ISB-NMPC: Interception-Oriented Spherical-Bearing Nonlinear Model Predictive Control for Quadrotors

Li Hong; Linkai Liu; Xiangyu Ren; Shuli Lv; Chen Min; Chunjiang Wu; Yujun Zhang; Dingchen Zeng

cs.ROOct 26, 2026

ISB-NMPC: Interception-Oriented Spherical-Bearing Nonlinear Model Predictive Control for Quadrotors

Authors: Li Hong, Linkai Liu, Xiangyu Ren, Shuli Lv, Chen Min, Chunjiang Wu, Yujun Zhang, Dingchen Zeng,

Organizations: Li Hong, Chen Min, and Yujun Zhang are with Shen Yuan Honors College, Beihang University, Beijing, China · Linkai Liu, Xiangyu Ren, Shuli Lv, Dingchen Zeng, and Quan Quan are with the School of Automation Science and Electrical Engineering, Beihang University, Beijing, China. · Chunjiang Wu is with the Hangzhou International Innovation Institute, Beihang University, Hangzhou, China.

Abstract

Quadrotor interceptors equipped with strapdown cameras offer a low-cost solution for physically countering unauthorized UAVs. However, this configuration inherently couples vehicle maneuvering and camera pointing, creating a conflict between rapid closing and maintaining target visibility. We present interception-oriented spherical-bearing nonlinear model predictive control (ISB-NMPC), which couples spherical-bearing prediction with nonlinear quadrotor dynamics to jointly optimize target-directed closing motion and visibility. An attitude-compensated extended Kalman filter on S^2 estimates target bearing motion, compensates for perception delay, and predicts target bearings to guide scale-adaptive detection. Across 30 paired simulation trials, ISB-NMPC achieves an interception success rate of 86.7%, the highest among the evaluated controllers, with a mean per-trial target-visible time of 99.11%. Outdoor flights demonstrate acquisition of a 30 cm target at approximately 150 m, with interceptor speed reaching 17 m/s in the long-range flight and approximately 14 m/s while pursuing a quadrotor-towed maneuvering target. The software and hardware are open source at https://github.com/HOLYNOTBAD/ISB-NMPC and https://github.com/HOLYNOTBAD/holydrone, respectively.

Figures & tables

Panel of Figure 1 — Fig. 1: Outdoor flight experiments with ISB-NMPC. Trajectories are colored by interceptor speed; insets show onboard views.

Fig. 2: Closing–visibility trade-off: target-directed acceleration tilts the strapdown camera and may reduce the target’s FOV margin.

Fig. 3: Onboard architecture integrating scale-adaptive detection, DC- $\mathbb{S}^{2}$ EKF bearing estimation, ISB-NMPC, and PX4 actuation.

Fig. 4: World, body, camera, and target frames, with spherical bearing $\mathbf{n}_{t}\in\mathbb{S}^{2}$ and image-plane projection. Axes $x$ , $y$ , and $z$ are red, green, and blue, respectively.

Fig. 6: Detection modes and timing of delay compensation and ROI prediction. Superscript $p$ denotes forward predictions from the latest posterior, without modifying the EKF state.

Fig. 5: DC- $\mathbb{S}^{2}$ EKF geometry: spherical back-projection, rotation compensation, propagation, and tangent-space correction. Bearings and tangent bases are shown schematically in the camera frame at measurement time.

Fig. 7: ISB-NMPC simulation trajectories: (a) all 30 trials, (b) selected successful trials, and (c) all failed trials. Colors indicate interceptor and target speeds; green markers denote interception and red crosses denote failure.

Metric	ISB- NMPC	PS-LOS	LOS- IBVS	Back- stepping
Interception performance
Success rate (%) $\uparrow$	86.7	63.3	6.7	33.3
Interception time (s) $\downarrow$	$25.75\pm 7.10$	$35.40\pm 15.28$	$15.51\pm 0.57$	$37.37\pm 5.55$
Minimum target range (m) $\downarrow$	$0.55\pm 0.55$	$1.40\pm 0.33$	$13.26\pm 11.67$	$13.59\pm 29.76$
Mean closing speed ( $\mathrm{m\,s^{-1}}$ ) $\uparrow$	$4.25\pm 1.04$	$3.02\pm 1.21$	$5.81\pm 1.09$	$2.11\pm 1.66$
Target visibility

TABLE I: Simulation comparison of interception controllers over 30 paired random-walk target-motion trials.

Fig. 8: Paired simulation trajectories: (a) ISB-NMPC, (b) PS-LOS, (c) LOS-IBVS, and (d) backstepping. All methods share target motion and initial geometry. Colors indicate speed; green markers denote interception and red crosses denote failure.

Fig. 9: Target image coordinates from online detections, offline results, and filtered estimates: $u$ (top) and $v$ (bottom). Right panels enlarge the highlighted intervals.

Fig. 10: Flight interception: onboard images at 0, 7, and 8.5 s (top); stacked MPC cost components and interceptor speed (right axis) below.

Quadrotor Control

Quadrotor control studies how to stabilize, guide, and adapt aerial robots under demanding flight conditions and physical constraints.

See all 127 papers

Robust Integrated Planning and Control for Quadrotors in Dynamic Environments via NMPC with CBF Penalties
May 31, 2026Zeinab Shayan, Mohammadreza Izadi, Reza FaieghiNonlinear MPC Control Barrier Functions
Autonomous Vehicles Laboratory, Department of Aerospace Engineering, Toronto Metropolitan University, Toronto, Canada.
SEP-NMPC: Safety Enhanced Passivity-Based Nonlinear Model Predictive Control for a UAV Slung Payload System
Mar 9, 2026Seyedreza Rezaei, Junjie Kang, Amaldev Haridevan +1Nonlinear MPC Quadrotor Control
Department of Earth and Space Science and Engineering, York University, Toronto, ON M3J 1P3, Canada
NMPP: Nonlinear Model Predictive Planning for Agile UAV Flight in Cluttered Environments
Oct 6, 2026Ondřej Procházka, Juraj Pauko, Robert Pěnička +1Constrained Motion Planning Nonlinear MPC
Multi-robot Systems Group, Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic

May 31, 2026J/K move · Enter open · S save

Robust Integrated Planning and Control for Quadrotors in Dynamic Environments via NMPC with CBF Penalties

Zeinab Shayan, Mohammadreza Izadi, Reza Faieghi

Autonomous Vehicles Laboratory, Department of Aerospace Engineering, Toronto Metropolitan University, Toronto, Canada.

Nonlinear MPC Control Barrier Functions Robust Control Quadrotor Control Dynamic Obstacle Avoidance

Open paper AskPDF arXiv

This paper presents a new robust integrated planning and control (IPC) strategy for multirotor uncrewed aerial vehicles. We propose a nonlinear model predictive control (NMPC) formulation that embeds control barrier functions (CBFs) as exponential penalties, improving feasibility while ensuring smooth obstacle avoidance under tight input bounds. The penalty weights provide a practical tuning knob to trade off tracking accuracy against avoidance aggressiveness. We enhance the system robustness by employing a high-gain disturbance observer (HGDO) to estimate and compensate for external disturbances. We also incorporate a Kalman filter (KF) for computationally efficient, real-time prediction of obstacle motion, enabling avoidance of moving obstacles. Comparative studies against both conventional NMPC and NMPC with hard CBF constraints, validated in Gazebo and hardware experiments, demonstrate superior feasibility, safety, and robustness. To the best of our knowledge, this is the first hardware-validated NMPC-CBF IPC framework, offering a practical step toward safe quadrotor deployment in dynamic environments.

Abstract

Quadrotor Control

Explore similar work

Robust Integrated Planning and Control for Quadrotors in Dynamic Environments via NMPC with CBF Penalties

SEP-NMPC: Safety Enhanced Passivity-Based Nonlinear Model Predictive Control for a UAV Slung Payload System

NMPP: Nonlinear Model Predictive Planning for Agile UAV Flight in Cluttered Environments