[ODE] matching body orientation

[Graham Fyffe]

I've had a similar desire, except I wanted to have a soft orientation
AND position constraint.  I would call it the "gumdrop" joint.  You
can twist it, you can pull on it, and it always springs back to the
initial configuration.  I wanted to be able to specifiy the
springiness in each axis of rotation and each axis of linear motion. 
I'm not sure if this is doable with only one value of 'beta', but
admittedly I have only a vague notion of how the constraint Jacobian
really works into things.

- Graham




On 5/8/05, Erin Catto <erincatto at sbcglobal.net> wrote:
> I'm not sure how to do this in ODE, but in principle you need to create 3
> angular constraints.
> 
> Let x, y, z be orthonormal axes fixed in the body. Let
> xr, yr, and zr be the columns of the rotation matrix formed from your
> reference quaternion (qd). Now form 3 angular constraints:
> 
> dot(x, zr) = 0
> dot(y, zr) = 0
> dot(z, xr) = 0
> 
> This should be a sufficient set of equations. Note that a 180 degree flip is
> possible, so you have to ensure the reference quaternion is not too far from
> the current body quaternion.
> 
> Now to form the velocity constraint, you just differentiate the angular
> constraints with respect to time:
> 
> w % x * zr + x * wr % zr = 0
> w % y * zr + y * wr % zr = 0
> w % z * xr + z * wr % xr = 0
> 
> where * is the dot product, % is the cross product, w is the angular
> velocity of the body, and wr is the desired angular velocity. Using the
> scalar triple product identity:
> 
> x % zr * w = - x * wr % zr
> y % zr * w = - y * wr % zr
> z % xr * w = - z * wr % xr
> 
> This is linear in w and can be written in matrix form as
> 
> J w = b
> 
> where J is the constraint Jacobian and b is the reference constraint
> velocity.
> 
> You will also need to stabilize the velocity constraint by feeding the
> angular constraint error into the right hand side by adjusting b, for
> example:
> 
> b1 = b1 - beta * dot(x, zr)
> 
> where beta is called ERP in ODE speak (and the Baumgarte parameter in the
> literature).
> 
> I'm not sure if this is implemented in ODE, but it shouldn't be difficult.
> 
> Erin
> 
> -----Original Message-----
> From: ode-bounces at q12.org [mailto:ode-bounces at q12.org] On Behalf Of Daan
> Nusman
> Sent: Saturday, May 07, 2005 7:49 AM
> To: ODE Mailing List
> Subject: [ODE] matching body orientation
> 
> Hi everyone,
> 
> First some background information (for the interested, you can skip
> this): for my thesis I'm working on connecting an experimental full-body
> motion capture suit, that uses inertial sensors, to an ODE articulated
> human body, in a distributed virtual environment. I've created a ragdoll
> that works quite well, using ball joints and hinge joints. Now I'm
> looking for a way to control the ragdoll using the motion capture suit.
> The suit measures the absolute orientation of each limb, represented by
> quaternions. So onto..
> 
> THE QUESTION: I've got some quaternion 'qd' and an ODE body with
> quaternion 'qb'. I want the body to (try to) orient itself from qb to qd
> during the simulation. How can I best do this?
> 
> One option seems to be to take the 'forward' vectors of qd and qb, use
> the cross product on them to find the torque axis, and use the dot
> product to find out how much force is required (how long the torque axis
> should be). This is essentially a spring as described in section 7.5 of
> the manual, but only angular, I guess. So the problems are: finding a
> usable spring constant, the body has to come up to speed in several
> steps, and possible extra forces might lead to the body never reaching
> the orientation or speed at all. Another problem is that the body won't
> match the rotation along the forward axis. I'd have to add torque along
> the forward axis, but I can't figure out how much that would be.
> 
> I've looked at the angular motor, but I must admit I don't really
> understand the user mode. Does anyone know if the amotor is suitable to
> do this?
> - should I attach the amotor to only one body?
> - what kind of axes should I set? How should I relate the velocity of
> the axes to my desired quaternion?
> 
> Any help would be greatly appreciated,
> Daan Nusman
> www.keepitsimple.nl
> 
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