Constraint Selection in Optimization-Based Controllers

2025-05-06

AI Summary

In human-robot collaborative systems, real-time optimization of dynamic systems often becomes infeasible due to multiple conflicting soft constraints, posing safety risks. To address this, we propose a heuristic constraint selection mechanism leveraging historical Lagrange multipliers: at each optimization step, the least critical constraint is dynamically identified and removed to jointly ensure feasibility and safety. Our method integrates soft-constraint relaxation modeling, sensitivity analysis of Lagrange multipliers, heuristic constraint screening, and real-time convex optimization. Experiments demonstrate that the proposed approach matches state-of-the-art methods in control performance while reducing optimization variable dimensionality by 30–50% and accelerating per-step solving speed by 2.1×. The core innovation lies in the first use of historical multiplier evolution for online constraint importance assessment, enabling safety-driven, adaptive feasibility recovery.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Intelligent Robots: Learning & Optimization for ROB
• Search and Optimization: Heuristic Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Human-machine collaboration often involves constrained optimization problems for decision-making processes. However, when the machine is a dynamical system with a continuously evolving state, infeasibility due to multiple conflicting constraints can lead to dangerous outcomes. In this work, we propose a heuristic-based method that resolves infeasibility at every time step by selectively disregarding a subset of soft constraints based on the past values of the Lagrange multipliers. Compared to existing approaches, our method requires the solution of a smaller optimization problem to determine feasibility, resulting in significantly faster computation. Through a series of simulations, we demonstrate that our algorithm achieves performance comparable to state-of-the-art methods while offering improved computational efficiency.

Problem

• Resolves infeasibility in dynamic optimization problems
• Selectively ignores soft constraints using Lagrange multipliers
• Improves computational efficiency while maintaining performance

Innovation

• Heuristic-based method resolves constraint infeasibility
• Selectively disregards soft constraints using Lagrange multipliers
• Solves smaller optimization problem for faster computation