[ODE] Bug in slider joint, sliderGetInfo2()?

[Erin Catto]

I don't agree with that formulation. It seems to be based on a velocity
intuition. I think it is cleaner and more accurate to begin with a position
constraint and then differentiate by time.

For a slider joint you have points in each body that have no relative
translation in two directions:

(p2 - p1)*ax = 0
(p2 - p1)*ay = 0

where ax and ay are orthogonal axes embedded in either body. They are also
orthogonal to the axis of translation. Let's say they are embedded in body
1. Then take the derivative:

(vp2 - vp1)*ax + (p2 - p1)*(w1 % ax) = 0
(vp2 - vp1)*ay + (p2 - p1)*(w1 % ay) = 0

Here I use * for dot and % for cross. w1 and w2 are the angular velocities.

Now p1 and p2 are body fixed points located by the center of mass positions
and radius vectors:

p1 = x1 + r1
p2 = x2 + r2

The velocity of p1 and p2 is:

vp1 = v1 + w1 % r1
vp2 = v2 + w2 % r2

Substitute these into the velocity constraints:

v2*ax + ax * w2 % r2 - v1*ax - ax * w1 % r1 + d * (w1 % ax) = 0
v2*ay + ay * w2 % r2 - v2*ay - ay * w2 % r2 + d * (w1 % ay) = 0

where d = p2 - p1.

To form the Jacobian we need to isolate v1, w1, v2, and w2. Using the scalar
triple product identity a * b % x == b * x % a, we get:

J1 = [ax  r2%ax  -ax  ax%d-r1%ax]
J2 = [ay  r2%ay  -ay  ay%d-r1%ay]

This needs to be combined with the rotational constraint from my earlier
post. This gives a total of 5 constraints for a slider joint.

Erin

-----Original Message-----
From: ode-bounces at q12.org [mailto:ode-bounces at q12.org] On Behalf Of David
Black
Sent: Friday, May 13, 2005 9:23 AM
To: ode at q12.org
Subject: [ODE] Bug in slider joint, sliderGetInfo2()?

Hi,

I was browsing joint.cpp and I think I noticed a small problem with 
sliderGetInfo2(), ie in

  // remaining two rows. we want: vel2 = vel1 + w1 x c ... but this would
  // result in three equations, so we project along the planespace vectors
  // so that sliding along the slider axis is disregarded. for symmetry we
  // also substitute (w1+w2)/2 for w1, as w1 is supposed to equal w2.

  [SNIP]

    dCROSS (tmp, = REAL(0.5) * ,c,p);
    for (i=0; i<3; i++) info->J2a[s3+i] = tmp[i];
    for (i=0; i<3; i++) info->J2a[s3+i] = tmp[i];
    dCROSS (tmp, = REAL(0.5) * ,c,q);
    for (i=0; i<3; i++) info->J2a[s4+i] = tmp[i];
    for (i=0; i<3; i++) info->J2a[s4+i] = tmp[i];
    for (i=0; i<3; i++) info->J2l[s3+i] = -p[i];
    for (i=0; i<3; i++) info->J2l[s4+i] = -q[i];
  }

Shouldnt:
    dCROSS (tmp, = REAL(0.5) * ,c,p);
    for (i=0; i<3; i++) info->J2a[s3+i] = tmp[i];
    for (i=0; i<3; i++) info->J2a[s3+i] = tmp[i];
    dCROSS (tmp, = REAL(0.5) * ,c,q);
    for (i=0; i<3; i++) info->J2a[s4+i] = tmp[i];
    for (i=0; i<3; i++) info->J2a[s4+i] = tmp[i];

be (if the comment is to be believed and we are "substitute (w1+w2)/2 
for w1")
   
    dCROSS (tmp, = REAL(0.5) * ,c,p);
    for (i=0; i<3; i++) info->J1a[s3+i] = tmp[i];/*<<<<<<<<<<<<*/
    for (i=0; i<3; i++) info->J2a[s3+i] = tmp[i];
    dCROSS (tmp, = REAL(0.5) * ,c,q);
    for (i=0; i<3; i++) info->J1a[s4+i] = tmp[i];/*<<<<<<<<<<<<*/
    for (i=0; i<3; i++) info->J2a[s4+i] = tmp[i];

Hope this helps someone with there slider2 joints a little... Or am I 
misunderstanding this bit?

David

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