辅导 7CCEMRKM ROBOT KINEMATICS ANALYSIS讲解 Python编程

Robot Kinematics & Motion Planning

7CCEMRKM

COURSE WORK

ROBOT KINEMATICS ANALYSIS

1 Introduction

In this coursework, you will work on tasks related to kinematics of a robot.

A report can be submitted as a single PDF document with a front cover page stating your name, your k number and your email address. In the report, you need describe your solutions, results, achievements, and experience learned. You may also need submit supplementary material of a short video and .xml file to demonstrate your results in task 3. You are also suggested to use Python programming to simplify and verify the matrix calculations in the tasks (optional), and you can include the Python code in .py in the submission as well. All the files need to be submitted as a .zip file to KEATS.

You are encouraged to discuss with other students on the coursework, but you need work on your report independently and plagiarism check will be conducted.

The coursework is worth 30% of the total mark for the module.

2 Task

Task 1 (40%): Consider the robot described by the D-H table below:

1) Draw a sketch of the robot defined in this D-H table, with link frames assigned to the robot.

2) Compute the translation part of the Forward Kinematics transform. bTee from the base of the robot to the end-effector.

3) Assume we require the end-effector to be at position [a, b, C]T , and we do not care about end-effector orientation. Derive the values for the robot joints q1 , q2 and q3 such that the end-effector achieves the desired position. Be sure to consider all possible solutions.

4) Compute the manipulator Jacobian with respect to end-effector position (and ignoring end-effector orientation). Find all the joint configurations where the Jacobian becomes singular.

Task 2 (40%): Fig. 1 shows a robot manipulator with three degrees of freedom. As shown in the figure, all three joints are revolute. Joint 1’s axis is not parallel to the other two. Instead, there is a twist of 90 degrees in magnitude between axes 1 and 2.

Fig. 1. A 3R nonplanar arm

1) Write down the D-H table of the robot manipulator.

2) Derive the kinematic equations of this three-link manipulator for bTw . Note that no l3need be defined.

3) Derive the inverse kinematics of this three-link manipulator.

4) Derive the Jacobian of the manipulator. Write in terms of a frame {4} located at the tip of the hand and having the same orientation as frame {3}.

Task 3 (20%): Build a robot model in MuJoCo. Follow the tutorial to modelingin MuJoCo and import one of the robot models in the model repository. Some common robots include: UR5e or UR3 robot arm by Universal Robots, Panda 7 DOF robot or Franka Research 3 by Franka Emika, IIWA by Kuka, Kinova3 by Kinova Robotics and Sawyer by Rethink Robotics.

1) Check the XML file of the robot model and draw a sketch of the robot;

2) Load the robot model, send the end-effector to a certain position [a, b, C]Tin space (e.g., [100, 35, 20]T ), and give an analysis of the movement (e.g., forward kinematics and inverse kinematics, singularity cases, but no detailed mathematical analysis is needed) in your report.

3 Report Requirement

• The report should be well written and well presented

o Very few typos/spelling/grammatical errors

o Use proper figure labels and captions

o Cite literature used as a basis of report

o Present your findings in a logical and intelligent way

• The report should touch on the various aspects listed above.

• The report should contain 8 — 12 pages of the main body of the report containing no more than 10 figures. This page limit does not include title sheet, table of contents, references or appendices. Additional figures may be presented in Appendices. Please use Times New Roman, 12 pt. when preparing report, and use 1.5 line spacing.