Robotics Project I: Furuta Pendulum Kinematics

The Furuta pendulum project forced me to learn Lee Algebra and was my first taste of using sympy for math. There were four questions in the project summarized below:

1. Resolve the position-level forward and inverse kinematics of the Furuta pendulum with the help of the coordinate systems shown as shown in the figure. Once you have the kinematic equations, answer the following questions...

2. Resolve the velocity-level forward and inverse kinematics of the Furuta pendulum and answer the following questions...

3. Implement the Furuta pendulum in MuJoCo and use its utility functions to verify all the kinematic equations you derived in Questions 1 and 2. Make sure that the frames that you define in MuJoCo match the ones given in the figure above.

4. Simulate the Furuta pendulum with MuJoCo using the fourth-order Runge-Kutta integrator for 15s under the action of gravity and a control torque on the first link given by

and record the motion of the system. Make the links cylindrical with a radius of 0.1m for the part of length d2 and 0.075m for the part with length d3...

Below you can find the full version of the instructions, the report, answers the individual questions and various other resources.