‫Welcome back.
‫So in the previous course, we, first of all had a carnival, and in that caramel we had two steering
‫wheel angles and we said that in this case, Delta one, the left steering wheel angle will be bigger
‫than Delta two.
‫And that is because we needed to have the angles that would make the wheels turn in such a way that
‫the car and all the wheels would have a common icy or instantaneous center of rotation.
‫And then what we did, we went from a car model to a bicycle model and then our bicycle model.
‫We only had one steering wheel angle.
‫Delta and s.m is center of mass.
‫And this is a common practice when extreme precision is not required.
‫The controller based on a bicycle model works well even for a four wheel car, because the difference
‫of the steering wheel angles Delta one minus Delta two is very small.
‫We then defined the longitudinal and the lateral velocities for the bicycle and we formulated the equations
‫of motion in the lateral direction.
‫And remember, there were two reference frames.
‫The first one was the fixed earth or inertial reference frame.
‫This is the frame that you're going to glue onto the ground and it's fixed to the ground.
‫It's not moving.
‫And then your car moves or your bicycle moves within this frame.
‫And then you also have a body frame, which we said we would glue onto the bicycle or car ride.
‫And then the longitudinal velocity was in the small X direction.
‫The lateral velocity was in the small Y direction.
‫We then took our equations of motion.
‫We applied the model of our bicycle to it, and then we got our state's basic equation where we had
‫two states.
‫Why dot, dot?
‫Why that was the lateral velocity in meters per second and that was then the angular velocity of the
‫car in radians per second.
‫And then what we did, we went from this state's basic equation system to this one.
‫So we expanded our state's base system.
‫We added two more states.
‫We had one additional state, which was the Oingo and another additional state, which was the big Y.
‫And this latter form here was used to compute the new states in the next sample time in the open loop
‫block right here in this control architecture.