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, Quan Quan
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.
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
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. 4: World, body, camera, and target frames, with spherical bearing nt∈S2 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- S2 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 (%) ↑
86.7
63.3
6.7
33.3
Interception time (s) ↓
25.75±7.10
35.40±15.28
15.51±0.57
37.37±5.55
Minimum target range (m) ↓
0.55±0.55
1.40±0.33
13.26±11.67
13.59±29.76
Mean closing speed ( ms−1 ) ↑
4.25±1.04
3.02±1.21
5.81±1.09
2.11±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.
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.
Zeinab Shayan, Mohammadreza Izadi, Reza Faieghi
Autonomous Vehicles Laboratory, Department of Aerospace Engineering, Toronto Metropolitan University, Toronto, Canada.
Model Predictive Control (MPC) is widely adopted for agile multirotor vehicles, yet achieving both stability and obstacle-free flight is particularly challenging when a payload is suspended beneath the airframe. This paper introduces a Safety Enhanced Passivity-Based Nonlinear MPC (SEP-NMPC) that provides formal guarantees of stability and safety for a quadrotor transporting a slung payload through cluttered environments. Stability is enforced by embedding a strict passivity inequality, which is derived from a shaped energy storage function with adaptive damping, directly into the NMPC. This formulation dissipates excess energy and ensures asymptotic convergence despite payload swings. Safety is guaranteed through high-order control barrier functions (HOCBFs) that render user-defined clearance sets forward-invariant, obliging both the quadrotor and the swinging payload to maintain separation while interacting with static and dynamic obstacles. The optimization remains quadratic-program compatible and is solved online at each sampling time without gain scheduling or heuristic switching. Extensive simulations and real-world experiments confirm stable payload transport, collision-free trajectories, and real-time feasibility across all tested scenarios. The SEP-NMPC framework therefore unifies passivity-based closed-loop stability with HOCBF-based safety guarantees for UAV slung-payload transportation.
Flying a quadrotor through a cluttered environment requires not only planning a collision-free reference trajectory based on perceived obstacles, but the reference also needs to be dynamically feasible and within the actuation limits of the vehicle, so that the controller can track it precisely. Existing methods either optimize a smooth polynomial inside a convex corridor, which limits agility, or treat obstacles as soft costs traded against tracking performance. We propose a Nonlinear Model Predictive Planning (NMPP) that imposes perceived obstacles as hard geometric constraints and hands a full-state reference to an obstacle-blind SE(3) controller. Our planner achieves a 58-67 % lower position RMSE than a linear Model Predictive Control trajectory planner and a 41-70 % lower RMSE than a polynomial trajectory planner. It also completes all forest flights with up to 9.5 m/s speed without collisions, and achieves 86 % flight success rate under a more aggressive speed profile where a state-of-the-art planner has only 26 % success rate. The real-world deployment showed reliable execution flying up to 5.5 m/s in an unknown cluttered environment.
Ondřej Procházka, Juraj Pauko, Robert Pěnička +1
Multi-robot Systems Group, Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic