johnlime/ik_lqr

Basic classical control theory-related projects regarding inverse kinematics and linear quadratic regulator control.

ik_lqr

Basic classical control theory-related projects.

Getting Started

Execute the following command in the main directory.

export PYTHONPATH=$PWD

Recommended Dependencies

python=3.8.12
numpy=1.21.2
tensorflow=2.7.0
matplotlib=3.5.1
control=0.9.1
gym=0.21.0
box2d-py=2.3.8
cma=3.2.2
scipy=1.8.0

Projects

Continuous Cartpole Control

• Control system modeled using gradient descent on $\dot x = Ax + Bu$
• Cartpole control solver
  • Manual eigenvalue placement
  • Search $T = A - BK$ that maximizes the return using CMA-ES
  • Continuous LQR
• Linear system classification analysis for $T$
• Demo:

python run/cartpole.py

https://github.com/johnlime/ik_lqr/tree/master/run/continuous_cartpole_dynamics

Discrete Cartpole Control [Suboptimal]

• Control system modeled using gradient descent on $x[t+1] = Ax[t] + Bu[t]$
• Cartpole control solver
  • Manual eigenvalue placement
  • Search $T = A - BK$ that maximizes the return using CMA-ES
  • Continuous and discrete LQR
• Linear system classification analysis for $T$

https://github.com/johnlime/ik_lqr/tree/master/run/discrete_cartpole_dynamics

Inverse Kinematics using Pseudoinverse of Jacobian

• Uses the "pigeon" environment
• Jacobian matrix calculated manually.
• Demo:

python run/pigeon_ik.py