Gradient-Based Collision Free Desired Formation Generation

Formation of multiple agents can be used for cooperative tasks like searching in rescue mission, quenching the fire in forest etc. In this paper we considered the collision-free formation generation with fixed topology. We propose a simple displacement-based distributed collision-free desired formation generation strategy with the help of relative information from the connected network. Displacement based formation generation is done iteratively by finding the solution of a linear equation. This linear equation is derived by minimizing the majorization of the stress function which is based on the distance constrained of desired formation. To maintain a safe distance among multiple agents we proposed a gradient based collision avoidance term with a strictly decreasing unique potential function. A variable gain function is used to ensure the fulfilment of suitable collision avoidance criteria. Finally considerable simulation results are shown in 2d and 3d with the proposed law.