Memory-Augmented Potential Field Theory: A Framework for Adaptive Control in Non-Convex Domains

2025-09-23

AI Summary

Randomized optimal control often converges to local optima in complex non-convex environments and lacks the capacity to learn from historical trajectories or adapt online. To address this, we propose a memory-augmented adaptive control framework that, for the first time, embeds historical trajectory experience into potential field theory—yielding a dynamic memory potential field capable of online modeling of state-space topology and adaptive policy refinement. Our approach requires no domain-specific prior knowledge or offline training, while guaranteeing both non-convex escape capability and asymptotic convergence. Integrated with Model Predictive Path Integral (MPPI) control for real-time optimization, it significantly improves control performance on challenging non-convex tasks. Extensive experiments demonstrate its effectiveness, robustness, and computational efficiency on high-dimensional, nonlinear systems—including robotic dynamics—under realistic constraints.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Search and Optimization: Sampling/Simulation-based Search
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Stochastic optimal control methods often struggle in complex non-convex landscapes, frequently becoming trapped in local optima due to their inability to learn from historical trajectory data. This paper introduces Memory-Augmented Potential Field Theory, a unified mathematical framework that integrates historical experience into stochastic optimal control. Our approach dynamically constructs memory-based potential fields that identify and encode key topological features of the state space, enabling controllers to automatically learn from past experiences and adapt their optimization strategy. We provide a theoretical analysis showing that memory-augmented potential fields possess non-convex escape properties, asymptotic convergence characteristics, and computational efficiency. We implement this theoretical framework in a Memory-Augmented Model Predictive Path Integral (MPPI) controller that demonstrates significantly improved performance in challenging non-convex environments. The framework represents a generalizable approach to experience-based learning within control systems (especially robotic dynamics), enhancing their ability to navigate complex state spaces without requiring specialized domain knowledge or extensive offline training.

Problem

• Overcoming local optima traps in stochastic optimal control for non-convex domains
• Integrating historical trajectory data into control systems for adaptive optimization
• Enabling controllers to learn from past experiences without extensive offline training

Innovation

• Memory-augmented potential fields encode state space topology
• Framework enables controllers to learn from past experiences
• Implementation in MPPI controller improves non-convex navigation