[ODE] fixed path constraint

Erin Catto erincatto at sbcglobal.net
Wed Jul 6 20:57:48 MST 2005


It is best to formulate constraints like other joints and let ODE's solver
compute the appropriate forces to make the body movements honor the
constraints.

A planar joint can be formed using three constraint equations:

- one to prevent motion along the plane normal
- two to prevent rotation perpendicular to the normal

dot(p2 - p1, n1) = 0
dot(tx2, n1) = 0
dot(ty2, n1) = 0

where

p1 = x1 + r1
p2 = x2 + r2

and

x1, x2: body positions
r1, r2: body anchor points
n1: plane normal bound to body 1
tx2, ty2: in plane basis vectors bound to body2

Now you just need to differentiate the constraint equations to get the
velocity Jacobians. These can be used to create a new joint in ODE.

Erin




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