Differential Flatness of Slider-Pusher Systems for Constrained Time Optimal Collision Free Path Planning

TL;DR

This paper demonstrates that slider-pusher systems are differentially flat under quasi-static and frictionless conditions, enabling a novel approach to collision-free path planning by decoupling geometry and velocity optimization.

Contribution

It introduces the differential flatness property for slider-pusher systems and develops a numerical method for constrained time optimal collision-free path planning based on this insight.

Findings

Differential flatness of slider-pusher systems established.

Path trajectories are invariant to velocity profile transformations.

A numerical approach for constrained time optimal path planning is proposed.

Abstract

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.