Obstacle avoidance in optimal formation geometry switching ?

We address the problem of dynamically switching the geometry of a formation of a number of undistinguishable agents. The need to switch formation geometry arises in situations when mission requirements change or there are obstacles or boundaries along the path for which the current geometry is inadequate. Here we propose a strategy to determine which agent should go to each of the new target positions, avoiding collisions among agents and assuming no agent communication. In addition, each agent can also modify its path by changing its curvature, which is a main distinguishing feature from previous work. Among all possible solutions we seek one that minimizes the total formation switching time, i.e. that minimizes the maximum time required by all agents to reach their positions in the new formation geometry. We describe an algorithm based on dynamic programming to solve this problem.