Generate the range data using the robot pose

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Reference no: EM132648584

49928 Design Optimisation for Manufacturing - University of Technology Sydney

Project: Nonlinear Programming

OBJECTIVE:

This project provides students an opportunity to apply the knowledge and problem solving skills obtained in the nonlinear programming and other optimisation techniques to a practical optimisation problem.

TASKS and REQUIREMENTS:
(1) Understand the optimisation problem;
(2) Develop the mathematical model;
(3) Applying the required optimisation techniques to solve the problem (if the optimisation techniques arc not specified in the problem, then any optimisation software, program or toolbox can be used);
(4) Perform other tasks as required.
(5) Write a project report.
(6) Only one of the group members need to submit in Canvas. However, all the group members should he able to explain the report and the code/files submitted. Some students might be selected to do a viva before the marks are given.
(7) Each student also needs to submit a separate one page report individually, talking about each group member's contribution in the group project with your justifications, and any individual reflection from the group project. This will be used to evaluate the individual contributions of each student.

Problem. Localisation using range only information

A simple two-dimensional robot localisation problem using range information can be formulated as an optimisation problem.

Suppose a mobile robot is navigating in an environment and it observes 4 landmarks. The (x,y) position of the 4 landmarks are known. The robot can only observe the range to the 4 landmarks. The range means the distance between the landmark and the robot. The problem is to estimate the robot position using the ranges and the landmark positions.

(I) Generate the range data using the robot pose and 4 landmark positions as shown in the following figure.

(2) Derive the model of the localisation problems with 4 landmarks; solve the problem: apply at least two different optimisation techniques/software and compare the results.

(3) Add some small noises on the range data and solve the problem again.

(4) Change the number of landmarks and their positions, formulate and solve another two problems.

(5) Discuss the conditions when the problem can or cannot be solved.

Attachment:- Figure.jpg

Reference no: EM132648584

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