Leaderless Time-To-Go Protocols for Same-Time Position Consensus

We propose three time-to-go consensus protocols to effect the same-time position consensus of multiple agents (or vehicles) to a destination. We prove same-time position consensus to occur through the use of control generated using each of the three protocols viz max-time, min-time, and achievable-time protocols using a backstepping-inspired speed modulation approach for a system of double integrators. Next, we formulate sufficient conditions on the graph communication network topology for consensus to occur through each protocol and propose a tokenized algorithm to effect same-time consensus in systems with arbitrary connected graph communication topologies using the achievable-time protocol. Finally, we verify our conclusions through numerical simulations to further ascertain the relevance of these protocols to diverse scenarios.