An Efficient Numerical Function Optimization Framework for Constrained Nonlinear Robotic Problems

2025-01-28

AI Summary

This paper addresses the challenge of optimizing constrained nonlinear black-box functions—lacking closed-form expressions—for real-time robot trajectory and control optimization. Method: We propose a model-free gradient-based optimization framework that uniquely integrates first-order gradient line search with a priority-aware constraint-handling mechanism based on null-space projection of the constraint Jacobian, requiring neither analytical gradients nor system derivatives. The method supports generic black-box function interfaces and is implemented efficiently in C++. Contributions/Results: (1) It achieves strict feasibility and high computational efficiency, overcoming traditional limitations that require explicit modeling or higher-order derivatives; (2) it delivers real-time performance—converging in milliseconds—across diverse robot dynamics and motion planning tasks; (3) an open-source implementation includes representative numerical experiments and standardized robotics benchmarks, demonstrating strong generalizability and engineering practicality.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Learning & Optimization for ROB
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• Robotics
• Optimization
• Complex Scenarios

Innovation

• Real-time Optimization
• Gradient and Priority Algorithm
• C++ Implementation