Abstract
A closed-form H2 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 H2 nonlinear control method that analytically fulfills the H2 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 H2 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 H2 proposed method, two testing scenarios, circular and S type reference trajectories, were applied to performance verification.
Highlights
Over the past few decades, scientific and technological progression and innovation have led to the universal application of wheeled mobile robots (WMRs) in daily life
Remark: Above the trajectory tracking problem of a swarm of WMRs for the analytic solution, one nonlinear time-varying Riccati-like equation can solve the H2 control performance index Equation (7)
From Equations (5) and (12), which are explicitly used to find out a closed-form solution, Ji2 (e, t) of this nonlinear time-varying Riccati-like equations and nonlinear differential equations are certainly complicated tasks
Summary
Over the past few decades, scientific and technological progression and innovation have led to the universal application of wheeled mobile robots (WMRs) in daily life. Considering the above statement, the subject of a nonlinear optimal control design must solve one nonlinear time-varying Riccati-like equation, which is very difficult to explain, and it is difficult to find out the solution This closed-form solution can be derived from the appropriately selected state variable transformation and tracking error dynamics analysis in this research. According to this closed-form solution, one nonlinear optimal control method contains a straightforward implementation structure for the trajectory tracking problem of a swarm of WMRs that can be constructed.
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