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Angles-Only Robust Trajectory Optimization for NRHO Rendezvous

This study demonstrates a robust trajectory optimization approach for rendezvous and proximity operations with angles-only navigation measurements. Often, sensors that directly measure relative range and velocity require communication or coordination between the chaser and target vehicle and can have limiting pointing accuracy, mass, or power requirements compared to angle measurement sensors. Thus, the capability to perform a rendezvous with only angle measurements can be advantageous for vehicle design and to improve robustness to failures. However, the well studied limitation of angles-only navigation in measuring range results in large uncertainties in the navigation system that must be reduced with chaser vehicle thrust maneuvers to induce observability in range for the navigation filter. This analysis presents a trajectory optimization problem for a lunar ascent rendezvous during a crewed lunar mission in a Near-Rectilinear Halo Orbit (NRHO) that is limited to only angle measurements. The objective of this study is to show that an angles-only rendezvous is feasible in an NRHO and to present the sensitivity to an assortment of constraints generated from a systematic optimization process using linear covariance analysis and particle swarm optimization. Linearized NRHO dynamics and linearized relative targeting are applied to use linear covariance analysis to determine the expected delta-v and trajectory dispersions due to initial state uncertainty, sensor errors, maneuver execution errors, and unmodeled dynamics. The delta-v and trajectory dispersions are passed into a particle swarm optimization algorithm to find the optimized maneuver profile that minimizes fuel use while satisfying constraints such as free drift and underburn to 3-sigma certainty. The trajectory constraints including time available, desired final uncertainty, and initial uncertainty are varied to ascertain sensitivity and desirable engineering trades.

Linear Covariance Analysis

Starling Formation-Flying Optical Experiment: Initial Operations and Flight Results

This paper presents initial flight results for angles-only navigation of a swarm of small spacecraft, conducted during the Starling Formation-Flying Optical Experiment (StarFOX). StarFOX is one of four experiments aboard the NASA Starling mission, which consists of four CubeSats launched in July 2023. Angles-only methods apply inter-satellite bearing angles obtained by on-board cameras for navigation, increasing satellite autonomy and enabling new mission concepts. Nevertheless, prior flight demonstrations have only featured one observer and target and have relied upon a-priori target orbit knowledge for initialization, translational maneuvers to resolve target range, and external absolute orbit updates to maintain convergence. StarFOX overcomes these limitations by applying the angles-only Absolute and Relative Trajectory Measurement System (ARTMS), which integrates three novel algorithms. Image Processing detects and tracks multiple targets in images, using multi-hypothesis methods and domain-specific kinematic modeling, and computes target bearing angles. Batch Orbit Determination computes initial swarm orbit estimates from bearing angle batches, via iterative batch least squares and sampling of the weakly observable target range. Sequential Orbit Determination leverages an adaptive, efficient unscented Kalman filter with nonlinear models to refine swarm state estimates over time. Multi-observer measurements shared over an intersatellite link are seamlessly fused to enable robust absolute and relative orbit determination. Initial StarFOX experiments are the first demonstrations of autonomous angles-only navigation for a satellite swarm, including multi-target and multi-observer relative navigation; autonomous initialization of navigation for unknown targets; and simultaneous absolute and relative orbit determination. Relative navigation accuracy of 1% (single observer) and 0.2% (multi-observer) of the inter-satellite range is achieved under challenging measurement conditions. Results demonstrate promising performance with regards to ongoing StarFOX campaigns and the application of angles-only navigation to future distributed missions.

Relative Navigation

Smallsat 2024 - Starling Cubesat Swarm Technology Demonstration Flight Results

The Starling swarm of four 6U CubeSats launched in July 2023 to test four key technologies to enable future swarm missions: 1) Mobile Ad-Hoc Networking (MANET) over a crosslink radio network 2) Autonomous onboard decision-making for operations 3) Optical-based absolute and relative navigation 4) Autonomous maneuver planning and execution The Starling team implemented the Better Approach to Mobile Ad-hoc Networking (B.A.T.M.A.N.) protocol to automatically manage the crosslink network of four satellites. The B.A.T.M.A.N. protocol uses a decentralized approach to managing a multi-hop mesh network of devices, in this case, a satellite swarm. The four satellites were able to successfully establish a network at multiple data rates and demonstrate file transfer and command issuance between spacecraft over the network. Starling incorporated Distributed Spacecraft Autonomy's (DSA) software to demonstrate onboard decision-making. The DSA software takes L1/L2 band GPS measurements and uses them to estimate the relative Total Electron Count (TEC) in the ionosphere. The onboard software then determines if there are any features of interest and provides that information to the other satellites over the crosslink network. The swarm of satellites then reaches a consensus on the optimal TEC observation strategy and adjusts its measurement collection tactics autonomously. The Starling Formation-Flying Optical Experiment (StarFOX), produced by Stanford's Space Rendezvous Laboratory, uses the onboard star trackers to collect images of the other swarm spacecraft and produce angles-only navigation estimates. This system is envisioned to be valuable in applications in which Global Navigation Satellite Systems (GNSS) are not available, such as in cis-lunar or deep space. StarFOX successfully applied its algorithms to multiple simultaneous spacecraft targets using the star tracker imagery. Finally, Starling used Emergent Space's Cluster Flight Application (CFA) software suite for the Reconfiguration and Orbit Maintenance Experiments Onboard (ROMEO) demonstration of autonomously planning and executing propulsive maneuvers. Large swarms will need to be able to maintain formation requirements with minimal operator involvement, especially as the size of the swarm scales up. Results from the ROMEO experiment are presented. Starling is funded by the Small Spacecraft Technology (SST) program out of NASA's Space Technology Mission Directorate (STMD).

distributed systems

Guidance and Navigation for Rendezvous and Proximity Operations with a Non-Cooperative Spacecraft at Geosynchronous Orbit

The feasibility and benefits of various spacecraft servicing concepts are currently being assessed, and all require that the servicer spacecraft perform rendezvous, proximity, and capture operations with the target spacecraft to be serviced. Many high-value spacecraft, which would be logical targets for servicing from an economic point of view, are located in geosynchronous orbit, a regime in which autonomous rendezvous and capture operations are not commonplace. Furthermore, existing GEO spacecraft were not designed to be serviced. Most do not have cooperative relative navigation sensors or docking features, and some servicing applications, such as de-orbiting of a non-functional spacecraft, entail rendezvous and capture with a spacecraft that may be non-functional or un-controlled. Several of these challenges have been explored via the design of a notional mission in which a nonfunctional satellite in geosynchronous orbit is captured by a servicer spacecraft and boosted into super-synchronous orbit for safe disposal. A strategy for autonomous rendezvous, proximity operations, and capture is developed, and the Orbit Determination Toolbox (ODTBX) is used to perform a relative navigation simulation to assess the feasibility of performing the rendezvous using a combination of angles-only and range measurements. Additionally, a method for designing efficient orbital rendezvous sequences for multiple target spacecraft is utilized to examine the capabilities of a servicer spacecraft to service multiple targets during the course of a single mission.

Barbee, Brent William