multi agent multi target Probabilistic Navigation Function

We issue the problem of cooperative control of
a swarm of autonomous mobile robots that are required
to intercept a set of moving targets while avoiding con-
tacts with dynamic obstacles. We introduce a Multi agent
Multi target (MAMT) simultaneous solution to the prob-
lems based on the Rimon and koditschek's Navigation
Function (NF) The MAMT-NF provides an analytic so-
lution, and guarantees a simultaneous interception of all
targets while collision between all two agents or between
agent and obstacles are avoided. In our previous work the
NF was extended to t for uncertain environment. Here
we implement the suggested solution for such scenarios
and we call it MAMT-PNF so, all targets are intercepted
while limiting the risk for collision to a predened value.
The complexity of the solution is linear with the number
of targets and agents, and therefore it is not limited to
small problems. Although the solution provided by the
NF or the PNF is not optimal, it provides simple and
ecient solution, making it suitable for a large range of
real time applications.