Mutual Information based communication aware path planning: A game theoretic perspective

This paper examines the problem of distributed path planning for a mobile sensor network comprised of communication-aware robots performing general information gathering missions. Mutual information is derived for distributed sensing over packet erasure channels that model multi-hop communication. We model distributed path planning as a non-cooperative game and derive utility functions that are optimized locally by each robot. Each robot computes the control input in a distributed manner that results in a combined action that can be bounded by the optimal centralized result by utilizing sub-modularity in certain cases. It is shown that when the communication model includes multi-hop communication to expand the coverage of the sensor network, the property of sub-modularity is lost. We further show that the additional global knowledge required for the local computation of utility functions can be learned by simple consensus approaches. Finally, we discuss a sampling approach to approximate the proposed utility functions in order to reduce the associated computational requirements.