This paper formulizes and solves a special class of trajectory optimization problems focusing on the optimization of different kind of agents which are coupled through reciprocal constraints. Searching for a solution to the problem at hand may not only stipulate planning a longer path for each agent, but also choosing slower travel speeds in order to coordinate multiple paths. A novel approach is formulated which uses the representation of a path by a telescopic antenna. The length and orientation of the antenna's sections are evolved by a genetic algorithm. The approach is demonstrated and studied through solving and simulating several path-planning problems.