@article {2020e-MicCenZacFra,
	title = {Hierarchical nonlinear control for multi-rotor asymptotic stabilization based on zero-moment direction},
	journal = {Automatica},
	year = {2020},
	abstract = {
We consider the hovering control problem for a class of multi-rotor aerial platforms with generically oriented propellers, characterized by intrinsically coupled translational and rotational dynamics. In doing this, we first discuss some assumptions guaranteeing the rejection of generic disturbance torques while compensating for the gravity force. These assumptions are translated into a geometric condition usually satisfied by both standard models and more general configurations. Then, we propose a control strategy based on the identification of a zero-moment direction for the exerted force and a dynamic state feedback linearization based on this preferential direction, which locally asymptotically stabilizes the platform to a static hovering condition. Stability properties of the control law are rigorously proved through Lyapunov-based methods and reduction theorems for the stability of nested sets. Asymptotic zeroing of the error dynamics and convergence to the static hovering condition are then confirmed by simulation results on a star-shaped hexarotor model with tilted propellers.},
	attachments = {https://homepages.laas.fr/afranchi/robotics/sites/default/files/2020e-MicCenZacFra.pdf},
	author = {Giulia Michieletto and Angelo Cenedese and Luca Zaccarian and Antonio Franchi}
}
@article {2019k-FurNaiZacFra,
	title = {Input Allocation for the Propeller-Based Overactuated Platform ROSPO},
	journal = {IEEE Trans. on Control Systems Technology},
	volume = {18},
	year = {2019},
	month = {11/2020},
	pages = {2720-2727},
	abstract = {We apply input allocation to a redundantly actu- ated platform driven by tilting aerodynamic propulsion units: the ROtor graSPing Omnidirectional (ROSPO). This platform represents a novel testbed for redundancy allocation designs in propeller driven platforms. The control solution is based on a hierarchical architecture, made of a high level controller for trajectory tracking, and a nonlinear input allocation algorithm. The algorithm exploits the input redundancy to take into account soft constraints associated to physical saturation limits of the actuators, and also induce reduced energy consumption. The actuator dynamics is fully taken into account in the framework and a rigorous proof of asymptotic tracking of time-varying references is guaranteed despite the impossibility of an instanta- neous force execution. The experiments on the ROSPO platform clearly show the practicability and effectiveness of the proposed approach, as well as its scalability with different degrees of over- actuation levels.},
	doi = {10.1109/TCST.2019.2944341},
	attachments = {https://homepages.laas.fr/afranchi/robotics/sites/default/files/2019k-FurNaiZacFra.pdf},
	author = {Michele Furci and Carlo Nainer and Luca Zaccarian and Antonio Franchi}
}
@conference {2017j-NaiFurSeuZacFra,
	title = {Hierarchical Control of the Over-Actuated ROSPO Platform via Static Input Allocation},
	booktitle = {20th IFAC World Congress},
	year = {2017},
	month = {07/2017},
	address = {Toulouse, France},
	abstract = {This paper addresses the problem of control allocation applied to an over-actuated hovercraft-type vehicle. A hierarchical control architecture, consisting of a high level controller for trajectory tracking, and a control allocation algorithm, is developed and proved to be effective in tracking a desired trajectory while optimizing some cost related to actuator constraints. The control allocation algorithm exploits the redundancy of the system in order to keep the actuator states inside their saturation limits and tries to minimize the power consumption of the propellers. Unlike other papers on control allocation, actuator dynamics is taken into account. The control architecture is tested through simulations that well illustrate the capabilities of the proposed control design},
	attachments = {https://homepages.laas.fr/afranchi/robotics/sites/default/files/2017j-NaiFurSeuZacFra-preprint.pdf},
	author = {Carlo Nainer and Michele Furci and Alexandre Seuret and Luca Zaccarian and Antonio Franchi}
}
@conference {2017i-MicCenZacFra,
	title = {Nonlinear Control of Multi-Rotor Aerial Vehicles Based on the Zero-Moment Direction},
	booktitle = {20th IFAC World Congress},
	year = {2017},
	month = {07/2017},
	address = {Toulouse, France},
	abstract = {A quaternion-based nonlinear control strategy is here presented to steer and keep a generic multi-rotor platform in a given reference position. Exploiting a state feedback structure, the proposed solution ensures the stabilization of the aerial vehicle so that its linear and angular velocity are zero and its attitude is constant. The main feature of the designed controller is the identification of a zero-moment direction in the feasible force space, i.e., a direction along which the control force intensity can be assigned independently of the control moment. The asymptotic convergence of the error dynamics is confirmed by simulation results on a hexarotor with tilted propellers.
},
	attachments = {https://homepages.laas.fr/afranchi/robotics/sites/default/files/2017i-MicCenZacFra-preprint.pdf},
	author = {Giulia Michieletto and Angelo Cenedese and Luca Zaccarian and Antonio Franchi}
}
@conference {2016m-SchFraZelRob,
	title = {A Rigidity-Based Decentralized Bearing Formation Controller for Groups of Quadrotor UAVs},
	booktitle = {2016 IEEE/RSJ Int. Conf. on Intelligent Robots and System},
	year = {2016},
	month = {10/2016},
	pages = {5099-5106},
	address = {Daejeon, South Korea},
	abstract = {This paper considers the problem of controlling a formation of quadrotor UAVs equipped with onboard cameras able to measure relative bearings in their local body frames w.r.t. neighboring UAVs. The control goal is twofold: (i) steering the agent group towards a formation defined in terms of desired bearings, and (ii) actuating the group motions in the {\textquoteleft}null-space{\textquoteright} of the current bearing formation. The proposed control strategy relies on an extension of the rigidity theory to the case of directed bearing frameworks in R 3{\texttimes}S1 . This extension allows to devise a decentralized bearing controller which, unlike most of the present literature, does not need presence of a common reference frame or of reciprocal bearing measurements for the agents. Simulation and experimental results are then presented for illustrating and validating the approach.},
	attachments = {https://homepages.laas.fr/afranchi/robotics/sites/default/files/2016m-SchFraZelRob-preprint.pdf , https://homepages.laas.fr/afranchi/robotics/sites/default/files/2016m-SchFraZelRob.mp4},
	author = {Fabrizio Schiano and Antonio Franchi and Daniel Zelazo and Paolo Robuffo Giordano}
}
@conference {2015k-ZelRobFra,
	title = {Bearing-Only Formation Control Using an SE(2) Rigidity Theory},
	booktitle = {54rd IEEE Conference on Decision and Control},
	year = {2015},
	month = {12/2015},
	pages = {6121-6126},
	address = {Osaka, Japan},
	attachments = {https://homepages.laas.fr/afranchi/robotics/sites/default/files/2015k-ZelRobFra-preprint.pdf},
	author = {Daniel Zelazo and Paolo Robuffo Giordano and Antonio Franchi}
}
@article {2014i-ZelRobBueFra,
	title = {Decentralized Rigidity Maintenance Control with Range Measurements for Multi-Robot Systems},
	journal = {The International Journal of Robotics Research},
	volume = {34},
	year = {2014},
	pages = {105-128},
	abstract = {This work proposes a fully decentralized strategy for maintaining the formation rigidity of a multi-robot system using only range measurements, while still allowing the graph topology to change freely over time. In this direction, a first contribution of this work is the new concept of weighted frameworks and rigidity, and of the rigidity eigenvalue, which when positive ensures the infinitesimal rigidity of a weighted framework. We then propose a distributed algorithm for estimating a common relative position reference frame amongst a team of robots with only range measurements in addition to one agent endowed with the capability of measuring the bearing to two other agents. This first estimation step is embedded into a subsequent distributed algorithm for estimating the rigidity eigenvalue associated with the weighted framework. The estimate of the rigidity eigenvalue is finally used to generate a local control action for each agent that both maintains the rigidity property and enforces additional constraints such as collision avoidance and sensing/communication range limits and occlusions. As an additional feature of our approach, the communication and sensing links among the robots are also left free to change over time while preserving rigidity of the whole framework. The proposed scheme is then experimentally validated with a robotic testbed consisting of 6 quadrotor UAVs operating in a cluttered environment.},
	keywords = {Motion control of multiple robots, Rigidity mainenance},
	attachments = {https://homepages.laas.fr/afranchi/robotics/sites/default/files/1309.0535v3.pdf , https://homepages.laas.fr/afranchi/robotics/sites/default/files/1309.0535v2.pdf},
	author = {Daniel Zelazo and Antonio Franchi and Heinrich H. B{\"u}lthoff and Paolo Robuffo Giordano}
}
@conference {2014f-ZelFraRob,
	title = {Rigidity Theory in SE(2) for Unscaled Relative Position Estimation using only Bearing},
	booktitle = {2014 European Control Conference},
	year = {2014},
	month = {06/2014},
	pages = {2703-2708},
	address = {Strasbourg, France},
	abstract = {This work considers the problem of estimating the unscaled relative positions of a multi-robot team in a common reference frame from bearing-only measurements. Each robot has access to a relative bearing measurement taken from the local body frame of the robot, and the robots have no knowledge of a common reference frame. An extension of rigidity theory is made for frameworks embedded in the special Euclidean group SE(2) = R^2  {\texttimes} S1. We introduce definitions describing rigidity for SE(2) frameworks and provide necessary and sufficient conditions for when such a framework is infinitesimally rigid in SE(2). We then introduce the directed bearing rigidity matrix and show that an SE(2) framework is infinitesimally rigid if and only if the rank of this matrix is equal to 2|V| - 4, where |V| is the number of agents in the ensemble. The directed bearing rigidity matrix and its properties are then used in the implementation and convergence proof of a distributed estimator to determine the unscaled relative positions in a common frame. Simulation results are given to support the
analysis.},
	keywords = {Localization of ground robots, Motion control of multiple robots, Rigidity mainenance},
	attachments = {https://homepages.laas.fr/afranchi/robotics/sites/default/files/2014f-ZelFraRob-preprint.pdf},
	author = {Daniel Zelazo and Antonio Franchi and Paolo Robuffo Giordano}
}
@conference {2012g-ZelFraAlgBueRob,
	title = {Rigidity Maintenance Control for Multi-Robot Systems},
	booktitle = {2012 Robotics: Science and Systems Conference},
	year = {2012},
	month = {07/2012},
	address = {Sydney, Australia},
	abstract = {Rigidity of formations in multi-robot systems is important for formation control, localization, and sensor fusion.  This work proposes a rigidity maintenance gradient controller for a multi-agent robot team.  To develop such a controller, we first provide an alternative characterization of the rigidity matrix and use that to introduce the novel concept of the rigidity eigenvalue.  We provide a necessary and sufficient condition relating the positivity of the rigidity eigenvalue to the rigidity of the formation.  The rigidity maintenance controller is based on the gradient of the rigidity eigenvalue with respect to each robot position.  This gradient has a naturally distributed structure, and is thus amenable to a distributed implementation.  Additional requirements such as obstacle and inter-agent collision avoidance, as well as typical constraints such as limited sensing/communication ranges and line-of-sight occlusions, are also explicitly considered.  Finally, we present a simulation with a group of seven quadrotor UAVs to demonstrate and validate the theoretical results.},
	keywords = {Decentralized control, Formation control, Motion control of multiple robots, Multi-robot systems, Rigidity mainenance},
	attachments = {https://homepages.laas.fr/afranchi/robotics/sites/default/files/2012g-ZelFraAlgBueRob-preprint.pdf},
	author = {Daniel Zelazo and Antonio Franchi and Frank Allg{\"o}wer and Heinrich H. B{\"u}lthoff and Paolo Robuffo Giordano}
}
