PID: proportional, integral, derivative.
It is a combination of 3 feedback mechanisms. Each is at different time scale: immediate, one interval, accumulative.
def run(robot, p,i,d, n=100, speed=1.0):
x_trajectory = []
y_trajectory = []
pre = robot.y
integral = 0
for j in range(n):
cte = robot.y
delta = cte -pre
pre = cte
integral += cte
steer = -p*cte - i*integral - d*delta
robot.move(steer, speed)
x_trajectory.append(robot.x)
y_trajectory.append(robot.y)
return x_trajectory, y_trajectory
A method to find the best hyperparameter is called “twiddle”. Each time apply a change to a single parameter if the error is not reduced, reduce the change amount.
def run(robot, params, n=100, speed=1.0):
x_trajectory = []
y_trajectory = []
err = 0
prev_cte = robot.y
int_cte = 0
p , d , i = params
for j in range(2 * n):
cte = robot.y
diff_cte = cte - prev_cte
int_cte += cte
prev_cte = cte
steer = -p * cte - d * diff_cte - i * int_cte
robot.move(steer, speed)
x_trajectory.append(robot.x)
y_trajectory.append(robot.y)
if j >= n: # discard the first n points to get more stable value
err += cte ** 2
return x_trajectory, y_trajectory, err / n
def twiddle(tol=0.2):
p = [0, 0, 0]
dp = [1, 1, 1]
robot = make_robot()
x_track, y_track, best_err = run(robot, p)
it = 0
while sum(dp) > tol:
it += 1
print("Iteration {}, best error = {}".format(it, best_err))
for i in range(len(p)):
for j in range(2):
if j==0:
p[i] += dp[i] # positive attempt
if j==1:
p[i] -= 2*dp[i] # negative attempt
robot = make_robot()
x_track, y_track, err = run(robot, p)
# works, record result,increase delta
if err < best_err:
best_err = err
dp[i] *= 1.1
print p, dp
break
# neither works, roll back, decrease delta
p[i] += dp[i]
dp[i] *= 0.9
print p, dp
return p, best_err
project
In the actual project, there is no fixed line for the car to approach. So we have to manually implement the twiddle method.
