Designing the trajectory of microsatellite swarms from the macro-micro perspective

Space: science and technology (2022). DOI: 10.34133/2022/9802195″ width=”800″ height=”530″/>

Diagram of collision avoidance between microsatellites. Credit: Space: Science & Technology (2022). DOI: 10.34133/2022/9802195

As an emerging multi-satellite cooperative flight mode, the microsatellite swarm has become an important future research problem for distributed space systems. It offers low costs, fast response and collaborative decision-making. To address swarm coordination for autonomous agents, a probabilistic escort approach was explored, which included sub-swarms with different mission objectives.

Probabilistic swarm guidance allows autonomous microsatellites to independently generate their individual trajectories so that the entire swarm converges to the desired distribution shape. However, avoiding crowds is essential to reduce the likelihood of collisions between microsatellites, which adds challenges to the design of the collision avoidance algorithm.

In a research paper recently published in Space: Science & TechnologyBing Xiao, of the School of Automation, Northwestern Polytechnical University, proposed a Centroidal Voronoi tessellation (CVT) and Model Predictive Control (MPC) based synthesis method, aiming to achieve macro-micro trajectory optimization of a microsatellite swarm.

The author formulated the transfer model of swarm microsatellites in 3D space and introduced the probabilistic swarm guidance law. Since it was essential to avoid crowds to reduce the probability of collisions between microsatellites, the safety analysis of collision avoidance was performed based on finding the lower limit of the minimum distance between all microsatellites at any time.

To determine the collision-free guidance trajectory of each microsatellite from its current position to the target space, a collision avoidance algorithm was needed. However, with high-level coordination using the macroscopic models, collision-free trajectories were very difficult to generate. Therefore, the author presented a synthesis method, in which the trajectory planning was divided into macro planning and micro planning.

Next, the author presented the details of macroplanning and microplanning of the microsatellite swarm, respectively. In the microsatellite swarm macro planning, the target position of each microsatellite was determined by the centroid generated by the CVT algorithm, and all microsatellites moved to the corresponding centroid until the algorithm converges.

The final distribution of the microsatellite swarm in space was obtained according to the location of the center of gravity. In the microplaning of the microsatellite swarm, MPC was used to generate the optimal trajectories for each step and finally reached the specified position in the target cube.

In particular, the author established the orbital dynamics model taking into account J2 disruption and implemented the convexification of collision avoidance constraints in the process of swarm reconfiguration. To achieve the real-time trajectory planning, model prediction control was introduced, which used receding horizon to update the optimal trajectories based on the current status information. Significantly, the proposed method can not only realize collision avoidance of microsatellite swarm maneuvers at the macro level, but also provide optimal trajectories for each microsatellite of swarming individuals at the micro level.

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Finally, the numerical simulation was performed to verify the proposed macro-micro trajectory planning method of microsatellite swarm. The author provided a virtual central microsatellite and designed a large-scale (300) microsatellite swarm with an omnidirectional flight configuration. The CVT algorithm was used to divide regions, thus determining the position of the microsatellites to be transmitted next.

Then one of the cubes was selected in the transfer process and CVT was performed on it to determine the transfer position of the microsatellite. After 50 iterations, a stable configuration was obtained and the position where the microsatellite moved at the next moment was determined. Due to the large scale of the microsatellite swarm, the process to reach the final configuration required many transitions.

To verify the proposed trajectory optimization based on model predictive control, one of the microsatellites was selected at some point from the initial point to the next desired target. The individual microsatellites can reach the desired point well. After the desired point was reached, the next iteration would be performed and due to the influence of the orbital dynamics, the microsatellite cannot remain the target without control constraints.

To make the mission of microsatellite swarm more practical, MPC was used in microplanning to improve the performance of microsatellite swarm in terms of fuel consumption and resource utilization. For example, simulation results on the collision-free guidance path of microsatellites confirmed the advantages of the planning scheme, which corresponded well with technical practice.


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More information:
Xiwei Wu et al, Centroidal Voronoi Tessellation and Model Predictive Control-based macro-micro trajectory optimization of microsatellite swarm, Space: Science & Technology (2022). DOI: 10.34133/2022/9802195

Provided by Beijing Institute of Technology Press Co., Ltd

Quote: Design of the trajectory of microsatellite swarms from the macro-micro perspective (2022, October 21) retrieved October 22, 2022 from https://phys.org/news/2022-10- trajectory-microsatellite-swarms-macro-micro-perspective. html

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