  Based on the convex force-motion polynomial model for quasi-static sliding,
we derive the kinematic contact model to determine the contact modes and
instantaneous object motion on a supporting surface given a position controlled
manipulator. The inherently stochastic object-to-surface friction distribution
is modelled by sampling physically consistent parameters from appropriate
distributions, with only one parameter to control the amount of noise. Thanks
to the high fidelity and smoothness of convex polynomial models, the mechanics
of patch contact is captured while being computationally efficient without mode
selection at support points. The motion equations for both single and multiple
frictional contacts are given. Simulation based on the model is validated with
robotic pushing and grasping experiments.
