HW4: Pincherx 100 Robot Arm's Pose in Its Zero Position and Transformation Matrices for Kinova's Gen3 Robot Arm - madibabaiasl/kinematics-robotic-arms-modern-approach GitHub Wiki

• Apply the concept of robot pose by identifying both position and orientation of a robot arm in its zero (home) position.
• Use homogeneous transformation matrices to represent the pose of the PincherX 100 and Kinova Gen3 robot arms.
• Practice connecting mathematical pose representations with real-world physical measurements using RViz and the actual hardware.
• Interpret and verify the relationship between simulation, technical drawings, and physical robot configuration.

By completing this homework, you will be able to:

• Represent a robot’s pose in its home position through a complete transformation matrix built from observed position and orientation data.
• Cross-check the transformation obtained from the calculation with physical measurements from the actual robot.
• Construct a series of transformation matrices for a multi-joint robot arm, showing how motion propagates through successive links.
• Explain the physical meaning of each transformation and confirm that the combined result matches the expected end-effector pose.
• Reflect thoughtfully on the connection between theoretical models and real robotic systems.

Understanding and verifying these transformations lays the groundwork for forward kinematics, where predicting the robot’s motion depends on chaining these matrices correctly. Whether you are programming an industrial manipulator or a mobile robot, this skill is at the core of every movement, calibration, and perception task in robotics.

• PincherX 100 Robot Arm

• Computer running Ubuntu 22.04

• ROS2 Humble

• RViz

One of the first steps to calculate the forward kinematics of an open-chain robot arm using screw theory is to find the pose in the zero position of the robot. We will calculate the full forward kinematics when studying screw theory but for now, let's complete one of the first strides.

Step 1. Launch the robot simulation in RViz as we learned in the previous activities.

• Put the robot in its home pose.

• Draw the schematic of the robot's base frame and end-effector frame or alternatively hide the robot and all other frames but the base and the end-effector frame from the left-hand side in RViz and take a screenshot to start with (5 points).

• Find the orientation of the end-effector frame w.r.t. the base frame in the robot's zero pose (home pose). This will give you the orientation part of the pose transformation matrix (5 points).

• Now use the robot's technical drawing (make sure you also verify that the measurements are correct on the physical robot) and find the position of the end-effector frame w.r.t the base frame. That will give you the position part of the transformation matrix (5 points).

This technical drawing is from Trossen Robotics Website.

• Complete the transformation matrix and call this matrix M which will give you the pose of the end-effector frame w.r.t the base frame in the robot's home position (8 points).

Step 2. Now put the physical robot in the home position and show that the matrix M makes sense. Show the measurements on the board that the robot is attached to (show that the pose is actually what you calculated) (8 points).

Kinova's Gen3 robot arm is an ultra-lightweight, modular, and adaptable robotic arm designed for research, education, and industrial applications. This robot arm has 7 degrees of freedom. The standard base and tool frames in this robot are depicted below:

The standard and tool frames of the Kinova's Gen3 robot arm.

Now for more practice, we want to find transformations between successive reference frames in this robot in the robot's zero pose. The successive frames in the 7-dof version of this robot with a spherical wrist can be depicted as below:

Successive reference frames in the Kinova's Gen3 robot arm.

Find the successive Transformation matrices ($T_{s1}, T_{12}, ..., T_{7e}$), where {s} is the base frame and {e} is the interface module frame (5.5 points for each of the matrices - 8 in total (44 points)).

• What is the transformation matrix describing the pose of the end-effector frame in the base frame? What is the easiest way to calculate this? Is this matrix what you expected (5 points)?

• Submit reports individually.
• Title, Name (5 points)
• Meeting the requirements of each part or question above that has points in front of it.
• Reflection: A short reflection on any interesting observations, surprises, difficulties, new directions that can be taken and any other feedback you may have (10 points)
• References: Note that utilizing (or not utilizing) AI should be disclosed here. You can use AI according to the allowed instances in the Syllabus. Also, 100% AI-generated content will get 0 (5 points).

Note: This activity is eligible for "best report" points in our reward system (see the reward system sheet for the criteria).