Performance Evaluation of a Vision Based Navigation Algorithm for CubeSat Docking Missions

The availability of structures that can autonomously assemble in orbit could have a key role in future space explorations and research. Thanks to the last 20 years of miniaturization in space technologies, CubeSats have emerged as the perfect tool for in-orbit demonstration missions. However, a successful docking mission between two CubeSats still represents an unmet challenge because of the high accuracy required in the last meters of this operation. In fact, during the final approach phase, the relative position and attitude of the two spacecrafts are coupled and all the 6 degrees of freedom of the chasing CubeSat must be estimated and controlled simultaneously. To perform this delicate relative motion, a Vision Based Navigation (VBN) solution represents the best available option. In this thesis, a simulator of CubeSat docking missions is designed. A 3U “chaser”, equipped with a monocular camera, approaches a “target”, equipped with a cross-shaped pattern of Light Emitting Diodes (LEDs). Three different LEDs patterns are studied. The target travels on a circular Low-Earth-Orbit and is considered perfectly aligned to its local orbital frame. The mission starts from a first Station Keeping point (SK0): it represents the position in which the handover between the Guidance Navigation and Control system that previously operated the chaser and the VBN system occurs. The VBN algorithm is mimicked by generating fake LEDs’ pictures based on the simulated real relative state. The LEDs’ position in pixels is then corrupted to account for the optical device noise and LEDs detection error. These noisy positions are fed to an Extended Kalman Filter which, using a linearized version of the coupled dynamics involved, performs simultaneous estimation and filtering of the state variables. The estimated state is used by a Linear Quadratic Regulator to generate the position and attitude control inputs for the chaser. These inputs are corrupted with realistic sources of disturbance and then returned to the chaser, thus closing the loop. The first goal of this thesis is to evaluate how the handover in SK0 affects the initialization of the VBN system. Simulations show how the choice of pattern doesn’t impact the handover performance, which is instead mostly affected by the residual relative velocities and rotation rates. The second goal is to understand how different LEDs pattern sizes and positions affect the final approach phase. Three patterns, different in size and location on the docking face, are tested. Simulations show that all three perform in a similar way, allowing the CubeSat to achieve docking with high precision. Therefore, using the proposed algorithm, the choice of pattern may be motivated by hardware requirements rather than by performance objectives. The final goal is to determine how the LEDs’ detection error in pixels affects the docking operation. This source of error mostly affects state estimation when the two CubeSats are distant, namely when the LEDs are seen very close to each other on the image plane. Therefore, the main consequence of this error is to slow down the VBN initialization process. In the worst-case scenario, the handover fails. Relaxing the handover and translation safety constraints allows the chaser to move in a less accurate way during the first couple of meters, until it reaches a range in which the effect of the LEDs detection error consistently reduces, leading to a successful docking.