Calculate Prediction Step: Quiz

Calculate Prediction Step Quiz

Calculate Prediction Step

Given the car’s last position was at (102 m, 65 m) with a heading of (5pi)/8 radians, the car’s velocity was 110 m / s, and the car’s yaw rate was pi/8 rad / s over the last 0.1 seconds, what is the car’s new position and heading?

(x, y, theta) = (97.59, 75.08, (51pi)/80)

(x, y, theta) = (101.93, 65.16, (51pi)/80)

(x, y, theta) = (101.84, 65.07, (51pi)/80)

(x, y, theta) = (97.79, 75.16, (49pi)/80)

SOLUTION:

(x, y, theta) = (97.59, 75.08, (51pi)/80)

Recall the equations for updating x, y and the yaw angle when the yaw rate is not equal to zero:

$x_f = x_0 + \dfrac{v}{ \dot{\theta}}[sin(\theta_0 + \dot{\theta}(dt)) - sin(\theta_0)]$

$y_f = y_0 + \dfrac{v}{ \dot{\theta}}[cos(\theta_0) - cos(\theta_0 + \dot{\theta}(dt))]$

$\theta_f = \theta_0 + \dot{\theta}(dt)$