UnderactuatedRobotics Save

I'll be implementing few algorithms in Underactuated Robotics and also solving some interesting problems

Table of Contents

• List of Custom Environments
• Quadrotor-2D
  • Trajectory Optimization on Quadrotor-2D
  • LQR on Quadrotor-2D
• CartPole Continuous
  • LQR on CartPole Contiunous
• Double Integrator
  • Value Iteration on Double Integrator
  • LQR on Double Integrator
  • Trajectory Optimization on Double Integrator
• Pendulum with Vibrating Base

List of Custom Environments

The below is a list of custom environments that I built using OpenAI gym, feel free to use them however you want

• Quadrotor-2D
• Horizontally Vibrating Pendulum
• Double Integrator

Quadrotor-2D

Consider here an extremely simple model of a quadrotor that is restricted to live in the plane. The equations of motion are almost trivial, since it is only a single rigid body, and certainly fit into our standard manipulator equations:

Trajectory Optimization on Quadrotor-2D

here

LQR on Quadrotor-2D

LQR here works essentially out of the box for Quadrotors, if linearized around a nominal fixed point (where the non-zero thrust from the propellers is balancing gravity). In this case nominal fixed point is

CartPole Continuous

The here task is to balance a simple pendulum around its unstable equilibrium, using only horizontal forces on the cart. Balancing the cart-pole system is used in many introductory courses in control because it can be accomplished with simple linear control (e.g. pole placement) techniques. Consider the full swing-up and balance control problem, which requires a full nonlinear control treatment.

LQR on CartPole Continuous

here

Double Integrator

Consider the double integrator system

If you would like a mechanical analog of the system, then you can think about this as a unit mass brick moving along the x-axis on a frictionless surface, with a control input which provides a horizontal force, u . The task is to find a policy for the system where, to regulate this brick to .

Value Iteration on Double Integrator

here

LQR on Double Integrator

here

Trajectory Optimization on Double Integrator

here

Pendulum with Vibrating Base

Consider here an actuated pendulum whose base (pivot of the rod) is forced to oscillate horizontally according to the harmonic law , where h denotes the amplitude of the oscillation and ω the frequency. The equation of motion for this system is

The goal is to design a time-dependent policy that makes the pendulum spin at constant velocity ,

below is the result through feedback cancellation,