Pose Control of a differential-drive robot via a Proportional-Derivative Controller considering only Kinematics of the robot is studied here along with a MATLAB Simulink Demo.
A derivative term in the forward path (acting on the error) will give bad response to a step input and noise. Wouldn't it be better to use velocity feedback instead?
You want your robot to move on a curved path, so one wheel has to rotate faster than the other one while they both move forward, so you use the same term v for both but you use plus and minus w to make the command rpm of the wheels be different. Angular velocity is equal to the linear velocity of the wheel centroid divided by the wheel radius if we assume no slipping happens. If you mean why adding v and w together since they are 2 different entities, there is actually a coefficient of 1 behind w (so it is like v + 1*w) but this 1 has a unit of length which allows for v and 1*w to be added together.
