In this paper, a novel hybrid control approach is used for trajectory-tracking control of wheeled mobile robotic manipulators (WMRMs) in the presence of model uncertainties and external disturbances. Due to the existence of nonholonomic constrains in wheeled mobile robots, the proposed controller should be able to tackle the challenge of underactuation in such systems. To attain this objective, the dynamic equations of motion for a WMRM are derived in closed form using the Gibbs–Appell (G-A) formulation, which is an efficient method for obtaining the dynamic motion equations of nonholonomic systems. Then, a novel control scheme is developed which is both optimal and robust and which enjoys updated gains under an adaptive law. In this regard, to benefit from the advantages of two distinct methods, a high-order sliding mode control (HOSMC) is employed as a robust controller with the aim of handling system uncertainties and a state-dependent Riccati equation (SDRE) is used as a nonlinear optimal controller. In order to systematically deal with system uncertainties and to avoid the manual calculation of the upper bound of uncertainties, the gain of HOSMC is updated via an adaptive law. The most important advantage of this novel approach over the existing methods is that not only is it robustly stable against external disturbances when controlling an uncertain nonlinear system but also optimal for a predefined quadratic cost function. Lyapunov stability theory is employed to verify the stability of the proposed controller. Finally, to demonstrate the superiority of this novel controller, computer simulation results for a WMRM are compared with those of an adaptive sliding mode controller. It can be observed that the proposed hybrid control approach is capable of optimizing control inputs while achieving stability for a WMRM in the presence of model uncertainties.

在本文中，一种新颖的混合控制方法被用于存在模型不确定性和外部干扰的轮式移动机器人操纵器（WMRM）的轨迹跟踪控制。由于轮式移动机器人中存在非完整约束，因此所提出的控制器应该能够应对此类系统中驱动不足的挑战。为了达到这个目的，使用吉布斯-阿佩尔（GA）公式以封闭形式导出WMRM的动态运动方程，这是获得非完整系统动态运动方程的有效方法。然后，开发了一种新颖的控制方案，该方案既最优又鲁棒，并且在自适应定律下享有更新的增益。在这方面，要受益于两种不同方法的优势，高阶滑模控制（HOSMC）被用作鲁棒控制器，旨在处理系统不确定性，而状态依赖的Riccati方程（SDRE）被用作非线性最优控制器。为了系统地处理系统不确定性并避免手动计算不确定性上限，HOSMC的增益通过自适应定律进行更新。这种新颖方法相对于现有方法的最重要优点是，不仅在控制不确定的非线性系统时，它对于外部干扰具有鲁棒的稳定性，而且对于预定义的二次成本函数而言，它也是最佳的。利用Lyapunov稳定性理论来验证所提出控制器的稳定性。最后，为了展示这种新型控制器的优越性，将WMRM的计算机仿真结果与自适应滑模控制器的仿真结果进行了比较。可以观察到，在存在模型不确定性的情况下，所提出的混合控制方法能够优化控制输入，同时实现WMRM的稳定性。