Background
The allocation matrix describes how the rotor inputs of a multirotor generate forces and torques on the vehicle. Controllers rely on this model to distribute the requested actuation among the available rotors.In practice, the nominal allocation matrix can differ from the true input-to-force relationship. Mounting inaccuracies, changes in rotor effectiveness, and aerodynamic interference can all affect this relationship. For omnidirectional and morphing multirotors, these effects can also vary significantly with the vehicle's configuration and operating conditions.
Experiments with an omnidirectional octa-rotor have shown that allocation-model errors can bias external-force estimates and cause loss of contact during physical interaction. Identifying allocation maps from free-flight data improved contact performance, including sliding along a cylindrical surface. [1]
A key challenge is that an inaccurate allocation model, sensor noise, and external forces can produce similar effects in the measured motion. Learning a useful model during flight therefore requires informative measurements and careful decisions about when to learn.
Objective
The objective of this thesis is to develop and experimentally validate a method for identifying the allocation matrix of a multirotor and using it in the control scheme in flight, with guaranteed closed-loop stability, physical-consistency and performance. The work will combine system identification, geometric control, real-time implementation, and experimental validation on the OmniMorph platform.
Expected outcomes
- An identification method for the allocation matrix.
- An assessment of which parameters can be reliably identified and which maneuvers provide sufficient excitation.
- A real-time implementation with physically meaningful parameter estimates.
- Simulation and hardware experiments evaluating whether identification improves tracking and allocation accuracy as operating conditions change.
- An assessment of the benefits and limitations of the identified model for physical-interaction tasks.
- Practical guidelines for estimator tuning, measurement filtering, and deciding when to update or retain the current allocation estimate.
Required or preferred skills
- A solid background in dynamical systems, control, linear algebra, and optimization.
- Experience with MATLAB, Python, or C++.
- Interest in system identification, geometric control, aerial robotics, and experimental work.
- Previous experience with state estimation, control allocation, or real-time robotic systems is beneficial.
Reference
[1] R. Veenstra, A. Ali, C. Gabellieri, and A. Franchi, "6D Physical Interaction with an Omnidirectional Aerial Robot," Drones, 10(2), 129, 2026.
https://doi.org/10.3390/drones10020129