Mobile Robotics - A Moving Robot in the Environment - Robotics Assignment Help

Assignment Task

There are two parts in this assignment:

Part I: Build and simulate the kinematic model of this robot (Demonstrate this part by tutorial sessions in Week 6

1. Derive kinematic equations for both types of mobile robots.

2. Using SIMULINK (a MATLAB toolbox) to build the kinematic models of the robots and simulate and demonstrate the behaviour of the vehicle subject to:

i. Constant driving velocity and a constant steering angle.

ii. Constant driving velocity and a linearly changing steering angle.

iii. Linearly changing driving velocity and linearly changing steering angle. It is assumed that the maximum driving velocity is (1.5+0.03G) m/s, the maximum driving acceleration is (0.2+0.01G) m/s2 , the maximum steering angle and steering velocity are p/4 rad, and 0.3 rad/s, respectively. (where G is your group number)

3. The robots are required to follow a trajectory. Plan the driving acceleration and steering velocity profiles for the front wheel steering and back wheel driving robot so that the robot will follow the path. Apply the same control profile to the front wheel steering and front wheel driving robot. Is the outcome the same? Why?

4. Present at least the following results in your report:

• Compare the results obtained from the two models and discuss the meaning of the results.

• Calculate the minimum radius of curvature of the circle the vehicle can drive around. Confirm this with simulation results.

Part II: Localisation using an Extended Kalman Filter (Demonstrate this part by tutorial sessions in Week 8. In this part, the tricycle-like mobile robot (shown in Figure 1) is assumed to use its front wheel to steer (a) and its back wheels to drive (v). The axial distance d is still (m) (to the nearest millimetre), where G is your group number. It is also assumed that the control inputs v and a are corrupted by Gaussian noises with zeros means and variances of ! " = 2.5 × 10#$ (m2 /sec2 ) and % " = 3.6 × 10#$("), 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 r and the angle b between the robot and the landmark. The variance of the sensor measurement is & " = 10#'(") and ( " = 7.26 × 10#)("). The robot is starting from an initial pose of [0,0,0], and the sampling time of the controller and sensor is 0.05 seconds. Only two landmarks, located at [3, 4] m and [4, 4] m are visible by the robot during the course of motion. The nominal input signals are v = 0.1 m/s and the steering angle a = 0.2 rad. Students are required in this part of the assignment to:

1. Derive the discrete time kinematic equation of the robot and the observation equations. Derive the equations for calculating the pose of the vehicle using the Extended Kalman filter (EKF) based on the measured range and bearing values.

2. Write a program in MATLAB to calculate the estimated positions of the vehicle using the EKF developed above. The actual control signals and the land mark measurements during the first 40 seconds of the robot motion will be provided on the vUWS site – the input signals are the same for all students (file name ‘contrlsig.mat’) and measurement values are group based (file name ‘measdat#.mat’, where # is the group number). These control and measurements have been affected by zero mean Gaussian noises with different variances, as stated earlier. The file ‘contrlsig.mat’ contains two rows – the first row is the input velocity and the second row is the input steering angle. The ‘measdat#.mat’ file contains 4 rows and the first 2 rows are corresponding to the range and the last 2 rows are bearing readings to the two landmarks.

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