Publications
1.
Fagiano, Lorenzo; Quack, Manfred; Bauer, Florian; Carnel, Lode; Oland, Espen
Autonomous Airborne Wind Energy Systems: Accomplishments and Challenges Journal Article
In: Annual Review of Control, Robotics, and Autonomous Systems, vol. 5, 2022.
@article{Fagiano2022,
title = {Autonomous Airborne Wind Energy Systems: Accomplishments and Challenges},
author = {Lorenzo Fagiano and Manfred Quack and Florian Bauer and Lode Carnel and Espen Oland},
url = {https://www.annualreviews.org/doi/abs/10.1146/annurev-control-042820-124658undefined
https://www.sas-lab.deib.polimi.it/wp-content/uploads/2021/12/2022-AWE_AR.pdf},
doi = {10.1146/annurev-control-042820-124658},
year = {2022},
date = {2022-05-02},
urldate = {2022-05-02},
journal = {Annual Review of Control, Robotics, and Autonomous Systems},
volume = {5},
abstract = {Airborne wind energy (AWE) is a fascinating technology to convert wind power into electricity with an autonomous tethered aircraft. Deemed a potentially game-changing solution, AWE is attracting the attention of policy makers and stakeholders with the promise of producing large amounts of cost-competitive electricity with wide applicability worldwide. Since the pioneering experimental endeavors in the years 2000–2010, there has been a clear technology convergence trend and steady progress in the field. Today, AWE systems can operate automatically with minimal supervision in all operational phases. A first product is also being commercialized. However, all-around fully autonomous operation still presents important fundamental challenges that are conceptually similar to those of other systems that promise to change our lives, such as fully autonomous passenger cars or service drones. At the same time, autonomous operation is necessary to enable large-scale AWE, thus combining challenging fundamental problems with high potential impact on society and the economy. This article describes the state of the art of this technology from a system perspective and with a critical view on some fundamental aspects, presents the latest automatic control results by prominent industrial players, and finally points out the most important challenges on the road to fully autonomous AWE systems.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Airborne wind energy (AWE) is a fascinating technology to convert wind power into electricity with an autonomous tethered aircraft. Deemed a potentially game-changing solution, AWE is attracting the attention of policy makers and stakeholders with the promise of producing large amounts of cost-competitive electricity with wide applicability worldwide. Since the pioneering experimental endeavors in the years 2000–2010, there has been a clear technology convergence trend and steady progress in the field. Today, AWE systems can operate automatically with minimal supervision in all operational phases. A first product is also being commercialized. However, all-around fully autonomous operation still presents important fundamental challenges that are conceptually similar to those of other systems that promise to change our lives, such as fully autonomous passenger cars or service drones. At the same time, autonomous operation is necessary to enable large-scale AWE, thus combining challenging fundamental problems with high potential impact on society and the economy. This article describes the state of the art of this technology from a system perspective and with a critical view on some fundamental aspects, presents the latest automatic control results by prominent industrial players, and finally points out the most important challenges on the road to fully autonomous AWE systems.
2.
Sabug, Lorenzo; Ruiz, Fredy; Fagiano, Lorenzo
SMGO-Δ: Balancing caution and reward in global optimization with black-box constraints Journal Article
In: Information Sciences, vol. 605, pp. 15-42, 2022, ISSN: 0020-0255.
@article{SABUG202215,
title = {SMGO-Δ: Balancing caution and reward in global optimization with black-box constraints},
author = {Lorenzo Sabug and Fredy Ruiz and Lorenzo Fagiano},
url = {https://www.sciencedirect.com/science/article/pii/S0020025522004376},
doi = {https://doi.org/10.1016/j.ins.2022.05.017},
issn = {0020-0255},
year = {2022},
date = {2022-01-01},
urldate = {2022-01-01},
journal = {Information Sciences},
volume = {605},
pages = {15-42},
abstract = {In numerous applications across all science and engineering areas, there are optimization problems where both the objective function and the constraints have no closed-form expression or are too complex to be managed analytically, so that they can only be evaluated through experiments. To address such issues, we design a global optimization technique for problems with black-box objective and constraints. Assuming Lipschitz continuity of the cost and constraint functions, a Set Membership framework is adopted to build a surrogate model of the optimization program, that is used for exploitation and exploration routines. The resulting algorithm, named Set Membership Global Optimization with black-box constraints (SMGO-Δ), features one tunable risk parameter, which the user can intuitively adjust to trade-off safety, exploitation, and exploration. The theoretical properties of the algorithm are derived, and the optimization performance is compared with representative techniques from the literature in several benchmarks. An extension to uncertain cost/constraint function outcomes is presented, too, as well as computational aspects. Lastly, the approach is tested and compared with constrained Bayesian optimization in a case study pertaining to model predictive control tuning for a servomechanism with disturbances and plant uncertainties, addressing practically-motivated task-level constraints.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In numerous applications across all science and engineering areas, there are optimization problems where both the objective function and the constraints have no closed-form expression or are too complex to be managed analytically, so that they can only be evaluated through experiments. To address such issues, we design a global optimization technique for problems with black-box objective and constraints. Assuming Lipschitz continuity of the cost and constraint functions, a Set Membership framework is adopted to build a surrogate model of the optimization program, that is used for exploitation and exploration routines. The resulting algorithm, named Set Membership Global Optimization with black-box constraints (SMGO-Δ), features one tunable risk parameter, which the user can intuitively adjust to trade-off safety, exploitation, and exploration. The theoretical properties of the algorithm are derived, and the optimization performance is compared with representative techniques from the literature in several benchmarks. An extension to uncertain cost/constraint function outcomes is presented, too, as well as computational aspects. Lastly, the approach is tested and compared with constrained Bayesian optimization in a case study pertaining to model predictive control tuning for a servomechanism with disturbances and plant uncertainties, addressing practically-motivated task-level constraints.
3.
Terzi, Enrico; Farina, Marcello; Fagiano, Lorenzo; Scattolini, Riccardo
Robust multi-rate predictive control using multi-step prediction models learned from data Journal Article
In: Automatica, vol. In press, available online, pp. 109852, 2021.
@article{Terzi2021,
title = {Robust multi-rate predictive control using multi-step prediction models learned from data},
author = {Enrico Terzi and Marcello Farina and Lorenzo Fagiano and Riccardo Scattolini},
doi = {10.1016/j.automatica.2021.109852},
year = {2021},
date = {2021-09-06},
urldate = {2021-09-06},
journal = {Automatica},
volume = {In press, available online},
pages = {109852},
abstract = {This note extends a recently proposed algorithm for model identification and robust model predictive control (MPC) of asymptotically stable, linear time-invariant systems subject to process and measurement disturbances. Independent output predictors for different horizon values are estimated with Set Membership methods. It is shown that the corresponding prediction error bounds are the least conservative in the considered model class. Then, a new multi-rate robust MPC algorithm is developed, employing said multi-step predictors to robustly enforce constraints and stability against disturbances and model uncertainty, and to reduce conservativeness. A simulation example illustrates the effectiveness of the approach.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
This note extends a recently proposed algorithm for model identification and robust model predictive control (MPC) of asymptotically stable, linear time-invariant systems subject to process and measurement disturbances. Independent output predictors for different horizon values are estimated with Set Membership methods. It is shown that the corresponding prediction error bounds are the least conservative in the considered model class. Then, a new multi-rate robust MPC algorithm is developed, employing said multi-step predictors to robustly enforce constraints and stability against disturbances and model uncertainty, and to reduce conservativeness. A simulation example illustrates the effectiveness of the approach.
4.
Sabug, Lorenzo Jr.; Ruiz, Fredy; Fagiano, Lorenzo
SMGO: A set membership approach to data-driven global optimization Journal Article
In: Automatica, vol. 133, pp. 109890, 2021.
@article{Sabug2021,
title = { SMGO: A set membership approach to data-driven global optimization},
author = {Lorenzo Jr. Sabug and Fredy Ruiz and Lorenzo Fagiano},
doi = {10.1016/j.automatica.2021.109890},
year = {2021},
date = {2021-08-24},
urldate = {2021-08-24},
journal = {Automatica},
volume = {133},
pages = {109890},
abstract = {Many science and engineering applications feature non-convex optimization problems where the objective function cannot be handled analytically, i.e. it is a black box. Examples include design optimization via experiments, or via costly finite elements simulations. To solve these problems, global optimization routines are used. These iterative techniques must trade-off exploitation close to the current best point with exploration of unseen regions of the search space. In this respect, a new global optimization strategy based on a Set Membership (SM) framework is proposed. Assuming Lipschitz continuity of the cost function, the approach employs SM concepts to decide whether to switch from an exploitation mode to an exploration one, and vice-versa. The resulting algorithm, named SMGO (Set Membership Global Optimization) is presented. Theoretical properties regarding convergence and computational complexity are derived, and implementation aspects are discussed. Finally, the SMGO performance is evaluated on a set of benchmark non-convex problems and compared with those of other global optimization approaches.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Many science and engineering applications feature non-convex optimization problems where the objective function cannot be handled analytically, i.e. it is a black box. Examples include design optimization via experiments, or via costly finite elements simulations. To solve these problems, global optimization routines are used. These iterative techniques must trade-off exploitation close to the current best point with exploration of unseen regions of the search space. In this respect, a new global optimization strategy based on a Set Membership (SM) framework is proposed. Assuming Lipschitz continuity of the cost function, the approach employs SM concepts to decide whether to switch from an exploitation mode to an exploration one, and vice-versa. The resulting algorithm, named SMGO (Set Membership Global Optimization) is presented. Theoretical properties regarding convergence and computational complexity are derived, and implementation aspects are discussed. Finally, the SMGO performance is evaluated on a set of benchmark non-convex problems and compared with those of other global optimization approaches.
5.
Leonardo Cecchin, Danilo Saccani; Fagiano, Lorenzo
G-BEAM: Graph-Based Exploration and Mapping for Autonomous Vehicles Conference
Proceedings of the 2021 Conference on Control Technology and Applications (CCTA), 2021, ISBN: 978-1-6654-3643-4.
@conference{nokeyf,
title = {G-BEAM: Graph-Based Exploration and Mapping for Autonomous Vehicles},
author = {Leonardo Cecchin, Danilo Saccani and Lorenzo Fagiano},
url = {https://ieeexplore.ieee.org/document/9659296},
isbn = {978-1-6654-3643-4},
year = {2021},
date = {2021-08-11},
urldate = {2021-08-11},
booktitle = {Proceedings of the 2021 Conference on Control Technology and Applications (CCTA)},
pages = {1011-1016},
abstract = {A novel solution to the problem of autonomous exploration and mapping of an unknown environment by an autonomous vehicle is presented. A hierarchical control system is adopted, where a low-level reactive controller manages obstacle avoidance, and two high-level strategies are in charge of mapping and navigation tasks. The decision strategy implemented at the high-level is named G-BEAM, standing for "Graph-Based Exploration And Mapping". It builds a reachability graph used both as a trajectory planning tool and as a map. The reachability graph representation requires less storage resources with respect to a more traditional occupancy-map. It can be directly exploited to compute the system's path towards a given target or unexplored locations. The latter are ranked according to the expected information gain that is realized when they are visited. Such information gain is then used in the cost function of the navigation strategy, which is based on a receding horizon concept. The graph is updated as the autonomous vehicle moves, exploiting the sensors' measurements in a novel approach based on polyhedral under-approximations of the feasible space. The controller has been successfully tested in various simulated environments. Comparison with other approaches in state of the art shows promising performance.},
keywords = {},
pubstate = {published},
tppubtype = {conference}
}
A novel solution to the problem of autonomous exploration and mapping of an unknown environment by an autonomous vehicle is presented. A hierarchical control system is adopted, where a low-level reactive controller manages obstacle avoidance, and two high-level strategies are in charge of mapping and navigation tasks. The decision strategy implemented at the high-level is named G-BEAM, standing for "Graph-Based Exploration And Mapping". It builds a reachability graph used both as a trajectory planning tool and as a map. The reachability graph representation requires less storage resources with respect to a more traditional occupancy-map. It can be directly exploited to compute the system's path towards a given target or unexplored locations. The latter are ranked according to the expected information gain that is realized when they are visited. Such information gain is then used in the cost function of the navigation strategy, which is based on a receding horizon concept. The graph is updated as the autonomous vehicle moves, exploiting the sensors' measurements in a novel approach based on polyhedral under-approximations of the feasible space. The controller has been successfully tested in various simulated environments. Comparison with other approaches in state of the art shows promising performance.
6.
Bolognini, Michele; Fagiano, Lorenzo
A Scalable Hierarchical Path Planning Technique for Autonomous Inspections with Multicopter Drones Conference
Proceedings of the 2021 European Control Conference (ECC), 2021, ISBN: 978-94-6384-236-5.
@conference{nokey,
title = {A Scalable Hierarchical Path Planning Technique for Autonomous Inspections with Multicopter Drones},
author = {Michele Bolognini and Lorenzo Fagiano},
isbn = {978-94-6384-236-5},
year = {2021},
date = {2021-07-02},
booktitle = {Proceedings of the 2021 European Control Conference (ECC)},
pages = {787-792},
abstract = {Multicopter drones equipped with cameras can perform rapid inspections of large buildings, including those with features that are difficult to reach, like bridge pylons. In such scenarios drones can be made autonomous by providing them with a method to choose a path that maximizes the collected information during the limited flight time allowed by the battery. It is therefore crucial to optimize the trajectories to minimize inspection time and energy consumption. The problem of finding an approximately optimal path passing through a series of desired inspection points in a three-dimensional environment with obstacles is considered. A hierarchical approach is proposed, where the space containing the inspection points is partitioned into different regions and multiple instances of the TSP (Travelling Salesman Problem) are solved, decreasing the overall complexity. An extended graph is used in the TSP formulaion, in order to tackle the problem of collision avoidance while planning the trajectory between point pairs. This approach leads to an efficient and scalable method capable of avoiding obstacles, and significantly reduces the time needed to find an optimal path with respect to non-hierarchical methods. Simulation results highlight these features.},
keywords = {},
pubstate = {published},
tppubtype = {conference}
}
Multicopter drones equipped with cameras can perform rapid inspections of large buildings, including those with features that are difficult to reach, like bridge pylons. In such scenarios drones can be made autonomous by providing them with a method to choose a path that maximizes the collected information during the limited flight time allowed by the battery. It is therefore crucial to optimize the trajectories to minimize inspection time and energy consumption. The problem of finding an approximately optimal path passing through a series of desired inspection points in a three-dimensional environment with obstacles is considered. A hierarchical approach is proposed, where the space containing the inspection points is partitioned into different regions and multiple instances of the TSP (Travelling Salesman Problem) are solved, decreasing the overall complexity. An extended graph is used in the TSP formulaion, in order to tackle the problem of collision avoidance while planning the trajectory between point pairs. This approach leads to an efficient and scalable method capable of avoiding obstacles, and significantly reduces the time needed to find an optimal path with respect to non-hierarchical methods. Simulation results highlight these features.
7.
Bolognini, Michele; Fagiano, Lorenzo; Limongelli, Maria Pina
An autonomous, multi-agent UAV platform for inspection of civil infrastructure Proceedings Article
In: Proceedings of the International Conference on Structural Health Monitoring of Intelligent Infrastructure, pp. 227-234, International Society for Structural Health Monitoring of Intelligent Infrastructure (ISHMII), Winnipeg, Manitoba, R3T 2N2, Canada, 2021, ISSN: 2564-3738.
@inproceedings{Bolognini2021,
title = {An autonomous, multi-agent UAV platform for inspection of civil infrastructure},
author = {Michele Bolognini and Lorenzo Fagiano and Maria Pina Limongelli},
url = {https://web.fe.up.pt/~shmii10//ficheiros/eBook_SHMII_2021.pdf},
issn = {2564-3738},
year = {2021},
date = {2021-07-02},
urldate = {2021-07-02},
booktitle = {Proceedings of the International Conference on Structural Health Monitoring of Intelligent Infrastructure},
volume = {1},
pages = {227-234},
publisher = {International Society for Structural Health Monitoring of Intelligent Infrastructure (ISHMII)},
address = {Winnipeg, Manitoba, R3T 2N2, Canada},
abstract = {UAVs (Unmanned Aerial Vehicles) are nowadays being used more and more in Structural Health Monitoring (SHM). Their versatility, speed, and manoeuvrability make them the ideal means to perform inspections autonomously and remotely, instead of relying on visual inspections carried out by human operators. Since commercial drones have limited flight times, the information collected in this short span must be maximised: to tackle the problem of gathering the maximum amount of data in the shortest possible time, we propose a platform where a central controller coordinates multiple UAVs. We address 1) the problem of generating points of interest, i.e., positions from which a sensor reading must be taken, given a 3D model of the structure, 2) the problem of assigning the points to the drones and finding the optimal traversal order of such points, in order to minimise the total flight time and make the best possible use of each drone's battery capacity. We decouple the two problems by first generating points of interest, starting from the structure's virtual model, and then feeding those points to a central mission planner that employs a linear programming formulation to find near-optimal trajectories for each agent, guaranteeing obstacle avoidance. We also address the issue of robustness of the whole system against the failure of an aircraft. We evaluate our method by applying it to the inspection of a virtual model of an existing building. We find that our approach yields good solutions in a reasonably short time, justifying its use as a robust mission planning algorithm.},
keywords = {},
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tppubtype = {inproceedings}
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UAVs (Unmanned Aerial Vehicles) are nowadays being used more and more in Structural Health Monitoring (SHM). Their versatility, speed, and manoeuvrability make them the ideal means to perform inspections autonomously and remotely, instead of relying on visual inspections carried out by human operators. Since commercial drones have limited flight times, the information collected in this short span must be maximised: to tackle the problem of gathering the maximum amount of data in the shortest possible time, we propose a platform where a central controller coordinates multiple UAVs. We address 1) the problem of generating points of interest, i.e., positions from which a sensor reading must be taken, given a 3D model of the structure, 2) the problem of assigning the points to the drones and finding the optimal traversal order of such points, in order to minimise the total flight time and make the best possible use of each drone's battery capacity. We decouple the two problems by first generating points of interest, starting from the structure's virtual model, and then feeding those points to a central mission planner that employs a linear programming formulation to find near-optimal trajectories for each agent, guaranteeing obstacle avoidance. We also address the issue of robustness of the whole system against the failure of an aircraft. We evaluate our method by applying it to the inspection of a virtual model of an existing building. We find that our approach yields good solutions in a reasonably short time, justifying its use as a robust mission planning algorithm.
8.
Saccani, Danilo; Fagiano, Lorenzo
Autonomous UAV Navigation in an Unknown Environment via Multi-Trajectory Model Predictive Control Conference
Proceedings of the 2021 European Control Conference (ECC), 2021, ISBN: 978-94-6384-236-5.
@conference{saccani2021autonomous,
title = {Autonomous UAV Navigation in an Unknown Environment via Multi-Trajectory Model Predictive Control},
author = {Danilo Saccani and Lorenzo Fagiano},
url = {https://ieeexplore.ieee.org/abstract/document/9655166?casa_token=pJMy5RZku8gAAAAA:5O3AjQKEFuotS5uMKRhw_R061FOWoNR8ZYkPRv9DqtI_1vjLhEAwlMr07Ry8X36DEkKVYYw
},
isbn = {978-94-6384-236-5},
year = {2021},
date = {2021-07-01},
urldate = {2021-07-01},
booktitle = {Proceedings of the 2021 European Control Conference (ECC)},
pages = {1577-1582},
abstract = {A novel model predictive control (MPC) formulation, named multi-trajectory MPC (mt-MPC), is presented and applied to the problem of autonomous navigation of an
unmanned aerial vehicle (UAV) in an unknown environment.
The UAV is equipped with a LiDAR sensor, providing only a partial description of the surroundings and resulting in time-varying constraints as the vehicle navigates among the obstacles.
The control system layout is hierarchical: the low-level loops stabilize the vehicle’s trajectories and track the set-points commanded by the high-level, mt-MPC controller.
The latter is required to plan the UAV trajectory trading off safety, i.e. to avoid collisions with the uncertain obstacles, and exploitation, i.e. to reach an assigned target location. To achieve this goal,
mt-MPC considers different future state trajectories in the same Finite Horizon Optimal Control Problem (FHOCP), enabling a partial decoupling between constraint satisfaction (safety) and
cost function minimization (exploitation). Recursive feasibility and, consequently, persistent obstacle avoidance guarantees are derived under the assumption of a time invariant environment.
The performance of the approach is studied in simulation and compared with that of a standard MPC, showing good improvement.},
keywords = {},
pubstate = {published},
tppubtype = {conference}
}
A novel model predictive control (MPC) formulation, named multi-trajectory MPC (mt-MPC), is presented and applied to the problem of autonomous navigation of an
unmanned aerial vehicle (UAV) in an unknown environment.
The UAV is equipped with a LiDAR sensor, providing only a partial description of the surroundings and resulting in time-varying constraints as the vehicle navigates among the obstacles.
The control system layout is hierarchical: the low-level loops stabilize the vehicle’s trajectories and track the set-points commanded by the high-level, mt-MPC controller.
The latter is required to plan the UAV trajectory trading off safety, i.e. to avoid collisions with the uncertain obstacles, and exploitation, i.e. to reach an assigned target location. To achieve this goal,
mt-MPC considers different future state trajectories in the same Finite Horizon Optimal Control Problem (FHOCP), enabling a partial decoupling between constraint satisfaction (safety) and
cost function minimization (exploitation). Recursive feasibility and, consequently, persistent obstacle avoidance guarantees are derived under the assumption of a time invariant environment.
The performance of the approach is studied in simulation and compared with that of a standard MPC, showing good improvement.
unmanned aerial vehicle (UAV) in an unknown environment.
The UAV is equipped with a LiDAR sensor, providing only a partial description of the surroundings and resulting in time-varying constraints as the vehicle navigates among the obstacles.
The control system layout is hierarchical: the low-level loops stabilize the vehicle’s trajectories and track the set-points commanded by the high-level, mt-MPC controller.
The latter is required to plan the UAV trajectory trading off safety, i.e. to avoid collisions with the uncertain obstacles, and exploitation, i.e. to reach an assigned target location. To achieve this goal,
mt-MPC considers different future state trajectories in the same Finite Horizon Optimal Control Problem (FHOCP), enabling a partial decoupling between constraint satisfaction (safety) and
cost function minimization (exploitation). Recursive feasibility and, consequently, persistent obstacle avoidance guarantees are derived under the assumption of a time invariant environment.
The performance of the approach is studied in simulation and compared with that of a standard MPC, showing good improvement.
9.
Bolognini, Michele; Fagiano, Lorenzo
Lidar-based navigation of tethered drone formations in an unknown environment Conference
IFAC-PapersOnLine, vol. 5, no. 2, Elsevier, 2020.
@conference{Bolognini2020,
title = {Lidar-based navigation of tethered drone formations in an unknown environment},
author = {Michele Bolognini and Lorenzo Fagiano},
url = {https://www.sciencedirect.com/science/article/pii/S2405896320330950
},
doi = {10.1016/j.ifacol.2020.12.2413},
year = {2020},
date = {2020-01-01},
urldate = {2020-01-01},
booktitle = {IFAC-PapersOnLine},
volume = {5},
number = {2},
pages = {9426-9431},
publisher = {Elsevier},
abstract = {The problem of navigating a formation of interconnected tethered drones, named STEM (System of TEthered Multicopters), in an unknown environment is considered. The tethers feed electrical power from a ground station to the drones and also serve as communication links. The presence of more than one interconnected drone provides enough degrees of freedom to navigate in a cluttered area. The leader drone in the formation must reach a given point of interest, while the followers must move accordingly, avoiding interference with the obstacles. The challenges are the uncertainty in the environment, with obstacles of unknown shape and position, the use of LiDAR (Light Detection And Ranging) sensors, providing only partial information of the surroundings of each drone, and the presence of the tethers, which must not impact with the obstacles and pose additional constraints to how the drones can move. To cope with these problems, a novel real-time planning algorithm based on numerical optimization is proposed: the reference position of each drone is chosen in a centralized way via a convex program, where the LiDAR scans are used to approximate the free space and the drones are moved towards suitably defined intermediate goals in order to eventually reach the point of interest. The approach is successfully tested in numerical simulations with a realistic model of the system.},
keywords = {},
pubstate = {published},
tppubtype = {conference}
}
The problem of navigating a formation of interconnected tethered drones, named STEM (System of TEthered Multicopters), in an unknown environment is considered. The tethers feed electrical power from a ground station to the drones and also serve as communication links. The presence of more than one interconnected drone provides enough degrees of freedom to navigate in a cluttered area. The leader drone in the formation must reach a given point of interest, while the followers must move accordingly, avoiding interference with the obstacles. The challenges are the uncertainty in the environment, with obstacles of unknown shape and position, the use of LiDAR (Light Detection And Ranging) sensors, providing only partial information of the surroundings of each drone, and the presence of the tethers, which must not impact with the obstacles and pose additional constraints to how the drones can move. To cope with these problems, a novel real-time planning algorithm based on numerical optimization is proposed: the reference position of each drone is chosen in a centralized way via a convex program, where the LiDAR scans are used to approximate the free space and the drones are moved towards suitably defined intermediate goals in order to eventually reach the point of interest. The approach is successfully tested in numerical simulations with a realistic model of the system.