The trajectory tracking control performance of non-holonomic wheeled mobile robots (NWMRs) is subject to non-holonomic constraints, system uncertainties, and external disturbances. This paper proposes a barrier function-based adaptive sliding mode control (BFASMC) method to provide high-precision, fast-response performance and robustness for NWMRs. Compared with the conventional adaptive sliding mode control, the proposed control strategy can guarantee that the sliding mode variables converge to a predefined neighborhood of origin with a predefined reaching time independent of the prior knowledge of the uncertainties and disturbances bounds. Another advantage of the proposed algorithm is that the control gains can be adaptively adjusted to follow the disturbances amplitudes thanks to the barrier function. The benefit is that the overestimation of control gain can be eliminated, resulting in chattering reduction. Moreover, a modified barrier function-like control gain is employed to prevent the input saturation problem due to the physical limit of the actuator. The stability analysis and comparative experiments demonstrate that the proposed BFASMC can ensure the pre-specified convergence performance of the NWMR system output variables and strong robustness against uncertainties/disturbances.

While designing control for a class of underactuated mechanical systems (UMSs), the uncertainty and the prescribed nonholonomic tracking trajectories should be taken into consideration. Uncertainty considered in this article is time varying and bounded, and the bound of uncertainty is described using the fuzzy set theory, namely, fuzzy UMSs. An analytical dynamics-based view is taken in which the prescribed tracking trajectories are viewed as servo constraints which can be linear, nonlinear, holonomic, and nonholonomic. Using this view, a novel closed form solution of adaptive robust control is found with leakage type adaptive law to guarantee deterministic system performance, including uniform boundedness and uniform ultimate boundedness. In order to find the optimal dual gain parameters of the designed control, a two-player cooperative game is proposed for which the Pareto optimality can always be guaranteed. The effectiveness of the proposed control is shown through numerical simulation of a two-wheeled inverted pendulum vehicle.

The main objective of this article is to address the position tracking control problem for permanent magnet linear motor by using a novel model-based robust control method. Specifically, based on the assumed upper bound of the lumped model uncertainties and external disturbances, we design a novel nonlinear control algorithm, which is characterized by error-based and model-based inheriting from traditional proportional-integral-derivative (PID) control and robust control. The proposed control can be considered as an improved PID control or a redesigned robust control, with simple implementation and practical effectiveness. Theoretical analysis is provided to demonstrate that the controller can guarantee the uniform boundedness and uniform ultimate boundedness of the system. Moreover, on the experimental platform, rapid controller prototyping cSPACE is designed to avoid long time programming and debugging, and provides great convenience for practical operation. Numerical simulations and real-time experimental results are finally presented to illustrate the effectiveness and the achievable control performance of the control design.

Laboratory experiments were conducted for falling U-chain, but explicit analytic form of the general equations of motion was not presented. Several modeling methods were developed for fish robots, however they just focused on the whole fish’s locomotion which does little favor to understand the detailed swimming behavior of fish. Udwadia-Kalaba theory is used to model these two multi-body systems and obtain explicit analytic equations of motion. For falling U-chain, the mass matrix is non-singular. Second-order constraints are used to get the constraint force and equations of motion and the numerical simulation is conducted. Simulation results show that the chain tip falls faster than the freely falling body. For fish robot, two-joint Carangiform fish robot is focused on. Quasi-steady wing theory is used to approximately calculate fluid lift force acting on the caudal fin. Based on the obtained explicit analytic equations of motion (the mass matrix is singular), propulsive characteristics of each part of the fish robot are obtained. Through these two cases of U chain and fish robot, how to use Udwadia-Kalaba equation to obtain the dynamical model is shown and the modeling methodology for multi-body systems is presented. It is also shown that Udwadia-Kalaba theory is applicable to systems whether or not their mass matrices are singular. In the whole process of applying Udwadia-Kalaba equation, Lagrangian multipliers and quasi-coordinates are not used. Udwadia-Kalaba theory is creatively applied to dynamical modeling of falling U-chain and fish robot problems and explicit analytic equations of motion are obtained.