Finding force required to apply a given angular acceleration from a given point and direction

Unity Engine
1

I’m trying to set up a physics-based “smart” flight system where you give a desired velocity and angular velocity and it uses its thrusters to match (I have another component to do more useful things like give it a position/angle rather than velocities). I’ve got all of the translational stuff down, but I’m having trouble figuring out how to calculate the force necessary per thruster to give it the desired angular velocity. Below is the commented translational code + the FixedUpdate that tells each of the thrusters what to do. Yes, the code is unoptimized and yes, I’m doing some stupid things for my own convenience. Sue me.

    void AdjustVelocity(Propulsion rocket, Vector3 tgVel)
    {
        rocket.Inp.Forward = 0;
        Vector3 up = Vector3.up;  // convenience shit, left over from when I was deciding whether or not I wanted to do everything in world space or object space (hint: I chose world space)
        Vector3 fwd = Vector3.forward;
        Vector3 right = Vector3.right;


        RelativeVelocity = (rocket.rig.velocity);  // debug/convenience shit - rocket.rig == the system's rigidbody
        AngularVelocity = (rocket.rig.angularVelocity);
        if (rocket.rig.useGravity)
        {
            RelativeVelocity += (Physics.gravity / 4f);  // make translations account for gravity - dunno why dividing by 4 works
        }


        rocket.Inp.Forward += (tgVel.z - RelativeVelocity.z) * Vector3.Dot(rocket.Origin.forward, fwd);  // tell the rocket's input controller what to do
        rocket.Inp.Forward += (tgVel.x - RelativeVelocity.x) * Vector3.Dot(rocket.Origin.forward, right);
        rocket.Inp.Forward += (tgVel.y - RelativeVelocity.y) * Vector3.Dot(rocket.Origin.forward, up);
    }


    void AdjustAngle(Propulsion rocket, Vector3 tgAng)
    {
        // snip help
    }


    void FixedUpdate()
    {
        for (int i = 0; i < Holders.Count; i++)  // Holders == List<Propulsion> == all thrusters attached to the root rigidbody
        {
            Propulsion rocket = Holders[i];  // Propulsion == thruster class
            if (!rocket || !rocket.enabled)
                continue;
            rocket.Inp.Forward = 0;  // rocket.Inp == input class, used in various places to
            // Adjust for angular velocity
            AdjustAngle(rocket, TargetAngularVelocity); // set up rotational forces
            rocket.ApplyForces();  // apply rotational forces


            // Adjust for translational velocity
            AdjustVelocity(rocket, TargetVelocity);  // set up translational forces
            rocket.ApplyForces();  // apply translational forces, done twice to accurately counteract rotations
        }
    }

The angular acceleration would be the angular difference between TargetAngularVelocity and rocket.rig.angularVelocity, but the question remains - how should I go about determining the force required to get there? I tried using F=T/(L*sin(theta)) where F = the force and T = the torque, but I’ve got a feeling I was doing it wrong - rotational dynamics isn’t exactly my strong point in physics. I spent a large portion of today kind of shooting in the dark to try to make it work, so any help would be greatly appreciated.

2

I’d take a leaf from how real rockets do it - use a PID controller pattern.

3

From what I understand, what I’m doing now is kind of the same concept as a PID controller (unless I’m misunderstanding what a PID controller actually does), and that doesn’t solve my issue. The issue I’m having is trying to programmatically determine which thrusters to fire based on their locations and forward vectors relative to the root object. For translation, this is easy because you can simply dot the forward vector and the world forward/up/right vectors to get a -1<x<1 value to see how much each thruster needs to fire to get there. However, rotation isn’t that simple, and that’s where I’m getting stuck. I was trying to reverse the torque equation to find how much each needs to fire, but that didn’t quite work (which I think is due to my lack of knowledge of rotational dynamics).

What my issue boils down to is how to determine the amount of force required from a point (in this case, a thruster) to apply the desired angular acceleration.