Coordinate systems

Unity is left-handed coordinate system with y-axis-up world frame while RaiSim is right-handed coordinate system with z-axis-up frame.

We follow RaiSim coordinate system to visualize RaiSim world. This can be done by the following code:

public static void SetTransform(GameObject obj, Vector3 rsPos, Quaternion rsQuat)
{
    // rsPos is position in RaiSim
    // rsQuat is quaternion in RaiSim
    
    var yaxis = rsQuat * new Vector3(0, 1.0f, 0);
    var zaxis = rsQuat * new Vector3(0, 0, 1.0f);

    Quaternion q = new Quaternion(0, 0, 0, 1);
    q.SetLookRotation(
        new Vector3(yaxis[0], -yaxis[2], yaxis[1]),
        new Vector3(-zaxis[0], zaxis[2], -zaxis[1])
    );

    obj.transform.localPosition = new Vector3(-rsPos.x, rsPos.z, -rsPos.y);
    obj.transform.localRotation = q;
}

In a short, we set Unity objects position as (-x_RS, z_RS, -y_RS) where subscript _RS indicates RaiSim position.