Nonlinear control for collision-free navigation of UAV fleet
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This paper presents the development of a cooperation scheme among unmanned aerial vehicle (UAV). Sliding mode control technique is used to guarantee that the set of robots can follow a reference trajectory and, in addition, will guarantee collision-free navigation of these autonomous vehicles. The analytical approach of the control strategy is shown, and the necessary conditions to guarantee the stability and governability of the multi-robot system are derived. The strategy and the derived conditions are tested using simulations, to demonstrate their effectiveness for collision-free navigation of an UAV fleet.
KeywordsSliding mode control Collision free navigation UAV coordination
Aerial robotics has been greatly developing in recent years, and this has made autonomous aerial vehicles or unmanned aerial vehicles (UAVs) gain many followers. In addition to the military use, there are many varied civil applications where this type of autonomous vehicles has gained ground, such as automation and technological support to agricultural work, filmography in general, support to rescue labors, the exploration of land even outside the planet, the tasks of recognition and supervision of bounded areas, the exploration of oil and minerals or the automated industrial transport and cargo.
In some of these cases, the use of a single autonomous vehicle is sufficient, but as the number and variety of applications increase, it has become necessary to integrate several of these vehicles to carry out the tasks in a more efficient and timely manner. For this reason, the present work focused on the development of a cooperation strategy between aerial robots based on nonlinear control techniques. It is demonstrated that the use of the nonlinear control technique known as control by sliding modes can be applied in tasks that require the coordinated navigation (without collisions) of several UAVs in a shared environment.
The main motivation for the development of this work was that its applications can benefit and impact clearly and directly the communities that are part of the social environment of the Pontificia Universidad Javeriana Cali (Colombia). These applications can range from the agro-industrial sector and the conservation of natural resources [3, 5, 8, 9, 13], as in search and rescue or in disaster prevention tasks, [7, 18], or applications to support sustainable urban development, such as those developed by [1, 14]. Another important application is the search and deactivation of antipersonnel mines, such as those mentioned in [2, 10, 12].
To solve the problem of collisions between autonomous robots, different investigations have been developed. In the case of aerial robots, several methods, techniques and theories based on generating trajectories prior to the flight have been implemented. For example, Maza  in his thesis presents a distributed architecture, composed of different modules that solve common problems that arise during the execution of multipurpose missions. In case of terrestrial robots, different approaches have been made, using different types of robot models. As an example of this, using the approach and theory of Lyapunov, Bacon et al.  proposed a law of control by sliding modes (SMC) in which the resulting decentralized control guides the robotic agents toward the coverage of an area within a target region that could be moving. The approach of the agents to the objective is asymptotic and without collisions. His work includes discussions on the stability of the controlled dynamics, as well as the abilities of rejection of disturbances, using linear models of holonomic robots. In the real world, robots possess dynamics that can be more complicated than those linear representations commonly used, so some authors like Zhai et al. , Listmann  and Ghommam  have included the problem of cooperation with non-holonomic robots. The approaches presented here offered clarity in some of the concepts related to conflict resolution and its application to the tasks and scenarios that were implemented.
This work shows the extension of results obtained for terrestrial robots (in a two-dimensional plane) to the three-dimensional case, necessary for the navigation of aerial robots. Using the results described previously, the effectiveness of SMC technique for a single non-holonomic terrestrial robot displacement control was checked, and is described by Torres et al. , as well as the verification of effectiveness of the same technique for the collision-free navigation of a set of terrestrial robots of this same type, as described by Martínez . The following section of this paper describes the way in which the problem of coordinated navigation between a group of aerial robots is approached, using the SMC technique, and then, the results of this approach are presented by means of simulations. Finally, some conclusions of the work developed are proposed, as well as a prospective of possible future developments.
2 Analytical approach of sliding mode control for coordinated flight in UAV
3 Results obtained on the navigation of a UAV fleet using sliding mode control
Design and control parameters for UAV
Design and control parameters for UAV
The nonlinear control technique, called sliding mode control, was effectively applied to command the trajectory followed by holonomic air robots, guaranteeing the stability and robustness of the controlled system.
The effectiveness of the sliding mode control was verified when used for the coordination of a group of holonomic aerial robots, including in the simulation tests the effects of the variability inherent to the position measurement system using GPS. The stability and robustness of the proposed solution were demonstrated.
The method proposed by Bacon  was extended for the control and safe navigation of robots in the plane \((R^2)\), to be able to use it in space \((R^3)\), and its effectiveness, stability and robustness were verified in simulated experiments with a fleet of aerial robots.
As a step to follow, we propose an analysis of the robustness of the control system proposed for a fleet of autonomous robots, considering the real conditions of the multi-robot system and validate these results with real experiments.
In addition, taking into account the robustness results verified with the use of the sliding mode control, it would be interesting to propose an analysis of the effect of the delays due to the communication systems of the robot fleet.
The authors are grateful for the support of the Pontificia Universidad Javeriana Cali (Colombia), through the financing of the project Experimental Platform for the Performance Evaluation of Multirobot Systems.
Compliance with ethical standards
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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