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This article uses the piecewise model and Kane’s method to present a procedure for studying impulsive motion of multibody systems. Impulsive motion occurs when the system is subject to either impulsive forces or impulsive constraints, or when subjected to both simultaneously. The Appellian classification of impulsive constraints and the corresponding equations of impulsive motion of the multibody system are discussed. The governing equations are derived based upon multibody formulation procedures developed by Huston. Constraint impulses associated with finite and impulsive constraints are incorporated into impact dynamical equations through the impulsive Lagrange multipliers. The kinetic energy change of the scleronomic multibody system due to the impact is derived. Newton’s impact law is treated as an impulsive constraint equation to study single-point frictionless collision between two multibody systems. Several examples are used to demonstrate and validate the procedure.

This paper presents a robust bounded control that prevents wheel skidding for an autonomous 4WS4WD vehicle under uncertain tire/road conditions with aerodynamic drag. Constraints on combined wheel slip are incorporated, a priori, in design to prevent skidding. A robust low‐and‐high gain technique is used to suppress the tracking error, and to enhance the utilization of the limited wheel slip. Simulation shows that, under uncertain tire/road conditions, with aerodynamic drag, the proposed control scheme can effectively limit the combined wheel slip, and it achieves the goal of path tracking. Moreover, the control inputs of wheel torque and wheel steering are coordinated well during vehicle cornering.

Constraining wheel slip can be applied to avoid vehicle skidding, especially on a slippery road. This paper presents an approach of constraining wheel slip for automatic path tracking control of 4WS/4WD vehicles. The approach integrates and limits the quasi-steady state of both the longitudinal and lateral wheel slips. A new control structure of wheel torque and wheel steering is proposed to transform the original constraint-tracking problem to that of state regulation with input constraint. For the transformed problem, a low-and-high gain technique and an integral compensator are introduced to construct the constrained controller, so that the utilization of the constrained wheel slip can be enhanced and the steady state error of tracking can be eliminated. Simulation shows that, on the snow road condition, the proposed scheme can render the 4WS/4WD vehicle tracking along the desired path within a prescribed threshold of wheel slip, and can provide satisfactory coordination between wheel torque and wheel steering

This paper presents a procedure for studying dynamics of multibodysystems subjected to impulsive constraints which may be either holonomicor nonholonomic. The procedure automatically incorporates the effects ofimpulsive constraints through its analysis. The governing equationsthemselves are developed from Kane's equations, using partial velocityvectors and partial angular velocity vectors. Explicit expressions forthe coefficients and terms of the governing equations are presented. Twosubcases are studied: (1) the constraints are instantaneously applied andcontinue to act; and (2) the constraints are instantaneously applied andlifted immediately after completion of impact. The internal impulses ateach joint and constraint impulses associated with the impulsiveconstraints are calculated. The procedure is checked with two examples,whose solutions are established.

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 configurations 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.