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This paper presents a distributed method for formation control of a homogeneous team of aerial or ground mobile robots navigating in environments with static and dynamic obstacles. Each robot in the team has a finite communication and visibility radius and shares information with its neighbors to coordinate. Our approach leverages both constrained optimization and multi-robot consensus to compute the parameters of the multi-robot formation. This ensures that the robots make progress and avoid collisions with static and moving obstacles. In particular, via distributed consensus, the robots compute (a) the convex hull of the robot positions, (b) the desired direction of movement and (c) a large convex region embedded in the four dimensional position-time free space. The robots then compute, via sequential convex programming, the locally optimal parameters for the formation to remain within the convex neighborhood of the robots. The method allows for reconfiguration. Each robot then navigates towards its assigned position in the target collision-free formation via an individual controller that accounts for its dynamics. This approach is efficient and scalable with the number of robots. We present an extensive evaluation of the communication requirements and verify the method in simulations with up to sixteen quadrotors. Lastly, we present experiments with four real quadrotors flying in formation in an environment with one moving human.

To be successful in multi-player drone racing, a player must not only follow the race track in an optimal way, but also compete with other drones through strategic blocking, faking, and opportunistic passing while avoiding collisions. Since unveiling one's own strategy to the adversaries is not desirable, this requires each player to independently predict the other players' future actions. Nash equilibria are a powerful tool to model this and similar multi-agent coordination problems in which the absence of communication impedes full coordination between the agents. In this paper, we propose a novel receding horizon planning algorithm that, exploiting sensitivity analysis within an iterated best response computational scheme, can approximate Nash equilibria in real time. We demonstrate that our solution effectively competes against alternative strategies in a large number of drone racing simulations.

Abstract-This paper presents a distributed method for navigating a team of robots in formation in 2D and 3D environments with static and dynamic obstacles. The robots are assumed to have a reduced communication and visibility radius and share information with their neighbors. Via distributed consensus the robots compute (a) the convex hull of the robot positions and (b) the largest convex region within free space. The robots then compute, via sequential convex programming, the locally optimal parameters for the formation within this convex neighborhood of the robots. Reconfiguration is allowed, when required, by considering a set of target formations. The robots navigate towards the target collision-free formation with individual local planners that account for their dynamics. The approach is efficient and scalable with the number of robots and performs well in simulations with up to sixteen quadrotors. I. INTRODUCTIONMuti-robot teams can be employed for various tasks, such as surveillance, inspection, or automated factories. In these scenarios, robots may be required to navigate in formation, for example for maintaining a communication network, for collaboratively handling an object, for surveilling an area or to improve navigation.Multi-robot navigation in formation has received extensive attention in the past, with many works considering obstaclefree scenarios. In [1] we leveraged efficient optimization techniques, namely quadratic programming, semi-definite programming and (non-linear) sequential quadratic programming to devise a centralized method for local navigation in formation. These techniques provided good computational efficiency, local guarantees and generality, and were employed at different stages of the method for local motion planning in formation among static and dynamic obstacles, albeit centralized.In this work we combine the optimization concepts presented in [1] with distributed consensus and geometric reasoning to achieve similar results in a distributed schema, where robots are no more centrally controlled, but instead have a limited field of view, and communicate with their immediate neighbors.