ENPM667 Project 1

An Optimal Control Approach to Robust Control of Robot Manipulators

Group of 2:

• Yashveer Jain : 119252864
• Mayank Sharma : 119203859

Overview:

With Uncertainty in state dynamics and input matrix, for Robot Manipulator, the controlling become difficult and there different ways to design controller, either using Robust Control Approach or Optimal Control Approach. Here we're implementing the paper which uses Optimal Control Approach i.e LQR controller to solve the Robust Control problem of Robot Manipulator.

Results for $\epsilon = 0$

Plot

Animation

Install dependencies

pip install -r requirements.txt

Run

python3 code/scara.py <path/to/store/result image file> <epsilon value b/w (0,1)>

• example:

python3 code/scara.py results/e_0.png 0

Note:

• If path argument are not given, then script will exit.
• By default
  • epsilon = 0 if epsilon argument is not given.
  • animation output = True, and need to set it to False manually in line 228 in the file, if animation is not needed.
• dt should be very small, currently we are using dt = 0.01.
• total time taken as 50 sec instead of 100 sec because of higher code runtime.
  • for changing total_time, in line 233, when calling method run_controller, you can give total_time as argument, [file](code/ scara.py).

Interactive code

Interactive code can be found here

Report

click here

Presentation

click here

Reference:

• Feng Lin and R. D. Brandt, "An optimal control approach to robust control of robot manipulators," in IEEE Transactions on Robotics and Automation, vol. 14, no. 1, pp. 69-77, Feb. 1998, doi: 10.1109/70.660845.
• https://automaticaddison.com/linear-quadratic-regulator-lqr-with-python-code-example/