⚡ electrical engineering

A Control Theoretic Study on Omnidirectional MAVs with Minimum Number of Actuators and No Internal Forces at Any Orientation

This paper proposes and validates a new class of omnidirectional multirotor aerial vehicles featuring a multi-body structure with passive joints, which achieves full pose controllability using a minimum number of unidirectional propellers and generates no internal forces at steady state through a derived dynamic model and feedback linearization control strategy.

Original authors: Ahmed Ali, Chiara Gabellieri, Antonio Franchi

Published 2026-07-30

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CC BY 4.0

Original authors: Ahmed Ali, Chiara Gabellieri, Antonio Franchi

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 the sky is a giant, invisible dance floor, and on it, tiny flying robots called drones are trying to perform. For a long time, these drones have been like clumsy dancers who can only move forward, backward, and spin in place. If they want to move sideways or tilt while flying, they have to twist their whole bodies awkwardly, which limits what they can do. This is because their "legs" (propellers) are all stuck pointing in the same direction, like a group of people trying to push a car while only facing forward. Scientists have been trying to build drones that can dance in any direction—sideways, upside down, or tilted—without losing their balance. This is called "omnidirectionality." The big challenge has been that making a drone do this usually requires adding too many motors, using heavy batteries, or wasting energy by fighting against itself just to stay still.

Now, picture a new kind of drone that solves this puzzle. Instead of a rigid box with fixed propellers, imagine a main body connected to arms by joints that allow them to swing, but with a specific resistance (viscous friction) rather than being completely loose. At the end of these arms are propeller units that are mounted fixed to the arms, not spinning freely on their own. The researchers behind this study, Ahmed Ali, Chiara Gabellieri, and Antonio Franchi, asked a bold question: Can we build a drone that can fly in any direction using the minimum number of motors possible, without wasting energy on internal fighting, and without needing propellers that can push and pull?

The paper proposes a new design for these "Multirotor Aerial Vehicles" (MAVs) that uses a clever trick. They suggest a structure where a main body is connected to several arms (links) via passive joints. These joints aren't powered by motors; they just let the arms swing, but they are subject to viscous friction. However, the arms are designed so that the weight of the arm and the push of the propeller create a natural balance. There are two versions of this idea: one where the arms just swing on their own (Type 1), and a more advanced version (Type 2) where at least one arm is actively controlled by a motor or a special pair of propellers that can push against each other to create a turning force.

The team found that the first version (Type 1) doesn't quite work for full freedom of movement; it's like a dancer who can spin but can't slide sideways. However, the second version (Type 2) is the star of the show. By using a smart control system (a mathematical recipe called "Input/Output Feedback Linearization"), they proved that this drone can control its position and tilt perfectly. It can hover in any orientation without generating any wasted internal forces (no fighting against itself) and uses only propellers that push in one direction, which are cheaper and more efficient.

The researchers didn't just dream this up; they built a mathematical model of the drone's physics and ran computer simulations to test it. They showed that with just the right number of inputs (equal to the number of ways the drone needs to move), the drone can stabilize itself and follow a path. They even tested how well it handles mistakes, like if the drone's weight is slightly different than expected or if a gust of wind hits it. The simulations showed that while the drone is sensitive to changes in its weight, it can still recover and fly well, especially if the wind changes quickly.

In short, this paper introduces a new, leaner way to build flying robots. It proves that you don't need a swarm of motors or expensive, reversible propellers to make a drone that can fly in any direction. By letting the drone's arms swing naturally (with controlled friction) and using a smart brain to control them, you get a machine that is lighter, cheaper, and more energy-efficient, capable of performing complex aerial dances that were previously impossible with standard designs. The authors are confident in their math and simulations, suggesting this is a solid step forward, though they note that real-world testing in a lab is the next big step to see if it flies as well in the real world as it does on the computer.

Technical Summary: Control Theoretic Study on Omnidirectional MAVs with Minimum Actuators

Problem Statement
Traditional Multirotor Aerial Vehicles (MAVs) typically feature coplanar, fixed-propeller configurations. This structural design couples translational and rotational dynamics, restricting the vehicle's ability to execute arbitrary pose trajectories (omnidirectionality). Existing solutions to achieve omnidirectionality often rely on one or more of the following: over-actuation (using more inputs than the Degrees of Freedom, DoF), reversible-thrust propellers, or the generation of significant internal forces at steady state (hovering). These approaches introduce drawbacks such as increased weight, cost, and energy waste due to internal force generation. The paper addresses the challenge of designing an MAV that achieves full omnidirectionality with a minimum number of control inputs (equal to the main body's DoF), using only unidirectional positive-thrust propellers, and generating no internal forces at equilibrium.

Methodology
The authors propose a new class of MAV designs featuring a multi-body structure where a main body is connected to links equipped with propellers via passive or active joints. Two specific configurations are analyzed in a 2D vertical plane:

Type 1: A main body connected to $N$ rigid links via passive, non-actuated joints subject to viscous friction.
Type 2: A variation where at least one link is connected via a moment-actuated friction-less joint. This actuation is achieved either by a direct servo motor (Option 1) or a coupled-rotor propeller module (Option 2) that uses differential thrust to control the joint moment.

The dynamic model is derived using the Euler-Lagrange approach, resulting in a control-affine nonlinear system. The authors analyze the system's omnidirectionality by examining the rank of the wrench Jacobian and the ability to generate arbitrary forces and moments while counteracting gravity.

To control the vehicle, the paper employs an Input/Output (I/O) Feedback Linearization strategy. The authors investigate the system's relative degree and decoupling matrix to determine if static or dynamic feedback linearization is possible. For Type 2 vehicles, a dynamic extension algorithm (DEA) is utilized to handle the singularity in the decoupling matrix, creating an extended system with a well-defined vector relative degree. The stability of the internal (zero) dynamics is also analyzed.

Key Contributions

Novel Design Concept: The paper introduces a MAV architecture that achieves full omnidirectionality with the minimum number of inputs (equal to the main body's 3 DoFs in 2D: $x, y, \phi$ ).
Theoretical Proofs:
- Theorem 1: Proves that Type 1 vehicles are neither statically nor dynamically I/O feedback linearizable, whereas Type 2 vehicles (specifically with $N=2$ ) are dynamically I/O feedback linearizable with stable zero dynamics.
- Proposition 1: Demonstrates that Type 1 vehicles are not omnidirectional at equilibrium, while Type 2 vehicles are Fully Omnidirectional (FOD), capable of applying non-zero total force in any direction with zero total moment.
Elimination of Internal Forces: The design ensures that at steady state (equilibrium), all propellers align vertically, producing zero horizontal forces and thus no internal forces, unlike many existing over-actuated designs.
Unidirectional Thrust: The system operates using only positive-thrust propellers, avoiding the complexity and energy cost of reversible-thrust mechanisms.

Results
Numerical simulations were conducted in MATLAB/Simulink to validate the controller design for a Type 2 vehicle ( $N=2$ ).

Pose Regulation: The controller successfully regulated the vehicle's pose to a desired target $(x_d, y_d, \phi_d)$ from various initial conditions, demonstrating convergence of both the main body states and the zero dynamics (passive joint variables).
Robustness Analysis:
- Parametric Uncertainty: The system showed sensitivity to mass parameters ( $m_p$ and $m_b$ ). Negative mismatches in mass estimation had the most significant impact on tracking performance. Inertial moment perturbations had minimal effect.
- External Disturbances: The closed-loop system demonstrated the ability to reject external disturbances. Performance was better against fast-varying disturbances compared to constant or low-frequency disturbances, where steady-state errors became more pronounced.

Significance and Claims
The authors claim this is the first presentation of a MAV concept that simultaneously possesses the following control-theoretic properties:

A number of control inputs equal to the main body's DoF (minimum actuation).
Full omnidirectionality (FOD).
Absence of internal forces at equilibrium.
Use of only unidirectional positive-thrust propellers.

The paper posits that translating this concept to the real world could result in MAVs that are cheaper, easier to build and maintain, and significantly more energy-efficient due to the elimination of internal forces and reversible thrust mechanisms. The study is presented as a 2D preliminary investigation intended to illustrate the concept and pave the way for future 3D extensions, robust controller design, and laboratory experiments.

Technical Summary: Control Theoretic Study on Omnidirectional MAVs with Minimum Actuators

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