Video Demos

Project Summary

Project objective

Derive and implement forward and inverse kinematics for a UR3e robot arm in order to solve a block puzzle 

Summary

This project was especially engaging because the lecture material aligned perfectly with our lab work, allowing us to apply newly learned math concepts to a real system. Learning linear algebra and immediately using it in practice made for an effective and rewarding experience.

We began with forward kinematics and coordinate frame transformations to establish a foundation. Once we understood these, we explored inverse kinematics and the different techniques roboticists use to handle problems with infinite or no solutions. In the lab, we derived these equations and verified their accuracy by commanding the robot to specific positions and physically measuring the end effector's coordinates. For our project, however, the inverse kinematics were simplified into a geometry problem due to set constraints. Once derived, we could precisely control the robot’s movements.

Takeaways

• Robot arms run into singularities frequently

• Linear algebra is incredibly powerful

• Keep a safe distance from robot arms

• Programming physical systems to function predictably and accurately is incredibly fulfilling

Forward Kinematics

Inverse Kinematics Derivation

Forward Kinematics are useful to know where the arm will be, but if you want to tell the arm to go somewhere, what are the 𝜃 values required for each joint? Inverse Kinematics is the method of calculating the angle of each joint in order for the arm to reach a desired position. This process is much more complex than Forward Kinematics, but in this project was simplified to a simple geometric solution.

Close form solution given certain constraints:

1. Elbow always up position between Links 3 and 5

2. Pitch and roll of the end effector are fixed 

3. Link 5 is always parallel to the baseplate

4. 𝜃5 is always -90

Note: The output 𝜃 values from the derived equations were tested by using Forward Kinematics to backcheck the input coordinates