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Goal Assignment and Trajectory Planning for Large Teams of Aerial Robots
"... Abstract—This paper presents a computationally tractable, resolutioncomplete algorithm for generating dynamically feasible trajectories for N interchangeable (identical) aerial robots navigating through cluttered known environments to M goal states. This is achieved by assigning the robots to goal ..."
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Abstract—This paper presents a computationally tractable, resolutioncomplete algorithm for generating dynamically feasible trajectories for N interchangeable (identical) aerial robots navigating through cluttered known environments to M goal states. This is achieved by assigning the robots to goal states while concurrently planning the trajectories for all robots. The algorithm minimizes the maximum cost over all robot trajectories. The computational complexity of this algorithm is shown to be cubic in the number of robots, substantially better than the expected exponential complexity associated with planning in the joint state space and the assignment of goals to robots. This algorithm can be used to plan motions and goals for tens of aerial robots, each in a 12dimensional state space. Finally, experimental trials are conducted with a team of six quadrotor robots navigating in a constrained threedimensional environment. I.
K.: Efficient multirobot motion planning for unlabeled discs in simple polygons
 CoRR
, 2013
"... Abstract. We consider the following motionplanning problem: we are given m unit discs in a simple polygon with n vertices, each at their own start position, and we want to move the discs to a given set of m target positions. Contrary to the standard (labeled) version of the problem, each disc is ..."
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Abstract. We consider the following motionplanning problem: we are given m unit discs in a simple polygon with n vertices, each at their own start position, and we want to move the discs to a given set of m target positions. Contrary to the standard (labeled) version of the problem, each disc is allowed to be moved to any target position, as long as in the end every target position is occupied. We show that this unlabeled version of the problem can be solved in
Shortest Path Set Induced Vertex Ordering and its Application to Distributed Distance Optimal Formation Path Planning and Control on Graphs
"... For the task of moving a group of indistinguishable agents on a connected graph with unit edge lengths into an arbitrary goal formation, it was shown that distance optimal paths can be computed to complete with a tight convergence time guarantee [30], using a fully centralized algorithm. In this stu ..."
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For the task of moving a group of indistinguishable agents on a connected graph with unit edge lengths into an arbitrary goal formation, it was shown that distance optimal paths can be computed to complete with a tight convergence time guarantee [30], using a fully centralized algorithm. In this study, we establish the existence of a more fundamental ordering of the vertices on the underlying graph network, induced by a fixed goal formation. The ordering leads to a simple distributed scheduling algorithm that assures the same convergence time. The vertex ordering also readily extends to more general graphs those with arbitrary integer capacities and edge lengths for which we again provide guarantees on the convergence time until the desired formation is achieved. Simulations, accessible via a web browser, confirm our theoretical developments.
Efficient Formation Path Planning on Large Graphs
"... Abstract—For the task of transferring a group of robots from one formation to another on a connected graph with unit edge lengths, we provide an efficient hierarchical algorithm that can complete goal assignment and path planning for 10,000 robots on a 250,000 vertex grid in under one second. In the ..."
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Abstract—For the task of transferring a group of robots from one formation to another on a connected graph with unit edge lengths, we provide an efficient hierarchical algorithm that can complete goal assignment and path planning for 10,000 robots on a 250,000 vertex grid in under one second. In the extreme, our algorithm can handle up to one million robots on a grid with one billion vertices in approximately 30 minutes. Perhaps more importantly, we prove that with high probability, the algorithm supplies paths with total distance within a constant multiple of the optimal total distance. Furthermore, our hierarchical method also allows these paths to be scheduled with a tight completion time guarantee. In practice, our implementation yields a total path distance less than two times of the true optimum and a much shorter completion time. I.
Virtual rigid bodies for coordinated agile maneuvering of teams of micro aerial vehicles
 in Robotics and Automation (ICRA), 2015 IEEE International Conference on. IEEE, 2015
"... Abstract — This paper proposes a method for controlling a team of quadrotor micro aerial vehicles to perform agile maneuvers while holding a fixed relative formation, as well as transitioning between a sequence of formations. The objective is to coordinate the quadrotors to fly in intricate interlac ..."
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Abstract — This paper proposes a method for controlling a team of quadrotor micro aerial vehicles to perform agile maneuvers while holding a fixed relative formation, as well as transitioning between a sequence of formations. The objective is to coordinate the quadrotors to fly in intricate interlaced patterns, similarly to an air show demonstration team. The paper proposes a new abstraction, called a Virtual Rigid Body, which allows the quadrotors to hold relative positions while executing agile maneuvers as a group. By planning trajectories for the Virtual Rigid Body in SE(3), trajectories for each quadrotor are obtained in order to maintain the desired formation during the maneuver. The paper also proposes a method for sequencing a series of Virtual Rigid Body formations, and automatically designing collision free transitions between successive formations, while the team simultaneously executes a trajectory in SE(3). The resulting sequence of formations and transitions gives trajectories that weave intricate designs while avoiding collisions. The method is demonstrated experimentally with three KMel K500 quadrotors flying in a motion capture environment. I.
Target Assignment in Robotic Networks: Distance Optimality Guarantees and Hierarchical Strategies
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1Motion Planning for Unlabeled Discs with Optimality Guarantees
"... Abstract—We study the problem of path planning for unlabeled (indistinguishable) unitdisc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guarantee ..."
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Abstract—We study the problem of path planning for unlabeled (indistinguishable) unitdisc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time Õ m4 +m2n2, where m is the number of robots and n is the total complexity of the workspace. Moreover, the total length of the returned solution is at most OPT+4m, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency. I.
1Target Assignment in Robotic Networks: Distance Optimality Guarantees and Hierarchical Strategies
"... Abstract—We study the problem of assigning a group of mobile robots to an equal number of distinct static targets, seeking to minimize the total distance traveled by all robots until each target is occupied by a robot. In the first half of our paper, the robots assume limited communication and targe ..."
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Abstract—We study the problem of assigning a group of mobile robots to an equal number of distinct static targets, seeking to minimize the total distance traveled by all robots until each target is occupied by a robot. In the first half of our paper, the robots assume limited communication and targetsensing range; otherwise, the robots have no prior knowledge of target locations. Under these assumptions, we present a necessary and sufficient condition under which true distance optimality can be achieved. Moreover, we provide an explicit, nonasymptotic formula for computing the number of robots needed for achieving distance optimality in terms of the robots ’ communication and targetsensing ranges with arbitrary guaranteed probabilities. We also show that the same bound is asymptotically tight. Because a large number of robots is required for guaranteeing distance optimality with high probability, in the second half of our study, we present suboptimal strategies when the number of robots cannot be freely chosen. Assuming that each robot is aware of all target locations, we first work under a hierarchical communication model such that at each hierarchy level, the workspace is partitioned into disjoint regions; robots can communicate with one another if and only if they belong to the same region. This communication model leads naturally to hierarchical strategies, which, under mild assumptions, yield constant approximations of true distanceoptimal solutions. We then revisit the rangebased communication model and show that combining hierarchical strategies with simple rendezvousbased strategies results in decentralized strategies which again achieve constant approximation ratios on distance optimality. Results from simulation show that the approximation ratio is as low as 1.4. I.