The Frugal Feeding Problem: Energy-efficient, multi-robot, multi-place rendezvous

We consider the problem of finding an energy-efficient route for a service robot to rendezvous with every member of a heterogeneous team of mobile worker robots. We analyze the general and special cases of the problem, finding it to be at least as hard as the travelling salesman problem. Decomposing the problem into two components: (i) an ordering of robot meetings; and (ii) finding an optimal set of meeting places given an ordering, we present useful solutions to part (ii) only. We propose and compare a discrete algorithm for the restricted meeting location case and two numerical algorithms for the continuous case with weighted Euclidean distance energy cost functions. Anticipating future work, we speculate briefly on suitable ordering heuristics and the need for an integrated method