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SUMMARYThis study deals with the problem of trajectory tracking of wheeled mobile robots (WMR's) under non-holonomic constraints and in the presence of model uncertainties. To solve this problem, the kinematic and dynamic models of a WMR are first derived by applying the recursive Gibbs–Appell method. Then, new kinematics- and dynamics-based multivariable controllers are analytically developed by using the predictive control approach. The control laws are optimally derived by minimizing a pointwise quadratic cost function for the predicted tracking errors of the WMR. The main feature of the obtained closed-form control laws is that online optimization is not needed for their implementation. The prediction time, as a free parameter in the control laws, makes it possible to achieve a compromise between tracking accuracy and implementable control inputs. Finally, the performance of the proposed controller is compared with that of a sliding mode controller, reported in the literature, through simulations of some trajectory tracking maneuvers.

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Shorter stopping distance and less deviation from the straight line are two requirements of vehicle safe braking on split-m roads. The first one is achieved by controlling the longitudinal slip of each wheel at its optimum value calculated by road conditions. However, in order to directly control the vehicle directional stability, a new multivariable controller is optimally developed for integrated active front steering (AFS) and direct yaw moment control. In an efficient way to manage two control inputs, the weights of the integrated optimal control law are online determined by fuzzy logics. These logics are defined using the stability index obtained by the phase plane analysis of nonlinear vehicle model. In this way, the required external yaw moment can be calculated for different driving conditions to only compensate the drawback of AFS for stabilising the vehicle system. The minimum usage of stabilising external yaw moment leads to the less reduction of maximum achievable braking forces of one side wheels and results the shorter stopping distance. By determination of the weighs in limit conditions, the integrated control law easily leads to the stand-alone braking control law. The simulation results carried out using a validated vehicle model demonstrate that the integrated control system has a better braking performance compared with the stand-alone braking system, reported in literature, to attain the shorter stopping distance with less lateral deviation on split-m roads.