Analysis & Assumptions What is the focus of assignment about? Analysis refers to the process of examining and evaluating relevant information to reach at some conclusion. Often during the analysis you may need to make certain assumptions. In this assignment you are required to analyze a system in order to predict its behavior. Certain assumptions are made to simplify the analysis, and their effect on the outcome is investigated. The Problem: Consider the ultrasonic sensor. Assume that the sensor is mounted in the center of the front side of the robot. The robot is programmed to stop if the sensor detects any obstacle. The robot is approaching, from a far distance, a wall with an open gate that is I m wide, along a line that goes straight through the center of the gate. The robot is only 15 cm wide. If the beam of the sensor is very narrow, the robot will pass through the gate, because it will not detect any obstacle in the way. But because of the significant beam width (as you noticed in class), the sensor may detect reflections from the wall and generate a "false alarm", causing the robot to stop and not go through the gate. You are required to analyze the situation in order to predict the behavior of your robot. Use the maximum detection range (R) of the sensor and the beam width () as measured in class. Make the following assumption (A): that the maximum range is the same at any beam angle within the detectable space. (a) Provide an illustrative sketch for the problem. Show all known quantities. (b) Carry out the analysis to find out if your robot will pass through the gate or not. (c) The narrower the beam the more expensive the sensor. If it is desired that the robot passes through a gate of any width without false alarm, would you insist on a sensor with a beam width close to zero, or can you tolerate some beam width? Why? (no quantitative answer required) (d) The assumption (A) is made to simplify the analysis. Practically, the range at the sides on the beam is shorter that that at the center. If we re-run the calculation with Assumption A removed, which of the following statement(s) is true? (i) If the robot passes with Assumption A imposed, it will pass when it is removed. (ii) If the robot does not pass with Assumption A imposed, it will not pass when it is removed. (iii) If the robot passes with Assumption A imposed, it may or may not pass when it is removed. (iii) If the robot does not pass with Assumption A imposed, it may or may not pass when it is removed.