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

The problem of specification of reference ephemeris (reference motion) using intersatellite range measurements on a given interval between spacecrafts of the space navigation system is formulated; observability for this problem is analyzed. Observability is the possibility of unambiguous determination of motion parameters of the orbital group of the space navigation system using known inter-satellite measurements on a given measurement interval. Linear approximate model describing the dependence between measurements and specified parameters are obtained for investigation of observability properties. In the framework of linear model problems of observability of motion of two any spacecrafts of the navigation system are studied using intersatellite range measurements.     

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...     

Further Results on the Observability of Quantum Systems Under General Measurement

In this paper, we present a collection of results on the observability of quantum mechanical systems, in the case the output is the result of a discrete nonselective measurement. By defining an effective observable, we extend previous results, on the Lie algebraic characterization of observable systems, to general measurements. Further results include the characterization of a ‘best probe’ (i.e. a minimally disturbing probe) in indirect measurement and a study of the relation between disturbance and observability in this case. We also discuss how the observability properties of a quantum system relate to the problem of state reconstruction. Extensions of the formalism to the case of selective measurements are also given.     

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.     

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.     

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.      

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.     

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.     

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。     

Vision-aided Estimation of Attitude,Velocity, and Inertial Measurement Bias for UAV Stabilization

This paper studies vision-aided inertial navigation of small-scale unmanned aerial vehicles (UAVs) in GPS-denied environments. The objectives of the navigation system are to firstly online estimate and compensate the unknown inertial measurement biases, secondly provide drift-free velocity and attitude estimates which are crucial for UAV stabilization control, and thirdly give relatively accurate position estimation such that the UAV is able to perform at least a short-term navigation when the GPS signal is not available. For the vision system, we do not presume maps or landmarks of the environment. The vision system should be able to work robustly even given low-resolution images (e.g., 160 ×120 pixels) of near homogeneous visual features. To achieve these objectives, we propose a novel homography-based vision-aided navigation system that adopts four common sensors: a low-cost inertial measurement unit, a downward-looking monocular camera, a barometer, and a compass. The measurements of the sensors are fused by an extended Kalman filter. Based on both analytical and numerical observability analyses of the navigation system, we theoretically verify that the proposed navigation system is able to achieve the navigation objectives. We also show comprehensive simulation and real flight experimental results to verify the effectiveness and robustness of the proposed navigation system.     

Bearing-only Cooperative Localization

In cooperative localization a group of robots exchange relative position measurements from their exteroceptive sensors and their motion information from interoceptive sensors to collectively estimate their position and heading. For the localization errors to be bounded, it is required that the system be observable, independent of the estimation technique being used. In this paper, we develop a test-bed of three ground robots, which are equipped with wheel encoders and omnidirectional cameras, to implement the bearing-only cooperative localization. The simulation and experimental results validate the observability conditions, derived in Sharma et al. (IEEE Trans Robot 28:2, 2011), for the complete observability of the bearing-only cooperative localization problem.     

Robust and Accurate Monocular Visual Navigation Combining IMU for a Quadrotor

In this paper, we present a multi-sensor fusion based monocular visual navigation system for a quadrotor with limited payload, power and computational resources. Our system is equipped with an inertial measurement unit (IMU), a sonar and a monocular down-looking camera. It is able to work well in GPS-denied and markerless environments. Different from most of the keyframe-based visual navigation systems, our system uses the information from both keyframes and keypoints in each frame. The GPU-based speeded up robust feature (SURF) is employed for feature detection and feature matching. Based on the flight characteristics of quadrotor, we propose a refined preliminary motion estimation algorithm combining IMU data. A multi-level judgment rule is then presented which is beneficial to hovering conditions and reduces the error accumulation effectively. By using the sonar sensor, the metric scale estimation problem has been solved. We also present the novel IMU+3P (IMU with three point correspondences) algorithm for accurate pose estimation. This algorithm transforms the 6-DOF pose estimation problem into a 4-DOF problem and can obtain more accurate results with less computation time. We perform the experiments of monocular visual navigation system in real indoor and outdoor environments. The results demonstrate that the monocular visual navigation system performing in real-time has robust and accurate navigation results of the quadrotor.      

Motion planning algorithms of an omni-directional mobile robot with active caster wheels

This work deals with motion planning algorithms of an omni-directional mobile robot with active caster wheels. A typical problem occurred in the motion control of such omni-directional mobile robot, which has been identified through experimental experiences, is skidding of the mobile wheel. It sometimes results in uncertain rotation of the steering wheel. To cope with this problem, a motion planning algorithm which resolves the skidding problem and uncertain motions of the steering wheel is mainly investigated. For navigation of the mobile robot, the posture of the omni-directional mobile robot is initially calculated using the odometry information. Then, the accuracy of the mobile robot’s odometry is measured through comparison of the odometry information and the external sensor measurement. Finally, for successful navigation of the mobile robot, a motion planning algorithm that employs kinematic redundancy resolution method is proposed. Through simulations and experimentation, the feasibility of proposed algorithms was verified.     

Autonomous Navigation of UAV in Foliage Environment

This paper presents a navigation system that enables small-scale unmanned aerial vehicles to navigate autonomously using a 2D laser range finder in foliage environment without GPS. The navigation framework consists of real-time dual layer control, navigation state estimation and online path planning. In particular, the inner loop of a quadrotor is stabilized using a commercial autopilot while the outer loop control is implemented using robust perfect tracking. The navigation state estimation consists of real-time onboard motion estimation and trajectory smoothing using the GraphSLAM technique. The onboard real-time motion estimation is achieved by a Kalman filter, fusing the planar velocity measurement from matching the consecutive scans of a laser range finder and the acceleration measurement of an inertial measurement unit. The trajectory histories from the real-time autonomous navigation together with the observed features are fed into a sliding-window based pose-graph optimization framework. The online path planning module finds an obstacle-free trajectory based the local measurement of the laser range finder. The performance of the proposed navigation system is demonstrated successfully on the autonomous navigation of a small-scale UAV in foliage environment.     

Distributed vision-aided cooperative localization and navigation based on three-view geometry

This paper presents a new method for distributed vision-aided cooperative localization and navigation for multiple inter-communicating autonomous vehicles based on three-view geometry constraints. Each vehicle is equipped with a standard inertial navigation system and an on-board camera only. In contrast to the traditional approach for cooperative localization, which is based on relative pose measurements, the proposed method formulates a measurement whenever the same scene is observed by different vehicles. Each such measurement is comprising of three images, which are not necessarily captured at the same time. The captured images, to which some navigation parameters are attached, are stored in repositories by some of the vehicles in the group. A graph-based approach is applied for calculating the correlation terms between the navigation parameters associated to images participating in the same measurement. The proposed method is examined using a statistical simulation and is further validated in an experiment that involved two vehicles in a holding pattern scenario. The experiments show that the cooperative three-view-based vision-aided navigation may considerably improve the performance of an inferior INS.     

Solving certain queueing problems modelled by toeplitz matrices

By using the concept of generating function associated with a Toeplitz matrix, we analyze existence conditions for the probability invariant vector π of certain stochastic semi-infinite Toeplitz-like matrices. An application to the shortest queue problem is shown. By exploiting the functional formulation given in terms of generating functions, we devise a weakly numerically stable algorithm for computing the probability invariant vector π. The algorithm is divided into three stages. At the first stage the zeros of a complex function are numerically computed by means of an extension of the Aberth method. At the second stage the first k components of π are computed by solving an interpolation problem, where k is a suitable constant associated with the matrix. Finally, at the third stage a triangular Toeplitz system is solved and its solution is refined by applying the power method or any other refinement method based on regular splittings. In the solution of the triangular Toeplitz system and at each step of the refinement method, special FFT-based techniques are applied in order to keep the arithmetic cost within the O(n log n) bound, where n is an upper bound to the number of the computed components. Numerical comparisons with the available algorithms show the effectiveness of our algorithm in a wide set of cases.     

Planar-Based Visual Inertial Navigation: Observability Analysis and Motion Estimation

In this paper, we address the problem of ego-motion estimation by fusing visual and inertial information. The hardware consists of an inertial measurement unit (IMU) and a monocular camera. The camera provides visual observations in the form of features on a horizontal plane. Exploiting the geometric constraint of features on the plane into visual and inertial data, we propose a novel closed form measurement model for this system. Our first contribution in this paper is an observability analysis of the proposed planar-based visual inertial navigation system (VINS). In particular, we prove that the system has only three unobservable states corresponding to global translations parallel to the plane, and rotation around the gravity vector. Hence, compared to general VINS, an advantage of using features on the horizontal plane is that the vertical translation along the normal of the plane becomes observable. As the second contribution, we present a state-space formulation for the pose estimation in the analyzed system and solve it via a modified unscented Kalman filter (UKF). Finally, the findings of the theoretical analysis and 6-DoF motion estimation are validated by simulations as well as using experimental data.     

Autonomous implementation of dynamic operations in a geostationary orbit. II. Synthesis of control algorithms

This study continues the series of papers devoted to the problems of autonomous operation of spacecraft in a geostationary orbit. The solution of the problem considered here assumes the formation of a set of algorithms for control processes in a closed autonomous spacecraft control and navigation system in a geostationary orbit. The paper is aimed at the formalization and solution of the new technical task of autonomous control during the spacecraft’s ascent to the given orbital position and remaining in this position. An important requirement is to provide the safe separation of several spacecraft in one orbital position. The control problem is solved using the combined optimization method developed by us; in this method, the control vector is divided into the synthesized and the programmed components taking into account the principle of the separation of the navigation and control problem in the stochastic approach. The motion’s models proposed in the previous paper are used to develop the control algorithms for a spacecraft’s ascent to the working position in a geostationary orbit and remaining in this position. The results of the algorithms simulating the ascent and maintaining for the exactly known state vector taking into account the random spread of the initial conditions and thrust are presented.     

Guaranteed Parameter Set Estimation for Exponential Sums: The Three-Terms Case

In this paper the problem of parameter estimation for exponential sums with three terms is considered. This task consists of finding the set of parameters (amplitudes as well as decay constants) such that the exponential sum attains values in specified intervals at prescribed time data points. These intervals represent uncertainties in the measurements. An interval variant of Prony’s method is given by which intervals can be found containing all the consistent values of the respective parameters. By the use of interval arithmetic these enclosures can also be guaranteed in the presence of rounding errors. Support from the Ministry of Education and Research of the Federal Republic of Germany under contract no. 1705803 and from the DAAD program PROCOPE under contract no. D/0205730 is gratefully acknowledged.