Fast Assignment of Pursuers to Intercept Stationary or Maneuvering Targets using Function Approximation

Core Concepts

This paper presents a neural network-based function approximator to efficiently compute the minimum time required for a pursuer to intercept a stationary or maneuvering target. This enables rapid construction of a cost matrix for solving an assignment problem that allocates pursuers to targets to minimize the maximum assigned intercept time.

Abstract

The paper considers two types of asset guarding engagements:

Assigning n pursuers to intercept n stationary targets
Assigning n pursuers to intercept n maneuvering targets guided by proportional navigation towards a single stationary asset

For each pursuer-target pair, an optimal control problem is formulated to determine the minimum time required for the pursuer to intercept the target. This involves solving a computationally expensive nonlinear optimal control problem.
To accelerate this process, the paper proposes using neural networks as function approximators. The neural networks are trained offline to predict:

Whether a pursuer can intercept a target
The minimum time required for a pursuer to intercept a target, given that interception is possible

The function approximators are then used to rapidly construct a cost matrix, which is input to a bottleneck assignment problem to determine the optimal assignment of pursuers to targets that minimizes the maximum assigned intercept time.
The paper demonstrates the effectiveness of this approach on simulated engagements of varying sizes (3x3, 5x5, 10x10) for both stationary and maneuvering targets. The function approximation method is able to compute the assignments orders of magnitude faster than the baseline method of solving the optimal control problems directly, while maintaining near-optimal assignment quality.
The paper also analyzes the robustness of the function approximators to variations in the maneuvering target's proportional navigation guidance law, showing that the approximators maintain good performance even when the targets use different guidance gains than those used in training.

Stats

The minimum time required for pursuer i to intercept target j is denoted as Ci,j.
The maximum of the assigned intercept times, Jbottleneck(C, Z), is the cost associated with a given assignment Z on cost matrix C.

Quotes

"The neural networks are trained offline, thus allowing for real-time online construction of cost matrices."
"In most cases, the approximators achieve assignments with optimal worst case intercept time."

Key Insights Distilled From

Fast Assignment in Asset-Guarding Engagements using Function Approximation

by Neelay Junna... at arxiv.org 04-15-2024

https://arxiv.org/pdf/2404.08086.pdf

Deeper Inquiries

How could this approach be extended to handle unbalanced assignment problems, where the number of pursuers and targets differ

In order to handle unbalanced assignment problems where the number of pursuers and targets differ, the approach presented in the context can be extended by incorporating a mechanism to dynamically adjust the number of pursuers or targets based on the specific scenario. This could involve introducing a step in the algorithm that evaluates the imbalance in the number of pursuers and targets and then adapts the assignment process accordingly. For instance, if there are more pursuers than targets, the algorithm could prioritize assigning multiple pursuers to the same target or allow for some pursuers to remain unassigned. On the other hand, if there are more targets than pursuers, the algorithm could consider assigning multiple targets to the same pursuer or introducing virtual pursuers to balance the assignment. By implementing such adaptive strategies, the approach can effectively handle unbalanced assignment problems while maintaining efficiency and accuracy in the assignment process.

What are some potential limitations or failure modes of the neural network-based function approximators, and how could they be addressed

While neural network-based function approximators offer significant advantages in terms of computational efficiency and real-time applicability, there are potential limitations and failure modes that need to be considered. One limitation is the generalization capability of the neural networks, as they may struggle to accurately approximate the minimum intercept times for pursuer-target pairs that significantly deviate from the training data distribution. This could lead to inaccuracies in the assignment process, especially in scenarios with complex dynamics or unforeseen variations. To address this, continuous monitoring and retraining of the neural networks with diverse and representative data can help improve their generalization performance and mitigate potential failure modes. Additionally, incorporating uncertainty estimation techniques, such as Bayesian neural networks, can provide insights into the reliability of the function approximations and enable more robust decision-making in the assignment process.

What other real-world applications beyond missile allocation could benefit from this type of rapid combinatorial optimization enabled by function approximation

Beyond missile allocation scenarios, there are several real-world applications that could benefit from the rapid combinatorial optimization enabled by function approximation techniques. One such application is in autonomous vehicle routing and scheduling, where vehicles need to be efficiently assigned to tasks or destinations based on dynamic environmental conditions and constraints. By leveraging function approximators, real-time optimization of vehicle assignments can be achieved, leading to improved traffic flow, reduced congestion, and enhanced overall system efficiency. Another application is in emergency response coordination, such as dispatching medical teams or resources to different locations during crises or disasters. The ability to quickly determine optimal assignments using function approximation can help streamline emergency response efforts, allocate resources effectively, and minimize response times. Additionally, in supply chain management, function approximation-based optimization can be utilized to optimize warehouse operations, distribution routes, and inventory management, leading to cost savings, improved logistics, and enhanced customer satisfaction. By applying the principles of rapid combinatorial optimization to these diverse real-world applications, significant operational efficiencies and performance enhancements can be achieved.