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# Ruling guidance an adaptive and dynamic haptic guide model

Alexis Boulay, David Daney, Margot Vulliez

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## To cite this version:

Alexis Boulay, David Daney, Margot Vulliez. Ruling guidance an adaptive and dynamic haptic guide model. MMT Symposium 2024 - Mechanism and Machine Theory Symposium, Jun 2024, Guimaraes, Portugal. p.383-384. hal-04776071

HAL Id: hal-04776071

https://inria.hal.science/hal-04776071v1

Submitted on 11 Nov 2024

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Distributed under a Creative Commons Attribution 4.0 International License
# RULING GUIDANCE AN ADAPTIVE AND DYNAMIC HAPTIC GUIDE MODEL

Alexis Boulay<fnref n="1" />,<fnref n="2" />, David Daney<fnref n="1" />, Margot Vulliez<fnref n="1" />

## 1 INTRODUCTION

Teleoperation is a method often used to carry out tasks in dangerous, inaccessible or sensitive environments where human's expertise and ability to adapt cannot be replaced by an autonomous robot. However, teleoperation also involves a split between the operator and the workspace. To counter this, haptic interfaces are used, transmitting the physical interactions of the robot with its environment via force feedback. The facility to generate forces, on the operator side, can also be exploited to help perform a task by the use of guiding forces. This work focuses on guiding the human through a novel guidance model, which can reproduce different modes of guidance, and be dynamically adjusted to the task, the environment, and the human interaction.

## 2 HAPTIC GUIDANCE

### 2.1 Related works

Known as virtual fixture, active constraint or virtual guide, a haptic guidance is a virtual geometric constraint used to generate a force feedback that help a user following a given behaviour [1]. The different guidance models in the literature are strongly linked to the tasks studied whether surgery [2], navigation [3] or pick&place [4]. Diversity of guidance can also be observed in contexts other than teleoperation, such as physical human-robot interaction [5] and programming by demonstration [6]. This dependence on task and context highlights that there is no unified formalism to model haptic guidance [1]. Yet, three common guidance models can be identified for the generation of guide: the use of spring-damper models (SD) [4], the definition of potential fields (PF) [7], and the establishment of restrictive zones with guiding tubes (GT) [8]. While these existing methods meet different needs, their generalization could be very helpful in generating guides that are better suited to the task, the environment, and the interaction with the operator. This work aims at defining a generic model that encompasses these conventional haptic guidance modes.

### 2.2 Haptic guidance expression

Any guidance force, $\mathbf{F}_g \in \mathbf{R}^3$, can be expressed through a virtual stiffness-damping model, as depicted in Eq. 1, with the stiffness and damping coefficients $\mathbf{K}_g \in \mathbf{R}^3$ and $\mathbf{B}_g \in \mathbf{R}^3$, the haptic device linear velocity in the cartesian space $\dot{\mathbf{X}}_h \in \mathbf{R}^3$, $d_g \in \mathbf{R}$ a distance threshold, $d_{dr} = ||\mathbf{X}_{dr} - \mathbf{X}_r||_2$ the distance between the robot position and the desired position and, $\Delta_{dr} \in \mathbf{R}^3$ a normalised vector, corresponding to the direction up to the desired position, as illustrated in Fig. 1. For the sake of simplicity, only translations are considered here, but the expression can be generalised to cartesian space by introducing distances between poses.

$$ \mathbf{F}_g = \mathbf{K}_g f(d_{dr}, d_g) \Delta_{dr} - \mathbf{B}_g \dot{\mathbf{X}}_h \quad (1) $$

With $f(d_{dr}, d_g) \in \mathbf{R}$ the attraction function that changes according to the type of guidance. SD is computed by $f_{SD}$, given by. Eq. 2, PF is computed by $f_{PF}$, given by Eq. 3, and GT is computed by $f_{GT}$, given by Eq. 4:

$$ f_{SD}(d_{dr}) = d_{dr} \quad (2) $$

$$ f_{PF}(d_{dr}, d_g) = \begin{cases} \frac{d_{dr}}{d_g^2} & \text{if } d_{dr} \le d_g \\ \frac{1}{d_{dr}} & \text{else} \end{cases} \quad (3) $$

$$ f_{GT}(d_{dr}, d_g) = \begin{cases} 0 & \text{if } d_{dr} \le d_g \\ (d_{dr} - d_g) & \text{else} \end{cases} \quad (4) $$

Each model of guidance has its pros and cons. Overall, SD prevents you from leaving the desired point/trajectory,

<footnote n="1">¹ Inria, Talence, France, {alexis.boulay@inria.fr; david.daney@inria.fr; margot.vulliez@inria.fr}</footnote>

<footnote n="2">² Farm3, Besançon, France, {alexis.boulay@farmcube.eu}</footnote>
GT lets you free around the desired point/trajectory until you reach a determined distance, and PF helps you find the desired point/trajectory while you can freely explore space. Yet GT and PF expressions have discontinuities, and SD makes it difficult for several objectives to coexist. Since each guidance has different specificity, it can be useful to change the guidance while executing a task.

### 3 RULING GUIDANCE

This work proposes the attraction function $f_{RG}$ given by Eq. 5. This expression of guidance, expressed as ruling guidance (RG) allows to switch easily and continuously between each type of guidance :

$$f_{RG}(d_{dr}, d_g, a, b, c) = a \frac{d_{dr}}{(d_g)^b} \exp(1 - \left(\frac{d_{dr}}{d_g}\right)^c) \quad (5)$$

With $(a, b, c) \in \mathbb{R}^3$ the parameters that allow to switch between usual guidance methods, as depicted in Fig. 1.

<figure><img src="image_4.png" /><figcaption>Figure 1: Classical guiding scenario (left) and common guiding methods compute with $f_{RG}$ (right).</figcaption></figure>

By implementing RG, it is possible to dynamically adapt the guidance, depending on the task, the environmental constraints or the user preferences. We could even explore intermediate guidance and propose an optimal haptic guide according to these parameters.

### 4 FUTURE WORK

Exploiting this equation will require a more in-depth study of existing guidance methods. In this objective, an experiment is planned to characterize the different guiding methods according to the workspace constraint. The aim of this experiment is also to identify metrics for evaluating operator interaction with the guide used. With this knowledge, we will then formulate an optimisation problem to exploit this function.

### REFERENCES

[1] S. A. Bowyer, B. L. Davies, and F. Rodriguez y Baena, "Active Constraints/Virtual Fixtures: A Survey", IEEE Transactions on Robotics, vol. 30, no. 1, p. 138-157, February 2014.

[2] Yang, Yongfei and al. "Safety Control Method of Robot-Assisted Cataract Surgery with Virtual Fixture and Virtual Force Feedback", in *J Intell Robot Syst*, vol. 97 no.1, January 2020.

[3] Lee, Kwang-Hyun and al., "Simultaneous Use of Autonomy guidance Haptic Feedback and Obstacle Avoiding Force Feedback for Mobile Robot Teleoperation", in *22nd ICCAS*, 2022.

[4] G. Raiola and al., "Co-manipulation with a library of virtual guiding fixtures", in *Auton Robot*, vol. 42, no. 5, p. 1037-1051, June 2018.

[5] Al-Saadi, Zaid and al., "Resolving Conflicts During Human-Robot Co-Manipulation" in *ACM/IEEE International Conference on HRI PROC*, 2023.

[6] Restrepo, Raiola and al., "Toward an Intuitive and Iterative 6D Virtual guide Programming Framework for Assisted Human-Robot Comanipulation", in *Robotica*, vol. 38, no. 10, p. 1778-1806, October 2020.

[7] A. Gottardi, S. Tortora, E. Tosello, and E. Menegatti, "Shared Control in Robot Teleoperation With Improved Potential Fields", in *IEEE Transactions on Human-Machine Systems*, vol. 52, no. 3, p. 410-422, June 2022.

[8] A. Bettini, P. Marayong, S. Lang, A. M. Okamura, and G. D. Hager, "Vision-assisted control for manipulation using virtual fixtures", in *IEEE Transactions on Robotics*, vol. 20, no. 6, p. 953-966, December 2004.