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The trajectory tracking control performance of the wheeled mobile robot (WMR) is subject to position constraints, system uncertainties, and external disturbances. This paper explores the mechanism of the position constraints (equality and inequality) and considers the system uncertainties to be time-varying but bounded with fuzzy prescribed bounds. To solve the position constraints and uncertainties problems, a cooperative game-oriented optimal robust control method is proposed to provide high-precision, fast-response performance and robustness for WMR. First, a creative diffeomorphism transformation is proposed to convert the bounded state variables (subject to inequality constraints) into unbounded state variables. Accordingly, a restructured WMR system with the new state variables is established, which is free from inequality constraints. The uncertainties' bound is described as a fuzzy number by employing fuzzy set theory, which builds the fuzzy dynamic system of the WMR. Second, the control goal for this study is to drive the WMR to follow the position constraints despite uncertainties. An optimal robust control is developed to guarantee that the tracking errors of the WMR converge to a predefined neighborhood of origin. Using Lyapunov stability analysis, a fuzzy performance index is constructed, including steady-state performance, time performance, and control effort. The fuzzy performance index is employed as the cost function based on the cooperative game theory. The optimal control design is formulated to seek the Pareto-optimal solution of control parameters. Finally, the stability analysis and comparative experiments demonstrate that the proposed control algorithm can ensure the WMR's superior trajectory tracking convergence performance and strong robustness against uncertainties/disturbances. [ABSTRACT FROM AUTHOR]

This article presents a novel optimal constraint‐following controller for uncertain mechanical systems (MSs). The MS's uncertainty is unknown (possibly time‐varying) and bounded, but the bound is unspecified. Employing the frame of Udwadia–Kalaba theory, we design a robust controller with two tunable control gains for MSs, which guarantees some deterministic performances. Assuming the constraints to be holonomic and periodic, we transform the controlled MSs and introduce an iterative feedback tuning method for optimizing the proposed controller. After optimization, the final control scheme can achieve the equilibrium between the system performance and control cost for an arbitrary single constraint period. Simulations on a two‐link rotational manipulator are provided at last to demonstrate the proposed approach. [ABSTRACT FROM AUTHOR]

This article proposes a novel Nash game‐theoretical optimal adaptive robust control design approach to address the constraint‐following control problem for the uncertain underactuated mechanical systems with fuzzy evidence theory. First, the uncertainty is considered bounded and the bound is unknown but lies in a specified fuzzy evidence number. Second, a deterministic adaptive robust control scheme is proposed based on the servo constraint following control method, which renders the uncertain underactuated mechanical system to follow the specified constraints accurately with deterministic performance (guarantee uniform boundedness and uniform ultimate boundedness). It is shown that the designed self‐adjusting leakage‐type adaptive law can compensate for the uncertainty and avoid overcompensation. Third, based on the performance analysis and the fuzzy evidence description of uncertainty, the Nash game theory is introduced into the multi‐parameter optimization design for the two tunable control gains selected as two players. The cost functions for two players are relevant to the system constraint‐following performance and control cost. Then we can obtain the optimal control gains by seeking the Nash equilibrium which is always proved to exist. Ultimately, the simulation results on the two‐wheeled self‐balancing robot demonstrate the availability of the proposed control scheme and the optimal design approach for the underactuated mechanical systems with uncertainties. [ABSTRACT FROM AUTHOR]