Formation Control of Multi-Agent Systems With Constrained Mismatched Compasses

Abstract

Due to inaccurate sensing results, the direction of the agent may be mismatched with each other, and constrained by a certain boundary condition, such that the directions of all the agents can not be aligned, e.g., the measurement biases or the drifts of sensors in inertial navigation. In this paper, such direction information, modeled as constrained mismatched compasses in the measurement or communication processes, has been considered for a kind of displacement-based formation control. To understand the introduced concept underlying how affects the system performance, several convex polytopes have been constructed to approximate rotation behaviors under the action of constrained mismatched compasses. The main aim of these polytopes is to recombine a larger convex region for containing the rotation behaviors, and is to further design a control gain matrix in view of the contracting mapping principle. The obtained results illustrate that all the agents can converge to the desired formation shape exponentially fast no matter whether the direction of each agent can be aligned with each other. Simulation is provided to verify the obtained results.