14. Parameter Optimization
Parameter Optimization - Artificial Intelligence for Robotics
In the following quiz you'll implement the twiddle algorithm for a PID controller. Additionally, the robot has a steering drift!
Start Quiz:
# ----------------
# User Instructions
#
# Implement twiddle as shown in the previous two videos.
# Your accumulated error should be very small!
#
# You don't have to use the exact values as shown in the video
# play around with different values! This quiz isn't graded just see
# how low of an error you can get.
#
# Try to get your error below 1.0e-10 with as few iterations
# as possible (too many iterations will cause a timeout).
#
# No cheating!
# ------------
import random
import numpy as np
import matplotlib.pyplot as plt
# ------------------------------------------------
#
# this is the Robot class
#
class Robot(object):
def __init__(self, length=20.0):
"""
Creates robot and initializes location/orientation to 0, 0, 0.
"""
self.x = 0.0
self.y = 0.0
self.orientation = 0.0
self.length = length
self.steering_noise = 0.0
self.distance_noise = 0.0
self.steering_drift = 0.0
def set(self, x, y, orientation):
"""
Sets a robot coordinate.
"""
self.x = x
self.y = y
self.orientation = orientation % (2.0 * np.pi)
def set_noise(self, steering_noise, distance_noise):
"""
Sets the noise parameters.
"""
# makes it possible to change the noise parameters
# this is often useful in particle filters
self.steering_noise = steering_noise
self.distance_noise = distance_noise
def set_steering_drift(self, drift):
"""
Sets the systematical steering drift parameter
"""
self.steering_drift = drift
def move(self, steering, distance, tolerance=0.001, max_steering_angle=np.pi / 4.0):
"""
steering = front wheel steering angle, limited by max_steering_angle
distance = total distance driven, most be non-negative
"""
if steering > max_steering_angle:
steering = max_steering_angle
if steering < -max_steering_angle:
steering = -max_steering_angle
if distance < 0.0:
distance = 0.0
# apply noise
steering2 = random.gauss(steering, self.steering_noise)
distance2 = random.gauss(distance, self.distance_noise)
# apply steering drift
steering2 += self.steering_drift
# Execute motion
turn = np.tan(steering2) * distance2 / self.length
if abs(turn) < tolerance:
# approximate by straight line motion
self.x += distance2 * np.cos(self.orientation)
self.y += distance2 * np.sin(self.orientation)
self.orientation = (self.orientation + turn) % (2.0 * np.pi)
else:
# approximate bicycle model for motion
radius = distance2 / turn
cx = self.x - (np.sin(self.orientation) * radius)
cy = self.y + (np.cos(self.orientation) * radius)
self.orientation = (self.orientation + turn) % (2.0 * np.pi)
self.x = cx + (np.sin(self.orientation) * radius)
self.y = cy - (np.cos(self.orientation) * radius)
def __repr__(self):
return '[x=%.5f y=%.5f orient=%.5f]' % (self.x, self.y, self.orientation)
############## ADD / MODIFY CODE BELOW ####################
# ------------------------------------------------------------------------
#
# run - does a single control run
def make_robot():
"""
Resets the robot back to the initial position and drift.
You'll want to call this after you call `run`.
"""
robot = Robot()
robot.set(0, 1, 0)
robot.set_steering_drift(10 / 180 * np.pi)
return robot
# NOTE: We use params instead of tau_p, tau_d, tau_i
def run(robot, params, n=100, speed=1.0):
x_trajectory = []
y_trajectory = []
err = 0
prev_cte = robot.y
int_cte = 0
for i in range(2 * n):
cte = robot.y
diff_cte = cte - prev_cte
int_cte += cte
prev_cte = cte
steer = -params[0] * cte - params[1] * diff_cte - params[2] * int_cte
robot.move(steer, speed)
x_trajectory.append(robot.x)
y_trajectory.append(robot.y)
if i >= n:
err += cte ** 2
return x_trajectory, y_trajectory, err / n
# Make this tolerance bigger if you are timing out!
def twiddle(tol=0.2):
# Don't forget to call `make_robot` before every call of `run`!
p = [0, 0, 0]
dp = [1, 1, 1]
robot = make_robot()
x_trajectory, y_trajectory, best_err = run(robot, p)
# TODO: twiddle loop here
return p, best_err
params, err = twiddle()
print("Final twiddle error = {}".format(err))
robot = make_robot()
x_trajectory, y_trajectory, err = run(robot, params)
n = len(x_trajectory)
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(8, 8))
ax1.plot(x_trajectory, y_trajectory, 'g', label='Twiddle PID controller')
ax1.plot(x_trajectory, np.zeros(n), 'r', label='reference')
INSTRUCTOR NOTE:
Twiddle notes: