Udwadia-Kalaba approach which presents a new, general and explicit equation of motion for constrained mechanical systems with holonomic or nonholonomic constraints is applied to the trajectory tracking control of the mobile robot in this paper. Unlike any other nonlinear control methods, the inspiration for this methodology which does not make any linearization or approximations comes from a different, though closely allied, field, namely analytical dynamics. The control torques required to control the mobile robot so that it precisely satisfies the trajectory requirements which are represented by an arbitrary (sufficiently smooth) function of time are obtained explicitly and in closed form by solving Udwadia-Kalaba equation. Numerical simulations are performed to show the simplicity, efficacy and accuracy of this closed-form method.

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In order to attain excellent stability and maneuverability to ensure safety and ride-comfort, the lateral velocity and yaw rate of a vehicle are expected to be controlled at any desired values simultaneously. A basic manipulation model of a vehicle with two degrees of freedom which requires two independent control inputs (front and rear steering angle) is constructed. In this model, we consider the mass and the moment of inertia of the vehicle are the uncertain parameters which are (possibly) fast-varying. However, no further information, except that the uncertainties are bounded, is assumed. Furthermore, the bound is unknown. An adaptive robust control methodology based on the Udwadia and Kalaba approach which guarantees uniform boundedness and uniform ultimate boundedness is proposed to drive the system to follow the pre-specified constraints approximately. The adaptive law is of leakage type which can adjust effectiveness of implementation.