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3D Guidance Law for Flexible Target Enclosing with Inherent Safety

Praveen Kumar Ranjan, Abhinav Sinha, Yongcan Cao

Abstract

In this paper, we address the problem of enclosing an arbitrarily moving target in three dimensions by a single pursuer while ensuring the pursuer's safety by preventing collisions with the target. The proposed guidance strategy steers the pursuer to a safe region of space surrounding and excluding the target, allowing it to maintain a certain distance from the latter while offering greater flexibility in positioning and converging to any orbit within this safe zone. We leverage the concept of the 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. Further, we demonstrate the effectiveness of the proposed guidance law in managing arbitrarily maneuvering targets and other uncertainties (such as vehicle/autopilot dynamics and external disturbances) by enabling the pursuer to consistently achieve stable global enclosing behaviors by switching between stable enclosing trajectories within the safe region whenever necessary, even in response to aggressive target maneuvers. To attest to the merits of our work, we conduct experimental tests with various plant models, including a high-fidelity quadrotor model within Software-in-the-loop (SITL) simulations, encompassing various challenging target maneuver scenarios and requiring only relative information for successful execution.

3D Guidance Law for Flexible Target Enclosing with Inherent Safety

Abstract

In this paper, we address the problem of enclosing an arbitrarily moving target in three dimensions by a single pursuer while ensuring the pursuer's safety by preventing collisions with the target. The proposed guidance strategy steers the pursuer to a safe region of space surrounding and excluding the target, allowing it to maintain a certain distance from the latter while offering greater flexibility in positioning and converging to any orbit within this safe zone. We leverage the concept of the 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. Further, we demonstrate the effectiveness of the proposed guidance law in managing arbitrarily maneuvering targets and other uncertainties (such as vehicle/autopilot dynamics and external disturbances) by enabling the pursuer to consistently achieve stable global enclosing behaviors by switching between stable enclosing trajectories within the safe region whenever necessary, even in response to aggressive target maneuvers. To attest to the merits of our work, we conduct experimental tests with various plant models, including a high-fidelity quadrotor model within Software-in-the-loop (SITL) simulations, encompassing various challenging target maneuver scenarios and requiring only relative information for successful execution.
Paper Structure (10 sections, 4 theorems, 11 equations, 6 figures)

This paper contains 10 sections, 4 theorems, 11 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Pursuer-Target relative kinematics
  4. Design of control objectives
  5. Main Results
  6. Design of the pursuer's linear speed
  7. Design of the pursuer's range controller
  8. Optimal Allocation of Lateral Acceleration Components
  9. Simulation Results
  10. Conclusions

Key Result

Lemma 1

TEE2009918 Consider the open sets, $\mathcal{Z}_1 \coloneqq \{z_1 \in \mathbb{R}, -a<z_1<b\} \subset \mathbb{R}$, $\mathcal{N}\coloneqq \mathbb{R} \times \mathcal{Z}_1 \subset \mathbb{R}^{2}$ and the system $\dot{\eta} = h(t,\eta)$, where $\eta \coloneqq[w, z_1]^\top \in \mathcal{N}$ and $h$ is piec

Figures (6)

  • Figure 1: Engagement geometry.
  • Figure 2: Pursuer's regions of operation.
  • Figure 3: SITL Setup.
  • Figure 4: Pursuer's trajectories for various target maneuvers.
  • Figure 5: Pursuer's error variables for various target maneuvers.
  • ...and 1 more figures

Theorems & Definitions (7)

  • Lemma 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof