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# A new unified and adaptive haptic guidance method, an exploratory user study

Alexis Boulay, Benjamin Camblor, Margot Vulliez, David Daney

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Alexis Boulay, Benjamin Camblor, Margot Vulliez, David Daney. A new unified and adaptive haptic guidance method, an exploratory user study. 2024. hal-04727078

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https://inria.hal.science/hal-04727078v1

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# A new unified and adaptive haptic guidance method, an exploratory user study

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

***Abstract***— In hazardous or inaccessible environments, teleoperation enables remote task execution. However, its effectiveness is hindered by reduced performance and an increased operator workload, primarily due to the lack of direct sensory feedback. To address this issue, haptic guidance, that provides a guiding force feedback through the haptic device, can enhance remote operations by directing the operator towards task goals. This method relies on both the environment and the operator, and its effectiveness is affected by their dynamics. Consequently, developing an adaptive guidance that responds to changing situations is essential for practical use.

This paper introduces a novel adaptive and unified haptic guidance, called ruling guidance, which can seamlessly switch between various guidance behaviors. To evaluate the proposed approach and bring out adaptation mechanisms, a user study assesses the impact of different haptic guidance methods on task performance, safety, comfort, and trust, in various vertical farming scenarios. The results show that ruling guidance effectively encompasses classical haptic guidance behaviors and provides mechanisms for adapting the guiding feedback to environmental conditions and human interactions.

## I. INTRODUCTION

Teleoperation allows remote task execution in environments inaccessible or hazardous to humans. While offering significant benefits, the physical separation between the operator and the workspace often leads to reduced performance and increased workload due to a lack of feedback.

Haptic guidance addresses these challenges by using haptic devices to apply forces that direct the operator toward a task goal. Known as virtual fixture [1] or active constraint [2] different haptic guidance methods coexist in the literature. They are designed to enhance performance by offering additional sensory information [3]. Nonetheless, their effectiveness depends on environmental knowledge, such as obstacles and goals' position, and some methods even require a task reference path, named a guide. However in dynamic or partially known environments, these requirements can lead to errors and reduced guidance assistance. Moreover, each haptic guidance method is not suitable for every situations, since different tasks and environments may require different approaches [4], and operators may have varying preferences from either guidance method and guide.

In this paper, we show how a unified and adaptive approach to haptic guidance methods can circumvent these problems. A new adaptive formulation is proposed to continuously switch between different guidance modalities. The study is motivated

by a vertical farming application, as depicted in figure 1, where agronomists are required to measure plant growth and to remotely take care of them. Because of plant diversity, their heterogeneous development and differing conditions based on each plant size and location, the environment and task requirements frequently change. Therefore, the guidance must be continuously adapted with respect to the dynamic of environmental conditions.

<figure><img src="image_3.png" /><figcaption>Fig. 1. In vertical farming, plants are arranged on a farming shelf in a climate-controlled room. To ensure correct agronomic monitoring, it is essential to take measurements on a regular basis, but plant growth makes this difficult. Teleoperation enhanced by haptic guidance could help the agronomists to remotely monitor the plants.</figcaption></figure>

A user study is conducted to evaluate our unified approach and highlight the impact of environmental conditions and human-robot interaction on different haptic guidance method, in terms of task performance and safety, as well as human comfort and trust.

Combined with metrics that can online evaluate the interaction, this novel approach makes it possible to optimally adapt the guidance for all scenarios and users.

## II. HAPTIC GUIDANCE METHODS

### A. A review of conventional haptic guidance methods

Haptic guidance, as depicted in figure 2, consists in helping the user to move in a given direction thanks to a force feedback $F_g \in \mathbb{R}^3$, which is either attractive or repulsive.

In the literature, several types of haptic guidance are commonly used. A potential-field feedback can attract the operator toward possible grabbing poses [5]. Similar potential fields can be used to create repulsive forces from obstacles and escape points to avoid local minima [6]. Virtual spring-damper models are often defined, for example between the user and a virtual cart which moves along a guide [7]. Such virtual spring-damper can also be used to follow a path that is changing depending on the user behaviour [8]. A virtual geometric

<footnote n="1">¹Farm3, 25000 Besançon, France alexis.boulay@farmcube.eu</footnote>

<footnote n="2">²Inria center of the University of Bordeaux, 33400 Talence, France, name.lastname@inria.fr</footnote>
object, such as a guiding tube [9] or a more complex polytope [10] can also be introduced to constrain the user motion within it. More complex guidance exist, such as geometric movement constraints generated with respect to the used tools [4], or restrictions in the use of some degrees of freedom to limit the user's motion [11].

Regarding our knowledge, no haptic guidance in the literature encompasses potential field, spring damper or guiding tube in a single model.

<figure><img src="image_4.png" /><figcaption>Fig. 2. A guiding force $\mathbf{F}_g$ is generated on the haptic device based on the distance between the controlled robot position $\mathbf{X}_r$ and an interest point which can be a goal $\mathbf{X}_g$, a position on a guide $\mathbf{X}_{d,r}$ or an obstacle $\mathbf{X}_o$.</figcaption></figure>

For the sake of simplicity, only $\mathbb{R}^3$ position/force are considered on the following models, but all expression can be generalised to $\mathbb{R}^6$ pose/wrench vectors in Cartesian space by computing distance between rigid-body poses [12].

Given a task interest point $\mathbf{X}_d \in \mathbb{R}^3$, that is either a target position $\mathbf{X}_g$, an obstacle position $\mathbf{X}_o$, or the orthogonal projection $\mathbf{X}_{d,r}$ of the current robot position $\mathbf{X}_r \in \mathbb{R}^3$ on a guide, the guiding force usually depends on the robot-to-target distance $d_{dr} \in \mathbb{R}^+$:

$$d_{dr} = \|\mathbf{X}_r - \mathbf{X}_d\|_2 \quad (1)$$

and on the direction-to-target unit vector $\mathbf{\Delta}_{dr} \in \mathbb{R}^3$:

$$\mathbf{\Delta}_{dr} = \frac{\mathbf{X}_r - \mathbf{X}_d}{d_{dr}} \quad (2)$$

The guiding force $\mathbf{F}_g$, can then be described as a stiffness-damping model, with the stiffness and damping gains $\mathbf{K}_g \in \mathbb{R}^3$ and $\mathbf{B}_g \in \mathbb{R}^3$, the haptic device linear velocity $\dot{\mathbf{X}}_h \in \mathbb{R}^3$ and a distance threshold $d_g \in \mathbb{R}^+$:

$$\mathbf{F}_g = \mathbf{K}_g f_{gm}(d_{dr}, d_g) \mathbf{\Delta}_{dr} - \mathbf{B}_g \dot{\mathbf{X}}_h \quad (3)$$

It is worth noting that all terms in equation (3), and in the following, are expressed in the same robot world frame. The haptic device position and velocity are, therefore, transformed from the haptic device to the robot frame.

The guidance function, $f_{gm}(d_{dr}, d_g) \in \mathbb{R}$ changes according to the $gm$ haptic guidance method employed. Three main functions, illustrated in figure 3, have been identified from the literature: $f_{SD}(d_{dr}, d_g)$, $f_{GT}(d_{dr}, d_g)$ and $f_{PF}(d_{dr}, d_g)$. The existence of many different functions highlights the lacks of a unified formalism in the field [13].

The spring-damper guidance method (SD) considers a path where the user is virtually attached by a spring-damper. The guiding force is proportional to the distance between the robot and the path, $\mathbf{X}_d = \mathbf{X}_{d,r}$:

$$f_{SD}(d_{dr}, 0) = d_{dr} \quad (4)$$

This method is mainly considered for highly-constrained tasks, such as in surgery [14], or to help new users to learn a path [15]. But, it is highly dependent on the guide.

The guiding tube guidance method (GT) also considers the orthogonal distance to a guide $\mathbf{X}_d = \mathbf{X}_{d,r}$, while it allows

free movements in a zone around it:

$$f_{GT}(d_{dr}, d_g) = \begin{cases} 0 & \text{if } d_{dr} \le d_g \\ (d_{dr} - d_g) & \text{else} \end{cases} \quad (5)$$

This method is often used to feedback virtual workspace limits or to provide a limited range of motion around a reference path [16]. However, it is also highly dependent on the knowledge of the environment (boundaries or guide).

The potential field guidance method (PF) directly considers attractive or repulsive points, which can be either goals $\mathbf{X}_d = \mathbf{X}_g$ or obstacles $\mathbf{X}_d = \mathbf{X}_o$:

$$f_{PF}(d_{dr}, d_g) = \begin{cases} \frac{d_{dr}}{d_g^2} & \text{if } d_{dr} \le d_g \\ \frac{1}{d_{dr}} & \text{else} \end{cases} \quad (6)$$

This method is often used when many goals or obstacles coexist, to let the user choose how to execute the task [17], or in large environments such as in navigation [18]. However, it may lead to the existence of local minimum in the attraction field.

<figure><img src="image_5.png" /><figcaption>Fig. 3. Using spring-damper guidance method (left), the force is proportional to the distance between $\mathbf{X}_r$ and the projected position $\mathbf{X}_{d,r}$ on a guide. Using guiding tube guidance method (center), the force is zero unless the distance between $\mathbf{X}_r$ and $\mathbf{X}_{d,r}$ is superior to a threshold $d_g$ from which the force proportionally increases. Using potential field guidance method (right), the force is inversely proportional to the distance between $\mathbf{X}_r$ and the goal position $\mathbf{X}_g$, unless it is inferior to a threshold $d_g$ from which the force proportionally decreases, repulsive obstacles can also be considered.</figcaption></figure>

All haptic guidance methods have specific features, advantages and drawbacks. Complex environments and tasks may require more than one guidance modality. [19] presents a method where a potential field attracts the user inside a guiding tube, then a new potential field encourages the user to move forward in the tube. The guidance gains can also be adapted according to far, near or close zones to the target [20].

The variety in the expressions of conventional guidance functions, and their inherent model discontinuities, underline the difficulty to get a method which could switch continuously from one function to another.

## B. Ruling guidance, a unified and adaptive haptic guidance method

To handle more complex scenarios and variations in environments, a new haptic guidance method should be introduced, as a way to change the guidance behavior. We propose a generic parameterized method: the ruling guidance (RG). It is expressed through the guidance function:

$$f_{RG}(d_{dr}, d_g, a, b, c) = a \frac{d_{dr}}{d_g b} e^{1 - \left(\frac{d_{dr}}{d_g}\right)^c} \quad (7)$$

where $\mathbf{X}_d$ can either be $\mathbf{X}_g$, $\mathbf{X}_o$ or $\mathbf{X}_{d,r}$. Setting the parameters $(a, b, c) \in \mathbb{R}$ reproduces classic haptic guidance methods, and switches from one to the other, as illustrated in figure 4.
<figure><img src="image_6.png" /><figcaption>Fig. 4. By tuning correctly the parameter $(a, b, c)$ of $f_{RG}$ it is possible to reproduce the behavior of the classic haptic guidance methods.</figcaption></figure>

The set of parameters $(a, b, c) = (1, 0, 0)$ exactly gives $f_{SD}$, and $(a, b, c) = (1, 1, 1)$ matches the PF continuous version given by [17]. It is more difficult to perfectly reproduce the GT behavior with a continuous function, but $(a, b, c) = (e^{-1}, 0, -1)$ makes a good approximation since:

$$f_{R\text{-}GT}(d_{dr}, d_g) = \begin{cases} 0 & \text{if } d_{dr} \to 0 \\ d_g e^{-1} & \text{if } d_{dr} = d_g \\ d_{dr} e^{d_{dr}} & \text{if } d_{dr} \gg d_g \end{cases} \quad (8)$$

The approximation error increases for high values of $d_g$, but this distance threshold usually stays equal to a small radius.

The ruling guidance function provides a continuous shift between the different conventional guidance methods. Along with the choice of $(a, b, c)$, that selects the guidance modality, the gains $K_g$, $B_g$ and the distance threshold $d_g$ should be properly tuned to get a safe behavior. Besides, while using PF it can be necessary to tune additional parameters $K_o$, $B_o$ and $d_o$ to generate repulsive feedback from obstacles. These parameters have a significant impact on the generated guiding force. It is important to select the right guidance modality and to tune it for the given task and teleoperation system. In addition, all users may not need the same tuning or prefer different guidance modes. Experts and beginners need different levels of assistance [21]. To adjust the guidance to these human factors, we must be able to evaluate user interaction, during the execution of a task.

### C. Evaluate the operator interaction

Evaluation methods of user experience are central in human-robot interaction. Lots of factors can be taken into account as reviewed by [22]. We consider four evaluation characteristics: task performance, safety, human comfort, and trust.

To assess these characteristics, subjective metrics can be collected using questionnaires. We have chosen the NASA-Raw Task Load Index (NASA-RTLX) [23], [24], which measures the perceived workload through a self-evaluation of mental demand, physical demand, temporal demand, performance, effort and frustration, and the Muir survey [25], which measures the operator trust in the robot behavior through 4 questions.

Objective metrics are used alongside the surveys. Performance is often measured through the scope of time completion [26], [27]. In the specific context of haptically-guided tasks, it is valuable to assess whether the user is moving within

the optimal guide direction. Considering the optimal guide as a discrete set $[X_\chi(1), ..., X_\chi(N)]$ where $\forall i \in [2; N]$, $X_\chi(i) \in \mathbb{R}^3$ is a point on the guide and $T_\chi(i) = X_\chi(i) - X_\chi(i-1)$, the tangent at this point, and by associating the projected position at time $t$, $X_{d,r}(t) \to X_\chi(k+1)$, the path following writes:

$$P_1(t) = \frac{T_\chi(k+1)^T u_h(t)}{\|T_\chi(k+1)\|_2} \quad \text{with } u_h(t) = \frac{\dot{X}_h(t)}{\|\dot{X}_h(t)\|_2} \quad (9)$$

Safety is assessed by the minimal obstacle distance, the distance from the robot end-effector to the nearest obstacle:

$$S_1(t) = \|\mathbf{X}_r(t) - \mathbf{X}_o\|_2 \quad (10)$$

From a physical point of view, human comfort is linked to the force feedback:

$$C_1(t) = \|\mathbf{F}_g(t)\|_2 \quad (11)$$

Human trust evaluation is different for every guidance. For SD and GT it is linked to the maximum force feedback:

$$T_1 = \max_{t \in [0; T]} (\|\mathbf{F}_g(t)\|_2) \quad (12)$$

For PF, the average force following describes trust as the alignment between the guiding force and the operator's motion direction:

$$T_2(t) = \mathbf{F}_g(t)^T \mathbf{u}_h(t) \quad \text{with} \quad \mathbf{u}_h(t) = \frac{\dot{\mathbf{X}}_h(t)}{\|\dot{\mathbf{X}}_h(t)\|_2} \quad (13)$$

Finding relevant objective metrics that can be computed online is crucial to develop dynamic adaptation methods of the haptic guidance based on the task interaction.

## III. HAPTICALLY-GUIDED TELEOPERATION FRAMEWORK

### A. Teleoperation bilateral controller

The proposed haptic guidance is implemented within a teleoperation bilateral controller, described in figure 5. The teleoperation framework can be divided into 2 parts: the haptic device control and the robot control. All communication between the components are ROS-based. The haptic device transmits human positions $X_h \in \mathbb{R}^3$ and velocity $\dot{X}_h \in \mathbb{R}^3$ data to a teleoperation communication hub and receives the desired force feedback $F_h^{des} \in \mathbb{R}^3$. The communication hub applies the transformations between haptic and robot spaces, with a scaling term $s_{h,r} \in \mathbb{R}$ and the transformation matrix from haptic to robot frames $T_{hr} \in \mathbb{R}^{4 \times 4}$, such as:

$$\mathbf{X}_r^{des} = s_{h,r} \mathbf{T}_{hr}^T \mathbf{X}_h \quad \text{and} \quad \mathbf{F}_h^{des} = \frac{1}{s_{h,r}} \mathbf{T}_{hr} \mathbf{F}_g \quad (14)$$

The robot desired position $X_r^{des}$ is input to a PD controller, that closes the loop in Cartesian space and outputs the desired velocity $\dot{X}_r^{des}$. The inverse kinematics is then written as a Quadratic Programming constrained optimization problem [28] that guarantees joint position, velocity, and acceleration limits and sets the joint velocity consign $\dot{\mathbf{q}}^{opt}$ to the robot.

### B. Haptic guidance module

The haptic guidance algorithm generates the guiding force $F_g$ according to equation (3). Selecting and tuning its parameters allows to switch between different guidance functions (see section II) toward chosen target points $X_d$. An external path planner generates the optimal guide $\chi$, on which the projection
<figure><img src="image_7.png" /><figcaption>Fig. 5. Haptic guidance teleoperation controller. A communication hub ensures data transformation and exchange between the local haptic device and robot controllers. The haptic guidance module provides parameters to continuously switch between guidance methods. It generates a guiding force $F_g$ based on the robot and haptic device states, environment information such as goal and obstacle positions $X_g, X_o$, and an external path planner and a projection module that computes the position $X_{d,r}$ on the optimal guide $\chi$.</figcaption></figure>

module orthogonally projects the robot position $X_{d,r}$. Goal and obstacle positions $X_g, X_o$ are given from external sources.

## IV. COMPARISON OF HAPTIC GUIDANCE METHODS IN VARIOUS ENVIRONMENTS, A USER STUDY

### A. *Objective and hypotheses*

A user study was designed to evaluate the interaction between an operator and different haptic guidance methods, on different plant inspection scenarios in vertical farming. The objective is to validate the following hypotheses:

**H1:** Ruling guidance appreciation is consistent with standard guidance methods.

**H2:** Haptic guidance methods appreciation varies regarding the faced environment. Spring damper is better suited for constrained environment, while potential field is more adapted to free environment and guiding tube won't really stand out but gives users more flexibility.

### B. *Experiment*

Twenty-eight volunteers were included in the user study. They have been enrolled through email lists and networking and none were familiar with the task. Eight participants have been removed for the study due to technical problems on data recording (8 F and 12 M after removal). The experiment was carried out with the agreement of an ethics committee. All participants completed a consent form to take part in the experiment and to use their data for the analysis of this work.

Participants were asked to quickly takes a picture of plants, within a 2-cm accuracy, while avoiding obstacles. Plants were placed on a vertical farming shelf with PVC tubes as obstacles. Participants were assisted by different haptic guidance methods across six scenarios {S1, ..., S6} illustrated in figure 6. S1 consists in a straight line. S2 makes the user avoid obstacles by one side. S3 forces the user to choose between two sides to avoid an obstacle. S4 presents a highly constrained path. S5 and S6 share the same goals as S2 and S3, but with haptic guidance that did not detect the obstacles. The experiment is organized into sessions, each consisting of four

<figure><img src="image_8.png" /><figcaption>Fig. 6. For the experiment the user teleoperates a robot to 4 plants through 6 different scenarios while avoiding tubes. S1 is a straight line. S2 forces to avoid obstacles. S3 can avoid an obstacle from 2 sides - the guide being randomly generated on one side only. S4 is a highly-constrained path. S5 and S6 have the same targets as S2 and S3 with guides that ignore obstacles.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. The robot (left) is remotely controlled by the operator (right) using the haptic interface, with visual feedback from 3 cameras (highlighted in color), in order to take photos of plants in a farming shelf.</figcaption></figure>

repetitions of a scenario. The first repetition has no guidance, while the next three ones use one of the three haptic guidance methods, selected in a constrained-random order. After each repetition, participants complete the NASA-RTLX and Muir surveys. Upon finishing the four repetitions, participants rank their preferences over the guidance methods. The experiment starts with 3 training sessions, with variation around the same specific training scenario, in the same order.

The operators remotely control a Panda Franka-Emika robot thanks to a Force Dimension Omega.7 haptic device. We
provide video feedback of three cameras (see figure 7), with a visual information about the target distance in the main screen.

### C. Variables and operational hypotheses

Two independent within-subject variables are manipulated during the experiment: scenario {S1, S2, S3, S4, S5, S6} and guidance methods {No guidance, Spring damper, Potential field, Guiding tube}. Every participant tested on a random order all possible combinations of these two variables. {S1, S2, S3, S4} provide situations to evaluate the performance of the different guidance methods under different levels of environment constraint. {S5, S6} provide situations to test the ability to detect and to override a guidance which does not take account of obstacles. An independent between-subject variable is also manipulated concerning the guiding tube {Classic-guiding tube, Ruling-guiding tube}, where half the participants tested one mode and half tested the other.

Subjective and objective data are collected throughout the experiment. The **NASA-RTLX** questionnaire measures perceived workload, with lower scores indicating less workload. **Miur's** questionnaire assesses trust in the robot, with higher scores reflecting greater trust. The **classification survey** asks participants to rank preferred guides for each scenario. **Time completion** associates smaller values with better performance. **Average path following** measures alignment between user motion and path direction, higher values indicate better performance. **Minimal obstacle distance** assesses safety, with larger distances indicating lower collision risk. **Guiding force standard deviation** reflects user comfort, with greater variation indicating discomfort. **Maximum force** results from user trust in GT and SD, where higher forces indicate deviation from the guide. For PF, trust is assessed via the **average force following**, lower values indicate less trust in the guiding force.

In accordance with the hypotheses proposed in section IV-A, the following operating hypotheses are defined:

H1: NASA-RTLX score should show no significant difference between R-GT and classic-GT in every scenario.

H2.1: SD should outperform in S4 and S2, PF in S1 and S3, and GT in S6 and S5; this should match the classification survey.

H2.2: PF should have better completion times in all scenarios; SD should excel in path following performance.

H2.3: PF should have lower safety minimal obstacle distances, SD higher, except in S5 and S6 where GT should be better.

H2.4: SD should globally have lower guiding force standard deviation, except in S5 and S6.

H2.5: PF should show different average force following in S5 and S6 compared to other scenarios; SD and GT should show maximum force variations.

## V. RESULTS & DISCUSSION

Rstudio software (version R 4.4.1) was used to carry out the statistical analysis. Results were considered significant at the 95% confidence level (i.e. p-value < 0.05). For each statistical test, the normality condition and the variance homogeneity

have been verified using Shapiro-Wilk and Levene tests. However, the tests have been run using two within-subject independent variables, each with more than two levels. Analyses were therefore performed using ANOVAs with a sphericity correction (Greenhouse-Geisser Correction) according to the result of an additional sphericity test (Mauchly test) whenever it was appropriate.

### A. Ruling guidance method as a substitute for classic haptic guidance method

A 2x6 mixed-design ANOVA between the guiding tube types (between-subject factor) and scenarios (within-subject factor) has been calculated to test their effect on the score to NASA-RTLX questionnaire to evaluate H1.1.

No effect of the guiding tube type ($F(1, 18) = 0.126, p = 0.727$) or intersection ($F(3.06, 55.15) = 0.866, p = 0.466$) was obtained for the score to NASA-RTLX. This means that the null hypothesis concerning the equality of NASA score averages cannot be rejected, which is consistent with the hypothesis H1: the two types of guiding tube (classic and ruling guidance) are similarly appreciated by participants.

### B. Appreciation of the different haptic guidance methods regarding environment constraint

#### 1) Classification survey

The classification survey, with worst and best guidance given in figure 8, shows two tendencies: User preferred guidance depends on the scenario, and PF is generally the most disliked. This second point could be explained by the random-order presentation of guidance in the experiment, where PF generates a force of attraction that can be surprising for the user and bias its appreciation. Still we can observe that PF appears as the most preferred guidance in S1 and S3 for several participants. In S2 the preference seems to be on SD and in S6 GT has a great score, which partially validate the hypothesis H2.1.

<figure><img src="image_10.png" /><figcaption>Fig. 8. Result of the classification survey about most preferred (left) and less preferred (right) guidance for each scenario.</figcaption></figure>

#### 2) Guidance evaluation

For the following hypotheses an example of the methodology used for all our dependent variables is proposed. Following this, table I summarizes the best (+) and worst (-) guidance methods for the different scenarios and evaluation metrics.

**Detailed study of time completion:** A 4x6 mixed-design ANOVA between the guidance methods' type (within-subject factor) and the scenarios (within-subject factor) has been calculated to test their effect on the participants time completion for each of their trials.
There was a significant main effect of the guidance methods on the time completion, $F(3, 57) = 10.36, p < 0.001$. Similarly, a significant main effect of scenario was observed, $F(2.43, 46.19) = 41.26, p < 0.001$. Furthermore, a significant effect of the interaction of the guidance methods and the scenario was found, $F(3.14, 59.67) = 5.55, p < 0.01$ on the time completion.

Post-hoc tests have been calculated, particularly on the interactions between the guidance methods and the scenarios. A Wilcoxon signed-rank test was conducted to compare the time completion across the guidance methods. The test was performed separately for each scenario, with Bonferroni adjustments applied for multiple comparisons.

Wilcoxon tests reveal lower task completion times in guidance potential field for S1 compared to guiding tube ($W = 209, p < 0.001$), spring damper ($W = 1, p < 0.001$) and no guidance ($W = 0, p < 0.001$) and for S3 compared to guiding tube ($W = 191, p < 0.01$), spring damper ($W = 41, p < 0.01$) and no guidance ($W = 24, p < 0.01$).

The tests also reveal higher completion times in no guidance for S1 compared with guiding tube ($W = 29, p < 0.05$), spring damper ($W = 22, p < 0.01$) and potential field ($W = 0, p < 0.001$) and for S4 compared with guiding tube ($W = 17, p < 0.01$), spring damper ($W = 0, p < 0.001$) and potential field ($W = 28, p < 0.05$).

Running the same tests and following this process for all evaluation metrics, we can fill the results in the table I.

<caption>TABLE I</caption>

THE TABLE SHOWS THE BEST (+) AND WORST (-) GUIDANCE METHODS FOR EACH SCENARIO BASED ON EVALUATION MEASURES. A GUIDANCE METHOD IN A CELL INDICATES SIGNIFICANT DIFFERENCES ($p < 0.05$) FROM OTHERS WHILE X MEANS NO SIGNIFICANT DIFFERENCES.

<table><thead><tr><th></th><th></th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th>S5</th><th>S6</th></tr></thead><tbody><tr><td rowspan="2">Completion time</td><td>+</td><td>PF</td><td>X</td><td>PF</td><td>X</td><td>X</td><td>X</td></tr><tr><td>-</td><td>NG</td><td>X</td><td>X</td><td>NG</td><td>X</td><td>X</td></tr><tr><td rowspan="2">Average path following</td><td>+</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>-</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td rowspan="2">Minimal obstacle distances</td><td>+</td><td>NA</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>-</td><td>X</td><td>X</td><td>X</td><td>X</td><td>PF</td><td>X</td></tr><tr><td rowspan="2">Force standard deviation</td><td>+</td><td>X</td><td>GT</td><td>X</td><td>GT</td><td>X</td><td>PF</td></tr><tr><td>-</td><td>X</td><td>X</td><td>X</td><td>X</td><td>GT</td><td>X</td></tr></tbody></table>

Regarding time completion, PF performs best in S1 (straight line) and S3 (where some participants disagreed with the guide's side token for SD and GT). Since scenarios started without guidance, the worst times were seen in no guidance. No guidance method stands out for average path following, as SD and GT are similar. They still performed better than PF in S1, S2, and S4. This supports hypothesis H2.2, indicating that constrained paths are more suitable for SD and GT compared to PF.

H2.3 is supported by PF being the least effective guide in S5. Although no significant difference was found in S6, PF was still less effective in scenarios where obstacles were not detected. Considering the entire experience, out of 27 crossed obstacles, 25 obstacles were crossed using PF, indicating PF's limitations in term of safety. For the other scenarios, haptic guidance method still provides good security feature.

Regarding guiding force standard deviation, GT is the most comfortable in S2 and S4, but the most uncomfortable in S5. PF's small force standard deviation in S6 is due to its limited force amplitude. However H2.4 is not validated, as SD consistently produces force, even if weak, suggesting that this metric may not be well-suited for this method.

### 3) Trust

To evaluate trust we study each guidance methods regarding the scenario as depicted in figure 9. Muir's questionnaire did not give any relevant result and will not be studied further.

<figure><img src="image_11.png" /><figcaption>Fig. 9. Trust is assessed through every scenario with maximum guiding force for GT and SD and with average force following for PF.</figcaption></figure>

H2.5 is confirmed for SD, with significant differences supporting it. Despite some participants resisting the guide in S3, which reduced the differences for the uses of GT through the different scenarios, a low maximum force remains a good indicator of trust. The average force following, on the other hand, demonstrates that PF is unsuitable for cluttered environments like S4, where the users mostly move in a near-zero field. However, as mentioned above, users often mistrust PF due to the unpredictable presentation of guidance, which complicates the conclusion about this metric's effectiveness in evaluating trust.

## VI. CONCLUSION

The results of our user experiment demonstrates that the proposed ruling guidance is a valuable unified approach, which properly encompasses the different guidance methods. It opens the use of intermediate guidance, as the parameterization allows to continuously vary the guidance function. The diversity of user preferences regarding the guidance and environment shows the importance of identifying adaptation metrics and methodology. We introduced useful performance, safety, comfort, and trust criteria to compare the different guidance methods. Future works will focus on adapting such metrics to dynamically adjust the guidance online during task execution.

## ACKNOWLEDGMENT

This material is based upon work supported by the ANRT (Association nationale de la recherche et de la technologie) with a CIFRE fellowship granted to Farm3. The authors thank Lucas Joseph for his help in designing the experiment.
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