An Efficient Numerical Function Optimization Framework for Constrained Nonlinear Robotic Problems

TL;DR

This paper introduces a real-time, constraint-agnostic numerical optimization framework for robotics, enabling efficient online trajectory and control input solutions without requiring analytical problem formulations.

Contribution

It presents a novel, gradient-based optimization method that handles constraints via nullspace projections, suitable for real-time robotic applications and implemented in C++.

Findings

Supports constrained block-box functions

Enables real-time trajectory optimization

Provides open-source implementation

Abstract

This paper presents a numerical function optimization framework designed for constrained optimization problems in robotics. The tool is designed with real-time considerations and is suitable for online trajectory and control input optimization problems. The proposed framework does not require any analytical representation of the problem and works with constrained block-box optimization functions. The method combines first-order gradient-based line search algorithms with constraint prioritization through nullspace projections onto constraint Jacobian space. The tool is implemented in C++ and provided online for community use, along with some numerical and robotic example implementations presented in this paper.