CODEWITHSUNDEEP
mathrotationquaternions
Suedocode
Suedocode

Reputation: 2534

Angular Velocity to rotate Heading towards Point

I have a 3D point in space, and I need to know how to pitch/yaw/roll my current heading (in the form of a 3d unit vector) to face a point. I am familiar with quaternions and rotation matrices, and I know how to represent the total rotation necessary to get my desired answer.

However, I only have control over pitch, yaw, and roll velocities (I can 'instantaneously' set their respective angular velocities), and only occasional updates on my new orientation (once every second or so). The end goal is to have some sort of PID controller (or three separates ones, but I suspect it won't work like that) controlling my current orientation. the end effect would be a slow (and hopefully convergent) wobble towards a steady state in the direction of my destination.

I have no idea how to convert the current desired quaternion/rotation matrix into a set of pitch-yaw-roll angular velocities (some sort of quaternion derivative or something?). I'm not even sure what to search for. I'm also uncertain how to apply a PID controller to this system, because I suspect there will need to be one controller for the trio as opposed to treating them each independently (although intuitively I feel this should be possible). Can anyone offer any guidance?

As a side note, if there is a solution that just involves a duo (pitch/yaw, roll/pitch, etc), then that works just fine too. I should only need 2 rotational degrees of freedom for this, but that is further from a realm that I am familiar with so I was less confident forming the question around it.

Upvotes: 1

Views: 1115

Answers (1)

Gouda
Gouda

Reputation: 1005

First take a look if your problem can be solved using quaternion SLERP [1], which can let you specify a scalar between 0 and 1 as the control to move from q1-->q2.

If you still need to control using the angular rotations then you can calculate the error quaternion as Nico Schertler suggested. From that error quaternion you can use the derivative property of the quaternion (Section 4 of http://www.ecsutton.ece.ufl.edu/ens/handouts/quaternions.pdf [2]) to work out the angular rates required.

I'm pretty sure that will work, but if it does not you can also look at using the SLERP derivative (eq. 23 of http://www.geometrictools.com/Documentation/Quaternions.pdf [3]) and equating that to the Right-Hand-Side of the equation in source [2] to again get angular rates. The disadvantage to this is that you need code implementations for the quaternion exponentiation and logarithm operations.

Upvotes: 0

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