This research presents an adaptive energy-saving H2 closed-form control approach to solve the nonlinear trajectory tracking problem of autonomous mobile robots (AMRs). The main contributions of this proposed design are as fol-lows: closed-form approach, simple structure of the control law, easy implemen-tation, and energy savings through trajectory tracking design of the controlled AMRs. It is difficult to mathematically obtained this adaptive H2 closed-form solution of AMRs. Therefore, through a series of mathematical analyses of the trajectory tracking error dynamics of the controlled AMRs, the trajectory tracking problem of AMRs can be transformed directly into a solvable problem, and an adaptive nonlinear optimal controller, which has an extremely simple form and energy-saving properties, can be found. Finally, two test trajectories, namely cir-cular and S-shaped reference trajectories, are adopted to verify the control performance of the proposed adaptive H2 closed-form control approach with respect to an investigated H2 closed-form control design.
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