Towards safe and optimal flight: Viability Kernel MPC for Fully Actuated Multirotor
Authors: Massimiliano Bertoni, Alberto Piccina, Gianni Lunardi, Elias Fontanari, Andrea Del Prete, Angelo Cenedese, Giulia Michieletto
Organizations: Department of Management and Engineering, University of Padova, Vicenza, Italy · Industrial Engineering Department, University of Trento, Trento, Italy · Department of Information Engineering, University of Padova, Padova, Italy · Department of Industrial Engineering, University of Padova, Padova, Italy
Industrial aerial robotics demands safety guarantees for navigation in unstructured environments while optimizing performance and computational efficiency. This paper presents a method for generating safe pose trajectories for fully actuated multirotors within a Model Predictive Control (MPC) framework, leveraging both viability theory and data-driven methods. Obstacle avoidance is enforced through dynamically computed axis-aligned bounding boxes, providing formal safety guarantees without exhaustive offline reachability analysis. Numerical simulations on a fully actuated tilted hexarotor validate the approach, demonstrating successful navigation in cluttered environments with real-time computational performance.
Figures & tables
Fig. 1 : Planar representative example of AABB (red area) in presence of obstacles (grey boxes).
Fig. 2 : Viability kernel for the α -Ted6R along only y -axis. Background color represents the outcomes of NN with red area identifying the viable set, black dots are the solution of the OCP ( 5 )
center [m]
dimensions [m]
obstacle
co,x
co,y
co,z
ℓo,x
ℓo,y
ℓo,z
1
2.0
0.0
0.5
0.5
2.0
2.0
2
−1.5
0.0
1.0
0.5
3.0
3.0
3
0.0
0.0
3.0
2.0
2.0
0.5
TABLE I : Obstacle parameters.
m
[kg]
mass
3.500
J
[kgm2]
inertia matrix
diag(0.155,0.147,0.251)
l
[m]
arm length
0.385
rp
[m]
propeller radius
0.172
r
[m]
safe radius
0.557
uˉ
[Hz2]
max squared spinning rate
1082
TABLE II : UAV platform parameters.
Fig. 3 : Pose trajectory tracking performance of the α -Ted6R using the terminal-constraint MPC with safe abort. 3Dview: red boxes indicate the time-varying AABBs, while gray blocks represent obstacles.
Fig. 4 : Pose trajectory tracking performance of the α -Ted6R using the terminal-constraint MPC with safe abort. States’ evolution (blue) over the reference (red).
Safe motion planning develops methods for robots and vehicles to reach goals while avoiding collisions and respecting dynamic and uncertainty constraints.
Department of Power Generation Technologies and Materials, Ricerca sul Sistema Energetico (RSE) S.p.A., 20134 Milan, Italy · Department of Cybernetics, Czech Technical University in Prague, 12135 Prague, Czech Republic