Lab Bonus

Overview

This is a bonus programming assignment following the topic of Forward Kinematics in Lab 4. The score of this assignment (100 bonus points) will be added as a 10% bonus. The problem is to derive and code the forward kinematics of the arm shown in Fig 4.18 in the textbook using the D-H formulation (50 points) and the PoE formula (50 points).

Please follow the instructions as listed below.

• Please use exactly the same file name and function name for submission.

• Note that this time you need to return the final transformation matrix T, as opposed to position only in Lab 4.

• There will be 5 test cases for each approach on autograder. All scripts will be double checked.

• It is required to use the PoE and the D-H parameters to solve the problem. In other words, PoE approach must be used in the forward_kinematics_poe.py script, and D-H approach must be used in the forward_kinematics_dh.py script. Otherwise penalty will apply and points will be deducted.

• Since this is a bonus, and to be fair with everyone, there will be no late submission option available, and we will not offer the kind of feedback we gave for Lab 4.

• No need to submit the lab report, as this is not a regular lab assignment.

Submission

1. Submission: individual submission via Gradescope

2. Due time: 11:59pm, Dec 11, Monday

3. Files to submit:

   • forward_kinematics_poe.py

   • forward_kinematics_dh.py

4. Grading rubric:

   • + 50 pts Product of Exponentials

   • + 50 pts D-H Parameters

Sample Code

• Two sample Python scripts are provided as follows.

  # forward_kinematics_poe.py
  import numpy as np
  from math import pi, cos, sin, sqrt
  import modern_robotics as mr
  
  def forward_kinematics_poe(joints, L):
      # input: length L and joint angles [theta1, theta2, theta3, theta4, theta5, theta6]
      # output: the final transformation matrix T (from frame {s} to frame {b})
      # complete the computation using Product of Exponentials
  
      return T
  

  # forward_kinematics_dh.py
  import numpy as np
  from math import pi, cos, sin, sqrt
  
  def forward_kinematics_dh(joints, L):
      # input: length L and joint angles [theta1, theta2, theta3, theta4, theta5, theta6]
      # output: the final transformation matrix T (from frame {s} to frame {b})
      # complete the computation using D-H Parameters
  
      return T
  

Specification

Figure 4.18 in the textbook is shown below.