# Acrobot Swing Up with MATLAB

## TL;DR

This paper demonstrates a trajectory optimization approach to solve the swing-up task for 2-link and 3-link acrobots using MATLAB, including derivation of equations and simulation of robot dynamics.

## Contribution

It introduces a manual derivation of acrobot dynamics and applies direct collocation for trajectory optimization in MATLAB, addressing both 2-link and 3-link configurations.

## Key findings

- Successful simulation of passive robot dynamics
- Effective trajectory optimization with bounds
- Validation of complex 3-link acrobot dynamics

## Abstract

This note presents a solution of the swing-up task of two acrobots using trajectory optimization method. The equations of motion for 2-link and 3-link acrobot are manually derived, and then form the dynamics of the robots. Numerical integration method is used to simulate the behaviour of passive robots, with the goal of showing the correctness of the complicated dynamics of the 3-link acrobot. Direct collocation method is used to optimize the trajectory of state and control of the robots with bounds on both.