Control Design of a Swarm of Intelligent Robots: A Closed-Form <i>H₂</i> Nonlinear Control Approach

A closed-form <i>H₂</i> approach of a nonlinear trajectory tracking design and practical implementation of a swarm of wheeled mobile robots (WMRs) is presented in this paper. For the nonlinear trajectory tracking problem of a swarm of WMRs, the design purpose is to point out a closed-form <i>H₂</i> nonlinear control method that analytically fulfills the <i>H₂</i> control performance index. The key and primary contribution of this research is a closed-form solution with a simple control structure for the trajectory tracking design of a swarm of WMRs is an absolute achievement and practical implementation. Generally, it is challenging to solve and find out the closed-form solution for this nonlinear trajectory tracking problem of a swarm of WMRs. Fortunately, through a sequence of mathematical operations for the trajectory tracking error dynamics between the control of a swarm of WMRs and desired trajectories, this <i>H₂</i> trajectory tracking problem is equal to solve the nonlinear time-varying Riccati-like equation. Additionally, the closed-form solution of this nonlinear time-varying Riccati-like equation will be acquired with a straightforward form. Finally, for simulation-controlled performance of this <i>H₂</i> proposed method, two testing scenarios, circular and S type reference trajectories, were applied to performance verification.

Abstract licence: CC BY

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