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The control based on dynamic model could improve the dynamic performance of manipulators and obtain better control effects than the control based on kinematic model. As manipulators are complex online multivariable systems, there are various uncertainties in different environments and working conditions. Accurate dynamic parameters are difficult to obtain in practical engineering applications. In this article, a controller is designed by combining the precise control torques obtained by the analytical dynamics method with the compensation control torques obtained by sliding mode method for trajectory tracking of the manipulator with bounded uncertainty. Precise control torques obtained from the Udwadia–Kalaba modeling method could be applied for the control of the ideal manipulator tracking the desired trajectory. Compensation control torques obtained from the sliding mode concept and the Lyapunov stability theory could be applied to compensate the uncertainties of parameters and external disturbances, thus enhancing the robustness of the system. By combining precise control torques with compensation control torques, the end point of the manipulator with uncertainty could track the end of the ideal manipulator and then track the desired trajectory. The simulation results of the three-link manipulator with uncertainty show that the control method can make the controlled target approach the desired trajectory in relatively small torque ranges and obtain high stability accuracy, and the chattering is effectively reduced at the stage of approaching the sliding mode surface.

The dynamic model is very important for the design of a wall-climbing robot and the final realization of its motion performance. The general process of dynamic modeling and expression equations of dynamic models are given for the wheeled wall-climbing robot based on the modeling method of the Udwadia-Phohomsiri equation. Firstly, the dynamic model of an unconstrained four-wheeled wall-climbing robot is constructed. Then, a trajectory constraint is defined, the rationality of the dynamic model for the unconstrained wall-climbing robot is verified by numerical simulation. Again, constraint equations under the conditions of synchronous toothed belt structure, non-lateral motion and nonslip between the driving wheel and the wall surface are established. Finally, the dynamic model of the unconstrained wall-climbing robot is gradually combined with constraint equations, and numerical simulations are implemented. Numerical simulation results verify the correctness of the wall-climbing robot model and constraint models, as well as the effectiveness and advantages of the modeling method.