In this paper, we apply a state-based computational model called Sum automaton to explore and model-check a given set of robotic tasks. Robotic processes often run concurrently and communicate with each other to accomplish a common goal. We begin from a specification of a set of robotic tasks in the form of communicating finite state machines. As opposed to the traditional product automaton, built from a given specification of communicating finite state machines (CFSMs), whose state-space explodes, we build a compressed model of sum automaton. The sum automaton is composed by simulating the specified set of CFSMS in global environment into a corresponding set of what are defined as communicating Minimal Prefix Machines (CMPMs). The states of CMPMs form a well-founded, partial order. This model truly represents sequence, choice and concurrency exhibited by the concurrent robotic system tasks. The model provides a sound platform for performing state exploration/model-checking without exponential state explosion to verify both safety and liveness properties of the given set of robotic tasks.