Time-Driven Dynamic MC Simulation of an AV: Consider an autonomous vehicle (AV) attempting to move in the "X direction" subject to random gusts of wind (blowing in the +- Y direction). Assume the AV has a mass of 2 kg and is traveling at a speed of 60 km/h. Assume that the impulse (change in momentum) imparted to the AV by the wind gusts over a period of 5 seconds is characterized by a normal distribution with a mean of 0 kg km/h and a standard deviation of 10 kg km/hr. (a) (2) Draw a schematic diagram of the system showing the AV, its motion, and the effect of the wind. (b) (2) Write down the equations of motion (in X and Y directions) for dt -5 sec. (c) (3) Develop and submit a MATLAB program that: Accepts the speed and mass of the AV, the time step size, the mean and standard deviation of the impulse delivered to the AV, the duration of the simulation (Ts), and number of bins. All units should be converted to MKS. Provides the following output: a. b. i. The final location of the AV (att Ts). ii. A 2-D plot of the trajectory of AV (at dt time intervals). (d) (3) Run the program for Ts- 100 s and 1,000 s and provide the resulting output below (text output should go in a table). (e) (4) Develop and submit a MATLAB program that: Accepts the speed and mass of the AV, the time step size, the mean and standard deviation of the impulse delivered to the AV, the duration of the simulation (Ts), the number of samples (Ns), and number of bins (Nb). All units should be converted to MKS. Provides the following output: a. b. wa 622 HW 4 MC Simulation-190212 (1) Compatibility Mode ailings Review View Help Tell me what you want to do Normal Heading 1 Tite SubtitieEmphasis Strong Lst Styles Paragraph deviation of the impulse delivered to the AV, the duration of the simulation (Ts). and number of bins. All units should be converted to MKS. b. Provides the following output The final location of the AV (att Ts). ii. i. A 2-D plot of the trajectory of AV (at dt time intervals). (d) (3) Run the program for Ts 100 s and 1,000 s and provide the resulting output below (text output should go in a table). (e) (4) Develop and submit a MATLAB program that: Accepts the speed and mass of the AV, the time step size, the mean and standard deviation of the impulse delivered to the AV, the duration of the simulation (Ts). the number of samples (Ns), and number of bins (Nb). All units should be a. converted to MKS. b. Provides the following output: i. The mean ending Y coordinate (in m), its associated standard deviation, and standard error in the mean. ii. A histogram graph showing the distribution of ending Y locations. (0 (4) Run the program for Ns 500, Ts 400 s and Nb-10 and provide the resulting output below (text output should go in a table). (g) (2) What do you conclude from the results table? (h) (2) Are these results consistent with the result you got from the simulation you developed in (c) and ran in (d)? Explain. (6) (2) What kind of distribution is suggested by the histogram? Explain. Is this surprising? Explain. 6) (1) How might this kind of simulation be used to evaluate the effectiveness of a self- correcting guidance algorithm? Time-Driven Dynamic MC Simulation of an AV: Consider an autonomous vehicle (AV) attempting to move in the "X direction" subject to random gusts of wind (blowing in the +- Y direction). Assume the AV has a mass of 2 kg and is traveling at a speed of 60 km/h. Assume that the impulse (change in momentum) imparted to the AV by the wind gusts over a period of 5 seconds is characterized by a normal distribution with a mean of 0 kg km/h and a standard deviation of 10 kg km/hr. (a) (2) Draw a schematic diagram of the system showing the AV, its motion, and the effect of the wind. (b) (2) Write down the equations of motion (in X and Y directions) for dt -5 sec. (c) (3) Develop and submit a MATLAB program that: Accepts the speed and mass of the AV, the time step size, the mean and standard deviation of the impulse delivered to the AV, the duration of the simulation (Ts), and number of bins. All units should be converted to MKS. Provides the following output: a. b. i. The final location of the AV (att Ts). ii. A 2-D plot of the trajectory of AV (at dt time intervals). (d) (3) Run the program for Ts- 100 s and 1,000 s and provide the resulting output below (text output should go in a table). (e) (4) Develop and submit a MATLAB program that: Accepts the speed and mass of the AV, the time step size, the mean and standard deviation of the impulse delivered to the AV, the duration of the simulation (Ts), the number of samples (Ns), and number of bins (Nb). All units should be converted to MKS. Provides the following output: a. b. wa 622 HW 4 MC Simulation-190212 (1) Compatibility Mode ailings Review View Help Tell me what you want to do Normal Heading 1 Tite SubtitieEmphasis Strong Lst Styles Paragraph deviation of the impulse delivered to the AV, the duration of the simulation (Ts). and number of bins. All units should be converted to MKS. b. Provides the following output The final location of the AV (att Ts). ii. i. A 2-D plot of the trajectory of AV (at dt time intervals). (d) (3) Run the program for Ts 100 s and 1,000 s and provide the resulting output below (text output should go in a table). (e) (4) Develop and submit a MATLAB program that: Accepts the speed and mass of the AV, the time step size, the mean and standard deviation of the impulse delivered to the AV, the duration of the simulation (Ts). the number of samples (Ns), and number of bins (Nb). All units should be a. converted to MKS. b. Provides the following output: i. The mean ending Y coordinate (in m), its associated standard deviation, and standard error in the mean. ii. A histogram graph showing the distribution of ending Y locations. (0 (4) Run the program for Ns 500, Ts 400 s and Nb-10 and provide the resulting output below (text output should go in a table). (g) (2) What do you conclude from the results table? (h) (2) Are these results consistent with the result you got from the simulation you developed in (c) and ran in (d)? Explain. (6) (2) What kind of distribution is suggested by the histogram? Explain. Is this surprising? Explain. 6) (1) How might this kind of simulation be used to evaluate the effectiveness of a self- correcting guidance algorithm
