the example of the soft lunar landing problem, a method for the numerical solution of optimal control problems based on this approximation procedure of the control function is described. Within the framework of the same example, the sensitivity of constraint functionals to the specification error of optimal parameters is investigated using three approaches as follows: 1) Pontryagin’s maximum principle (both numerically and theoretically); 2) the control parametrization technique in combination with the method of sliding nodes; 3) the newly proposed method. A comparative analysis is performed that confirms the effectiveness of the third method.

Waypoint Constrained Multi-Phase Optimal Guidance of Spacecraft for Soft Lunar Landing

A waypoint constrained multi-phase nonlinear optimal guidance scheme is presented in this paper for the soft landing of a spacecraft on the Lunar surface by using the recently developed computationally efficient Generalized Model Predictive Static Programming (G-MPSP). The proposed guidance ensures that the spacecraft passes through two waypoints, which is a strong requirement to facilitate proper landing site detection by the on-board camera for mission safety. Constraints that are required at the waypoints as well as at the terminal point include position, velocity, and attitude of the spacecraft. In addition to successfully meeting these hard constraints, the G-MPSP guidance also minimizes the fuel consumption, which is a very good advantage. An optimal final time selection procedure is also presented in this paper to facilitate minimization of fuel requirement to the best extent possible. Extensive simulation studies have been carried out with various perturbations to illustrate the effectiveness of the algorithm. Finally, processor-in-loop simulation has been carried out, which demonstrates the feasibility of on-board implementation of the proposed guidance.

Fuel-optimal control for soft lunar landing based on a quadratic regularization approach

This paper considers a fuel-optimal control problem for soft lunar landing. Firstly, the fuel-optimal control problem is formulated as an optimal control problem of constrained nonlinear systems with a novel piecewise state linear feedback controller, which can be transformed into an optimal control problem of switched systems. However, it is difficult to solve this fuel-optimal control problem analytically by using conventional optimization techniques due to its nonlinear nature and the existence of the continuous-time inequality constraint. Next, to obtain the numerical solution of the fuel-optimal control problem, a numerical computation method is developed by using a quadratic regularization approach with a cubic sufficient-descent condition. Convergence results indicate that the proposed algorithm is convergent. Finally, a numerical experiment shows that the proposed algorithm is more effective than the existing method.

Trajectory optimization for lunar soft landing with complex constraints

A unified trajectory optimization framework with initialization strategies is proposed in this paper for lunar soft landing for various missions with specific requirements. Two main missions of interest are Apollo-like Landing from low lunar orbit and Vertical Takeoff Vertical Landing (a promising mobility method) on the lunar surface. The trajectory optimization is characterized by difficulties arising from discontinuous thrust, multi-phase connections, jump of attitude angle, and obstacles avoidance. Here R-function is applied to deal with the discontinuities of thrust, checkpoint constraints are introduced to connect multiple landing phases, attitude angular rate is designed to get rid of radical changes, and safeguards are imposed to avoid collision with obstacles. The resulting dynamic problems are generally with complex constraints. The unified framework based on Gauss Pseudospectral Method (GPM) and Nonlinear Programming (NLP) solver are designed to solve the problems efficiently. Advanced initialization strategies are developed to enhance both the convergence and computation efficiency. Numerical results demonstrate the adaptability of the framework for various landing missions, and the performance of successful solution of difficult dynamic problems.

Multi-objective optimization on the shock absorber design for the lunar probe using nondominated sorting genetic algorithm II

In this article, the design on the shock absorber of the lunar probe soft landing can be considered as a single- or multi-objective optimization problem. Here, the optimized objective parameters include the maximum toppling stability, defined as Dmin, and the minimum stroke of primary strut energy absorption, SPmax. However, the two optimized variables are conflict objectives. In order to give an overall consideration about the multi-performances of landing, the multi-objective optimization strategy is proposed and nondominated sorting genetic algorithm II is employed to find the best decision parameters of the shock absorber design. To conduct the optimizations, firstly, the worst landing cases and safety boundaries for both toppling and primary strut energy absorptions are obtained by the computer simulation experiments. Both single- and multi-objective optimizations are then implemented aiming to expand the stability boundary. The results show that the landing stability is effectively improved after optimizations, and also demonstrate that the multi-objective optimization strategy is superior to that of the single-objective optimization.

Self calibration of the stereo vision system of the Chang’e-3 lunar rover based on the bundle block adjustment

The Chang’e-3 was the first lunar soft landing probe of China. It was composed of the lander and the lunar rover. The Chang’e-3 successful landed in the northwest of the Mare Imbrium in December 14, 2013. The lunar rover completed the movement, imaging and geological survey after landing. The lunar rover equipped with a stereo vision system which was made up of the Navcam system, the mast mechanism and the inertial measurement unit (IMU). The Navcam system composed of two cameras with the fixed focal length. The mast mechanism was a robot with three revolute joints. The stereo vision system was used to determine the position of the lunar rover, generate the digital elevation models (DEM) of the surrounding region and plan the moving paths of the lunar rover. The stereo vision system must be calibrated before use. The control field could be built to calibrate the stereo vision system in the laboratory on the earth. However, the parameters of the stereo vision system would change after the launch, the orbital changes, the braking and the landing. Therefore, the stereo vision system should be self calibrated on the moon. An integrated self calibration method based on the bundle block adjustment is proposed in this paper. The bundle block adjustment uses each bundle of ray as the basic adjustment unit and the adjustment is implemented in the whole photogrammetric region. The stereo vision system can be self calibrated with the proposed method under the unknown lunar environment and all parameters can be estimated simultaneously. The experiment was conducted in the ground lunar simulation field. The proposed method was compared with other methods such as the CAHVOR method, the vanishing point method, the Denavit-Hartenberg method, the factorization method and the weighted least-squares method. The analyzed result proved that the accuracy of the proposed method was superior to those of other methods. Finally, the proposed method was practical used to self calibrate the stereo vision system of the Chang’e-3 lunar rover on the moon.

Equivalent mechanical model of large-amplitude liquid sloshing under time-dependent lateral excitations in low-gravity conditions

Subjected to external lateral excitations, large-amplitude sloshing may take place in propellant tanks, especially for spacecraft in low-gravity conditions, such as landers in the process of hover and obstacle avoidance during lunar soft landing. Due to lateral force of the order of gravity in magnitude, the amplitude of liquid sloshing becomes too big for the traditional equivalent model to be accurate. Therefore, a new equivalent mechanical model, denominated the “composite model”, that can address large-amplitude lateral sloshing in partially filled spherical tanks is established in this paper, with both translational and rotational excitations considered. The hypothesis of liquid equilibrium position following equivalent gravity is first proposed. By decomposing the large-amplitude motion of a liquid into bulk motion following the equivalent gravity and additional small-amplitude sloshing, a better simulation of large-amplitude liquid sloshing is presented. The effectiveness and accuracy of the model are verified by comparing the slosh forces and moments to results of the traditional model and CFD software.