# Control of Painlev\'e Paradox in a Robotic System

## TL;DR

This paper investigates the Painlevé paradox in a two-link robotic system in contact with a moving belt, analyzing its dynamics and designing control strategies to prevent instability and undesired lift-off.

## Contribution

It provides a bifurcation analysis of the Painlevé paradox in a realistic robot setup and proposes a hybrid force/motion control scheme to mitigate its effects.

## Key findings

- Hybrid control outperforms PID in preventing bouncing motions.
- Bifurcation analysis reveals conditions leading to the Painlevé paradox.
- Control strategies can effectively stabilize the robot against paradox-induced instability.

## Abstract

The Painlev\'e paradox is a phenomenon that causes instability in mechanical systems subjects to unilateral constraints. While earlier studies were mostly focused on abstract theoretical settings, recent work confirmed the occurrence of the paradox in realistic set-ups. In this paper, we investigate the dynamics and presence of the Painlev\'e phenomenon in a twolinks robot in contact with a moving belt, through a bifurcation study. Then, we use the results of this analysis to inform the design of control strategies able to keep the robot sliding on the belt and avoid the onset of undesired lift-off. To this aim, through numerical simulations, we synthesise and compare a PID strategy and a hybrid force/motion control scheme, finding that the latter is able to guarantee better performance and avoid the onset of bouncing motion due to the Painlev\'e phenomenon.