Future missions involving the interaction of multiple satellites presentincreasingly demanding relative navigation requirements which mustbe achieved autonomously using limited onboard resources. Vision-based navigation techniques deliver an effective response to theseneeds by providing an inherently passive, robust, and high-dynamicrange capability which uses simple sensors that are already on boardmost spacecraft. Furthermore, because of their low cost, low powerconsumption, and small form factor as compared with other metrologysystems, these sensors enable accurate relative navigation whilecomplementing the current trend of spacecraft miniaturization.

State-of-the-art Blue Canyon Technology Standard NST (left) and Sinclair (center)star trackers. Overlaid images taken of a target spacecraft during the ARGONexperiment (right) using a DTU star tracker.

Motivation

Abstract #

20980123

Research goal: Enable accurate and robust angles-only estimationof the target’s relative motion in arbitrarily eccentric orbits, withoutrequiring reconfiguration maneuvers for observability improvement.Design strategies for responding to the challenges:• Parameterize relative orbital motion using mean Relative Orbital

Elements (ROE): 𝛿𝒙 = 𝛿𝑎, 𝛿𝜆, 𝛿𝑒𝑥 , 𝛿𝑒𝑦, 𝛿𝑖𝑥, 𝛿𝑖𝑦 . This choice

allows relevant perturbations like 𝐽2 and atmospheric drag to beseamlessly included in the dynamics. Furthermore, the weakobservability is largely decoupled to one element (𝛿𝜆).

• Improve dynamical observability by exploiting the nonlinearitiesrelating mean ROE to osculating ROE in the Unscented KalmanFilter measurement model. The osculating ROE short-periodoscillations encode separation-dependent features (see figurebelow) that disambiguate the weakly observable range.

• Supplement reduced onboard dynamics model with adaptiveprocess noise tuning online using an innovation-covariancematching technique. By improving the process model,measurement trends observed by the sensor are assimilated intoimproved state estimates.

• Derive method for angles-only initial relative orbit determinationfor accurate filter initialization in eccentric, 𝐽2-perturbed orbits.

Osculating (blue) and mean (red) ROE trends beginning from initial conditions (Xand O markers, respectively). Mean separation varies from -20 km to 0 km.

Maneuver-Free Angles-Only Navigation

Angles-only navigation algorithm verification architecture using the opticalstimulator testbed with far-range camera in the loop.

Optical stimulator testbed, including OLED monitor, collimating optic, and far-rangecamera test article. Under provisional patent 62/413757 as of 10/27/2016.

ROE estimation errors and 1-𝜎 bounds using an adaptive UKF. Measurements areobtained from a far-range navigation camera in the loop. Relative trajectoryapproaches from 20km down to approximately 5km in near-circular low Earth orbit.

Navigation Algorithm Verification

This research focuses on the far-range angles-only relativenavigation problem, where an observing spacecraft uses a set ofbearing angles to determine the relative orbital motion of a target.In this scenario, constrained dynamical observability makes itdifficult or impossible to estimate the full 6D relative state fromsequences of 2D measurements. A common solution is toconducted known orbital maneuvers to change the bearing angletrends, but this has the undesired effect of strongly coupling themaneuver-planning and navigation tasks. Finally, nearly all existingresearch studies are confined to near-circular orbit applications.

Challenges and State-of-the-Art

Josh Sullivan, Connor Beierle, Simone D’Amico

Space Rendezvous Laboratory{jasulliv, cbeierle, damicos} @ stanford.edu

slab.stanford.edu Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305

Autonomous Far-Range Vision-Based Rendezvous with a Target Space Object

References1. Beierle, Sullivan, and D’Amico, High-Fidelity Verification of Vision-Based Sensors for Inertial and Far-Range

Spaceborne Navigation, 26th International Symposium on Space Flight Dynamics, Matsuyama, Japan, June3-9, 2017.

2. Sullivan and D’Amico, Nonlinear Kalman Filtering for Improved Angles-Only Navigation Using RelativeOrbital Elements, Journal of Guidance, Control, and Dynamics Special Kalman Issue, 2017.

3. Sullivan and D’Amico, Adaptive Filtering for Maneuver-Free Angles-Only Navigation in Eccentric Orbits,27th AAS/AIAA Space Flight Mechanics Meeting, San Antonio, Texas, February 5-9, 2017.

4. Beierle and D’Amico, High-Dynamic Range Optical Stimulator for Spaceborne Vision Applications, Journalof Spacecraft and Rockets, 2017.