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
FI,FB
Inertial and body-fixed frames
ξ=[x,y,z]⊤,ξ˙
Position and velocity in FI
R∈SO(3),ω
Attitude; body angular velocity
γ=[α,β]⊤
Payload swing angles ( xz/yz planes)
pQ=ξ,pL
Quadrotor / payload positions
mQ,mL,l,g
Quadrotor/payload masses; cable length; gravity
TABLE I: Notation (core symbols)
Fig. 2: Coordinate frames and configuration of a quadrotor with a slung payload: the inertial frame FI with origin O , the body-fixed frame FB , cable length l , and swing angles α (in xz plane) and β (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 w1,w2,w3 are marked.
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 dmin .
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 ( ∣α∣,∣β∣ )
54.94∘
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)
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.
This paper presents a safety-critical centralized nonlinear model predictive control (NMPC) framework for cooperative payload transportation by two quadrupedal robots. The interconnected robot-payload system is modeled as a discrete-time nonlinear differential-algebraic system, capturing the coupled dynamics through holonomic constraints and interaction wrenches. To ensure safety in complex environments, we develop a control barrier function (CBF)-based NMPC formulation that enforces collision avoidance constraints for both the robots and the payload. The proposed approach retains the interaction wrenches as decision variables, resulting in a structured DAE-constrained optimal control problem that enables efficient real-time implementation. The effectiveness of the algorithm is validated through extensive hardware experiments on two Unitree Go2 platforms performing cooperative payload transportation in cluttered environments under mass and inertia uncertainty and external push disturbances.
Ruturaj S. Sambhus, Yicheng Zeng, Kapi Ketan Mehta +2
R.S. Sambhus, Y. Zeng, K. K. Mehta, and K. Akbari Hamed are with the Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA · J. Kim is with The University of Texas at El Paso, El Paso, TX 79968, USA
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