Be sure to read lab instructions carefully. When asked questions in the lab, responses should be full english sentences.

Learning objectives:

• Practice with Python
• Practice with Pixi, a modern software package manager
• Learning to use inverse kinematics solver
• Learning to work with URDF files
• Learning to use visualization as a way to debug inverse kinematics solutions and URDF files

First, we must install a package manager to install software for us. Pixi is a relatively new cross-platform package management tool that will come in handy this quarter as we work with various robotic systems. It is especially good for managing Python packages and dependencies.

To install pixi on linux, run the following command in a shell:

curl -fsSL https://pixi.sh/install.sh | sh

or use wget:

wget -qO- https://pixi.sh/install.sh | sh

See the Pixi website above for install instructions on other platforms.

In this repository, run pixi install to initialize the packages we will need.

Run pixi shell to start a shell with our software. Work in this shell for the rest of the lab.

URDF stands for Unified Robot Description Format. It is an XML-based text format for representing a robot model. The full specification can be found here.

There are many tools for creating, viewing, and editing URDF files. One is included in this pixi package.

Try running

yourdfpy ./ur5/ur5_gripper.urdf

and a window should open, allowing you to inspect the robot model.

Open the URDF file in a text editor and inspect the file. As you may notice, these files are not the nicest to read and write by humans.

Our URDF file was created from a "xacro" file, a macro language for describing XML. Inspect the xacro file here.

1. From the xacro file, can you determine the lengths of each link of the robot arm? What are the lengths? Given these, as well as the visualization of our robot arm in yourdfpy, what do you think the maximum range of the robot arm is (approximately)? Note that units are in meters.

In a terminal, run pixi run setup then jupyter lab. The second commmand will open a browser window. This is the Jupyter Lab interface.

Click the "497 Kernel" button in the top of the home page.

Then, use the sidebar to open the file my_IK.ipynb. Execute cells of code in order, from top to bottom, using the Shift + Enter keys.

Play around with different target end effector positions, and see what effect they have on the resulting robot arm poses.

2. Can you get your robot end effector to the maximum range you estimated in Q1, along any of the x/y/z axes? Why or why not?

3. Write code to find and visualize the 3D volume of points that are reachable by the robot arm. Hints: the forward kinematics function gives you the actual position of the end effector for a given target position. The target position is visualized as a red dot in the original plotting code. You want to randomly sample from points on a large sphere around the robot, and attempt to get the robot to reach those points, such that the arm is fully "stretched". Record the resulting points, and visualize. You may want the "Convex Hull" method in the "scipy" library, as well as the method plot_trisurf from the matplotlib library. AI is allowed for producing the visualization code, but not for sampling from the sphere. Sampling points on the surface of a sphere is a non-trivial problem.

4. Define and visualize a plane in the space with the robot arm; the plane should not intersect the robot arm when all the joints are set to zero position. Write code to determine if any part of the robot arm is intersecting the plane for an arbitrary pose of the robot arm, and include at least three test cases for your method.

5. Write code to generate a trajectory that starts from the robot arm at zero position, and moves the end effector in such a way that the end effector approaches very near to the plane, but no part of the robot arm intersects the plane. Create an mp4 animation of your robot arm moving (either directly in python, or by saving multiple .png files to disk and animating the series of png files with a program like ffmpeg, and submit along with your writeup.

Hint: manually define a few "safe" waypoints, starting from the zero position. Look at the inverse kinematics module and try setting the starting_nodes_angles using previous "safe" solutions. You may also try setting the orientation mode.

(Extra credit) Visualize the trajectory of the robot end effector by "tracing a line" in your visualization, and make the robot arm "draw something" on the plane.