This paper proposes a decentralized approach for solving the problem of moving a swarm of agents into a desired formation. We propose a decentralized assignment algorithm which prescribes goals to each agent using only local information. The assignment results are then used to generate energy-optimal trajectories for each agent which have guaranteed collision avoidance through safety constraints. We present the conditions for optimality and discuss the robustness of the solution. The efficacy of the proposed approach is validated through a numerical case study to characterize the framework's performance on a set of dynamic goals.
Recently an energy-optimal decentralized approach to the desired formation problem was presented by @cite_13 . In this case a set of algorithms is described to solve the decoupled optimal assignment and trajectory generation problems in a distributed manner. This is achieved through a global assignment auction and convexified optimal trajectory algorithm, which is robust to agent failures and disconnected groups of agents.
@cite_13
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This paper presents a distributed, guidance and control algorithm for reconfiguring swarms composed of hundreds to thousands of agents with limited communication and computation capabilities. This algorithm solves both the optimal assignment and collision-free trajectory generation for robotic swarms, in an integrated manner, when given the desired shape of the swarm without pre-assigned terminal positions. The optimal assignment problem is solved using a distributed auction assignment that can vary the number of target positions in the assignment, and the collision-free trajectories are generated using sequential convex programming. Finally, model predictive control is used to solve the assignment and trajectory generation in real time using a receding horizon. The model predictive control formulation uses current state measurements to resolve for the optimal assignment and trajectory. The implementation of the distributed auction algorithm and sequential convex programming using model predictive control produces the swarm assignment and trajectory optimization SATO algorithm that transfers a swarm of robots or vehicles to a desired shape in a distributed fashion. Once the desired shape is uploaded to the swarm, the algorithm determines where each robot goes and how it should get there in a fuel-efficient, collision-free manner. Results of flight experiments using multiple quadcopters show the effectiveness of the proposed SATO algorithm. This paper presents a joint market structure for energy, spinning reserves and VAR support in a multiarea setting. It is based on a cooptimization that can simultaneously optimize all three commodities across the "seams". An auxiliary problem principle based decomposition scheme is applied to the overall optimization for coordinating interchanges of energy and ancillary services between control areas. The proposed decomposition approach preserves independent dispatching for neighboring areas while achieves overall optimum. Nodal prices for energy and opportunity cost payments to forgone energy profit due to providing reserves and VAR support are also addressed. We believe the algorithm is of particular interest in the restructuring electricity industry for resolving seams issues. An illustrative example of a modified IEEE 30-bus system is used to demonstrate the validity of proposed algorithm. In this paper, a novel decentralized task allocation algorithm based on the Hungarian approach is proposed. The proposed algorithm guarantees an optimal solution as long as the agent network is connected, i.e., the second smallest eigenvalue of the Laplacian matrix of the agent graph is greater than zero. In order to show the motivation of the proposed algorithm, the original centralized auction and Hungarian algorithms are compared in terms of the converging speed versus the number of agents. The result shows the superiority of the Hungarian algorithm in scalability over the auction algorithm. Then, the performance of the proposed decentralized Hungarian-Based algorithm (DHBA) is compared with the consensus-based auction algorithm (CBAA) under different situations, including different number of agents and different network topologies. The simulation results show that DHBA outperforms CBAA in all cases on the basis of the converging speed, the optimality of assignments, and the computational time. In this paper, we consider the problem of concurrent assignment and planning of trajectories (which we denote Capt) for a team of robots. This problem involves simultaneously addressing two challenges: (1) the combinatorially complex problem of finding a suitable assignment of robots to goal locations, and (2) the generation of collision-free, time parameterized trajectories for every robot. We consider the Capt problem for unlabeled (interchangeable) robots and propose algorithmic solutions to two variations of the Capt problem. The first algorithm, c-Capt, is a provably correct, complete, centralized algorithm which guarantees collision-free optimal solutions to the Capt problem in an obstacle-free environment. To achieve these strong claims, c-Capt exploits the synergy obtained by combining the two subproblems of assignment and trajectory generation to provide computationally tractable solutions for large numbers of robots. We then propose a decentralized solution to the Capt problem through d-Capt, a decentralized algorithm that provides suboptimal results compared to c-Capt . We illustrate the algorithms and resulting performance through simulation and experimentation.