Dojo simulates systems in maximal coordinates.
For a mechanism with M
joints and N
bodies, the maximal representation z
can be efficiently converted to minimal coordinates:
where y^{(j)}
depends on the degree and type of joint. Note: this minimal representation does not stack coordinates followed by velocities, which is a common convention; instead, coordinates and velocities are grouped by joint.
Each minimal state comprises:
coordinates p
and velocities w
for both translational and rotational degrees of freedom.
In the case of a floating-base joint, the minimal-representation orientation is converted to modified Rodrigues parameters from a unit quaternion.