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‫Welcome back.

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‫So in the previous course, we, first of all had a carnival, and in that caramel we had two steering

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‫wheel angles and we said that in this case, Delta one, the left steering wheel angle will be bigger

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‫than Delta two.

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‫And that is because we needed to have the angles that would make the wheels turn in such a way that

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‫the car and all the wheels would have a common icy or instantaneous center of rotation.

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‫And then what we did, we went from a car model to a bicycle model and then our bicycle model.

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‫We only had one steering wheel angle.

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‫Delta and s.m is center of mass.

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‫And this is a common practice when extreme precision is not required.

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‫The controller based on a bicycle model works well even for a four wheel car, because the difference

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‫of the steering wheel angles Delta one minus Delta two is very small.

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‫We then defined the longitudinal and the lateral velocities for the bicycle and we formulated the equations

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‫of motion in the lateral direction.

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‫And remember, there were two reference frames.

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‫The first one was the fixed earth or inertial reference frame.

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‫This is the frame that you're going to glue onto the ground and it's fixed to the ground.

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‫It's not moving.

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‫And then your car moves or your bicycle moves within this frame.

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‫And then you also have a body frame, which we said we would glue onto the bicycle or car ride.

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‫And then the longitudinal velocity was in the small X direction.

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‫The lateral velocity was in the small Y direction.

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‫We then took our equations of motion.

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‫We applied the model of our bicycle to it, and then we got our state's basic equation where we had

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‫two states.

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‫Why dot, dot?

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‫Why that was the lateral velocity in meters per second and that was then the angular velocity of the

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‫car in radians per second.

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‫And then what we did, we went from this state's basic equation system to this one.

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‫So we expanded our state's base system.

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‫We added two more states.

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‫We had one additional state, which was the Oingo and another additional state, which was the big Y.

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‫And this latter form here was used to compute the new states in the next sample time in the open loop

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‫block right here in this control architecture.