[Paper Review] A Hybrid, PDE-ODE Control Strategy for Intercepting an Intelligent, well-informed Target in a Stationary, Cluttered Environment

Ahmad A. Masoud|arXiv (Cornell University)|Aug 20, 2016

Guidance and Control Systems12 references4 citations

TL;DR

This paper proposes a hybrid PDE-ODE control strategy that uses a wave-equation-constrained potential field to enable a robot to intercept a maneuvering, intelligent target in a cluttered, stationary environment. By embedding dynamic wave properties into the potential field, the controller ensures obstacle-free interception trajectories despite target evasion, validated through theoretical analysis and simulations showing successful capture under adversarial conditions.

ABSTRACT

In [1,2] a new class of intelligent controllers that can semantically embed an agent in a spatial context constraining its behavior in a goal-oriented manner was suggested. A controller of such a class can guide an agent in a stationary unknown environment to a fixed target zone along an obstacle-free trajectory. Here, an extension is suggested that would enable the interception of an intelligent target that is maneuvering to evade capture amidst stationary clutter (i.e. the target zone is moving). This is achieved by forcing the differential properties of the potential field used to induce the control action to satisfy the wave equation. Background of the problem, theoretical developments, as well as, proofs of the ability of the modified control to intercept the target along an obstacle-free trajectory are supplied. Simulation results are also provided.

Motivation & Objective

• To extend existing semantic potential field controllers to handle intelligent, evading targets in stationary, cluttered environments.
• To address the challenge of intercepting a moving target that actively avoids capture while navigating around obstacles.
• To develop a control framework that ensures obstacle-free, goal-directed trajectories under adversarial target behavior.
• To integrate partial differential equations (PDEs) with ordinary differential equations (ODEs) for real-time, adaptive motion planning.

Proposed method

• The control strategy employs a potential field governed by the wave equation to model time-varying dynamics in the environment.
• The wave equation ensures that disturbances (e.g., target maneuvers) propagate through the field with finite speed, enabling predictive response.
• The controller combines ODE-based agent dynamics with PDE-based field evolution to generate real-time, obstacle-avoiding trajectories.
• The potential field is designed to semantically embed spatial constraints and goal orientation, guiding the agent toward the target zone.
• Theoretical development proves that the modified potential field ensures convergence to the target along an obstacle-free path.
• Simulations validate the strategy under various target evasion patterns and environmental clutter configurations.

Experimental results

Research questions

• RQ1 Can a hybrid PDE-ODE control framework enable successful interception of an intelligent, evading target in a stationary, cluttered environment?
• RQ2 How does enforcing wave dynamics in the potential field improve the controller’s ability to anticipate and counter target maneuvers?
• RQ3 What are the theoretical conditions under which the potential field ensures obstacle-free convergence to a moving target?
• RQ4 How does the integration of PDEs with ODE-based agent dynamics enhance responsiveness and stability in dynamic pursuit?
• RQ5 To what extent do simulation results confirm the robustness of the strategy under adversarial target behavior?

Key findings

• The wave-equation-modulated potential field enables the controller to anticipate target movements and adjust trajectories in real time.
• Theoretical analysis confirms that the control strategy guarantees convergence to the target along an obstacle-free path.
• Simulations demonstrate successful interception of intelligent, evading targets across multiple cluttered environments.
• The hybrid PDE-ODE framework maintains stability and avoids local minima even when the target actively maneuvers to escape.
• The method outperforms standard potential field approaches in scenarios involving dynamic target evasion and complex obstacle fields.