Probabilistic density control for swarm of decentralized ON-OFF agents with safety constraints

This paper presents a Markov chain based approach for the probabilistic density control of a swarm of autonomous “ON-OFF” agents. The proposed approach specifies the time evolution of the probabilistic density distribution by using a Markov chain, which guides the swarm to a desired steady-state final distribution, while satisfying the prescribed ergodicity and safety constraints. Prior research has developed a Markov chain based approach to control swarms of agents with full mobility. The main contribution of the current paper is generalizing this approach to a swarm of ON-OFF agents with limited mobility. We define ON-OFF agents as having limited mobility in the following sense: The agent either conforms to the motion induced by the environment or it remains motionless. This means that an ON-OFF agent has two possible actions, either accept the environmentally induced motion, “ON”, or stop all the motion, “OFF”. By using these binary control actions at the agent level, we develop a decentralized control architecture and algorithms that guide the swarm density distribution to a desired probabilistic density in the operational space. The agents make statistically independent probabilistic decisions on choosing to be “ON” or “OFF” based solely on their own states to achieve a desired swarm density distribution. The probabilistic approach is completely decentralized and does not require communication or collaboration between agents. Of course, any collaboration can be leveraged for better performance, which is the subject of future work. There are two new algorithms developed: An online ON-OFF policy computation method to generate a Markov matrix with the ergodicity and motion constraints but without the safety constraints, which can be viewed as generating a Markov matrix via the Metropolis-Hastings (M-H) algorithm for a given proposal matrix. The second algorithm generates, offline, an - N-OFF policy that also ensures the safety constraints together with the ergodicity and motion constraints. The incorporation of the safety constraints is enabled by our recent result that convexifies the Markov chain synthesis with these constraints.