  In this work we show that the differential kinematics of slider-pusher
systems are differentially flat assuming quasi-static behaviour and
frictionless contact. Second we demonstrate that the state trajectories are
invariant to time-differential transformations of the path parametrizing
coordinate. For one this property allows to impose arbitrary velocity profiles
on the slider without impacting the geometry of the state trajectory. This
property implies that certain path planning problems may be decomposed
approximately into a strictly geometric path planning and an auxiliary
throughput speed optimization problem. Building on these insights we elaborate
a numerical approach tailored to constrained time optimal collision free path
planning and apply it to the slider-pusher system.
