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In this part, thetricycle-like mobile robot (shown in Figure 1) is assumed to useits front wheel to steer (a) and to drive (v)

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In this part, thetricycle-like mobile robot (shown in Figure 1) is assumed to useits front wheel to steer (a) and to drive (v). The axial distance dis still0.5(m). It is also assumed that the control inputs vand aare corrupted by Gaussian noises with zeros means and variances of and , respectively.In order to estimate the robot position accurately, external land marks are used to provide measurements that can infer the pose of the robot. Assume that a laser range finder is attached to the centre of the rear wheel axis (as shown in Figure 1). The laser sensor measures the distance rand the angle bbetween the robot and the landmark. It is assumed that the laser sensor can only measure a distance within2 m. and an angle of within from the heading direction of the car.The variancesof the sensor measurement areand .The laser readings will be given as a vector that contains two (2) columns, the first column being the range reading, and the second column being the angle (bearing) reading. The number of rows returned from the sensor depend on how many landmarks the sensor can 'see'. In addition, the order of the vectoris given as the smallest (most negative) angle being the first row and the largest (most positive) angle being the last row.It is assumed that the robot could be anywherein the space of, , and . The robot is driven by the nominal input signals of velocity v= 0.1 m/sand the steering angle a= 0.2 rad. It is also assumed thatthe sampling time of the controller and sensor is 0.05 seconds. There arefourlandmarksin this space. They are located at [2, 2.5] m[3, 2.5] m, [3, 2] mand [3, 1] m. Students are required in this part of the assignment to:1.Derive the Particle Filter (PF) algorithmfor calculating the pose of the vehicle using the measured range and bearing values.Write the MATLAB program to implement this algorithm.2.Completeand demonstrate the working of PFin MATLAB to estimatethepositions of the vehicle.Students will be provided with two files:•The actual vehicle position during the first 10 seconds of the robot motion will beprovidedon the vUWS site-the car posesare given infile name 'carpose.mat'. The car poses are generated using the nominal control velocity and steering anglewith zero mean Gaussian noises with different variances, as stated earlier.The 'carpose.mat' file contains 3rows that represent the car's x, y and qvalue at each time step -total of 201 columns that represent 0 -10 seconds at 0.05 second interval.•A MATLAB function called "sensor.m" that provides the noisy sensor reading as in a real robot situation. The function will return the sensor reading in a row vector form -each row corresponding to one landmark. The order of the row is sorted according tothe bearing reading. Type "help sensor"in MATLAB command window or read the comments in "sensor.m"for more details.3.Present at least the following resultsin your report:•Plot and compare the pose results obtained from the particlefilter with the actual data.•Plot and compare the estimation errors in xy and qfrom the particlefilter and the actual pose.•Comment on the effectiveness (or ineffectiveness) of the filter