# How do I apply PID to CFrame lerping?

So I saw the tutorial based on PID and I was amazed at how you can apply it to non-physics based objects like a GUI.

I think it would be really cool if I could apply it to CFrame lerping in order to obtain physics like results specifically for moving a turret so it oscillates and feels more realistic and doesn’t always 100% match the target.

Here’s the resource I’m wanting to apply PID to, you can download it experiment if you want.

Here is the code bit related to lerping.

if step and self.ConstantSpeed then
local angularDistance = VectorUtil.AngleBetween(currentRotation.LookVector,goalRotationCFrame.LookVector)
local estimatedTime = self.AngularSpeed/angularDistance
elseif step then
end

local newRotationCF = currentRotation:lerp(goalRotationCFrame, adjustedLerpAlpha or self.LerpAlpha)

self.JointMotor6D.C0 = CFrame.new(originalC0Position)*newRotationCF

So yeah given two CFrames the current and the goal how can I adjust the lerp alpha in a RunService connection to apply a “Force” through PID.

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NVM, it’s not possible with the current setup because of how lerping towards the goal works where it’ll only be in a value of 0-1 so it’s hard to find the directionality of the angular velocity we want to control with PID and apply to the current rotation.

I’ll take a break from this problem for now, I believe the solution is to align the CFrame axis like how the AlignOrientation bodymover works by getting the rotation between two vectors of the axis of the attachments.

This is a really cool idea! I might give it a shot and add it as an example use case. If I do I’ll comment here

Edit: it works quite well, but it definitely needs a PD controller to deal with the oscillations. But with a PD controller it’s super cool! I’ll probably use it as the main example when I cover D control.

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Found the solution, using everyone’s favorite axis angle rotation representation

All CFrames no AlignOrientation

Code
local RunService = game:GetService("RunService")

local part = script.Parent
local target = workspace.gun.Target --random part in a model

function p_controller(kP, set_point, process_value)
local e = set_point - process_value
local CO = kP * e
return CO
end

local partAngularVelocity = Vector3.new(0,0,0)
local goal = Vector3.new()

RunService.Heartbeat:Connect(function(dt)
local partCF = part.CFrame
local targetCF = target.CFrame
local differenceCF = partCF:ToObjectSpace(targetCF)
local axis, angle = differenceCF:ToAxisAngle()
--obtain rotation difference in form of torque
--axis is well yeah rotation axis
local test = axis*angle
--go towards goal rotation of zero difference
local outputAcceleration = p_controller(0.1,goal,test)

--add torque difference into the parts current velocity
partAngularVelocity += -outputAcceleration*dt

--Convert current angular velocity into CFrame representation
local newaxis = partAngularVelocity.Unit
local newangle = partAngularVelocity.Magnitude

local stuff
-- if there is a rotation or else it's a .Unit Nil error
if newaxis == newaxis then
stuff = CFrame.fromAxisAngle(newaxis,newangle)
else
stuff = CFrame.new()
end
part.CFrame *= stuff-stuff.Position

end)

Yeah, it definitely needs something to stop the oscillations. but wow it does look smooth as if it has physics enabled. Seems like D control will be required looking forward to your follow up tutorial!

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Nice!

Here’s what I’ve come up with, it only rotates on the yaw axis, I was thinking it’d be interesting to have yaw and pitch be different “hinges” / Motor6Ds:

TurretController
local RunS = game:GetService("RunService")
local PIDController = require(game.ServerStorage.PIDController)
PIDController.update_time_on(RunS.Heartbeat)

local turret = script.Parent
local turretBase = turret.Base
local yawBase = turret.YawAssembly.YawBase
local yawMotor = turret.Base.YawMotor6D

local target = game.Workspace.Target

local yaw_velocity = 0
local yaw_controller = PIDController.new_PID_controller(10, 0, 3, .1)

RunS.Heartbeat:Wait()

RunS.Heartbeat:Connect(function(dt)
local object_horizontal_offset = yawBase.CFrame:PointToObjectSpace(target.Position)
local object_yaw_angle = math.atan2(-object_horizontal_offset.X, -object_horizontal_offset.Z)

local yaw_force = yaw_controller(0, object_yaw_angle)
yaw_velocity += yaw_force * dt

yawMotor.C1 *= CFrame.Angles(0, yaw_velocity * dt, 0)
end)
PIDController Module

local t = tick()

local update_c

function update_time()
t = tick()
end

function update_time_on(event)
if update_c then
update_c:Disconnect()
end

update_c = event:Connect(update_time)

return update_c

end

function new_P_controller(kP)
return function(SP, PV)
local e = SP - PV
return kP * e
end
end

function new_I_controller(kI, example_value)
local prev_t = t
local sum_e = 0 * (example_value or 0)

return function(SP, PV)
local dt = t - prev_t
prev_t = t

local e = SP - PV

sum_e += e * dt
return kI * sum_e
end

end

function new_D_controller(kD, initial_error)
local prev_t = t
local prev_e = initial_error

return function(SP, PV)
local dt = t - prev_t
prev_t = t

local e = PV - SP
local de = e - prev_e

local de_dt = de / dt

prev_e = e
return kD * -de_dt
end

end

function new_PID_controller(kP, kI, kD, initial_error)
local P_controller = new_P_controller(kP)
local I_controller = new_I_controller(kI, initial_error)
local D_controller = new_D_controller(kD, initial_error)

return function(SP, PV)
return P_controller(SP, PV)
+ I_controller(SP, PV)
+ D_controller(SP, PV)
end

end

local Module = {
update_time = update_time,
update_time_on = update_time_on,
new_P_controller = new_P_controller,
new_I_controller = new_I_controller,
new_D_controller = new_D_controller,
new_PID_controller = new_PID_controller,
}
return Module

I haven’t put the PID module on the tutorial thing because I’m not quite happy with it yet, I want to polish it a bit more before releasing it properly.

EDIT: Added the pitch Motor6D w/ a separate controller, here’s a video:

... and here's the updated TurretController

local RunS = game:GetService("RunService")
local PIDController = require(game.ServerStorage.PIDController)
PIDController.update_time_on(RunS.Heartbeat)

local turret = script.Parent
local yawBase = turret.YawAssembly.YawBase
local pitchBase = turret.YawAssembly.PitchAssembly.PitchBase
local yawMotor = turret.YawBase.YawMotor6D
local pitchMotor = turret.YawAssembly.PitchBase.PitchMotor6D

local target = game.Workspace.Target

local yaw_velocity = 0
local pitch_velocity = 0
local yaw_controller = PIDController.new_PID_controller(8, 0, 5, .1)
local pitch_controller = PIDController.new_PID_controller(10, 0, 2, .1)

RunS.Heartbeat:Wait()

RunS.Heartbeat:Connect(function(dt)
local object_yaw_offset = yawBase.CFrame:PointToObjectSpace(target.Position)
local object_yaw_angle = math.atan2(-object_yaw_offset.X, -object_yaw_offset.Z)
local yaw_force = yaw_controller(0, object_yaw_angle)
yaw_velocity += yaw_force * dt
yawMotor.C1 *= CFrame.Angles(0, yaw_velocity * dt, 0)

local object_pitch_offset = pitchBase.CFrame:PointToObjectSpace(target.Position)
local object_pitch_angle = math.atan2(object_pitch_offset.Y, -object_pitch_offset.Z)
local pitch_force = pitch_controller(0, object_pitch_angle)
pitch_velocity += pitch_force * dt
pitchMotor.C1 *= CFrame.Angles(pitch_velocity * dt, 0, 0)
end)

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