A preprint reports a drone controller reaching a target pose in simulation while navigating around static obstacles, even though the target was not initially inside the obstacle-free box available to the system. The approach combines viability theory with data-driven model predictive control, or MPC, to generate pose trajectories for a fully actuated multirotor.
The paper frames the work as a methodological proof of concept for safety-aware control under state and input constraints. It uses dynamically computed axis-aligned bounding boxes to impose obstacle constraints without exhaustive offline reachability analysis.
A map of viable states
The key idea is a viability kernel, a calculated region of states used to assess whether the system can still meet its constraints. VBOC computes a conservative numerical approximation of that region, and a neural network encodes it offline for real-time evaluation.
That network has two hidden layers of 512 units each and was trained on 200,000 samples.
The hard terminal constraint is intended to leave each feasible solution with a state from which a safe equilibrium can be reached. The paper describes this as supporting a safe abort under persistent infeasibility. If an MPC solution is infeasible, the procedure applies the last feasible control sequence and triggers the abort maneuver when a counter reaches the MPC horizon.
Moving boundaries around obstacles
Obstacle avoidance uses dynamically computed axis-aligned bounding boxes, or AABBs. The paper presents this design as offering formal safety guarantees without exhaustive offline reachability analysis.
During navigation, the AABB was updated as new regions were discovered. Its z component showed a temporary plateau from 0.8 to 1.4 seconds, when the safety sphere became tangent to an AABB face.
The timing test
The reported test used the fully actuated, cant-tilted α-Ted6R hexarotor, with its dynamics integrated at 0.1 milliseconds. The document is an arXiv version 1 preprint dated 26 Aug 2026. No physical-flight validation is supplied, so the result is limited to the numerical scenario reported.
The MPC configuration used a horizon of 60 steps, a 20-millisecond sampling period and a fixed simulation duration of 5 seconds.
Reported iteration time averaged 1.00 milliseconds, peaked at 11.72 milliseconds and bottomed out at 0.12 milliseconds. It was consistently below the imposed sampling period.
What the simulation leaves open
In the viability-region comparison, the neural network's predicted region closely matched the solutions of the paper's optimal-control problem. The explicit comparison was restricted to a y-axis case, and no numerical error metric was reported.
The paper notes that the viability-kernel approximation is not necessarily control-invariant in general, although it can still be used to provide safety guarantees within the MPC framework.
The obstacle-free boxes carry another trade-off. Their greedy shrinking prioritizes computational efficiency over global optimality and may produce sub-optimal configurations in geometrically complex environments.
Taken together, the evidence is an early simulation proof of concept. The analysis reports no independent controller or planner comparison and no repeated-scenario success rate, so it does not establish how reliably the method would perform beyond the reported case.
The authors identify dynamic obstacles, advanced perception or learning components, less conservative obstacle-free representations and more efficient safety-aware optimization as future directions.
The work was partially supported by the European Union NextGenerationEU Mission 4 Component 2 project STARLIT (CUP C53D23000520006).
Paper data and sources
Original title: Towards safe and optimal flight: Viability Kernel MPC for Fully Actuated Multirotor
Authors: Massimiliano Bertoni, Alberto Piccina, Gianni Lunardi et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text