||We address the problem of dynamically switching the geometry of a formation of a
number of undistinguishable agents, while avoiding collisions among agents and with external
obstacles. 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, in order to avoid obstacles, 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.