Helicopter Auto-Hover: Solve the Challenge in Minimal Time

[zazz0000]

Homework Statement

Auto-Hover instructions for the AI

Relevant Equations

Uncertain at this time

Hello again everybody.
Encountered another challenge with the helicopter game we've been writing.

For sake of simplicity, let's consider this to be a one-dimensional problem.
I have a helicopter traveling at speed V and an arbitrary pitch angle A.
The acceleration of the helicopter is defined thrust t and mass m as t * cos(A) / m.
The pitch rate has a max of dA_MAX, and a maximum rate of change of ddA_MAX.
Also there's simplified air drag R = ½v^2 * dragCoefficient, although that might be a needless complication for this problem.

The goal is to provide AI instructions to come to a hover in as little time as possible.
So basically achieve V=0 and A=0 simultaneously.

Made a little animation to show the approximate scenario:

Any ideas would be appreciated.
Thanks in advance everybody.

 

[FactChecker]

A game doesn't need to have all the physics right, it just needs to appear believable. Your image shown is good enough. The actual physics and any associated AI control system (or real modern control system of any sort) would be much, much more complicated than necessary.

 

[zazz0000]

@FactChecker Appreciate your response.
The slight issue is that the game already has all the physics mentioned above in place. I certainly already have some number "cheats" in the game, but I guess this is where I would like to draw the line.
While the biggest reason for me posting here is to find a solution, there is a secondary motive, and that is to engage brilliant minds in a problem they have not faced before.

A great example is this thread of mine from some time ago:
Solving for ballistic trajectory

As cool as it was to get a solution for what seems to be a somewhat unique problem, observing the collective brainstorm that happened around it was much more enjoyable.

 

[FactChecker]

I can imagine what kind of deep water such a question would get into in this forum. There are a lot of experts here. If possible, can you describe what kind of physical models and controls are used in video games? I can't imagine it is the same as would be used in the real design of modern control laws.

 

[256bits]

Homework Statement:: Auto-Hover instructions for the AI
Relevant Equations:: Uncertain at this time

I have a helicopter traveling at speed V

V should have some relationship with pitch angle.

 

[zazz0000]

@256bits

The relationship of V to pitch angle (A) is the acceleration of the helicopter.
The acceleration of the helicopter is t * cos(A) / m, where t (thrust) and m (mass).
Both t and m are constant, so those can be disregarded, so we just have acceleration = cos(A)

Hope that makes sense,
Thanks

 

[256bits]

@256bits

The relationship of V to pitch angle (A) is the acceleration of the helicopter.
The acceleration of the helicopter is t * cos(A) / m, where t (thrust) and m (mass).
Both t and m are constant, so those can be disregarded, so we just have acceleration = cos(A)

Hope that makes sense,
Thanks

I don't get it.
Constant acceleration means the velocity of the helicopter is continuously changing due to the constant thrust T at pitch angle A.

 

[zazz0000]

@256bits

Hope I can clarify the problem a bit.
First the goal, which is to achieve a state where dV, V, and A are simultaneously equal to 0 in as little time t as possible.

So I believe that can be expressed as ₀∫^tdV dt = _{initial 0}∫^tsin(A) dt = -V_initial, at least if we disregard air drag R for now

In order to achieve that, I believe we need to find A_final, which is the greatest pitch angle made during the maneuver, occurring right before leveling the craft. If that angle is too high, the craft will drift backwards after levelling, too small and the craft drifts forward.

@FactChecker
Other than a simplified drag system, the physics are actually fairly realistic. It relies on NVidia Physx, a popular and common engine. Could you specify what I could be missing in what is already given?

 

[rcgldr]

One issue is that helicopter in steady forward flight needs to be pitched down a bit to compensate for drag. Another issue is what is the thrust to weight ratio of the helicopter, which will limit the maximum angle that can be used for acceleration | deceleration. In the case of model aerobatic helicopters, the thrust to weight ratio is quite high, as seen in this video (skip to 18 seconds into the video):

 

[256bits]

Hope I can clarify the problem a bit.
First the goal, which is to achieve a state where dV, V, and A are simultaneously equal to 0 in as little time t as possible.

what you can do, is to make a table of results for the ai to look up the necessary pitch vs velocity. Assume that both forward and backward pitches act symmetrically on acceleration.

start from a hovering 0 velocity, do a pitch and record the velocity and acceleration for a period of time t.
work up to maximum pitch, recording results of v and t vs pitch to make the table.

then for deceleration,, the AI looks up from the table the necessary pitch characteristic to come to a hover.