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

Seyedreza Rezaei; Junjie Kang; Amaldev Haridevan; Jinjun Shan

cs.ROMar 9, 2026

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

Authors: Seyedreza Rezaei, Junjie Kang, Amaldev Haridevan, Jinjun Shan

Organizations: Department of Earth and Space Science and Engineering, York University, Toronto, ON M3J 1P3, Canada

Abstract

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.

Figures & tables

Fig. 1: Illustration of a quadrotor with a slung payload navigating in a cluttered environment. The swinging load expands the effective geometry, motivating the need for stability and safety-aware control.

Symbol	Meaning
$\mathcal{F}_{I},\ \mathcal{F}_{B}$	Inertial and body-fixed frames
$\xi=[x,y,z]^{\top},\ \dot{\xi}$	Position and velocity in $\mathcal{F}_{I}$
$R\in SO(3),\ \omega$	Attitude; body angular velocity
$\gamma=[\alpha,\beta]^{\top}$	Payload swing angles ( $xz/yz$ planes)
$p_{Q}=\xi,\ p_{L}$	Quadrotor / payload positions
$m_{Q},\ m_{L},\ l,\ g$	Quadrotor/payload masses; cable length; gravity

TABLE I: Notation (core symbols)

Panel of Figure 3 — Fig. 2: Coordinate frames and configuration of a quadrotor with a slung payload: the inertial frame $\mathcal{F}_{I}$ with origin $O$ , the body-fixed frame $\mathcal{F}_{B}$ , cable length $l$ , and swing angles $\alpha$ (in $xz$ plane) and $\beta$ (in $yz$ plane).

Fig. 3: Block diagram of the proposed SEP-NMPC framework, where state and obstacle data are fed into the optimal control problem (OCP) enforcing passivity (stability) and HOCBF (safety) constraints to generate control inputs for safe, stable trajectory tracking.

Fig. 4: Top-view trajectories of the quadrotor–payload system. The quadrotor path is a solid curve color-coded by planar speed (see colorbar), while the payload path is the red dashed curve. Circular red disks denote obstacle positions; waypoints $w_{1},w_{2},w_{3}$ are marked.

Panel of Figure 6 — Fig. 5: Dynamic obstacle scenario. Left: Reciprocal avoidance between the ego quadrotor–payload system (black/grey) and two moving intruder drones (red/green), with dashed lines indicating the maintained safety corridors. Right: Position trajectories of the quadrotor (blue), payload (red), and target (green, dotted) along the $x$ -, $y$ -, and $z$ -axes.

Fig. 6: Representative safety margins during dynamic obstacle avoidance: (a) payload-obstacle 1 and (b) drone-obstacle 2, both compared against the enforced minimum distance $d_{\min}$ .

Fig. 7: Top-view trajectories from real-world experiments with a single obstacle. Each subplot shows 20 repeated trials, color-coded by time. Top row: (left) 1st-order CBF without passivity, (middle) state-constraint without passivity, (right) high-order CBF (HOCBF) without passivity. Bottom row: (left) 1st-order CBF with passivity, (middle) state-constraint with passivity, (right) proposed SEP–NMPC with high-order CBF and passivity. Without passivity, both CBF and state-constraint approaches show boundary violations and inconsistent convergence. HOCBF restores feasibility but overshoot persists. Adding passivity improves smoothness and safety, while SEP-NMPC achieves the most reliable avoidance and convergence.

Method	Viol./Infeas.	Overshoot (#)	Solve [ms]
State Constraint only	16 / 19	0	5.26
State Constraint + Passivity	14 / 17	0	7.75
1st-Order CBF only	6 / 18	0	4.90
1st-Order CBF + Passivity	6 / 8	3	7.52
High-Order CBF only	0 / 0	4	5.06
SEP-NMPC	0 / 0	0	8.74

TABLE II: Ablation on single-obstacle case (20 runs).

Metric	Result
Success rate	20/20
Min clearance (median)	0.53 m (IQR 0.51–0.55)
Max swing angle ( $\|\alpha\|,\|\beta\|$ )	$54.94^{\circ}$
Tracking RMSE xyz	0.035 m (median)
Solver time	8.74 ms (median)
Overruns $>$ 10 ms	0%

TABLE III: Experimental Results of SEP-NMPC (Single-Obstacle, 20 Trials)

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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

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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

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