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.
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.