Organizations: Department of Robotics Engineering, Worcester Polytechnic Institute, Worcester, MA 01609 USA · Nanyang Technological University, Singapore
Safety-critical quadrotor navigation in cluttered environments typically relies on hierarchical architectures in which a high-level safety filter modifies position references that are then tracked by a separate attitude controller. However, this separation can create a mismatch between translational safety objectives and attitude evolution. To address this gap, we propose a safety controller based on fourth-order control barrier functions (CBFs) that explicitly incorporates the full nonlinear quadrotor dynamics, including attitude dynamics and torque-level actuation. Furthermore, we apply the integral high-order CBF technique to resolve the mixed-relative degree issue in the derived constraint formulation. The resulting formulation enforces obstacle-avoidance constraints while optimizing control torques, granting the safety layer direct authority over attitude behavior and eliminating the hierarchical disconnect inherent in reference-tracking safety filters. We validate the approaches in both high-fidelity simulation and real-world flight experiments, demonstrating reliable constraint satisfaction and successful obstacle avoidance. These results suggest that torque-level high-order CBFs provide a practical pathway to provably safer quadrotor navigation under full rigid-body dynamics.
Figures & tables
Fig. 1: The quadrotor flight trajectory with the fourth-order CBF-QP for obstacle avoidance.
Fig. 2: System convention definition: W and B denote the inertial frame and the body frame respectively.
Fig. 3: The cascaded control structure: the nominal NMPC controller and the CBF-QP safety filter
Fig. 4: One example obstacle layout at each clutter level, with n=12 (top), n=20 (middle), and n=28 (bottom). The red dashed line is the minimum-snap reference trajectory, the red disk marks the start position, and the red star marks the goal. Green cylinders and orange spheres are obstacles, and the gray box is the flight volume enforced by the boundary constraints.
Fig. 5: The fourth-order CBF-QP records no collision at any clutter level. Outcome of 100 randomly generated environments per obstacle count n , reported as the percentage of trials ending in success, collision, and deadlock. A trial counts as a success when the quadrotor reaches the goal region without contacting an obstacle. Every remaining trial is a deadlock, in which the quadrotor stops on an obstacle boundary without violating the safety constraint.
Fig. 6: Schematic illustration of the cluttered real-world experiment environment.
Fig. 7: Three-dimensional visualization of the three measured quadrotor trajectories and the cluttered obstacle environment.
Fig. 8: Comparison of the CBFs value h across three flights.
Safety-critical control designs controllers that keep physical systems within hard safety constraints despite uncertainty, disturbances, and limited actuation.
We study high-order safety-critical control of quadrotor teams under bounded inputs and pairwise collision-avoidance constraints. Squared-distance barriers may lose thrust effectiveness when the relative displacement is orthogonal to the available thrust directions, while nonsingular constraints may still be jointly infeasible under shared bounds. We characterize both phenomena through pairwise effectiveness and aggregate feasibility measures. A torque-aware dynamic extension exposes attitude torques in a fourth-order barrier and prevents the extended-input row from vanishing under positive thrust. Gaussian processes directly learn the fourth-order HOCBF residual, providing robust margins without differentiating unknown perturbations. Under residual-bound and persistent-feasibility assumptions, the resulting QP guarantees collision avoidance and recovers the nominal input whenever it satisfies the robust safety and actuator constraints.
Omayra Yago Nieto, Leonardo Colombo
Universidad Polit´ecnica de Madrid, Spain · Centre for Automation and Robotics (CSIC-UPM), Ctra. M300 Campo Real, Km 0,200, Arganda del Rey - 28500 Madrid, Spain
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 investigates the optimal safety control problem of nonlinear control systems by proposing novel high-order control barrier functions (HOCBFs). Different from zeroing HOCBFs, two novel HOCBFs are derived and the safety controllers are designed in an explicit way. Next, we implement vector Lyapunov function approach to propose a novel high-order control Lyapunov function (HOCLF) for the stabilization control problem. The relations between the proposed and existing HOCBFs are discussed. Afterwards, the compatibility of the proposed HOCLF and HOCBF is addressed to guarantee the stabilization and safety control objectives simultaneously, and thus the optimal controller is established. Finally, a numerical example from the navigation problem of quadrotors is presented to illustrate the efficacy of the derived results.
Neng Li, Zuodong Pan, Jiaxing Wang +2
Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, Dalian University of Technology, Dalian 116024, China