3D Guidance Law for Safely Enclosing a Moving Target with Maximal Coverage

Core Concepts

The proposed 3D guidance law allows a pursuer (UAV) to safely enclose an arbitrarily moving target while providing maximal coverage around the target.

Abstract

The paper presents a 3D guidance law for a pursuer (UAV) to enclose an arbitrarily moving target with maximal coverage while ensuring the pursuer's safety. The key highlights are:

The guidance strategy steers the pursuer to a safe region of space surrounding the target, allowing it to maintain a certain distance from the target while offering greater flexibility in positioning and converging to any orbit within this safe zone.

The approach uses nonholonomic constraints to model the vehicles with accelerations as control inputs and coupled engagement kinematics to craft the pursuer's guidance law.

The Lyapunov Barrier Function is leveraged to constrain the distance between the pursuer and the target within asymmetric bounds, thereby ensuring the pursuer's safety within the predefined region.

The proposed guidance law guarantees the global convergence of the range error with respect to the predefined state constraints, ensuring the pursuer remains within the safe region surrounding the target.

The guidance law only requires relative information between the pursuer and the target, making it suitable for GPS-denied environments.

The effectiveness and robustness of the algorithm are validated through high-fidelity quadrotor simulations under various challenging target maneuver scenarios.

Stats

The pursuer's desired linear speed is 5 m/s.
The desired proximity between the pursuer and the target is 8 m.
The safe region for the pursuer is defined by the bounds 5 m ≤ r ≤ 15 m.

Quotes

"Our approach is distinguished by the use of nonholonomic constraints to model vehicles with accelerations serving as control inputs and coupled engagement kinematics to craft the pursuer's guidance law meticulously."
"We leverage the concept of Lyapunov Barrier Function as a powerful tool to constrain the distance between the pursuer and the target within asymmetric bounds, thereby ensuring the pursuer's safety within the predefined region."

Key Insights Distilled From

3D Guidance Law for Maximal Coverage and Target Enclosing with Inherent Safety

by Praveen Kuma... at arxiv.org 04-26-2024

https://arxiv.org/pdf/2404.16312.pdf

Deeper Inquiries

How can the proposed guidance law be extended to handle multiple pursuers enclosing a single target or multiple targets

The proposed guidance law can be extended to handle multiple pursuers enclosing a single target or multiple targets by implementing a coordination strategy among the pursuers. Each pursuer can follow the same guidance law to maintain a safe distance from the target(s) while maximizing coverage. To avoid collisions between pursuers, a communication protocol can be established to ensure that they do not converge on the same path or orbit. Additionally, the guidance law can be modified to include rules for pursuer-pursuer interactions, such as maintaining a minimum separation distance or coordinating movements to enclose the target(s) efficiently.

What are the potential limitations of the approach in terms of handling external disturbances or sensor uncertainties

The approach may have limitations in handling external disturbances or sensor uncertainties, as these factors can affect the accuracy of the relative information used for control. External disturbances, such as wind gusts or sudden changes in the target's trajectory, can lead to deviations in the pursuer's motion and potentially compromise the safety and enclosing behavior. Sensor uncertainties, including measurement noise or limited sensor range, can introduce errors in the relative information used for control, impacting the effectiveness of the guidance law. To address these limitations, robust control techniques, such as adaptive control or Kalman filtering, can be integrated to account for uncertainties and disturbances in the system.

How can the guidance law be further optimized to minimize the overall energy expenditure of the pursuer during the enclosing maneuver

To further optimize the guidance law and minimize the overall energy expenditure of the pursuer during the enclosing maneuver, several strategies can be implemented:

Trajectory Planning: Incorporate trajectory planning algorithms to generate energy-efficient paths for the pursuer to enclose the target(s) while considering constraints on acceleration and velocity.
Dynamic Programming: Utilize dynamic programming techniques to optimize the pursuer's control inputs over time, considering energy consumption as a cost function to be minimized.
Online Optimization: Implement online optimization algorithms, such as model predictive control, to continuously adjust the pursuer's control inputs based on real-time information and energy constraints.
Energy-Aware Control: Develop energy-aware control strategies that dynamically adjust the pursuer's speed and acceleration based on the energy consumption rate, ensuring efficient use of resources while enclosing the target(s).
Sensor Fusion: Integrate sensor fusion techniques to improve the accuracy of relative information and reduce uncertainties, enabling more precise control actions and energy-efficient maneuvers.