Designing the path of swarms of small satellites from a macro-micro point of view

The microsatellite swarm is an important future research topic for distributed space systems because it is a new way for multiple satellites to fly together. It is cheap, responds quickly, and lets people work together to make decisions. A probabilistic guidance approach with sub-swarms with different mission goals has been looked into as a way for autonomous agents to work together in swarms.

Probabilistic swarm guidance lets self-driving microsatellites plan their own paths independently so that the whole swarm moves toward the shape of the desired distribution. But it’s important to keep microsatellites from getting too close to each other so they don’t crash into each other. This makes designing the algorithm to avoid collisions more difficult.

In a research paper that was just published in Space: Science & Technology, Bing Xiao from the School of Automation at Northwestern Polytechnical University proposed a method that uses Centroidal Voronoi tessellation (CVT) and Model Predictive Control (MPC) to optimize the paths of a group of microsatellites.

The author made a model of how swarms of small satellites move through 3D space and introduced the probabilistic swarm guidance law. After that, since it was important to keep microsatellites from getting too close to each other to avoid collisions, the safety analysis of collision avoidance was based on finding the minimum distance between all microsatellites at any given time.

A collision avoidance algorithm was needed to figure out the safest way for each microsatellite to move from where it is now to where it needs to go. But with high-level coordination that used macroscopic models, it was hard to make paths that didn’t hit anything. So, the author came up with a synthesis method in which the planning of a trajectory was split into two parts: macro-planning and micro-planning.

The author then talked about the details of both the big and small plans for the microsatellite swarm. In the macro-planning of a swarm of microsatellites, each microsatellite’s target position was set by the CVT algorithm’s centroid, and all microsatellites moved toward their respective centroids until the algorithm reached a point of convergence.

The location of the centroid was used to figure out how the microsatellites should be spread out in space. The MPC was used in the micro-planning of the microsatellite swarm to find the best paths for each step so that the swarm would end up in the right place in the target cube.

In particular, the author set up an orbital dynamics model that took J2 perturbation into account and used convexification of collision avoidance constraints during the swarm reconfiguration process. A model of predictive control was used to update the best paths based on the current state of the system and a receding horizon. This made it possible to plan trajectories in real time. Importantly, the proposed method can not only keep microsatellites from running into each other at the macro level, but it can also find the best path for each individual microsatellite at the micro level.

Lastly, a numerical simulation was done to test the proposed method for planning the paths of a group of microsatellites. The author created a virtual central microsatellite and a large-scale swarm of 300 microsatellites that can fly in any direction. The CVT algorithm was used to split up regions and figure out where the microsatellites needed to be moved to next.

Then, during the transfer process, one of the cubes was chosen and CVT was done on it to find out where the microsatellite was moving to. After 50 iterations, a stable configuration was found, and the next position of the microsatellite was figured out. Because there were so many microsatellites, getting to the final configuration took a long time and a lot of changes.

To test the proposed trajectory optimization based on model predictive control, one of the microsatellites was sent from the starting point to the next desired target point at a certain time. The microsatellites can all get to where they need to go. After the target point was reached, the next iteration would happen. Because orbital dynamics can change, the microsatellite might not stay at the target point if there were no controls.

MPC was used in micro-planning to improve the performance of microsatellite swarms in terms of fuel use and resource use. This made the mission of the microsatellite swarm more useful. So, the benefits of the planning scheme, which was in line with engineering practice, were confirmed by simulation results about microsatellite’s paths that avoided collisions.

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