Enhancements to the DIDO Optimal Control Toolbox

TL;DR

This paper details recent mathematical and algorithmic enhancements to the DIDO optimal control toolbox, demonstrating its improved ability to solve complex, real-world problems beyond aerospace, including robotics and quantum control.

Contribution

It introduces internal algorithmic improvements to DIDO, enhancing its capability to escape local minima and handle diverse, complex optimal control problems.

Findings

Enhanced DIDO algorithms can escape local minima in trajectory optimization.

The toolbox now supports a wider range of applications including robotics and quantum control.

Demonstrated improved performance on a robotics challenge problem.

Abstract

In 2020, DIDO$^\copyright$ turned 20! The software package emerged in 2001 as a basic, user-friendly MATLAB$^\circledR$ teaching-tool to illustrate the various nuances of Pontryagin's Principle but quickly rose to prominence in 2007 after NASA announced it had executed a globally optimal maneuver using DIDO. Since then, the toolbox has grown in applications well beyond its aerospace roots: from solving problems in quantum control to ushering rapid, nonlinear sensitivity-analysis in designing high-performance automobiles. Most recently, it has been used to solve continuous-time traveling-salesman problems. Over the last two decades, DIDO's algorithms have evolved from their simple use of generic nonlinear programming solvers to a multifaceted engagement of fast spectral Hamiltonian programming techniques. A description of the internal enhancements to DIDO that define its mathematics and algorithms are described in this paper. A challenge example problem from robotics is included to showcase how the latest version of DIDO is capable of escaping the trappings of a ``local minimum'' that ensnare many other trajectory optimization methods.