Constrained Multi-Agent Optimization with Unbounded Information Delay

A multi-agent system (MAS) consists of a group of agents that solve a common task through cooperation. Many problems arising in this setting can be formulated as distributed constrained optimization. In recent work, we considered the unconstrained version of the problem. In particular, we developed a theory to understand distributed gradient-based optimization methods, wherein the local (state) information is communicated via a lossy wireless network. A key contribution of the theory is that the information delay could be  unbounded, however, it does not consider constraints. In this work, we present preliminary experimental results aimed towards extending the aforementioned work to the constrained  setting. First, the constrained optimization problem is transformed into an unconstrained one using the penalty-based method. Then, we employ the distributed gradient approach from  our previous work to solve the unconstrained optimization in a decentralized manner. The illustrative experiments are based on autonomous pattern formation tasks for robotic swarms.  The (simulated) robots cooperate to form a specified pattern (line, circle), with the constraint that the distances between neighboring robots equal a given constant.