Three-dimensional trajectory optimization of soft lunar landings from the parking orbit with considerations of the landing site

Minimum fuel, three-dimensional trajectory optimization from a parking orbit considering the desired landing site is addressed for soft lunar landings. The landing site is determined by the final longitude and latitude; therefore, a two-dimensional approach is limited and a three-dimensional approach is required. In addition, the landing site is not usually considered when performing lunar landing trajectory optimizations, but should be considered in order to design more accurate and realistic lunar landing trajectories. A Legendre pseudospectral (PS) method is used to discretize the trajectory optimization problem as a nonlinear programming (NLP) problem. Because the lunar landing consists of three phases including a de-orbit burn, a transfer orbit phase, and a powered descent phase, the lunar landing problem is regarded as a multiphase problem. Thus, a PS knotting method is also used to manage the multiphase problem, and C code for Feasible Sequential Quadratic Programming (CFSQP) using a sequential quadratic programming (SQP) algorithm is employed as a numerical solver after formulating the problem as an NLP problem. The optimal solutions obtained satisfy all constraints as well as the desired landing site, and the solutions are verified through a feasibility check.     

An algorithm and observability research of autonomous navigation and joint attitude determination in asteroid exploration descent stage

In this paper, an autonomous relative navigation and joint attitude determination algorithm in asteroid exploration descent stage is researched based on feature point information of perpendicular asteroid surface image observed by optical navigation camera, distance vectors from spacecraft to asteroid measured by three angled installed lidars and relative velocity increment measured by accelerometer when the relative distance vector to the centroid of asteroid can not be obtained. The inertial attitude of spacecraft is determined by sun vector, star vectors and inertial angular velocity respectively measured by sun sensor, star trackers and inertial reference unit. Also, in order to obtain measurement error model transferred from sensor noise, a covariance matrix solver considering error correlation is presented via the error model of normalized vector to first order. Numerical simulation and improved observability evaluation of filtering are undertaken to discuss the results of complete sensor observation and weak observation of lidars, and verify the effectiveness of the presented relative navigation and attitude determination algorithm.     

Autonomous real-time landing site selection for Venus and Titan using Evolutionary Fuzzy Cognitive Maps

Future science-driven landing missions, conceived to collect in situ data on regions of planetary bodies that have the highest potential to yield important scientific discoveries, will require a higher degree of autonomy. The latter includes the ability of the spacecraft to autonomously select the landing site using real-time data acquired during the descent phase. This paper presents the development of an Evolutionary Fuzzy Cognitive Map (E-FCM) model that implements an artificial intelligence system capable of autonomously selecting a landing site with the highest potential for scientific discoveries constrained by the requirement of soft landing in a region with safe terrains. The proposed E-FCM evolves its internal states and interconnections as a function of real-time data collected during the descent phase, therefore improving the decision process as more accurate information becomes available. The E-FCM is constructed using knowledge accumulated by planetary experts and it is tested on scenarios that simulate the decision process during the descent phase toward the Hyndla Regio on Venus. The E-FCM is shown to quickly reach conclusions that are consistent with what would be the choice of a planetary expert if the scientist were presented with the same information. The proposed methodology is fast and efficient and may be suitable for on-board spacecraft implementation and real-time decision making during the course of robotic exploration of the Solar System.     

小行星433 Eros本体悬停轨道的稳定控制

研究了近地小行星433 Eros本体悬停轨道的稳定控制问题.用三轴椭球体模型近似Eros引力场分布,建立了航天器在其引力场内的动力学模型,并且应用等加速度变截距时变滑模控制设计了悬停控制器.该方法的滑模面选取与常规滑模控制不同,且不存在到达阶段.仿真分析从不同的初始条件和悬停条件入手,验证控制器的有效性,并讨论了航天器的速度与控制加速度的幅值随滑模面切换时间的变化情况.     

SLAM-Based Navigation Scheme for Pinpoint Landing on Small Celestial Body

Addressing the need for robust pinpoint landing capabilities, this paper proposes a monocular navigation scheme based on the Rao-Blackwellized particle filter simultaneous localization and mapping (SLAM) approach. The proposed online navigation scheme provides attitude and position (or pose) estimation during the approach, descent, and landing phase for small celestial body missions. This approach relies on one navigation camera and potentially sparse readings from one or more range sensors (e.g. LIDAR (Light Detection And Ranging)). The concept of the proposed navigation scheme is to maintain several hypotheses of the most likely spacecraft pose and landmarks position and to feed the most likely one to the spacecraft controller at any given time. The proposed system uses a double staged Monte-Carlo simulation that represents the population of all possible spacecraft motions between two camera images taken at successive time steps, and that samples this population over all possible scaling factors, converting each relative motion to world-scaled coordinates in the process. The purpose of this Monte-Carlo based visual pose estimation approach is to offer an alternative solution to the drift error and inaccuracy problems of SLAM kinematic models, odometry motion models, and other conventional dead reckoning techniques.     

轨道方程平滑方法在轨道预报中的应用

航天器的轨道预报和落点预报等信息处理对预报起始点的速度精度要求很高.由于非合作测量设备通常不具备测速能力,通常采用多项式平滑微分和卡尔曼滤波等传统方法计算的速度参数精度较差,造成航天器轨道预报精度不高.为提高航天器轨道预报初始点的坐标和速度参数精度,依据自由段轨道符合椭圆轨道方程这一事实,提出使用轨道方程来拟合航天器自由段轨道的方法,可以很好地消弱目标测量数据中随机误差的影响,提供稳定且精度较高的轨道预报结果.本方法可用于航天器轨道预报和落点预报的数据处理.     

Apollo LM guidance computer software for the final lunar descent

In all manned lunar landings to date, the lunar module Commander has taken partial manual control of the spacecraft during the final stage of the descent, below roughly 500 ft altitude. Because of the irregularity of the lunar surface and the inevitability of some error in the on-board estimate of the spacecraft's position with respect to the local terrain, fully automatic landings, with men aboard, cannot be anticipated until landing fields are prepared on the moon.This report describes programs developed at the Charles Stark Draper Laboratory, MIT, for use in the LM's guidance computer during the final descent. At this time computational demands on the on-board computer are at a maximum, and particularly close interaction with the crew is necessary. The emphasis is on the design of the computer software rather than on justification of the particular guidance algorithms employed. After the computer and the mission have been introduced, the current configuration of the final landing programs and an advanced version developed experimentally by the author are described.     

Numerical problems in modelling of collision in sliding systems subjected to seismic excitations

The study addresses collision in sliding systems subjected to seismic excitations. The collision is modelled according to the impact laws of the mechanics of particles using coefficient of restitution to account for energy losses (Newton's hypothesis). An analytical solution in a small time interval after the collision is constructed viewing the sliding velocity. When constructing numerical solutions, it is assumed that the friction force does not change its sign within one step of integration. If at end of the time step, velocity with an opposite sign is calculated, the obtained solution is incorrect, because the result contradicts the accepted constant sign of the friction force during the time step. To avoid these problems expressions are derived for the magnitude of the time step in which a mathematically correct solution will have place. Recommendations are formulated for numerical simulation of collision in sliding systems subjected to seismic excitations. The obtained correct numerical solutions using the Coulomb model are compared with numerical results from the velocity model of friction forces. It is shown that the velocity model provides the possibility to avoid automatically the above numerical problems by use of its correctness condition.     

Sliding-Mode-Based Attitude Tracking Control of Spacecraft Under Reaction Wheel Uncertainties

The attitude tracking operations of an on-orbit spacecraft with degraded performance exhibited by potential actuator uncertainties (including failures and misalignments) can be extraordinarily challenging. Thus, the control law development for the attitude tracking task of spacecraft subject to actuator (namely reaction wheel) uncertainties is addressed in this paper. More specially, the attitude dynamics model of the spacecraft is firstly established under actuator failures and misalignment (without a small angle approximation operation). Then, a new non-singular sliding manifold with fixed time convergence and anti-unwinding properties is proposed, and an adaptive sliding mode control (SMC) strategy is introduced to handle actuator uncertainties, model uncertainties and external disturbances simultaneously. Among this, an explicit misalignment angles range that could be treated herein is offered. Lyapunov-based stability analyses are employed to verify that the reaching phase of the sliding manifold is completed in finite time, and the attitude tracking errors are ensured to converge to a small region of the closest equilibrium point in fixed time once the sliding manifold enters the reaching phase. Finally, the beneficial features of the designed controller are manifested via detailed numerical simulation tests.      

Application of generalised neural network for aircraft landing control system

 It is observed that landing performance is the most typical phase of an aircraft performance. During landing operation the stability and controllability are the major considerations. To achieve a safe landing, an aircraft has to be controlled in such a way that its wheels touch the ground comfortably and gently within the paved surface of the runway. The conventional control theory found very successful in solving well defined problems, which are described precisely with definite and clearly mentioned boundaries. In real life systems the boundaries can't be defined clearly and conventional controller does not give satisfactory results. Whenever, an aircraft deviates from its glide path (gliding angle) during landing operation, it will affect the landing field, landing area as well as touch down point on the runway. To control correct gliding angle (glide path) of an aircraft while landing, various traditional controllers like PID controller or state space controller as well as maneuvering of pilots are used, but due to the presence of non-linearities of actuators and pilots these controllers do not give satisfactory results. Since artificial neural network can be used as an intelligent control technique and are able to control the correct gliding angle i.e. correct gliding path of an aircraft while landing through learning which can easily accommodate the aforesaid non-linearities. The existing neural network has various drawbacks such as large training time, large number of neurons and hidden layers required to deal with complex problems. To overcome these drawbacks and develop a non-linear controller for aircraft landing system a generalized neural network has been developed.     

基于非金属材料减振设计的小型空间飞行器模态分析

为有效改善发射过程中飞行器有效载荷的动力学环境,以某小型空间飞行器为例,基于转接框结构提出非金属材料减振设计方案．在有限元模型中采用考虑剪切变形的梁单元模拟非金属材料减振器,对飞行器的动特性进行数值仿真分析和试验验证．结果表明仿真结果与试验结果基本一致．     

ADRC Law of Spacecraft Rendezvous and Docking in Final Approach Phase

This article addresses the high-precision coordinated control problem of spacecraft autonomous rendezvous and docking, which couple the relative position and attitude in the final approach phase. The coupled dynamics equations of the tracking-target spacecrafts is derived by using dual quaternions. Then, a cascade Active Disturbance Rejection Controller is proposed, by which the extended state observer and nonlinear error feedback law is designed, the virtual value on which the actual control volume tracking is calculated to ensure the finite time convergence of the relative position and attitude tracking errors in spite of parametric uncertainties and external disturbances. Finally, numerical simulations are performed to demonstrate that the proposed approaches, which can avoid the coupling effect and restrain the interference, can track the target spacecraft in a relatively short period of time, and the control precision can satisfy the requirements of docking.     

基于恢复系数的碰撞过程模型分析

论述了恢复系数的含义及作用,并在此基础上介绍了几种碰撞过程模型.通过详细推导恢复系数与模型参数之间的关系,使得不同的碰撞过程模型可统一用恢复系数表示能量损失,并用接触刚度表示变形.这也阐明了碰撞过程模型与刚性模型之间的区别和联系,把动态接触理论和古典碰撞理论统一了起来.通过对一个单球碰撞系统进行数值仿真,不仅验证了关系推导的正确性,而且对各种模型从精度、效率、微观接触过程等方面进行了比较.     

Decentralised finite-time attitude synchronisation and tracking control for rigid spacecraft

The problem of finite-time attitude synchronisation and tracking for a group of rigid spacecraft nonlinear dynamics is investigated in this paper. First of all, in the presence of environmental disturbance, a novel decentralised control law is proposed to ensure that the spacecraft attitude error dynamics can converge to the sliding surface in finite time; then the final practical finite-time stability of the attitude error dynamics can be guaranteed in small regions. Furthermore, a modified finite-time control law is proposed to address the control chattering. The control law can guarantee a group of spacecraft to attain desired time-varying attitude and angular velocity while maintaining attitude synchronisation with other spacecraft in the formation. Simulation examples are provided to illustrate the feasibility of the control algorithm presented in this paper.     

Delay time compensation based on coefficient of restitution for collision hybrid motion simulator

A hybrid motion simulator embeds a hardware experiment in a numerical simulation loop. However, it is often subjected to the inherent problem of an energy increase in the collision of two pieces of hardware in a loop because of the delay time. This paper proposes a delay time compensation method based on contact dynamics model for a collision hybrid motion simulator under delay time and establishes a compensation method for coupled translational and rotational motion. The model developed in this paper describes linear uniform motion of a floating object during the period of the delay time until the force and torque are observed and non-linear motion according to environmental stiffness after the initial delay time period in contact. By using the above model, compensation parameters are designed based on desired coefficient of restitution with iterative calculation. The proposed method achieves accurate delay time compensation and simultaneously realizes a variable desired coefficient of restitution over a wide range of frequencies. Furthermore, the compensation method for multi-dimensional motion is established under the assumption that the friction effect is very small. The efficiency of the proposed method is verified through collision experiments for the coupled motion in two dimensions.     

Advances in trajectory optimization for space vehicle control

Space mission design places a premium on cost and operational efficiency. The search for new science and life beyond Earth calls for spacecraft that can deliver scientific payloads to geologically rich yet hazardous landing sites. At the same time, the last four decades of optimization research have put a suite of powerful optimization tools at the fingertips of the controls engineer. As we enter the new decade, optimization theory, algorithms, and software tooling have reached a critical mass to start seeing serious application in space vehicle guidance and control systems. This survey paper provides a detailed overview of recent advances, successes, and promising directions for optimization-based space vehicle control. The considered applications include planetary landing, rendezvous and proximity operations, small body landing, constrained attitude reorientation, endo-atmospheric flight including ascent and reentry, and orbit transfer and injection. The primary focus is on the last ten years of progress, which have seen a veritable rise in the number of applications using three core technologies: lossless convexification, sequential convex programming, and model predictive control. The reader will come away with a well-rounded understanding of the state-of-the-art in each space vehicle control application, and will be well positioned to tackle important current open problems using convex optimization as a core technology.     

Robust adaptive backstepping control for autonomous spacecraft proximity maneuvers

The control problem of autonomous proximity phase during rendezvous and docking is studied for a chaser spacecraft subject to parametric uncertainty and unknown external disturbance approaching to a tumbling non-cooperative space target. A coupled relative motion model is established for the autonomous spacecraft proximity missions based on the relative motion information and chaser’s motion information. Based on the cascaded structure of the six degrees-of-freedom coupled model, the backstepping technology combined with element-wise and norm-wise adaptive control methods is used to design a relative position controller firstly, then the same method is also applied to the design of the relative attitude controller. Asymptotic stability is proven uniformly for the six degrees-of-freedom closed-loop system, and the performance of the controlled overall system is demonstrated via a representative numerical example.     

On the continuous contact force models for soft materials in multibody dynamics

A general and comprehensive analysis on the continuous contact force models for soft materials in multibody dynamics is presented throughout this work. The force models are developed based on the foundation of the Hertz law together with a hysteresis damping parameter that accounts for the energy dissipation during the contact process. In a simple way, these contact force models are based on the analysis and development of three main issues: (i) the dissipated energy associated with the coefficient of restitution that includes the balance of kinetic energy and the conservation of the linear momentum between the initial and final instant of contact; (ii) the stored elastic energy, representing part of initial kinetic energy, which is evaluated as the work done by the contact force developed during the contact process; (iii) the dissipated energy due to internal damping, which is evaluated by modeling the contact process as a single degree-of- freedom system to obtain a hysteresis damping factor. This factor takes into account the geometrical and material properties, as well as the kinematic characteristics of the contacting bodies. This approach has the great merit that can be used for contact problems involving materials with low or moderate values of coefficient of restitution and, therefore, accommodate high amount of energy dissipation. In addition, the resulting contact force model is suitable to be included into the equations of motion of a multibody system and contributes to their stable numerical resolution. A demonstrative example of application is used to provide the results that support the analysis and discussion of procedures and methodologies described in this work.     

Autonomous Adaptive Control System for Airplane Landing

The paper presents a new autonomous adaptive system for the control of airplanes during landing in longitudinal plane. For the first stage of landing in longitudinal plane, the main variables to be controlled are the glide slope angle and longitudinal velocity; during the second main stage of landing in longitudinal plane, the vertical velocity error and the airplane's longitudinal velocity are controlled. The new robust control architecture has linear subsystems, for which the relative degrees are calculated; the new architecture will also consists of a dynamic compensator, a linear observer, and two reference models, their design being accomplished with respect to the calculated relative degrees. The signal estimated by the observer is useful for training a neural network – an adaptive subsystem of the architecture that provides the adaptive component of the control law. In the case of actuators having nonlinear dynamics, pseudo control hedging blocks are used to cancel the adapting difficulties of the neural networks. The new adaptive architecture is software implemented and validated by complex numerical simulations.