17_bicycle_example_2018_10_09_blank-1.pdf - Control Design From Start to Finish Why front wheel steering MECH 412 System Dynamics and Control Prof James

17_bicycle_example_2018_10_09_blank-1.pdf - Control Design...

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Control Design From Start to Finish Why front wheel steering? MECH 412 - System Dynamics and Control Prof. James Richard Forbes McGill University, Department of Mechanical Engineering October 9, 2018 1/22
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Front wheel steering versus rear wheel steering: where’s my racing combine! I We will show that a front-wheel steered vehicle is much easier to control than a rear-wheel steered vehicle. I Early on in the days of “vehicle development” it was not obvious that front-wheel steering was far superior from a control perspective. I Note, although our discussion is focused on autonomous driving , historically the controller was “the driver” (or “the pilot”). I Trial and error (i.e., a lot of building, testing, and tinkering of vehicle prototypes) lead to the conclusion that a vehicle should be front-wheel steered. I But why? Why is a rear-wheel steered vehicle so bad? Can a rear-wheel steered vehicle be controlled at all? 2/22
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A Similar Example Figure: X-29 versus CF-18 Hornet. X-29 has forward swept wings. (Credit: wikipidia.) I X-29 is open-loop unstable; can’t fly without a feedback control system. I Well, why bother with a forward swept wing then? I Highly maneuverable . 3/22
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A “Soviet” Example Figure: SU-47 versus SU-35. SU-37 has forward swept wings. (Credit: wikipidia.) Whatever Uncle Sam does, . . . 4/22
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Simplified Model - The Bicycle Model x 1 x 2 x 3 v r f s Figure: “Bicycle model” of a vehicle. I Point r : rear wheel contact point. I Point f : front wheel contact point. I Distance between points r and f is ` w (wheelbase). I Distance between points r and s is ` d . 5/22
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Bicycle Model Kinematics I Kinematics are ˙ x 1 ( t ) = cos x 3 ( t ) , ˙ x 2 ( t ) = sin x 3 ( t ) , ˙ x 3 ( t ) = ` w tan v ( t ) , where I x 1 is the horizontal position of point r (i.e., the “ x ” position), I x 2 is the vertical position of point r (i.e., the “ y ” position), I x 3 is the heading angle (i.e., “ ”), I v is the steering angle, and I is the velocity. I Measure x 2 and x 3 . I Control input is v , the steering angle. I Control output (regulated output) is z ( t ) = x 2 ( t ) + ` d sin x 3 ( t ) , a nonlinear function of the measurements.
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