Trajectory Tracking Control with Heterogeneous Input Delay in Multi-Agent System

Abstract

In this paper we present a protocol to track a general trajectory for a multi-agent system in the presence of heterogeneous constant finite input delays. We consider two different multi-agent cases: agents with single-integrator and double-integrator dynamics. For the single-integrator case, we assume that the velocity along the desired trajectory is known to all agents for all time. Similar assumption is made only for the acceleration along the desired trajectory for the double-integrator case. It is assumed that at least one agent has the complete information about the desired trajectory for all time. The tracking strategy comprises of a consensus-based estimator and a simple independent tracking controller for each agent in the system. Only the state estimates are exchanged among the agents. The communication graph for the multi-agent system along with the desired trajectory has a rooted directed spanning tree with the desired trajectory being the root. The proposed tracking strategy ensures asymptotic convergence of the multi-agent system. The controller and estimator gains do not depend on the edge weights of the graph. The chosen controller gains of individual agent are bounded by their respective input delays. We present a particular form of control gains in order to achieve a desired possible exponential convergence rate and maximize the upper bound of the convergence rate for these selective gains. Finally, we present simulation results to substantiate the effectiveness of the proposed methodology. Comparison of the proposed strategy with the existing work in the literature show a better performance.

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