Study of observability of motion of an orbital group of navigation space system using intersatellite range measurements. II

This study continues the analysis of observability of the problem of refinement of motion parameters of an orbital group of navigation spacecrafts using intersatellite range measurements on a given interval initiated in [1]. The analysis is performed in the framework of linear models connecting measured and refined parameters on a measurement interval. A number of theorems and corollaries concerning the properties of observability in the problem of refinement of motion parameters using intersatellite range measurements for the cases of three and all navigation spacecrafts of the orbital group are proved. It is shown that all motion parameters of an orbital group cannot be refined in a unique way using intersatellite range measurements between navigation spacecrafts, and three parameters are always “unobservable”. Recommendations for construction of onboard algorithm for intersatellite measurement processing are given.     

舰载武器惯导系统传递对准仿真验证的研究

针对传统船用惯导系统采用理想运动状态对传递对准方案进行仿真验证的问题,提出了引入舰船空间运动模型的传递对准仿真验证方法。通过舰船空间运动模型提供接近真实运动环境的空间运动参数,并实现了空间运动信息至惯性敏感信息的正确转换,给出了各模块的空间变换算法转换流程。"速度+姿态"子惯导传递对准模块的仿真精度优于0.05°,证明了仿真验证系统变换算法的正确性。该研究设计为开展其它领域的传递对准仿真验证提供了有效的参考依据。     

Single range observability for cooperative underactuated underwater vehicles

The paper addresses the single range observability analysis of a kinematics model of cooperating underactuated underwater vehicles. Teams of underwater vehicles that communicate with each other may be able to access and exchange their relative distances through, by example, acoustic signal time-of-flight measurements. Such relative distance measurements together with vehicle’s attitude and velocity information may be used onboard to implement a navigation filter to estimate the vehicle’s relative positions and orientations. A pre-requisite for successfully designing such navigation filters is to assess the systems observability properties. Contrary to the majority of existing studies on single range observability, the paper considers a more realistic underactuated kinematics model for slender body autonomous underwater vehicles rather than a simple point mass model. The paper extends previous results building on an augmented state technique allowing to reformulate the nonlinear observability problem in terms of a linear time varying one. As a result, all possible (globally) unobservable motions are characterized in terms of the systems’ initial conditions and velocity commands within the class of interest. The fundamental results reported are also illustrated by numerical simulations providing evidence of different motions generating the same output, namely lacking observability.     

Autonomous navigation system of near-Earth spacecraft

An autonomous navigation system for near-Earth spacecraft is described; this system allows determination of the satellite orbit and prediction of its motion parameters. Radio navigation measurements of GLONASS and GPS satellite systems are used for this purpose. The autonomous navigation system is designated for operation on near-Earth orbits which do not go beyond the navigation areas of GLONASS and/or GPS and on orbits with large eccentricity whose apocenter is at a distance of 50–70 thousand km from the Earth’s surface. The developed methods and algorithms for orbit determination are based on the application of laws of motion dynamics of a spacecraft directly at processing primary phase measurements of the carrier frequency and code pseudo-range using an extended measurement base. Algorithms for determination of motion parameters of the spacecraft and results of simulation and operation of a model system are presented. The possibility of creation of an onboard autonomous navigation system with precision and reliability higher than those of the ground measuring complex is demonstrated.     

Navigation of a subsatellite of a space cable system

A method for the navigation of an object of a space cable system, a subsatellite, that does not have its own navigation means and is connected with the master space spacecraft of the bunch by an elastic weightless cable is considered. A method for estimating the location of the subsatellite based on information about the tension force of the cable is proposed, and the problems of observability of the location parameters are investigated. The results of simulating the process of estimating the subsatellite location under various conditions are presented (under the presence and absence of measurements of the cable tension and under the assumption that the cable is constantly tensed under the conditions of its loosing, etc.).     

Single range aided navigation and source localization: Observability and filter design

This paper addresses the problems of navigation and source localization by mobile agents based on the range to a single source, in addition to relative velocity readings. The contribution of the paper is two-fold: (i) necessary and sufficient conditions on the observability of the nonlinear system are derived, which are useful for trajectory planning and motion control of the agent; and (ii) a nonlinear system, which given the input and output of the system is regarded as linear time-varying, is proposed and a Kalman filter is applied to successfully estimate the system state. Simulation results are presented in the presence of realistic measurement noise that illustrate the performance achieved with the proposed solution.     

基于UWB辅助的多无人机惯导定位误差校正方法

针对卫星导航拒止的复杂环境下多无人机编队飞行只依赖惯性导航无法长时间导航的问题,提出一种超宽带(UWB,ultra wide band)辅助的惯导定位误差校正方法;给出UWB测距原理的同时建立了无人机机体坐标系下的惯导相对距离解算模型;在惯导误差模型的基础上,以惯导误差和UWB测距信息分别作为状态量和观测量,设计出惯导误差校正的扩展卡尔曼滤波模型;以两架无人机为例对算法进行仿真验证,仿真结果表明相较于纯惯导定位,该方法在东北天三个方向的最大定位误差不超过1 m,速度均方根误差值不超过0.01 m/s,很好地抑制了惯导系统速度和位置的误差发散,为解决无人机编队在卫星拒止环境中的定位问题提供参考思路。     

近地小行星仅测角相对导航可观性判据

针对近地小行星仅测角相对导航系统的非线性可观测性分析问题,本文基于非线性系统局部弱可观性理论给出了新的可观测性判据.首先,通过分析非线性系统李导数的共有属性,给出了李导数梯度空间的共有子空间.进一步,利用该共有子空间和非线性系统局部弱可观性定义给出了新的可观性判据.经理论证明,该判据适用于非线性系统任意阶李导数,并且给出的可观性结论可与高阶可观性矩阵秩判据的结论等价.与传统的秩判据相比,该判据具有无需进行高阶李导数运算,无需进行高维矩阵运算的优点.因此该判据适合在轨计算,具有一定的工程价值.最后仿真结果验证了可观性判据的有效性.     

On Consistency of Subspace Methods for System Identification

Subspace methods for identification of linear time-invariant dynamical systems typically consist of two main steps. First, a so-called subspace estimate is constructed. This first step usually consists of estimating the range space of the extended observability matrix. Secondly, an estimate of system parameters is obtained, based on the subspace estimate. In this paper, the consistency of a large class of methods for estimating the extended observability matrix is analyzed. Persistence of excitation conditions on the input signal are given which guarantee consistent estimates for systems with only measurement noise. For systems with process noise, it is shown that a persistence of excitation condition on the input is not sufficient. More precisely, an example for which the subspace methods fail to give a consistent estimate of the transfer function is given. This failure occurs even if the input is persistently exciting of any order. It is also shown that this problem can be eliminated if stronger conditions on the input signal are imposed.     

Segmentation of bathymetric profiles and terrain matching for underwater vehicle navigation

A terrain-based underwater navigation using sonar bathymetric profiles is presented. It deals with matching high-resolution local depth maps against a large on-board reference map. The matching algorithm locates the local depth map within the a priori known larger map to determine the absolute position and heading of the vehicle. Two separate approaches for this problem are presented. The first uses a contour-based representation of depth maps. Contours are extracted from both local and reference maps. Invariant attributes under rigid plane transformation are associated with each contour point, so that the problem is reduced to a point-based matching algorithm: given two point sets, find correspondences and estimate transformation between the two sets. We shall particularly focus on the formalism of partial differential equations, which is used to smooth depth maps in a morphologically invariant way and to obtain anisotropic contours. The second approach is also based on a correspondence algorithm. Here, discriminant parameters are associated with each local map and the correspondence is established in the parameter space. The extraction of discriminant parameters is based on a wavelet packet analysis. Their discriminant power and robustness are analysed. In order to reduce the space of possible robot locations, an area of localization is first delimited by a crude method. A finer interpolation follows, using a neural network. Both methods have been designed keeping in mind limited computational load in order to board future systems on small operational robots and they have been tested using a real terrain model of the Var underwater canyon (France); a multibeam sounder simulator is used in the first approach in order to simulate sonar performances as well as bathymetric image deformations due to errors in short-term navigation.     

多航天器相对轨道与姿态耦合分布式自适应协同控制

基于一致性理论,在有向通讯拓扑结构下对多航天器系统相对轨道及姿态的耦合协同控制问题进行了研究.本文考虑近地航天器相对轨道的非线性方程以及用罗德里格参数描述的航天器姿态运动方程,建立了考虑控制输入耦合的六自由度航天器运动模型.在仅有部分跟随航天器可获取参考状态(记为领航航天器)的情形下,针对航天器存在未建模动态以及外部环境干扰等问题,提出了一种基于切比雪夫神经网络(Chebyshev neural networks,CNN)的自适应增益控制律,使得各跟随航天器在轨道交会的同时姿态保持一致.因为每个航天器上的控制算法仅依赖其自身及相邻航天器的信息,因此控制算法是分布式的.同时考虑到航天器之间的相对速度及相对角速度难以测量,提出了无需相对速度及角速度信息的分布式自适应协同控制律使得各航天器保持一定的队形且具有期望的相对指向.最后对6颗航天器的编队飞行进行了仿真分析,仿真结果表明本文设计的分布式自适应协同控制律是有效可行的.     

交会对接视觉相对导航系统半物理仿真

飞行器自主交会对接最终逼近段,通过视觉导航系统可以精确测量两飞行器在对接过程中的相对位置和姿态。根据飞行动力学建立相对导航观测模型和状态模型;设计基于微型可见光对接敏感器的相对导航算法;应用扩展卡尔曼滤波器(EKF),并采用simulink软件模块建立相对导航算法的模型;采用实验室的光电组合测量与相对导航系统成功的进行了地面半物理仿真。实验结果表明,导航半实物系统能够为两个交会对接航天器提供足够精度的相对运动状态信息。     

Cooperative Localization of AUVs Using Moving Horizon Estimation

This paper studies the localization problem of autonomous underwater vehicles (AUVs) constrained by limited size, power and payload. Such AUVs cannot be equipped with heavy sensors which makes their underwater localization problem difficult. The proposed cooperative localization algorithm is performed by using a single surface mobile beacon which provides range measurement to bound the localization error. The main contribution of this paper is twofold: 1) The observability of single beacon based localization is first analyzed in the context of nonlinear discrete time system, deriving a sufficient condition on observability. It is further compared with observability of linearized system to verify that a nonlinear state estimation is necessary. 2) Moving horizon estimation is integrated with extended Kalman filter (EKF) for three dimensional localization using single beacon, which can alleviate the computational complexity, impose various constraints and make use of several previous range measurements for each estimation. The observability and improved localization accuracy of the localization algorithm are verified by extensive numerical simulation compared with EKF.      

Progressive learning and its application to robot impedancelearning

An approach to learning control using an excitation scheduling technique is developed and applied to an impedance learning problem for fast robotic assembly. Traditional adaptive and learning controls incur instability depending on the reference inputs provided to the system. This technique avoids instability by progressively increasing the level of system excitation. Called progressive learning, it uses scheduled excitation inputs that allow the system to learn quasistatic parameters associated with slow input commands first, followed by the learning of dynamic parameters excited by fast input commands. As learning progresses, the system is exposed to a broader range of input excitation, which nonetheless does not incur instability and unwanted erratic responses. In robotic assembly, learning starts with a slow, quasistatic motion and goes to a fast, dynamic motion. During this process, the stiffness terms involved in the impedance controller are learned first, then the damping terms and finally by the inertial terms. The impedance learning problem is formulated as a model-based, gradient following reinforcement learning. The method allows the suppression of excessive parameter changes and thereby stabilizes learning. By gradually increasing the motion speed command, the internal model as well as the control parameters can be learned effectively within a focused, local area in the large parameter space, which is then gradually expanded as speed increases. Several strategies for motion speed scheduling are also addressed.     

磁导航AGV纠偏控制模型的研究与设计

针对轮式移动机器人循迹偏差问题,以差速驱动型AGV为研究对象,基于LQR(LinearQuadratic Regulator)线性二次型最优控制算法设计磁导航AGV纠偏控制器,控制AGV速度实现循迹跟踪。通过对磁导航AGV偏差建模,将决定AGV运行的驱动电机线性化,建立其状态空间模型,判别系统能控、能观性;同时用Matlab进行仿真设计,实验得到最佳Q、R完成最优控制器设计;通过Simulink设计基于LQR最优控制算法的AGV纠偏控制系统模型,并与传统PID控制算法进行对比分析表明,论文设计的基于LQR算法纠偏控制模型具有更好的收敛性和实时响应性。     

Research on the strategy of angles-only relative navigation for autonomous rendezvous

This paper considers the problem of angles-only relative navigation for autonomous rendezvous. Methods for determining degree of observability (DOO) and latent range information of orbital maneuver are proposed for analyzing and enhancing the precision of relative position and velocity estimation. The equations of angles-only relative navigation are set forth on the condition that optical camera is the only viable sensor for relative measurement, and expressions for the DOO of relative navigation are obtain...     

Quantitative measure of observability for linear stochastic systems

In this study we define a new observability measure for stochastic systems: the mutual information between the state sequence and the corresponding measurement sequence for a given time horizon. Although the definition is given for a general system representation, the paper focuses on the linear time invariant Gaussian case. Some basic analytical results are derived for this special case. The measure is extended to the observability of a subspace of the state space, specifically an individual state and/or the modes of the system. A single measurement system represented in the observable canonical form is examined in detail. A recursive form of the observability measure for a finite time horizon is derived. The possibility of using this form for designing a sensor selection algorithm is demonstrated by two examples.     

基于瞬态相对模型的轨道机动目标运动参数估计

空问目标可能存在未知的机动,针对该类目标相对导航问题,提出一种基于瞬态相对模型的运动参数估计方法.该方法依据轨道密切性思想,在瞬态意义下建立相对运动模型和机动辨识算法,然后通过密切轨道到参考轨道的量测变换对冻结时间模型进行状态滤波,可为目标机动下的自主导航提供所需的相对状态与目标机动参数估值.误差分析表明,所得估值偏差均有界.仿真验证了该方法在目标存在机动情况下的有效性和一般性.     

Structural identifiability and observability of compartmental models of the COVID-19 pandemic

The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted their limitations. If some parameters and/or state variables of a model cannot be determined from output measurements, its ability to yield correct insights – as well as the possibility of controlling the system – may be compromised. Epidemic dynamics are commonly analysed using compartmental models, and many variations of such models have been used for analysing and predicting the evolution of the COVID-19 pandemic. In this paper we survey the different models proposed in the literature, assembling a list of 36 model structures and assessing their ability to provide reliable information. We address the problem using the control theoretic concepts of structural identifiability and observability. Since some parameters can vary during the course of an epidemic, we consider both the constant and time-varying parameter assumptions. We analyse the structural identifiability and observability of all of the models, considering all plausible choices of outputs and time-varying parameters, which leads us to analyse 255 different model versions. We classify the models according to their structural identifiability and observability under the different assumptions and discuss the implications of the results. We also illustrate with an example several alternative ways of remedying the lack of observability of a model. Our analyses provide guidelines for choosing the most informative model for each purpose, taking into account the available knowledge and measurements.     

Significance of observation strategy on the design of robot calibration experiments

This article examines the factors influencing the identification and observability of kinematic parameters during robot calibration. A generalized calibration experiment has been simulated using two different identification techniques. Details of the identification techniques and considerations for implementing them using standard IMSL routines are presented. The factors considered during the simulations include: initial estimates of parameters, measurement accuracy and noise, encoder resolution and uncertainty, selection of measurement configurations, number of measurements, and range of motion of the joints during observations. Results are tabulated for the various cases and suggestions are made for the design of robot calibration experiments.