Date: January 29, 2024

Topic: Bicycle Model Representation

Recall

Cars can be approximated by a bicycle model

We can steer the car (turning angle) or move forward (forward movement)

Notes

From Bicycle to Car

Approximating cars from a bicycle

• We use the bicycle to approximate how a car moves (car has twice the wheels of a bicycle, but same motion range)

Bicycle Model Controls

• Turning the front wheel to the left has a positive steering angle, vice versa
• Forward movement is measured from the rear axle in point A to point B - the rear axle is fixed
• Position is taken from the rear axle

Robot Pose

• Robots have position ($x,y$) and orientation $\theta$
• A and C, B and E have the same orientations respectively
• D and E have the same position
• None of them have the same pose (otherwise they will be on top of each other)

<aside> 💡 Steering angle $\alpha$ references the front wheel angle from where the car is facing, orientation $\theta$ is the angle of the car relative to the $x$-axis

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In a straight motion, we can use trigonometry to get the new position since no turning is done.

In compound motion, 2 circular tracks will be left behind

Movement

Simple Movement (Diagonal Motion)

• We can either turn the robot or make it move forward
• Use trigonometry to calculate the distance moved in either axis, and add it to the original position
• In a straight movement, 1 track will be left by the wheels

Compound Movement (Turning angle + forward motion)

• 2 tracks will be left behind in compound motion.
  • The front wheel creates the outer track
  • The back wheel creates the inner track

<aside> 📌 SUMMARY: Approximating a car with a bicycle model allows us to calculate the new offset from a center given the length of the car, orientation and the steering angle for a set distance

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