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
\[ \tau = -15 sgn \dot{\theta_2} \]
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.
Final Design Report
A detailed technical report exhaustively detailing all math and reasoning, assumes a high degree of familiarity with subject matter.
Open
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Video of the Simulation
Here is a video of me running the Jupyter notebook for question 4, it shows the simulation and the graphs created by it.
