[1letterunixname]

Hand-waving about "people" == "simpler" == "better" aside, read about TCAS.

Humans in the loop are a SPoF if they're there:

1. Solely to read information over a lossy, slow medium like analog radio. Digital data between ground and air systems should be the primary means of comms with voice radio as a backup channel for clarification and stating intent.

2. To flawlessly plan and avoid collisions between dozens of objects moving at high speed in 4 dimensions. Never going to happen. These should be done and verified mechanically, continuously.

Humans should be guiding and assisting mechanical, reliable automation of decision-making rather than playing telephone or doing long division on paper when calculators exist.

[hef19898]

>> four dimensions

You're sure about that?

[defrost]

They likely mean { X, Y, Z, T } three spatial dimensions and time which are four orthogonal dimensions.

That said, it makes the "moving in" redundant and is shy a few dimensions if you want to go full descriptive phase space diagraming given velocity and acceleration in each spatial dimension are missing.

[hef19898]

It is still just changing vectors and speed in three dimensional space so...

[defrost]

I suggest you take your objections up with the authors of, say,

A Four-Dimensional Space-Time Automatic Obstacle Avoidance Trajectory Planning Method for Multi-UAV Cooperative Formation Flight

or any number of other similar papers.

Many prefer to think of an objects path as a trajectory in space-time (four dmensions) and for two ojects to "collide" their paths must coincide within that 4-D space within an Epsilon for some value of WTF.

Other common examples of working in N dimensional spaces for values of N bigger than someones mother include: https://en.wikipedia.org/wiki/Phase_space

[hef19898]

I never considered time as a 4th dimension in that sense. TIL.

Fun fact, now I can claim to plan in the 4th dimension by using lead times in supply chain planning!

[thaumasiotes]

But as ... you yourself ... note above, the planes aren't moving in four dimensions. If time is one of the dimensions, all the planes are doing is existing.

[defrost]

A plane (P1)'s past positions and projected future positions form a continuous path in R^4 (four dimensional euclidean space).

Another plane (P2)'s travel through various {X,Y,Z} positions at various times forms another path in R^4.

If those paths come close to each other then P1 and P2 are close in both space and time - ie. they are very close to a collision.

Collision detection and avoidance is problem laid out and (hopefully) solved in an R^4 euclidean space.

(at the very least - throw in some more independant variables that parameterise motion and you've got a higher order puzzle

Eg: Collision avoidance for two robot arms with 6 or 7 degrees of freedom each is a maze solving puzze in 12 or 14 dimensions).