Memory-Augmented Potential Field Theory: A Framework for Adaptive Control in Non-Convex Domains
This addresses the problem of adaptive control in complex non-convex domains, especially for robotic dynamics, by enabling experience-based learning without specialized domain knowledge, though it appears incremental as it builds on existing control methods.
The paper tackles the problem of stochastic optimal control methods getting trapped in local optima in non-convex landscapes by introducing Memory-Augmented Potential Field Theory, a framework that integrates historical experience to dynamically construct memory-based potential fields, resulting in significantly improved performance in challenging non-convex environments.
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.