The formula for the base's velocity and the wheel's velocity should be derived so that forward should be in the direction of +x_b of the base and negative side way in the direction of +y_b of the base. The rotation is positive respecting the right-handed system. The only missing info is the direction of the rollers. See below
Based on Coppeliasim, I've determined the positive directions of the wheels, and I have shown them in the picture. When the wheel rotates counter-clock wise, the linear velocity in the negative direction of the base's frame. The problem I have with the above configuration is that I always end up with reverse movement in terms of y-axis and rotation. Any suggestions regarding the rollers?
