BicycleMotion.md (1137B)
1 # Bicycle Motion 2 3 **Source:** Probabilistic Robotics 4 5 **Chapter:** 5 6 7 **Definition:** Bicycle motion is a motion system that accounts for two wheels along with the rotation of the front wheel. 8 9 Given that car wheels are generally not independent wrt their lateral counterparts, this model can be used to model the motion of cars. 10 11 ## The Model 12 13 ### Controls 14 15 There are two controls, the steering angle ($\alpha$), and the forward movement ($d$). 16 17 #### Steering Angle 18 19 Positive steering angle is angling the wheels to the left. 20 21 Negative steering angle is angling the wheels to the right. 22 23 If we consider a top down view of a car where the car is facing to our right, we the steering angle matches our notion of radians on a unit circle. 24 25 #### Forward Movement 26 27 The forward movement describes the distance the robot will travel in a given step. 28 29 ### Pose 30 31 The pose of a robot is described by the (x,y) coordinates and theta. 32 33 ## Position Calculation 34 35 ### Basic Movement 36 37 This is simple trig. 38 39 $y_{dist} = sin(\theta) * d$ 40 $x_{dist} = cos(\theta) * d$ 41 42 $y_{new} = y + y_{dist}$ 43 $x_{new} = x + x_{dist}$ 44 45 This assumes no steering angle.