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arXiv · 2511.04246

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

Sander De Witte·Tom Lefebvre·Thomas Neve·Andras Retzler·Guillaume Crevecoeur
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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

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Sander De Witte, Tom Lefebvre, Thomas Neve, Andras Retzler, Guillaume Crevecoeur. 2025-11-06. Differential Flatness of Quasi-Static Slider-Pusher Models with Applications in Control. https://arxiv.org/abs/2511.04246

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