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December 22, 2017 07:04
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| # ------------ | |
| # https://classroom.udacity.com/courses/cs373/lessons/48736210/concepts/486838410923 | |
| # ------------ | |
| # User Instructions | |
| # | |
| # In this problem you will implement a more manageable | |
| # version of graph SLAM in 2 dimensions. | |
| # | |
| # Define a function, online_slam, that takes 5 inputs: | |
| # data, N, num_landmarks, motion_noise, and | |
| # measurement_noise--just as was done in the last | |
| # programming assignment of unit 6. This function | |
| # must return TWO matrices, mu and the final Omega. | |
| # | |
| # Just as with the quiz, your matrices should have x | |
| # and y interlaced, so if there were two poses and 2 | |
| # landmarks, mu would look like: | |
| # | |
| # mu = matrix([[Px0], | |
| # [Py0], | |
| # [Px1], | |
| # [Py1], | |
| # [Lx0], | |
| # [Ly0], | |
| # [Lx1], | |
| # [Ly1]]) | |
| # | |
| # Enter your code at line 566. | |
| # ----------- | |
| # Testing | |
| # | |
| # You have two methods for testing your code. | |
| # | |
| # 1) You can make your own data with the make_data | |
| # function. Then you can run it through the | |
| # provided slam routine and check to see that your | |
| # online_slam function gives the same estimated | |
| # final robot pose and landmark positions. | |
| # 2) You can use the solution_check function at the | |
| # bottom of this document to check your code | |
| # for the two provided test cases. The grading | |
| # will be almost identical to this function, so | |
| # if you pass both test cases, you should be | |
| # marked correct on the homework. | |
| from math import * | |
| import random | |
| # ------------------------------------------------ | |
| # | |
| # this is the matrix class | |
| # we use it because it makes it easier to collect constraints in GraphSLAM | |
| # and to calculate solutions (albeit inefficiently) | |
| # | |
| class matrix: | |
| # implements basic operations of a matrix class | |
| # ------------ | |
| # | |
| # initialization - can be called with an initial matrix | |
| # | |
| def __init__(self, value = [[]]): | |
| self.value = value | |
| self.dimx = len(value) | |
| self.dimy = len(value[0]) | |
| if value == [[]]: | |
| self.dimx = 0 | |
| # ----------- | |
| # | |
| # defines matrix equality - returns true if corresponding elements | |
| # in two matrices are within epsilon of each other. | |
| # | |
| def __eq__(self, other): | |
| epsilon = 0.01 | |
| if self.dimx != other.dimx or self.dimy != other.dimy: | |
| return False | |
| for i in range(self.dimx): | |
| for j in range(self.dimy): | |
| if abs(self.value[i][j] - other.value[i][j]) > epsilon: | |
| return False | |
| return True | |
| def __ne__(self, other): | |
| return not (self == other) | |
| # ------------ | |
| # | |
| # makes matrix of a certain size and sets each element to zero | |
| # | |
| def zero(self, dimx, dimy): | |
| if dimy == 0: | |
| dimy = dimx | |
| # check if valid dimensions | |
| if dimx < 1 or dimy < 1: | |
| raise ValueError, "Invalid size of matrix" | |
| else: | |
| self.dimx = dimx | |
| self.dimy = dimy | |
| self.value = [[0.0 for row in range(dimy)] for col in range(dimx)] | |
| # ------------ | |
| # | |
| # makes matrix of a certain (square) size and turns matrix into identity matrix | |
| # | |
| def identity(self, dim): | |
| # check if valid dimension | |
| if dim < 1: | |
| raise ValueError, "Invalid size of matrix" | |
| else: | |
| self.dimx = dim | |
| self.dimy = dim | |
| self.value = [[0.0 for row in range(dim)] for col in range(dim)] | |
| for i in range(dim): | |
| self.value[i][i] = 1.0 | |
| # ------------ | |
| # | |
| # prints out values of matrix | |
| # | |
| def show(self, txt = ''): | |
| for i in range(len(self.value)): | |
| print txt + '['+ ', '.join('%.3f'%x for x in self.value[i]) + ']' | |
| print ' ' | |
| # ------------ | |
| # | |
| # defines elmement-wise matrix addition. Both matrices must be of equal dimensions | |
| # | |
| def __add__(self, other): | |
| # check if correct dimensions | |
| if self.dimx != other.dimx or self.dimx != other.dimx: | |
| raise ValueError, "Matrices must be of equal dimension to add" | |
| else: | |
| # add if correct dimensions | |
| res = matrix() | |
| res.zero(self.dimx, self.dimy) | |
| for i in range(self.dimx): | |
| for j in range(self.dimy): | |
| res.value[i][j] = self.value[i][j] + other.value[i][j] | |
| return res | |
| # ------------ | |
| # | |
| # defines elmement-wise matrix subtraction. Both matrices must be of equal dimensions | |
| # | |
| def __sub__(self, other): | |
| # check if correct dimensions | |
| if self.dimx != other.dimx or self.dimx != other.dimx: | |
| raise ValueError, "Matrices must be of equal dimension to subtract" | |
| else: | |
| # subtract if correct dimensions | |
| res = matrix() | |
| res.zero(self.dimx, self.dimy) | |
| for i in range(self.dimx): | |
| for j in range(self.dimy): | |
| res.value[i][j] = self.value[i][j] - other.value[i][j] | |
| return res | |
| # ------------ | |
| # | |
| # defines multiplication. Both matrices must be of fitting dimensions | |
| # | |
| def __mul__(self, other): | |
| # check if correct dimensions | |
| if self.dimy != other.dimx: | |
| raise ValueError, "Matrices must be m*n and n*p to multiply" | |
| else: | |
| # multiply if correct dimensions | |
| res = matrix() | |
| res.zero(self.dimx, other.dimy) | |
| for i in range(self.dimx): | |
| for j in range(other.dimy): | |
| for k in range(self.dimy): | |
| res.value[i][j] += self.value[i][k] * other.value[k][j] | |
| return res | |
| # ------------ | |
| # | |
| # returns a matrix transpose | |
| # | |
| def transpose(self): | |
| # compute transpose | |
| res = matrix() | |
| res.zero(self.dimy, self.dimx) | |
| for i in range(self.dimx): | |
| for j in range(self.dimy): | |
| res.value[j][i] = self.value[i][j] | |
| return res | |
| # ------------ | |
| # | |
| # creates a new matrix from the existing matrix elements. | |
| # | |
| # Example: | |
| # l = matrix([[ 1, 2, 3, 4, 5], | |
| # [ 6, 7, 8, 9, 10], | |
| # [11, 12, 13, 14, 15]]) | |
| # | |
| # l.take([0, 2], [0, 2, 3]) | |
| # | |
| # results in: | |
| # | |
| # [[1, 3, 4], | |
| # [11, 13, 14]] | |
| # | |
| # | |
| # take is used to remove rows and columns from existing matrices | |
| # list1/list2 define a sequence of rows/columns that shall be taken | |
| # is no list2 is provided, then list2 is set to list1 (good for symmetric matrices) | |
| # | |
| def take(self, list1, list2 = []): | |
| if list2 == []: | |
| list2 = list1 | |
| if len(list1) > self.dimx or len(list2) > self.dimy: | |
| raise ValueError, "list invalid in take()" | |
| res = matrix() | |
| res.zero(len(list1), len(list2)) | |
| for i in range(len(list1)): | |
| for j in range(len(list2)): | |
| res.value[i][j] = self.value[list1[i]][list2[j]] | |
| return res | |
| # ------------ | |
| # | |
| # creates a new matrix from the existing matrix elements. | |
| # | |
| # Example: | |
| # l = matrix([[1, 2, 3], | |
| # [4, 5, 6]]) | |
| # | |
| # l.expand(3, 5, [0, 2], [0, 2, 3]) | |
| # | |
| # results in: | |
| # | |
| # [[1, 0, 2, 3, 0], | |
| # [0, 0, 0, 0, 0], | |
| # [4, 0, 5, 6, 0]] | |
| # | |
| # expand is used to introduce new rows and columns into an existing matrix | |
| # list1/list2 are the new indexes of row/columns in which the matrix | |
| # elements are being mapped. Elements for rows and columns | |
| # that are not listed in list1/list2 | |
| # will be initialized by 0.0. | |
| # | |
| def expand(self, dimx, dimy, list1, list2 = []): | |
| if list2 == []: | |
| list2 = list1 | |
| if len(list1) > self.dimx or len(list2) > self.dimy: | |
| raise ValueError, "list invalid in expand()" | |
| res = matrix() | |
| res.zero(dimx, dimy) | |
| for i in range(len(list1)): | |
| for j in range(len(list2)): | |
| res.value[list1[i]][list2[j]] = self.value[i][j] | |
| return res | |
| # ------------ | |
| # | |
| # Computes the upper triangular Cholesky factorization of | |
| # a positive definite matrix. | |
| # This code is based on http://adorio-research.org/wordpress/?p=4560 | |
| def Cholesky(self, ztol= 1.0e-5): | |
| res = matrix() | |
| res.zero(self.dimx, self.dimx) | |
| for i in range(self.dimx): | |
| S = sum([(res.value[k][i])**2 for k in range(i)]) | |
| d = self.value[i][i] - S | |
| if abs(d) < ztol: | |
| res.value[i][i] = 0.0 | |
| else: | |
| if d < 0.0: | |
| raise ValueError, "Matrix not positive-definite" | |
| res.value[i][i] = sqrt(d) | |
| for j in range(i+1, self.dimx): | |
| S = sum([res.value[k][i] * res.value[k][j] for k in range(i)]) | |
| if abs(S) < ztol: | |
| S = 0.0 | |
| res.value[i][j] = (self.value[i][j] - S)/res.value[i][i] | |
| return res | |
| # ------------ | |
| # | |
| # Computes inverse of matrix given its Cholesky upper Triangular | |
| # decomposition of matrix. | |
| # This code is based on http://adorio-research.org/wordpress/?p=4560 | |
| def CholeskyInverse(self): | |
| # Computes inverse of matrix given its Cholesky upper Triangular | |
| # decomposition of matrix. | |
| # This code is based on http://adorio-research.org/wordpress/?p=4560 | |
| res = matrix() | |
| res.zero(self.dimx, self.dimx) | |
| # Backward step for inverse. | |
| for j in reversed(range(self.dimx)): | |
| tjj = self.value[j][j] | |
| S = sum([self.value[j][k]*res.value[j][k] for k in range(j+1, self.dimx)]) | |
| res.value[j][j] = 1.0/ tjj**2 - S/ tjj | |
| for i in reversed(range(j)): | |
| res.value[j][i] = res.value[i][j] = \ | |
| -sum([self.value[i][k]*res.value[k][j] for k in \ | |
| range(i+1,self.dimx)])/self.value[i][i] | |
| return res | |
| # ------------ | |
| # | |
| # comutes and returns the inverse of a square matrix | |
| # | |
| def inverse(self): | |
| aux = self.Cholesky() | |
| res = aux.CholeskyInverse() | |
| return res | |
| # ------------ | |
| # | |
| # prints matrix (needs work!) | |
| # | |
| def __repr__(self): | |
| return repr(self.value) | |
| # ###################################################################### | |
| # ------------------------------------------------ | |
| # | |
| # this is the robot class | |
| # | |
| # our robot lives in x-y space, and its motion is | |
| # pointed in a random direction. It moves on a straight line | |
| # until is comes close to a wall at which point it turns | |
| # away from the wall and continues to move. | |
| # | |
| # For measurements, it simply senses the x- and y-distance | |
| # to landmarks. This is different from range and bearing as | |
| # commonly studies in the literature, but this makes it much | |
| # easier to implement the essentials of SLAM without | |
| # cluttered math | |
| # | |
| class robot: | |
| # -------- | |
| # init: | |
| # creates robot and initializes location to 0, 0 | |
| # | |
| def __init__(self, world_size = 100.0, measurement_range = 30.0, | |
| motion_noise = 1.0, measurement_noise = 1.0): | |
| self.measurement_noise = 0.0 | |
| self.world_size = world_size | |
| self.measurement_range = measurement_range | |
| self.x = world_size / 2.0 | |
| self.y = world_size / 2.0 | |
| self.motion_noise = motion_noise | |
| self.measurement_noise = measurement_noise | |
| self.landmarks = [] | |
| self.num_landmarks = 0 | |
| def rand(self): | |
| return random.random() * 2.0 - 1.0 | |
| # -------- | |
| # | |
| # make random landmarks located in the world | |
| # | |
| def make_landmarks(self, num_landmarks): | |
| self.landmarks = [] | |
| for i in range(num_landmarks): | |
| self.landmarks.append([round(random.random() * self.world_size), | |
| round(random.random() * self.world_size)]) | |
| self.num_landmarks = num_landmarks | |
| # -------- | |
| # | |
| # move: attempts to move robot by dx, dy. If outside world | |
| # boundary, then the move does nothing and instead returns failure | |
| # | |
| def move(self, dx, dy): | |
| x = self.x + dx + self.rand() * self.motion_noise | |
| y = self.y + dy + self.rand() * self.motion_noise | |
| if x < 0.0 or x > self.world_size or y < 0.0 or y > self.world_size: | |
| return False | |
| else: | |
| self.x = x | |
| self.y = y | |
| return True | |
| # -------- | |
| # | |
| # sense: returns x- and y- distances to landmarks within visibility range | |
| # because not all landmarks may be in this range, the list of measurements | |
| # is of variable length. Set measurement_range to -1 if you want all | |
| # landmarks to be visible at all times | |
| # | |
| def sense(self): | |
| Z = [] | |
| for i in range(self.num_landmarks): | |
| dx = self.landmarks[i][0] - self.x + self.rand() * self.measurement_noise | |
| dy = self.landmarks[i][1] - self.y + self.rand() * self.measurement_noise | |
| if self.measurement_range < 0.0 or abs(dx) + abs(dy) <= self.measurement_range: | |
| Z.append([i, dx, dy]) | |
| return Z | |
| # -------- | |
| # | |
| # print robot location | |
| # | |
| def __repr__(self): | |
| return 'Robot: [x=%.5f y=%.5f]' % (self.x, self.y) | |
| # ###################################################################### | |
| # -------- | |
| # this routine makes the robot data | |
| # | |
| def make_data(N, num_landmarks, world_size, measurement_range, motion_noise, | |
| measurement_noise, distance): | |
| complete = False | |
| while not complete: | |
| data = [] | |
| # make robot and landmarks | |
| r = robot(world_size, measurement_range, motion_noise, measurement_noise) | |
| r.make_landmarks(num_landmarks) | |
| seen = [False for row in range(num_landmarks)] | |
| # guess an initial motion | |
| orientation = random.random() * 2.0 * pi | |
| dx = cos(orientation) * distance | |
| dy = sin(orientation) * distance | |
| for k in range(N-1): | |
| # sense | |
| Z = r.sense() | |
| # check off all landmarks that were observed | |
| for i in range(len(Z)): | |
| seen[Z[i][0]] = True | |
| # move | |
| while not r.move(dx, dy): | |
| # if we'd be leaving the robot world, pick instead a new direction | |
| orientation = random.random() * 2.0 * pi | |
| dx = cos(orientation) * distance | |
| dy = sin(orientation) * distance | |
| # memorize data | |
| data.append([Z, [dx, dy]]) | |
| # we are done when all landmarks were observed; otherwise re-run | |
| complete = (sum(seen) == num_landmarks) | |
| print ' ' | |
| print 'Landmarks: ', r.landmarks | |
| print r | |
| return data | |
| # ###################################################################### | |
| # -------------------------------- | |
| # | |
| # full_slam - retains entire path and all landmarks | |
| # Feel free to use this for comparison. | |
| # | |
| def slam(data, N, num_landmarks, motion_noise, measurement_noise): | |
| # Set the dimension of the filter | |
| dim = 2 * (N + num_landmarks) | |
| # make the constraint information matrix and vector | |
| Omega = matrix() | |
| Omega.zero(dim, dim) | |
| Omega.value[0][0] = 1.0 | |
| Omega.value[1][1] = 1.0 | |
| Xi = matrix() | |
| Xi.zero(dim, 1) | |
| Xi.value[0][0] = world_size / 2.0 | |
| Xi.value[1][0] = world_size / 2.0 | |
| # process the data | |
| for k in range(len(data)): | |
| # n is the index of the robot pose in the matrix/vector | |
| n = k * 2 | |
| measurement = data[k][0] | |
| motion = data[k][1] | |
| # integrate the measurements | |
| for i in range(len(measurement)): | |
| # m is the index of the landmark coordinate in the matrix/vector | |
| m = 2 * (N + measurement[i][0]) | |
| # update the information maxtrix/vector based on the measurement | |
| for b in range(2): | |
| Omega.value[n+b][n+b] += 1.0 / measurement_noise | |
| Omega.value[m+b][m+b] += 1.0 / measurement_noise | |
| Omega.value[n+b][m+b] += -1.0 / measurement_noise | |
| Omega.value[m+b][n+b] += -1.0 / measurement_noise | |
| Xi.value[n+b][0] += -measurement[i][1+b] / measurement_noise | |
| Xi.value[m+b][0] += measurement[i][1+b] / measurement_noise | |
| # update the information maxtrix/vector based on the robot motion | |
| for b in range(4): | |
| Omega.value[n+b][n+b] += 1.0 / motion_noise | |
| for b in range(2): | |
| Omega.value[n+b ][n+b+2] += -1.0 / motion_noise | |
| Omega.value[n+b+2][n+b ] += -1.0 / motion_noise | |
| Xi.value[n+b ][0] += -motion[b] / motion_noise | |
| Xi.value[n+b+2][0] += motion[b] / motion_noise | |
| # compute best estimate | |
| mu = Omega.inverse() * Xi | |
| # return the result | |
| return mu | |
| # -------------------------------- | |
| # | |
| # online_slam - retains all landmarks but only most recent robot pose | |
| # | |
| def online_slam(data, N, num_landmarks, motion_noise, measurement_noise): | |
| # | |
| # | |
| # Enter your code here! | |
| # | |
| # | |
| dim = 2*num_landmarks+2 | |
| Omega = matrix() | |
| Omega.zero(dim,dim) | |
| Xi = matrix() | |
| Xi.zero(dim,1) | |
| Omega.value[0][0] = 1.0 | |
| Omega.value[1][1] = 1.0 | |
| Xi.value[0][0] = 50.0 | |
| Xi.value[1][0] = 50.0 | |
| for Z,[dx,dy] in data: | |
| Omega = Omega.expand(dim+2,dim+2,[0,1]+range(4,dim+2)) | |
| Xi = Xi.expand(dim+2,1,[0,1]+range(4,dim+2),[0]) | |
| # for xt, xt+1 | |
| Omega.value[0][0] += 1/motion_noise | |
| Omega.value[0][2] += -1/motion_noise | |
| Xi.value[0][0] += -dx/motion_noise | |
| Omega.value[2][0] += -1/motion_noise | |
| Omega.value[2][2] += 1/motion_noise | |
| Xi.value[2][0] += dx/motion_noise | |
| # for yt, yt+1 | |
| Omega.value[1][1] += 1/motion_noise | |
| Omega.value[1][3] += -1/motion_noise | |
| Xi.value[1][0] += -dy/motion_noise | |
| Omega.value[3][1] += -1/motion_noise | |
| Omega.value[3][3] += 1/motion_noise | |
| Xi.value[3][0] += dy/motion_noise | |
| for i,zx,zy in Z: | |
| # for x,zx | |
| Omega.value[0][0] += 1/measurement_noise | |
| Omega.value[0][4+2*i] += -1/measurement_noise | |
| Xi.value[0][0] += -zx/measurement_noise | |
| Omega.value[4+2*i][0] += -1/measurement_noise | |
| Omega.value[4+2*i][4+2*i] += 1/measurement_noise | |
| Xi.value[4+2*i][0] += zx/measurement_noise | |
| #for y,zy | |
| Omega.value[1][1] += 1/measurement_noise | |
| Omega.value[1][4+2*i+1] += -1/measurement_noise | |
| Xi.value[1][0] += -zy/measurement_noise | |
| Omega.value[4+2*i+1][1] += -1/measurement_noise | |
| Omega.value[4+2*i+1][4+2*i+1] += 1/measurement_noise | |
| Xi.value[4+2*i+1][0] += zy/measurement_noise | |
| # get new omega, A, B, C | |
| newlist = range(2, len(Omega.value)) | |
| A = Omega.take([0,1], newlist) | |
| B = Omega.take([0,1],[0,1]) | |
| C = Xi.take([0,1],[0]) | |
| Omega = Omega.take(newlist, newlist) - A.transpose() * B.inverse() * A | |
| Xi = Xi.take(newlist,[0]) - A.transpose() * B.inverse() * C | |
| mu = Omega.inverse() * Xi | |
| return mu, Omega # make sure you return both of these matrices to be marked correct. | |
| # -------------------------------- | |
| # | |
| # print the result of SLAM, the robot pose(s) and the landmarks | |
| # | |
| def print_result(N, num_landmarks, result): | |
| print 'Estimated Pose(s):' | |
| for i in range(N): | |
| print ' ['+ ', '.join('%.3f'%x for x in result.value[2*i]) + ', ' \ | |
| + ', '.join('%.3f'%x for x in result.value[2*i+1]) +']' | |
| print 'Estimated Landmarks:' | |
| for i in range(num_landmarks): | |
| print ' ['+ ', '.join('%.3f'%x for x in result.value[2*(N+i)]) + ', ' \ | |
| + ', '.join('%.3f'%x for x in result.value[2*(N+i)+1]) +']' | |
| # ------------------------------------------------------------------------ | |
| # | |
| # Main routines | |
| # | |
| num_landmarks = 5 # number of landmarks | |
| N = 20 # time steps | |
| world_size = 100.0 # size of world | |
| measurement_range = 50.0 # range at which we can sense landmarks | |
| motion_noise = 2.0 # noise in robot motion | |
| measurement_noise = 2.0 # noise in the measurements | |
| distance = 20.0 # distance by which robot (intends to) move each iteratation | |
| # Uncomment the following three lines to run the full slam routine. | |
| #data = make_data(N, num_landmarks, world_size, measurement_range, motion_noise, measurement_noise, distance) | |
| #result = slam(data, N, num_landmarks, motion_noise, measurement_noise) | |
| #print_result(N, num_landmarks, result) | |
| # Uncomment the following three lines to run the online_slam routine. | |
| data = make_data(N, num_landmarks, world_size, measurement_range, motion_noise, measurement_noise, distance) | |
| result = online_slam(data, N, num_landmarks, motion_noise, measurement_noise) | |
| print_result(1, num_landmarks, result[0]) | |
| ########################################################## | |
| # ------------ | |
| # TESTING | |
| # | |
| # Uncomment one of the test cases below to check that your | |
| # online_slam function works as expected. | |
| def solution_check(result, answer_mu, answer_omega): | |
| if len(result) != 2: | |
| print "Your function must return TWO matrices, mu and Omega" | |
| return False | |
| user_mu = result[0] | |
| user_omega = result[1] | |
| if user_mu.dimx == answer_omega.dimx and user_mu.dimy == answer_omega.dimy: | |
| print "It looks like you returned your results in the wrong order. Make sure to return mu then Omega." | |
| return False | |
| if user_mu.dimx != answer_mu.dimx or user_mu.dimy != answer_mu.dimy: | |
| print "Your mu matrix doesn't have the correct dimensions. Mu should be a", answer_mu.dimx, " x ", answer_mu.dimy, "matrix." | |
| return False | |
| else: | |
| print "Mu has correct dimensions." | |
| if user_omega.dimx != answer_omega.dimx or user_omega.dimy != answer_omega.dimy: | |
| print "Your Omega matrix doesn't have the correct dimensions. Omega should be a", answer_omega.dimx, " x ", answer_omega.dimy, "matrix." | |
| return False | |
| else: | |
| print "Omega has correct dimensions." | |
| if user_mu != answer_mu: | |
| print "Mu has incorrect entries." | |
| return False | |
| else: | |
| print "Mu correct." | |
| if user_omega != answer_omega: | |
| print "Omega has incorrect entries." | |
| return False | |
| else: | |
| print "Omega correct." | |
| print "Test case passed!" | |
| return True | |
| # ----------- | |
| # Test Case 1 | |
| testdata1 = [[[[1, 21.796713239511305, 25.32184135169971], [2, 15.067410969755826, -27.599928007267906]], [16.4522379034509, -11.372065246394495]], | |
| [[[1, 6.1286996178786755, 35.70844618389858], [2, -0.7470113490937167, -17.709326161950294]], [16.4522379034509, -11.372065246394495]], | |
| [[[0, 16.305692184072235, -11.72765549112342], [2, -17.49244296888888, -5.371360408288514]], [16.4522379034509, -11.372065246394495]], | |
| [[[0, -0.6443452578030207, -2.542378369361001], [2, -32.17857547483552, 6.778675958806988]], [-16.66697847355152, 11.054945886894709]]] | |
| answer_mu1 = matrix([[81.63549976607898], | |
| [27.175270706192254], | |
| [98.09737507003692], | |
| [14.556272940621195], | |
| [71.97926631050574], | |
| [75.07644206765099], | |
| [65.30397603859097], | |
| [22.150809430682695]]) | |
| answer_omega1 = matrix([[0.36603773584905663, 0.0, -0.169811320754717, 0.0, -0.011320754716981133, 0.0, -0.1811320754716981, 0.0], | |
| [0.0, 0.36603773584905663, 0.0, -0.169811320754717, 0.0, -0.011320754716981133, 0.0, -0.1811320754716981], | |
| [-0.169811320754717, 0.0, 0.6509433962264151, 0.0, -0.05660377358490567, 0.0, -0.40566037735849064, 0.0], | |
| [0.0, -0.169811320754717, 0.0, 0.6509433962264151, 0.0, -0.05660377358490567, 0.0, -0.40566037735849064], | |
| [-0.011320754716981133, 0.0, -0.05660377358490567, 0.0, 0.6962264150943396, 0.0, -0.360377358490566, 0.0], | |
| [0.0, -0.011320754716981133, 0.0, -0.05660377358490567, 0.0, 0.6962264150943396, 0.0, -0.360377358490566], | |
| [-0.1811320754716981, 0.0, -0.4056603773584906, 0.0, -0.360377358490566, 0.0, 1.2339622641509433, 0.0], | |
| [0.0, -0.1811320754716981, 0.0, -0.4056603773584906, 0.0, -0.360377358490566, 0.0, 1.2339622641509433]]) | |
| # result = online_slam(testdata1, 5, 3, 2.0, 2.0) | |
| # solution_check(result, answer_mu1, answer_omega1) | |
| # ----------- | |
| # Test Case 2 | |
| testdata2 = [[[[0, 12.637647070797396, 17.45189715769647], [1, 10.432982633935133, -25.49437383412288]], [17.232472057089492, 10.150955955063045]], | |
| [[[0, -4.104607680013634, 11.41471295488775], [1, -2.6421937245699176, -30.500310738397154]], [17.232472057089492, 10.150955955063045]], | |
| [[[0, -27.157759429499166, -1.9907376178358271], [1, -23.19841267128686, -43.2248146183254]], [-17.10510363812527, 10.364141523975523]], | |
| [[[0, -2.7880265859173763, -16.41914969572965], [1, -3.6771540967943794, -54.29943770172535]], [-17.10510363812527, 10.364141523975523]], | |
| [[[0, 10.844236516370763, -27.19190207903398], [1, 14.728670653019343, -63.53743222490458]], [14.192077112147086, -14.09201714598981]]] | |
| answer_mu2 = matrix([[63.37479912250136], | |
| [78.17644539069596], | |
| [61.33207502170053], | |
| [67.10699675357239], | |
| [62.57455560221361], | |
| [27.042758786080363]]) | |
| answer_omega2 = matrix([[0.22871751620895048, 0.0, -0.11351536555795691, 0.0, -0.11351536555795691, 0.0], | |
| [0.0, 0.22871751620895048, 0.0, -0.11351536555795691, 0.0, -0.11351536555795691], | |
| [-0.11351536555795691, 0.0, 0.7867205207948973, 0.0, -0.46327947920510265, 0.0], | |
| [0.0, -0.11351536555795691, 0.0, 0.7867205207948973, 0.0, -0.46327947920510265], | |
| [-0.11351536555795691, 0.0, -0.46327947920510265, 0.0, 0.7867205207948973, 0.0], | |
| [0.0, -0.11351536555795691, 0.0, -0.46327947920510265, 0.0, 0.7867205207948973]]) | |
| #result = online_slam(testdata2, 6, 2, 3.0, 4.0) | |
| #solution_check(result, answer_mu2, answer_omega2) | |
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