A previous article described the formation of a UAV swarm when aligning to a point, line and plane. While the shape formations in these cases are known, the size depends on the number of units in the formation, the minimum distance between units, the presence of external infringements and constraints and the margin required to maintain from such constraints. The article also described the ability to distribute drones to spread as close to the constraints using self-organizing maps which is essentially drawing each unit to the nearest real-world element that imposes a constraint. This establishes the maximum boundaries for the space that the UAV swarm occupies with the core being provided by the point, line, or plane that the units must align to. Given the minimum-maximum combination and the various thresholds for the factors cited, the size of the shape for the UAV swarm at a point of time can be determined.

This article argues that the vectorization, clustering and model does not just apply to the UAV swarm formation in space but also applies to maintaining a balance between constraints and sizing and determining the quality of the formation, using Vector-Search-as-a-judge.  The idea is borrowed from LLM-as-a-judge which helps to constantly evaluate and monitor many AI applications of various LLMs used for specific domains including Retrieval Augmented Generation aka RAG based chatbots. By virtue of automated evaluation with over 80% agreement on human judgements and a simple 1 to 5 grading scale, the balance between constraints and sizing can be consistently evaluated and even enforced. It may not be at par with human grading and might require several auto-evaluation samples but these can be conducted virtually without any actual flights of UAV swarms. A good choice of hyperparameters is sufficient to ensure reproducibility, single-answer grading, and reasoning about the grading process. Emitting the metrics for correctness, comprehensiveness and readability is sufficient in this regard. The overall workflow for this judge is also similar to the self-organizing map in terms of data preparation, indexing relevant data, and information retrieval.

As with all AI models, it is important to ensure AI safety and security to include a diverse set of data and to leverage the proper separation of the read-write and read-only accesses needed between the model and the judge. Use of a feedback loop to emit the gradings as telemetry and its inclusion into the feedback loop for the model when deciding on the formation shape and size, albeit optional, can ensure the parameters of remaining under the constraints imposed is always met.

The shape and size of the UAV formation is deterministic at a point of time but how it changes over time depends on the selection of waypoints between source and destination as well as the duration permitted for the swarm to move collectively or stream through and regroup at the waypoint. A smooth trajectory was formed between the waypoints and each unit could adhere to the trajectory by tolerating formation variations.

Perhaps, the biggest contribution of the vectorization of all constraints in a landscape is that a selection of waypoints offering the least resistance for the UAV swarm to keep its shape and size to pass through can be determined by an inverse metric to the one that was used for self-organizing maps.