Optimal Control Strategy for an Acrobot

Utilizing Direct Collocation (DIRCOL) for dynamic trajectory planning and control in a two-link acrobot.

Overview

This project explores the development of an Optimal Control Strategy for an acrobot designed to perform trapeze-style jumping. By employing Direct Collocation (DIRCOL) method, the acrobot was programmed to swing, release, and catch successive trapeze bars with precise control. The system dynamics and constraints were carefully modeled to reflect real-world scenarios, and a quadratic cost function was optimized for energy efficiency and trajectory accuracy.

AcRobot System

Objectives

  • Develop a robust control strategy for an under-actuated two-link robot.
  • Enable the acrobot to perform dynamic transitions between swinging and flying phases.
  • Optimize the system using free-time intervals for enhanced trajectory precision.
  • Minimize energy consumption while achieving smooth motion.

Dynamics Modeling

The acrobot is modeled as a two-link robot with:

  • Revolute joints connecting the links.
  • A gripper as the end effector.
  • Swinging and flying phases were analyzed separately.

Equations were derived using the Euler-Lagrange formulation

The acrobot gathering momentum in the swinging phase
The acrobot in the flying phase, heading to the next bar
Landing onto the next trapeze

Highlights

  • Free-Time Optimization: The system dynamically adjusted phase durations, improving efficiency.
  • Trajectory Accuracy: Achieved seamless transitions between trapeze bars.
  • Energy Efficiency: Quadratic cost functions minimized control efforts.