Source

udacity373_code / unit6 / u6-7_parameters.py

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
# -----------
# User Instructions
#
# The point of this exercise is to find the optimal
# parameters! You can write a twiddle function or you
# can use any other method
# that you like. Since we don't know what the optimal
# parameters are, we will be very loose with the 
# grading. If you find parameters that work well, post 
# them in the forums!
#
# Note: when we first released this problem, we 
# included a twiddle function. But that's no fun!
# Try coding up your own parameter optimization
# and see how quickly you can get to the goal.
#
# You can find the parameters at line 581.
 
from math import *
import random


# don't change the noise paameters

steering_noise    = 0.1
distance_noise    = 0.03
measurement_noise = 0.3


class plan:

    # --------
    # init: 
    #    creates an empty plan
    #

    def __init__(self, grid, init, goal, cost = 1):
        self.cost = cost
        self.grid = grid
        self.init = init
        self.goal = goal
        self.make_heuristic(grid, goal, self.cost)
        self.path = []
        self.spath = []

    # --------
    #
    # make heuristic function for a grid
        
    def make_heuristic(self, grid, goal, cost):
        self.heuristic = [[0 for row in range(len(grid[0]))] 
                          for col in range(len(grid))]
        for i in range(len(self.grid)):    
            for j in range(len(self.grid[0])):
                self.heuristic[i][j] = abs(i - self.goal[0]) + \
                    abs(j - self.goal[1])



    # ------------------------------------------------
    # 
    # A* for searching a path to the goal
    #
    #

    def astar(self):


        if self.heuristic == []:
            raise ValueError, "Heuristic must be defined to run A*"

        # internal motion parameters
        delta = [[-1,  0], # go up
                 [ 0,  -1], # go left
                 [ 1,  0], # go down
                 [ 0,  1]] # do right


        # open list elements are of the type: [f, g, h, x, y]

        closed = [[0 for row in range(len(self.grid[0]))] 
                  for col in range(len(self.grid))]
        action = [[0 for row in range(len(self.grid[0]))] 
                  for col in range(len(self.grid))]

        closed[self.init[0]][self.init[1]] = 1


        x = self.init[0]
        y = self.init[1]
        h = self.heuristic[x][y]
        g = 0
        f = g + h

        open = [[f, g, h, x, y]]

        found  = False # flag that is set when search complete
        resign = False # flag set if we can't find expand
        count  = 0


        while not found and not resign:

            # check if we still have elements on the open list
            if len(open) == 0:
                resign = True
                print '###### Search terminated without success'
                
            else:
                # remove node from list
                open.sort()
                open.reverse()
                next = open.pop()
                x = next[3]
                y = next[4]
                g = next[1]

            # check if we are done

            if x == goal[0] and y == goal[1]:
                found = True
                # print '###### A* search successful'

            else:
                # expand winning element and add to new open list
                for i in range(len(delta)):
                    x2 = x + delta[i][0]
                    y2 = y + delta[i][1]
                    if x2 >= 0 and x2 < len(self.grid) and y2 >= 0 \
                            and y2 < len(self.grid[0]):
                        if closed[x2][y2] == 0 and self.grid[x2][y2] == 0:
                            g2 = g + self.cost
                            h2 = self.heuristic[x2][y2]
                            f2 = g2 + h2
                            open.append([f2, g2, h2, x2, y2])
                            closed[x2][y2] = 1
                            action[x2][y2] = i

            count += 1

        # extract the path



        invpath = []
        x = self.goal[0]
        y = self.goal[1]
        invpath.append([x, y])
        while x != self.init[0] or y != self.init[1]:
            x2 = x - delta[action[x][y]][0]
            y2 = y - delta[action[x][y]][1]
            x = x2
            y = y2
            invpath.append([x, y])

        self.path = []
        for i in range(len(invpath)):
            self.path.append(invpath[len(invpath) - 1 - i])




    # ------------------------------------------------
    # 
    # this is the smoothing function
    #

  


    def smooth(self, weight_data = 0.1, weight_smooth = 0.1, 
               tolerance = 0.000001):

        if self.path == []:
            raise ValueError, "Run A* first before smoothing path"

        self.spath = [[0 for row in range(len(self.path[0]))] \
                           for col in range(len(self.path))]
        for i in range(len(self.path)):
            for j in range(len(self.path[0])):
                self.spath[i][j] = self.path[i][j]

        change = tolerance
        while change >= tolerance:
            change = 0.0
            for i in range(1, len(self.path)-1):
                for j in range(len(self.path[0])):
                    aux = self.spath[i][j]
                    
                    self.spath[i][j] += weight_data * \
                        (self.path[i][j] - self.spath[i][j])
                    
                    self.spath[i][j] += weight_smooth * \
                        (self.spath[i-1][j] + self.spath[i+1][j] 
                         - (2.0 * self.spath[i][j]))
                    if i >= 2:
                        self.spath[i][j] += 0.5 * weight_smooth * \
                            (2.0 * self.spath[i-1][j] - self.spath[i-2][j] 
                             - self.spath[i][j])
                    if i <= len(self.path) - 3:
                        self.spath[i][j] += 0.5 * weight_smooth * \
                            (2.0 * self.spath[i+1][j] - self.spath[i+2][j] 
                             - self.spath[i][j])
                
            change += abs(aux - self.spath[i][j])
                






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

class robot:

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

    def __init__(self, length = 0.5):
        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.measurement_noise = 0.0
        self.num_collisions    = 0
        self.num_steps         = 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, new_m_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)
        self.measurement_noise = float(new_m_noise)

    # --------
    # check: 
    #    checks of the robot pose collides with an obstacle, or
    # is too far outside the plane

    def check_collision(self, grid):
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 1:
                    dist = sqrt((self.x - float(i)) ** 2 + 
                                (self.y - float(j)) ** 2)
                    if dist < 0.5:
                        self.num_collisions += 1
                        return False
        return True
        
    def check_goal(self, goal, threshold = 1.0):
        dist =  sqrt((float(goal[0]) - self.x) ** 2 + (float(goal[1]) - self.y) ** 2)
        return dist < threshold
        
    # --------
    # move: 
    #    steering = front wheel steering angle, limited by max_steering_angle
    #    distance = total distance driven, most be non-negative

    def move(self, grid, 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.measurement_noise = self.measurement_noise
        res.num_collisions    = self.num_collisions
        res.num_steps         = self.num_steps + 1

        # apply noise
        steering2 = random.gauss(steering, self.steering_noise)
        distance2 = random.gauss(distance, self.distance_noise)


        # 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)

        # check for collision
        # res.check_collision(grid)

        return res

    # --------
    # sense: 
    #    

    def sense(self):

        return [random.gauss(self.x, self.measurement_noise),
                random.gauss(self.y, self.measurement_noise)]

    # --------
    # measurement_prob
    #    computes the probability of a measurement
    # 

    def measurement_prob(self, measurement):

        # compute errors
        error_x = measurement[0] - self.x
        error_y = measurement[1] - self.y

        # calculate Gaussian
        error = exp(- (error_x ** 2) / (self.measurement_noise ** 2) / 2.0) \
            / sqrt(2.0 * pi * (self.measurement_noise ** 2))
        error *= exp(- (error_y ** 2) / (self.measurement_noise ** 2) / 2.0) \
            / sqrt(2.0 * pi * (self.measurement_noise ** 2))

        return error



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






# ------------------------------------------------
# 
# this is the particle filter class
#

class particles:

    # --------
    # init: 
    #	creates particle set with given initial position
    #

    def __init__(self, x, y, theta, 
                 steering_noise, distance_noise, measurement_noise, N = 100):
        self.N = N
        self.steering_noise    = steering_noise
        self.distance_noise    = distance_noise
        self.measurement_noise = measurement_noise
        
        self.data = []
        for i in range(self.N):
            r = robot()
            r.set(x, y, theta)
            r.set_noise(steering_noise, distance_noise, measurement_noise)
            self.data.append(r)


    # --------
    #
    # extract position from a particle set
    # 
    
    def get_position(self):
        x = 0.0
        y = 0.0
        orientation = 0.0

        for i in range(self.N):
            x += self.data[i].x
            y += self.data[i].y
            # orientation is tricky because it is cyclic. By normalizing
            # around the first particle we are somewhat more robust to
            # the 0=2pi problem
            orientation += (((self.data[i].orientation
                              - self.data[0].orientation + pi) % (2.0 * pi)) 
                            + self.data[0].orientation - pi)
        return [x / self.N, y / self.N, orientation / self.N]

    # --------
    #
    # motion of the particles
    # 

    def move(self, grid, steer, speed):
        newdata = []

        for i in range(self.N):
            r = self.data[i].move(grid, steer, speed)
            newdata.append(r)
        self.data = newdata

    # --------
    #
    # sensing and resampling
    # 

    def sense(self, Z):
        w = []
        for i in range(self.N):
            w.append(self.data[i].measurement_prob(Z))

        # resampling (careful, this is using shallow copy)
        p3 = []
        index = int(random.random() * self.N)
        beta = 0.0
        mw = max(w)

        for i in range(self.N):
            beta += random.random() * 2.0 * mw
            while beta > w[index]:
                beta -= w[index]
                index = (index + 1) % self.N
            p3.append(self.data[index])
        self.data = p3

    



    

# --------
#
# run:  runs control program for the robot
#


def run(grid, goal, spath, params, printflag = False, speed = 0.1, timeout = 1000):

    myrobot = robot()
    myrobot.set(0., 0., 0.)
    myrobot.set_noise(steering_noise, distance_noise, measurement_noise)
    filter = particles(myrobot.x, myrobot.y, myrobot.orientation,
                       steering_noise, distance_noise, measurement_noise)

    cte  = 0.0
    err  = 0.0
    N    = 0

    index = 0 # index into the path
    
    while not myrobot.check_goal(goal) and N < timeout:

        diff_cte = - cte


        # ----------------------------------------
        # compute the CTE

        # start with the present robot estimate
        estimate = filter.get_position()

        # some basic vector calculations
        dx = spath[index+1][0] - spath[index][0]
        dy = spath[index+1][1] - spath[index][1]
        drx = estimate[0] - spath[index][0]
        dry = estimate[1] - spath[index][1]
        
        # u is the robot estimate projectes onto the path segment
        u = (drx * dx + dry * dy) / (dx * dx + dy * dy)
        
        # the cte is the estimate projected onto the normal of the path segment
        cte = (dry * dx - drx * dy) / (dx * dx + dy * dy)
        
        # pick the next path segment
        if u > 1.0 and index < len(spath) - 1:
            index += 1
        

        # ----------------------------------------


        diff_cte += cte

        steer = - params[0] * cte - params[1] * diff_cte 

        myrobot = myrobot.move(grid, steer, speed)
        filter.move(grid, steer, speed)

        Z = myrobot.sense()
        filter.sense(Z)

        if not myrobot.check_collision(grid):
            print '##### Collision ####'

        err += (cte ** 2)
        N += 1

        if printflag:
            print myrobot, cte, index, u

    return [myrobot.check_goal(goal), myrobot.num_collisions, myrobot.num_steps]


# ------------------------------------------------
# 
# this is our main routine
#

def main(grid, init, goal, steering_noise, distance_noise, measurement_noise, 
     weight_data, weight_smooth, p_gain, d_gain):

    path = plan(grid, init, goal)
    path.astar()
    path.smooth(weight_data, weight_smooth)
    return run(grid, goal, path.spath, [p_gain, d_gain])

    


# ------------------------------------------------
# 
# input data and parameters
#


# grid format:
#   0 = navigable space
#   1 = occupied space

grid = [[0, 1, 0, 0, 0, 0],
        [0, 1, 0, 1, 1, 0],
        [0, 1, 0, 1, 0, 0],
        [0, 0, 0, 1, 0, 1],
        [0, 1, 0, 1, 0, 0]]


init = [0, 0]
goal = [len(grid)-1, len(grid[0])-1]


steering_noise    = 0.1
distance_noise    = 0.03
measurement_noise = 0.3

#### ADJUST THESE PARAMETERS ######

weight_data       = 0.3
weight_smooth     = 0.1
p_gain            = 1.0
d_gain            = 3.0

###################################
    
print main(grid, init, goal, steering_noise, distance_noise, measurement_noise, 
           weight_data, weight_smooth, p_gain, d_gain)
Tip: Filter by directory path e.g. /media app.js to search for public/media/app.js.
Tip: Use camelCasing e.g. ProjME to search for ProjectModifiedEvent.java.
Tip: Filter by extension type e.g. /repo .js to search for all .js files in the /repo directory.
Tip: Separate your search with spaces e.g. /ssh pom.xml to search for src/ssh/pom.xml.
Tip: Use ↑ and ↓ arrow keys to navigate and return to view the file.
Tip: You can also navigate files with Ctrl+j (next) and Ctrl+k (previous) and view the file with Ctrl+o.
Tip: You can also navigate files with Alt+j (next) and Alt+k (previous) and view the file with Alt+o.