This paper presents a robust bounded controller that prevents an autonomous 4WS4WD vehicle from wheel skidding in presence of uncertainties of both tire/road condition and aerodynamic drag. For eliminating the steady-state error of path tracking, this control scheme incorporates integral compensation into a robust low-and high-gain technique, which in our earlier work has been introduced to achieve the anti-skidding. In comparison, this new proposed scheme ensures the path-tracking error can vanish asymptotically without incurring high-frequency chattering in the control signals. Simulation shows that, under the uncertainty effects, the proposed controller effectively limits the combined wheel slip and achieves the asymptotic path tracking. Moreover, the control inputs of wheel torque and wheel steering are coordinated well in response to this new control scheme.

This paper presents a computational procedure for studying collisions of multibody systems. It combines the procedures of impact analysis and the methods of modern multibody dynamics (including the use of Kane's equations, lower body arrays, generalized speeds, and differentiation algorithms). By assuming the duration of impact to be very short and that the con®gurations of the systems have only small changes during the colliding process, we can automatically generate the governing dynamical equations. By using Newton's impact law, the partial velocities of the contact points determine impulse force components. Then by back substituting into the governing equations, the changes of velocities during the collision, the components of internal impulses, and the subsequent motions of the systems after collision may be determined.

In Part 1 of these two companion papers, the spatial system kinematic and dynamic equations are developed using the Cartesian and elastic coordinates in order to maintain the generality of the formulation. This allows introducing general forcing functions and adding and/or deleting kinematic constraints. In control applications, however, it is desirable to determine the joint forces associated with the joint variables. On the other hand the use of the joint coordinates to formulate the dynamic equations leads to a complex recursive formulation based on loop closure equations. In this paper a velocity transformation technique applicable to spatial multibody systems that consist of interconnected rigid and deformable bodies is developed. The Cartesian variables are expressed in terms of the joint and elastic variables. The resulting kinematic relationships are then employed to determine the joint forces associated with the joint variables. A spatial robot manipulator that manipulates an object is presented as a numerical example to exemplify the development presented in this paper.

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