Angles-only Navigation Research Articles

Robust trajectory planning for non-cooperative target rendezvous based on closed-loop uncertainty analysis

A robust trajectory planning method for non-cooperative target rendezvous is investigated based on closed-loop uncertainty analysis. The proposed method addresses the issue that uncertainties affect the optimality of objective functions and the reliability of constraints. Considering multiple uncertainties, a stochastic optimal rendezvous model with a robustness performance index and chance constraints is presented with line-of-sight dynamics. The guidance model, angles-only navigation model and control model are derived, and uncertainty propagation equations for closed-loop GN&C system is proposed by using linear covariance analysis. The stochastic optimal rendezvous model is transformed into a robust optimal rendezvous model by using 3-σ of the random variables. The genetic algorithm is used to solve the robust trajectory planning problem, and a series of examples demonstrate that the robust maneuver solution can be significantly better than the solution corresponding to deterministic trajectory optimization problem.

Aiding Angles-Only Navigation with Illumination Telemetry to Resolve Weak Observability

This paper introduces the discrete measurement transition update (DMTU), a reformulation of the Kalman filter measurement update that is capable of processing discrete data. DMTU is applied to illumination data onboard a spacecraft to create a new observable for space navigation systems. It is shown that combining this new observable with intersatellite angle measurements creates an autonomous navigation system (Angles and Illumination Data Navigation [AIDnav]) capable of resolving the absolute orbits of both spacecraft. This novel navigation system is extremely low size, weight, and power, relying only on hardware already found on most spacecraft. It does not require cooperative spacecraft or more than one observer, nor does it require orbits or maneuvers that maximize observability. The performance of AIDnav is studied in a Monte Carlo simulation for a potential distributed Mars mission, and it is shown to be capable of determining an orbit with an average converged state error of 86 m and . This method of navigation is viable for many different orbital regimes, but is ideal for ride-along interplanetary missions, which will always have a nearby target to observe and an external source of navigation before capturing into orbit at the destination central body.

Observability analysis and optimization for angles-only navigation of distributed space systems

Angles-only navigation methods are compelling for distributed space systems (DSS) such as swarms and constellations. However, complex dependencies between state observability and system parameters present a challenging design problem. This paper proposes a unified angles-only observability analysis and design framework enabling designers of a DSS to 1) analytically determine whether its orbit state is observable, 2) numerically estimate its expected navigation performance, and 3) intelligently optimize the system to meet navigation requirements. First, a new system measurement topology representation is proposed for which analytic orbit observability can be assessed via a set of graphical conditions. Second, methods for numeric estimation of the achievable state covariance are augmented with auxiliary state variables, dynamics uncertainty, and measurement availability constraints. Third, a system cost function is developed and the topological and numeric methods are placed within a quasi-Newton optimization framework to enable automatic system design. The optimization is applied to a distributed science swarm and a space situational awareness constellation in lunar orbit. Both scenarios converge to a global cost minimum and output designs that achieve user requirements under realistic measurement conditions and constraints. Combined analytic and numeric methods therefore presents a powerful tool for design of angles-only DSS.

Starling Formation-Flying Optical Experiment (StarFOX): System Design and Preflight Verification

The Starling Formation-Flying Optical Experiment (StarFOX) is intended as the first on-orbit demonstration of autonomous distributed angles-only navigation for spacecraft swarms. StarFOX applies the angles-only Absolute and Relative Trajectory System (ARTMS), a navigation architecture consisting of three innovative algorithms: image processing, which identifies and tracks multiple targets in images from a single camera without a priori relative orbit knowledge; batch orbit determination, which autonomously initializes orbit estimates for visible swarm members; and sequential orbit determination, which continuously refines the swarm state by fusing measurements from multiple observers exchanged over an intersatellite link. Nonlinear dynamics and measurement models provide sufficient observability to estimate absolute orbits, relative orbits, and auxiliary states using only bearing angles without maneuvers. StarFOX will be conducted using a four-CubeSat swarm as part of the NASA Starling mission, and simulations of experiment scenarios demonstrate that ARTMS meets mission performance requirements. Results indicate that mean bearing angle errors are below 35′′ (), initial target range errors are below 20% of true separation, and steady-state range errors are below 2% (). Absolute orbit estimation accuracy is on the order of 100 m. Hardware-in-the-loop tests display robust navigation under a variety of conditions, enabling autonomous, ubiquitous navigation with minimal ground interaction for future distributed missions.

Optical simulator design for hardware in loop testing of medium and long range angles-only navigation of spacecraft

设计了一种航天器中远距仅测角导航硬件在环测试的光学模拟器，可对仅测角导航视觉传感器的硬件、软件和算法的性能及可靠性进行验证。首先对该光学模拟器进行了系统描述，包括硬件组成和星图模拟软件设计。硬件选用的都是商用、现成的部组件，可大幅节约研发成本，缩短开发周期。其次，重点阐述屏幕亮度与恒星星等之间的关系，以及该光学模拟器的光学原理。最后对该光学模拟器的星图模拟进行实验测试，并介绍了一种基于Clohessy-Wiltshire (CW)方程的仅测角导航模型，用于硬件在环测试。验证了几何校正后的光学模拟器完全满足航天器中远距仅测角导航硬件在环测试要求，并得出相对于几何校正前，终端时刻的相对位置精度提高了25.5%，相对速度精度提高了31.3%。

Feasibility analysis of angles-only navigation algorithm with multisensor data fusion for spacecraft noncooperative rendezvous

Feasibility analysis of angles-only navigation algorithm with multisensor data fusion for spacecraft noncooperative rendezvous

Review of Angles-Only Navigation Technique for Spacecraft Autonomous Rendezvous and Docking

Review of Angles-Only Navigation Technique for Spacecraft Autonomous Rendezvous and Docking

Deep reinforcement learning for rendezvous guidance with enhanced angles-only observability

This research studies the application of reinforcement learning in spacecraft angles-only rendezvous guidance in the presence of multiple constraints and uncertainties. To apply a standard reinforcement learning framework, a stochastic optimal control problem is constructed as a time-discrete Markov decision process, and the observability of angles-only navigation is included in the construction of a reward function. A proximal policy optimization algorithm is used to train a deep neural network (DNN) to map observations of spacecraft state to an optimal control strategy. The trained guidance control network provides a robust nominal orbit and the corresponding closed-loop guidance law, which has the potential to improve the performance of closed-loop navigation, guidance and control. Numerical simulation results are given for an example of far-rendezvous approach guidance. The influence of different weights of the observability term in the reward function on the optimal control strategy is studied. The robustness of the obtained closed-loop control law is evaluated and verified through Monte Carlo simulations in disturbed scenarios.

Multi-objective optimization of angles-only navigation and closed-loop guidance control for spacecraft autonomous noncooperative rendezvous

In this paper, the angles-only navigation and closed-loop guidance control for spacecraft autonomous noncooperative rendezvous in geosynchronous Earth orbit (GEO) are studied, and a multi-objective optimization model is established considering various constraints. The optimization objectives include the total flight time, the total fuel cost, and the observability of angles-only navigation. First of all, the angles-only navigation model is established, including relative dynamics and Line-of-Sight (LoS) measurement models. Then, the closed-loop guidance control covariance is analyzed, and the navigation and control covariance analysis models are established. And then, a multi-objective optimization model is established, including the objective functions, optimization variables, constraints, and the mathematical model. After that, a crowding mechanism based on vector space model (VSM) is proposed to improve the fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II, and a VSM-NSGA-II is constructed to solve the proposed multi-objective optimization model. Finally, a set of Pareto optimal solutions are simulated and analyzed by using closed-loop guidance control covariance analysis and Monte Carlo simulation, thereby proving the effectiveness of the multi-objective optimization model proposed in this paper.

Autonomous angles-only multitarget tracking for spacecraft swarms

This paper presents a new algorithm for autonomous multitarget tracking of resident space objects using optical angles-only measurements from a spaceborne observer. To enable autonomous angles-only navigation of spacecraft swarms, observers must identify and track multiple known or unknown target space objects in view, without reliance on a-priori relative orbit knowledge. Extremely high tracking precision is necessary despite low measurement frequencies and limited computational resources. The new ’Spacecraft Angles-only MUltitarget tracking System’ (SAMUS) algorithm has been developed to meet these objectives and constraints. It combines domain-specific modeling of target kinematics with multi-hypothesis techniques to autonomously track multiple unknown targets using only sequential camera images. A measurement transform ensures that target motion in the observer reference frame follows a consistent parametric model; curve fitting is used to predict track behavior; and kinematic track gating and scoring criteria improve the efficiency and accuracy of the multi-hypothesis approach. Monte Carlo testing with high-fidelity simulations demonstrates close to 100% data association precision and high recall across a range of multi-spacecraft formations, in both near-circular and eccentric orbits. Tracking is maintained in the presence of eclipse periods, significant measurement noise, and partially known swarm maneuvers. A comparison to other tracking algorithms reveals strong advantages in precision, robustness and computation time, crucial for spaceborne angles-only navigation.

Generalized Angles-Only Navigation Architecture for Autonomous Distributed Space Systems

This paper addresses the development and verification of an estimation architecture for autonomous relative navigation in multi-satellite systems using angles-only measurements. Unlike traditional angles-only navigation approaches, which are generally hindered by poor handling of observability constraints, this prototype solution is designed to be flexible and applicable to a multitude of relevant missions. The estimator converges accurately and robustly in varying orbital environments without requiring maneuvers by exploiting system nonlinearities using an unscented Kalman filter that is streamlined by formulating the measurement and dynamics models using relative orbital elements. While the majority of prior work has focused on only solving for the relative motion of a single target, the approach here enables estimation of several additional parameters. Key design trades are evaluated for estimating additive sensor biases, target ballistic properties in environments with strong nonconservative perturbations, adaptive process noise statistics, and the absolute orbit of the observing satellite. The architecture is generalized for relative navigation with multiple targets, and for decentralized estimation using multiple coordinated observers. These filter strategies are used to inform the development of a novel on-orbit demonstration of angles-only navigation known as the Starling Formation-flying Optical eXperiment (StarFOX) in partnership with NASA. Key hardware-in-the-loop algorithm verification results for StarFOX-specific scenarios are provided.

An Angles-Only Navigation and Control Scheme for Noncooperative Rendezvous Operations

The use of vision sensors for noncooperative rendezvous operations is attractive, especially for microspacecraft, because vision sensors are usually of small size, light weight, and low cost but provide rich information. However, vision-based rendezvous operations are extremely challenging. It is difficult for vision sensors to accurately measure the relative distance between a chaser spacecraft and a noncooperative target. In this paper, we propose a systematic angles-only navigation and control scheme for noncooperative rendezvous operations. The scheme is a hybrid framework that combines offline trajectory planning that integrates observability condition and online trajectory tracking based on nonlinear model predictive control. A navigation filter is used in the online trajectory tracking to estimate the relative motion by using only angle measurements. In the scheme, the chaser spacecraft can closely track the desired trajectory and simultaneously guarantee the estimation accuracy of the navigation filter. This paper provides a general and practical framework for angles-only rendezvous operations and the effectiveness is verified by extensive simulations.

Precise Angles-Only Navigation for Noncooperative Proximity Operation With Application to Tethered Space Robot

For microspacecraft that have limited payload capability, the potential use of vision sensors (e.g., cameras) has been already recognized in noncooperative proximity operation. However, vision-based relative navigation is difficult, because vision sensors have the limitation to accurately measure distance information. In this paper, we propose an angles-only navigation and control framework for noncooperative proximity operation. The framework is especially suitable for challenging long-range proximity operation, where only the line-of-sight angles of the target can be obtained. Within the proposed framework, the spacecraft not only estimates its current orbital position precisely with only angle measurements but also approaches to a noncooperative target by following desired attitude and orbital motions. The framework combines an off-line motion planning and an online navigation and control that is based on model predictive control (MPC) and time delay control (TDC). The study is with application to tethered space robot. Extensive simulations illustrate the effectiveness of the proposed framework.

Onboard Target Searching Strategy During Lost in Space Situations in Angles-Only Navigation Active Space Debris Removal

During the transition from ground-based to on-board relative navigation, active space debris removal faces the so-called lost in space problem where the target’s orbital parameters are known to a limited degree making its detection and identification among the other visible objects challenging. Being non-cooperative, the target is also assumed to be non-responsive to communication methods. Seven target search strategies are developed and evaluated using Monte-Carlo analysis. It is shown that one of the proposed methods, stepping-sweeping, can insure detection of the target within several minutes with a 99.9% success rate using either a single optical/infra-red camera payload. A sensitivity analysis was conducted on both the camera parameters and the detection success condition and reveals that this target search strategy is robust against initial position uncertainties. It is also applicable to all the common relative trajectories for orbital proximity operations. The developed tool can also be used for sensor parameters as well as search strategy key parameters selection.

Observability criterion of angles-only navigation for spacecraft proximity operations

This research studies the angles-only relative navigation problem for spacecraft proximity operations when the camera offset from the vehicle center-of-mass allows for range observability. Emphasis is placed on developing an analytic observability criterion for the camera offset within the context of the Clohessy-Wiltshire (CW) dynamics and evaluating the performance of the navigation algorithm in nonlinear dynamics environment. Further, the newly observability criterion is mathematically derived by changing the analyzing problem of the nonlinear observability into the solving problem of linear equations, and the criterion can be a powerful guideline to be followed to install the camera and execute attitude maneuvers. Moreover, navigation filtering algorithm based on an Unscented Kalman Filter and systematic nonlinear Monte Carlo simulation framework are established to verify the analytic observability criterion and evaluate the performance of the proposed algorithm through typical proximity missions. The sensitivity of the navigation accuracy to spacecraft trajectories and camera offset is presented and discussed. The conclusion is that the camera offset is required to have out-of-plane component and cannot be parallel to the line-of-sight vector in order to supply range observability.

Corrigendum to “Time and Covariance Threshold Triggered Optimal Uncooperative Rendezvous Using Angles-Only Navigation”

Corrigendum to “Time and Covariance Threshold Triggered Optimal Uncooperative Rendezvous Using Angles-Only Navigation”

Optimal range observability maneuvers of a spacecraft formation using angles-only navigation

The work presented in this paper leverages existing progress in angles-only navigation to develop optimal range observability maneuvers and trajectory planning methods for spacecraft formations under constrained relative orbital motion. Relative motion is modeled in the Clohessy-Wiltshire frame for proximity operations of multiple chaser spacecraft about a non-cooperative resident-space-object (RSO).The objective of the optimization is to maximize range observability of the RSO from each of the chaser spacecraft in the formation. Each chaser spacecraft transfers between an initial and a final trajectory with respect to the RSO on an intermediate trajectory. Optimal range observability is sought during the transfer. A two-burn impulsive maneuver pair is used to 1) take the chaser spacecraft from the initial to the transfer trajectory and 2) to acquire the final trajectory. By parameterizing the relative states of each chaser using relative orbit elements, the system of equations governing the optimization problem is expressed in terms of a single time varying relative orbital element per spacecraft, per target trajectory. The free parameters are constrained in terms of the fuel used per burn, collision avoidance with the RSO, and collision avoidance with other members of the formation. Lighting (eclipse) and field of view (optical) obstructions by neighboring celestial bodies are considered as well.A representative scenario for a single spacecraft is presented for ease of visualization and to illustrate the cost and constraints in a single 3D map. The method presented hereafter has been extended to a formation of arbitrary cardinality; however, the results shown are those of a three-spacecraft formation. Examples are then given for distinctive formations of three spacecraft. For each example, the optimal burns are determined given the initial and target trajectories of each member in the formation.

Flight demonstration of spaceborne real-time angles-only navigation to a noncooperative target in low earth orbit

The paper describes the onboard vision-based navigation software employed during the DLR's AVANTI experiment and presents its flight performance. The navigation task relies on a dedicated target detection module in charge of extracting the line-of-sight observations from the images taken by a monocular camera. The recognition of the target is based on the kinematic identification of its trajectory over a sequence of images. Subsequently, the resulting angles-only measurements are validated dynamically and processed by an Extended Kalman Filter to derive in real-time the relative state estimate. A computationally light implementation of the filter is achieved by the use of an analytical relative motion model. Two autonomous rendezvous to a noncooperative object have been performed in orbit, first from 13 km to 1 km separation, then from 3 km to 50 m. Despite the poor visibility conditions and the strong orbit perturbations encountered at low altitude, the filter was able to supply the onboard guidance and control algorithms with accurate and reliable relative state estimation, enabling thus a safe and smooth approach.

Nonlinear Kalman Filtering for Improved Angles-Only Navigation Using Relative Orbital Elements

This paper addresses the design and validation of an accurate estimation architecture for autonomous angles-only navigation in orbits of arbitrary eccentricity. The proposed filtering strategy overcomes the major deficiencies of existing approaches in the literature, which mainly focus on applications in near-circular orbits and generally suffer from poor dynamical observability due to linearizing the filter dynamics and measurement models. Consequently, traditional angles-only navigation solutions require conducting known orbital maneuvers to reconcile the ambiguous range. In contrast, the algorithms developed in this work enable accurate maneuver-free reconstruction of the relative orbital motion. This is done through the full exploitation of nonlinearities in the measurement model using the unscented Kalman filter to improve dynamical observability and filter performance. The filter estimates mean relative orbit elements, adopting a state transition matrix subject to secular and long-period perturbation effects to decouple observable from unobservable parameters. The complete state is then reconciled with the angle measurements in the measurement model through a nonlinear transformation that includes the conversion from mean to osculating orbital elements. The resulting linear dynamics model is supplemented by either first-order Gauss–Markov processes (that is, differential empirical accelerations) or by a covariance-matching approach to online adaptive process noise tuning to increase performance at minimal computational complexity. Finally, the estimation architecture is completed by a novel deterministic algorithm for batch initial relative orbit determination to accurately initialize the sequential filter.

Time and Covariance Threshold Triggered Optimal Uncooperative Rendezvous Using Angles-Only Navigation

A time and covariance threshold triggered optimal maneuver planning method is proposed for orbital rendezvous using angles-only navigation (AON). In the context of Yamanaka-Ankersen orbital relative motion equations, the square root unscented Kalman filter (SRUKF) AON algorithm is developed to compute the relative state estimations from a low-volume/mass, power saving, and low-cost optical/infrared camera’s observations. Multi-impulsive Hill guidance law is employed in closed-loop linear covariance analysis model, based on which the quantitative relative position robustness and relative velocity robustness index are defined. By balancing fuel consumption, relative position robustness, and relative velocity robustness, we developed a time and covariance threshold triggered two-level optimal maneuver planning method, showing how these results correlate to past methods and missions and how they could potentially influence future ones. Numerical simulation proved that it is feasible to control the spacecraft with a two-line element- (TLE-) level uncertain, 34.6% of range, initial relative state to a 100 m v-bar relative station keeping point, at where the trajectory dispersion reduces to 3.5% of range, under a 30% data gap per revolution on account of the eclipse. Comparing with the traditional time triggered maneuver planning method, the final relative position accuracy is improved by one order and the relative trajectory robustness and collision probability are obviously improved and reduced, respectively.