Differential Flatness of Quasi-Static Slider-Pusher Models with Applications in Control

TL;DR

This paper explores the differential flatness of planar slider-pusher systems under quasi-static assumptions, enabling new control strategies validated through simulations and real-world experiments.

Contribution

It introduces a differential kinematic model for slider-pusher systems and demonstrates flatness with the center of mass as a flat output, facilitating control design.

Findings

Slider-pusher systems exhibit differential flatness with the center of mass as a flat output.

Proposed control strategies achieve effective trajectory tracking in simulations and experiments.

The quasi-static model applies broadly to various slider shapes and pusher geometries.

Abstract

This paper investigates the dynamic properties of planar slider-pusher systems as a motion primitive in manipulation tasks. To that end, we construct a differential kinematic model deriving from the limit surface approach under the quasi-static assumption and with negligible contact friction. The quasi-static model applies to generic slider shapes and circular pusher geometries, enabling a differential kinematic representation of the system. From this model, we analyze differential flatness - a property advantageous for control synthesis and planning - and find that slider-pusher systems with polygon sliders and circular pushers exhibit flatness with the centre of mass as a flat output. Leveraging this property, we propose two control strategies for trajectory tracking: a cascaded quasi-static feedback strategy and a dynamic feedback linearization approach. We validate these strategies through closed-loop simulations incorporating perturbed models and input noise, as well as experimental results using a physical setup with a finger-like pusher and vision-based state detection. The real-world experiments confirm the applicability of the simulation gains, highlighting the potential of the proposed methods for