⚡ electrical engineering

Towards safe and optimal flight: Viability Kernel MPC for Fully Actuated Multirotor

This paper proposes a Viability Kernel Model Predictive Control framework for fully actuated multirotors that ensures safe, real-time navigation in unstructured environments by leveraging data-driven methods and dynamically computed bounding boxes for obstacle avoidance without exhaustive offline analysis.

Original authors: Massimiliano Bertoni, Alberto Piccina, Gianni Lunardi, Elias Fontanari, Andrea Del Prete, Angelo Cenedese, Giulia Michieletto

Published 2026-08-27

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CC BY 4.0

Original authors: Massimiliano Bertoni, Alberto Piccina, Gianni Lunardi, Elias Fontanari, Andrea Del Prete, Angelo Cenedese, Giulia Michieletto

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a drone that can fly not just in open skies, but through a cluttered warehouse, weaving between pillars, pipes, and moving machinery without ever crashing. For years, the dream of autonomous aerial robots has been held back by a simple, terrifying reality: if the computer running the drone makes a single wrong guess about where an obstacle is, the machine could spin out of control and hit something. Current safety systems often react too late, checking for collisions only after the drone has already committed to a dangerous path. To move from simple surveillance in empty fields to complex work in crowded spaces, engineers needed a way to guarantee that at every single moment, the drone has a safe way to stop or turn around, no matter what happens next.

This is the challenge tackled by a team of researchers from universities in Italy, who have developed a new way to guide fully actuated multirotor drones through messy environments. Unlike standard drones that can only push air down to move up and tilt to move sideways, these advanced machines can push air in any direction, allowing them to move sideways, spin, and hover with equal precision. The researchers' breakthrough lies in combining two powerful ideas: a mathematical concept called "viability," which asks "is there any way to stay safe from here?", and a predictive control system that plans the drone's next moves. Instead of just trying to avoid the next obstacle, their system constantly checks that the drone is always in a position where it can safely come to a complete stop or execute a pre-planned emergency landing if the path ahead suddenly becomes blocked.

The core of their method involves a clever trick to handle the complexity of the drone's physics. Calculating every possible future path for a drone in a crowded room is too slow for a computer to do in real time. To solve this, the team used a data-driven approach. They first ran thousands of simulations offline to map out the "safe zone" for the drone—a specific set of positions and speeds from which the machine could always reach a safe stop. They then taught an artificial intelligence, specifically a neural network, to recognize this safe zone instantly. Think of this neural network as a highly trained pilot who can glance at the drone's current speed and location and immediately know, "Yes, we are still in a safe spot," or "No, we are getting too close to the edge of safety," without needing to run a complex calculation.

In their experiments, the researchers tested this system on a unique six-rotor drone called the α-Ted6R, designed with tilted propellers to give it full control over its movement. They placed the drone in a simulated environment filled with static obstacles, such as large boxes and pillars, and asked it to navigate to a specific target point. As the drone flew, the computer continuously updated a virtual "safety box" around it, shrinking this box dynamically to fit the available space between obstacles. At every step, the system checked if the drone's predicted future position remained inside the safe zone identified by the neural network. If the drone ever found itself in a situation where the planned path was blocked and no safe stop was possible, the system had a built-in "safe abort" mechanism. This would immediately trigger a pre-calculated emergency maneuver, guiding the drone to a safe halt rather than letting it crash.

The results of the simulation were striking. The drone successfully navigated through the cluttered space, reaching its target while avoiding all obstacles. Even when the drone's path was temporarily blocked by a safety margin touching a virtual wall, the system adjusted its speed and direction to find a way through without losing stability. The computational performance was fast enough for real-world use, with the system making decisions in about one millisecond on average, well within the time limits required for smooth flight. The researchers demonstrated that by embedding this "safety guarantee" directly into the planning process, they could allow the drone to operate in complex, unstructured environments with a level of confidence that previous methods could not provide.

This work does not claim to have solved every problem in aerial robotics, nor does it yet prove the system works in the real world with moving people or shifting debris. However, the simulations provide a strong proof of concept. They show that it is possible to create a flight controller that is not just reactive, but fundamentally safe by design. By ensuring that the drone is always in a state where a safe future exists, the system removes the fear of the "unrecoverable state" that has long plagued autonomous flight. The path forward, as the authors note, involves testing these ideas in more dynamic environments and refining how the drone perceives its surroundings, but the foundation laid here suggests a future where drones can work alongside humans in our most crowded and complicated spaces.

Technical Summary: Viability Kernel MPC for Fully Actuated Multirotor

Problem Statement
The paper addresses the challenge of navigating fully actuated multirotors in cluttered, unstructured environments while guaranteeing safety and optimizing performance. Current industrial aerial robotics are largely limited to open-area surveillance due to a lack of robust safety guarantees for complex scenarios involving static obstacles and proximity to humans. Existing safety approaches often suffer from two main limitations: they either ensure only short-term collision avoidance without guaranteeing long-term system viability, or they rely on computationally expensive offline reachability analyses that do not scale well to high-dimensional, nonlinear systems. Furthermore, safety is frequently treated as a reactive constraint rather than an intrinsic property of the control architecture.

Methodology
The authors propose a Model Predictive Control (MPC) framework that integrates Viability Theory with data-driven methods to generate safe pose trajectories. The core methodology consists of three main components:

Viability Kernel Approximation via VBOC:
The system utilizes the Viability-Boundary Optimal Control (VBOC) approach to compute a conservative numerical approximation of the viability kernel ( $\hat{V}$ ). The viability kernel is defined as the set of states from which the system can be driven to a safe equilibrium while satisfying state and input constraints indefinitely.
- Offline Computation: An Optimal Control Problem (OCP) is solved over a finite horizon to identify the boundary of the viability kernel. This OCP maximizes the initial twist norm along a specific direction subject to dynamic constraints, input saturation (rotor limits), and state constraints.
- Neural Network Encoding: To enable real-time evaluation, the computed viability kernel boundary is encoded into a Neural Network (NN). The NN takes Euler angles, twist direction, and Axis-Aligned Bounding Box (AABB) parameters as inputs and outputs the maximum viable twist norm. This allows for computationally efficient viability checks during online operation.
Dynamic Obstacle Representation (AABB):
Unlike methods requiring exhaustive offline analysis, obstacle avoidance is enforced through dynamically computed, obstacle-free Axis-Aligned Bounding Boxes (AABB).
- A greedy shrinking algorithm is employed to compute a collision-free AABB ( $B^*$ ) around the multirotor. This algorithm iteratively shrinks the largest feasible box by displacing faces that intersect with obstacles until no collisions remain.
- This approach provides formal safety guarantees without pre-computing reachability sets for every possible environment configuration.
Terminal-Constrained MPC with Safe Abort:
The viability kernel approximation is embedded into the MPC formulation as a hard terminal constraint.
- Constraint: The predicted final state ( $x_N$ ) at the end of the MPC horizon must belong to the viability kernel ( $x_N \in \hat{V}$ ). This ensures that every feasible solution contains a state from which a safe equilibrium can be reached.
- Safe Abort Mechanism: If the MPC problem becomes infeasible (e.g., due to unexpected obstacles or constraints), the system triggers a "safe abort." It applies the last feasible control sequence and tracks the time steps until the previously planned viable terminal state is reached. Once reached, a predefined abort maneuver (solving a specific OCP to reach equilibrium) is executed, guaranteeing the system does not enter an unsafe state.

Key Contributions
The paper formalizes two primary contributions:

The numerical approximation of the viability kernel for a fully actuated multirotor navigating in cluttered environments, explicitly accounting for propeller saturation and obstacle-induced constraints via a dynamically computed AABB.
The integration of this approximation into a terminally constrained MPC framework, which guarantees a certified safe fallback state in the event of control infeasibility, thereby enabling a robust safe abort mechanism.

Results
The approach was validated through numerical simulations using a fully actuated $\alpha$ -Ted6R (a tilted hexarotor with six propellers) navigating a cluttered environment with static obstacles.

Trajectory Tracking: The system successfully navigated from an initial state to a target pose ( $\xi_r = [2, 0, 5, 0, 0, 0]^\top$ ) while avoiding obstacles, even when the target was initially outside the immediate obstacle-free box.
NN Accuracy: The Neural Network prediction of the viability kernel closely matched the solutions of the offline OCP, validating its ability to accurately encode the viability boundary.
Computational Performance: The method demonstrated real-time capability with an average iteration time of 1.00 ms (maximum 11.72 ms), well below the 20 ms sampling period. This efficiency is attributed to the NN encoding of the viability kernel and the tractable greedy AABB algorithm.
Dynamic Adaptation: The system dynamically updated the AABB as the robot moved, discovering new free space and adjusting the trajectory accordingly.

Significance and Claims
The authors position this work as a methodological proof of concept. The significance lies in providing safety guarantees for fully actuated multirotors in cluttered environments without relying on exhaustive offline reachability analysis. By embedding viability theory directly into the control loop via a neural network, the framework ensures that the system always retains a path to a safe equilibrium, even in the presence of persistent infeasibilities.

The paper modestly frames this as a foundational study. It acknowledges that the current box-based approach (AABB) is conservative and suggests that future work could explore more accurate representations of obstacle-free regions, extensions to environments with dynamic obstacles, and the integration of advanced perception or learning-based components.

Technical Summary: Viability Kernel MPC for Fully Actuated Multirotor

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