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

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 (7)

• Figure 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.
• Figure 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).
• Figure 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.
• Figure 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.
• Figure 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.

Theorems & Definitions (1)

• Remark 1