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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.