Planar-Sector LOS Guidance for Interception of Agile Targets with Lifting-Wing Quadcopters

Planar-Sector Line-of-Sight guidance for lifting-wing quadcopters enables robust image-based interception of agile targets by relaxing conventional conical constraints to preserve maneuverability while reducing aerodynamic penalties.

The gist

A novel Planar-Sector Line-ofSight (PS-LOS) guidance law, combined with a two-layer control architecture and a delaycompensated Extended Kalman Filter (EKF), successfully achieves long-range interception of unpredictably agile targets up to 138 m using lifting-wing quadcopters.

Platform and Perception

The research focuses on deploying a lifting-wing quadcopter platform, which combines the advantages of conventional quadrotors and tail-sitter UAVs, offering higher flight speeds, lower energy consumption, and substantially longer range. The system utilizes a fixed monocular camera for perception. To handle measurement latency inherent in visual systems (0.13 to 0.16 s), a delay-compensated EKF is employed to provide low-latency, continuous target estimates. This filter fuses high-rate IMU propagation with delayed monocular feature updates, ensuring that the estimation remains accurate even when image features are temporarily lost during agile motion.

PS-LOS Guidance Law

The core innovation is the Planar-Sector Line-ofSight (PS-LOS) constraint, which relaxes the FOV-centered conic designs used in prior work. This strategy constrains the LOS to a planar sector aligned with the camera symmetry plane—tight along the image’s horizontal axis but relaxed along the vertical axis. Formally, it is defined by:

SPS = n in S 2 such that n T hdn < sin(αlon), and n T vdn <= sin(αlat).

This constraint directly addresses Challenge 1 (FOV-induced thrust and acceleration limits) and Challenge 3 (irregular lateral and vertical target accelerations). The theoretical foundation, established in Lemma 1, shows that two orthogonal attitude angles — roll ϕ and pitch θ are sufficient to steer the acceleration toward any desired direction while maintaining LOS within the Planar-Sector region.

Control Architecture

The interception controller employs a two-layer architecture: an outer-loop thrust/LOS law and an inner-loop attitude tracker with coordinated-turn compensation.

1. The outer loop utilizes a composite Lyapunov function to design the command, enforcing sector invariance (maintaining the PS-LOS constraint) while driving the vehicle toward the target. The desired thrust command is given by:

e frd = − Re l l fa − e fg − m (− c1 evr − c2 z4 − epr − Kh∥pr∥ I − ntn T t nhd−Kv∥pr∥ I− ntn T t nvd,

where the terms involving (I - ntn T t) produce corrections tangent to the LOS manifold and realize the barrier effect on z1, z2.

2. The inner loop tracks this thrust command by aligning the body thrust axis with the desired direction using a Rodrigues construction to determine a required tilt angle. A feedback law of bω2 = − cω zω is used to ensure attitude tracking error convergence.

Aerodynamic Efficiency and Stability

A key theoretical benefit of PS-LOS is its impact on aerodynamics: The PS-LOS confines the required maneuvering forces within the symmetry plane, which reduces aerodynamic penalties because sideslip maneuvers are inefficient for lifting-wing platforms. Furthermore, a coordinated-turn correction is implemented to blend desired yaw rate for sideslip compensation with the nominal attitude command, ensuring that high flight speeds do not compromise efficiency. Stability is formally guaranteed by a composite Lyapunov analysis (Theorem 1), which proves sector invariance and asymptotic convergence of the relative position, ensuring that if the initial condition satisfies the constraint, pr → 0 as t → ∞.

Experimental Validation

Outdoor flight experiments validated the method against unpredictable agile targets under irregular lateral and vertical accelerations. The results demonstrated a 90% interception success rate for static targets and a 71% success rate for dynamic targets. Notably, the proposed approach achieved substantially greater interception range (138 m v.s. 55 m) compared to previous quadrotor-based IBVS baselines, proving its robustness in challenging conditions including wind gusts of Beaufort 2–5. The DC-EKF performance showed that it accurately predicts target position approximately 0.1 ∼ 0.2 s before the visual feature measurements arrive, effectively compensating for delay and maintaining continuity during frame drops.

Performance Comparison

The proposed controller significantly outperforms previous methodologies in range and robustness, as summarized in Table II:

**Compared to [8], our work yields substantially greater interception range (138 m v.s.

As a fastidious researcher, I have analyzed this paper, Planar-Sector LOS Guidance for Interception of Agile Targets with Lifting-Wing Quadcopters. The core contribution lies in moving beyond conventional Line-of-Sight (LOS) constraints (conical regions) to a more maneuverable planar sector constraint (PS-LOS) specifically tailored for lifting-wing platforms.

Here are the specific improvements and what the resulting AI system can achieve:

The proposed framework enhances existing Image-Based Visual Servoing (IBVS) systems by integrating platform-specific dynamics with advanced geometric guidance laws, resulting in a highly robust and agile interception system.

1. Refined Guidance Law for Agility:

The introduction of the Planar-Sector Line-of-Sight (PS-LOS) constraint replaces restrictive conical constraints with a planar sector aligned with the camera symmetry plane.

2. Enhanced Maneuverability Envelope:

The PS-LOS formulation mathematically proves that only two attitude angles (roll and pitch) are sufficient to steer the thrust vector toward any desired target direction, while maintaining LOS within the sector. This enlarges the feasible acceleration set compared to traditional methods, effectively removing a significant performance gap between the interceptor and agile targets.

3. Aerodynamically Efficient Control:

The PS-LOS constraint confines required maneuvering forces primarily within the vehicle's symmetry plane. This minimizes sideslip maneuvers, which are aerodynamically inefficient for lifting-wing quadcopters, leading to reduced aerodynamic penalties while preserving high control agility.

4. Two-Layer Hierarchical Control Architecture:

The system implements a sophisticated two-layer controller:

a. Outer Loop (Thrust/LOS Law): Uses Barrier Lyapunov Functions and PS-LOS error terms to enforce the sector invariance constraint while simultaneously driving the vehicle toward the target position and velocity (using relative position/velocity errors).

b. Inner Loop (Attitude Tracker with Coordinated-Turn Compensation): Tracks the thrust command, incorporating a coordinated turn correction term that compensates for high flight speeds and sideslip inefficiencies, ensuring smooth and efficient attitude tracking.

5. Low-Latency State Estimation:

The integration of a Delay-Compensated Extended Kalman Filter (DC-EKF) addresses the inherent latency in monocular visual sensing (0.13–0.16s). The DC-EKF fuses high-rate Inertial Measurement Unit (IMU) propagation with delayed image feature updates, allowing for continuous, low-latency target state estimation even during aggressive maneuvers or temporary loss of visual tracking.

The improved AI system can perform the following:

1. Precision Interception of Unpredictable Targets: The system can reliably intercept agile targets exhibiting significant lateral and vertical accelerations (as validated up to 138 m) in outdoor environments, outperforming baseline quadrotor IBVS methods in both range and robustness.

2. Robustness Against Environmental Disturbances: It maintains accurate tracking under challenging conditions, including strong winds (Beaufort 2–5), by effectively incorporating dynamic disturbances into the state estimation loop via the DC-EKF.

3. High-Speed, Energy-Efficient Tracking: The coordinated-turn compensation ensures that at high speeds (up to 10.8 m/s), the vehicle maintains aerodynamic efficiency by minimizing energy waste from sideslip, while still executing rapid acceleration and precise maneuvers dictated by the PS-LOS law.

4. Real-Time Autonomous Engagement: The combination of low-latency estimation and robust guidance allows for near real-time decision-making in interceptor UAVs, enabling autonomous capture of non-cooperative targets without relying on pre-defined flight paths or GPS.