PID 路径跟踪

单车模型

# --------------
# User Instructions
#
# Define a function cte in the robot class that will
# compute the crosstrack error for a robot on a
# racetrack with a shape as described in the video.
#
# You will need to base your error calculation on
# the robot's location on the track. Remember that
# the robot will be traveling to the right on the
# upper straight segment and to the left on the lower
# straight segment.
#
# --------------
# Grading Notes
#
# We will be testing your cte function directly by
# calling it with different robot locations and making
# sure that it returns the correct crosstrack error.

from math import *
import random


# ------------------------------------------------
#
# this is the robot class
#

class robot:

    # --------
    # init:
    #    creates robot and initializes location/orientation to 0, 0, 0
    #

    def __init__(self, length=20.0):
        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

    # --------
    # set:
    #	sets a robot coordinate
    #

    def set(self, new_x, new_y, new_orientation):

        self.x = float(new_x)
        self.y = float(new_y)
        self.orientation = float(new_orientation) % (2.0 * pi)

    # --------
    # set_noise:
    #	sets the noise parameters
    #

    def set_noise(self, new_s_noise, new_d_noise):
        # makes it possible to change the noise parameters
        # this is often useful in particle filters
        self.steering_noise = float(new_s_noise)
        self.distance_noise = float(new_d_noise)

    # --------
    # set_steering_drift:
    #	sets the systematical steering drift parameter
    #

    def set_steering_drift(self, drift):
        self.steering_drift = drift

    # --------
    # move:
    #    steering = front wheel steering angle, limited by max_steering_angle
    #    distance = total distance driven, most be non-negative

    def move(self, steering, distance,
             tolerance=0.001, max_steering_angle=pi / 4.0):

        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

        # make a new copy
        res = robot()
        res.length = self.length
        res.steering_noise = self.steering_noise
        res.distance_noise = self.distance_noise
        res.steering_drift = self.steering_drift

        # 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 = tan(steering2) * distance2 / res.length

        if abs(turn) < tolerance:

            # approximate by straight line motion

            res.x = self.x + (distance2 * cos(self.orientation))
            res.y = self.y + (distance2 * sin(self.orientation))
            res.orientation = (self.orientation + turn) % (2.0 * pi)

        else:

            # approximate bicycle model for motion

            radius = distance2 / turn
            cx = self.x - (sin(self.orientation) * radius)
            cy = self.y + (cos(self.orientation) * radius)
            res.orientation = (self.orientation + turn) % (2.0 * pi)
            res.x = cx + (sin(res.orientation) * radius)
            res.y = cy - (cos(res.orientation) * radius)

        return res

    def __repr__(self):
        return '[x=%.5f y=%.5f orient=%.5f]' % (self.x, self.y, self.orientation)

    ############## ONLY ADD / MODIFY CODE BELOW THIS LINE ####################
    
    def dist2(self, x, y):
        return sqrt((self.x - x)**2 +(self.y - y)**2)

    def cte(self, radius):

        if self.x < radius:
            cte = self.dist2(radius, radius) - radius
        elif self.x > 3*radius:
            cte = self.dist2(3* radius, radius) - radius
        elif self.y > radius:
            cte = self.y - 2*radius
        else:
            cte = -self.y
                
        return cte

PID

# ------------------------------------------------------------------------
#
# run - does a single control run.


def run(params, radius, printflag=False):
    myrobot = robot()
    myrobot.set(0.0, radius, pi / 2.0)
    speed = 1.0  # motion distance is equal to speed (we assume time = 1)
    err = 0.0
    int_crosstrack_error = 0.0
    N = 200
    path = []

    crosstrack_error = myrobot.cte(radius)  # You need to define the cte function!

    for i in range(N * 2):
        path.append([myrobot.x, myrobot.y])
        diff_crosstrack_error = - crosstrack_error
        crosstrack_error = myrobot.cte(radius)
        diff_crosstrack_error += crosstrack_error
        int_crosstrack_error += crosstrack_error
        steer = - params[0] * crosstrack_error \
                - params[1] * diff_crosstrack_error \
                - params[2] * int_crosstrack_error
        myrobot = myrobot.move(steer, speed)
        if i >= N:
            err += crosstrack_error ** 2
        if printflag:
            print(myrobot)
    
    draw_path(path)
    return err / float(N)


radius = 25.0
params = [10.0, 15.0, 0] # pid
err = run(params, radius, True)
print('\nFinal parameters: ', params, '\n ->', err)

参数调优

def twiddle(init_params):
    
    # k 次平均误差
    def k_run_err(K, params):
        err = 0
        for k in range(K):
            err += run(params, radius)
        err = float(err) / float(K)
        return err
    
    n_params = len(init_params)
    dparams = [1.0 for row in range(n_params)] # 参数浮动范围
    params = [0.0 for row in range(n_params)]
    K = 10

    for i in range(n_params):
        params[i] = init_params[i]

    best_error = k_run_err(K, params)
    print(best_error)

    n = 0
    while sum(dparams) > 0.0000001:
        for i in range(len(params)):
            params[i] += dparams[i]
            err = k_run_err(K, params)
            print(err)
            
            if err < best_error:
                best_error = err
                dparams[i] *= 1.1
            else:
                params[i] -= 2.0 * dparams[i]
                err = k_run_err(K, params)
                print(err)
                
                if err < best_error:
                    best_error = err
                    dparams[i] *= 1.1
                else:
                    params[i] += dparams[i]
                    dparams[i] *= 0.5
        n += 1
        print('Twiddle #', n, params, ' -> ', best_error)
    print(' ')
    return params