Embodied Tentacle: Mapping Design to Control of Non-Analogous Body Parts with the Human Body

Manipulating a non-humanoid body using a mapping approach that translates human body activity into different structural movements enables users to perform tasks that are difficult with their innate bodies. However, a key challenge is how to design an effective mapping to control non-analogous body parts with the human body. To address this challenge, we designed an articulated virtual arm and investigated the effect of mapping methods on a user’s manipulation experience. Specifically, we developed an unbranched 12-joint virtual arm with an octopus-like appearance. Using this arm, we conducted a user study to compare the effects of several mapping methods with different arrangements on task performance and subjective evaluations of embodiment and user preference. As a result, we identified three important factors in mapping: “Visual and Configurational Similarity”, “Kinematics Suitability for the User”, and “Correspondence with Everyday Actions.” Based on these findings, we discuss a mapping design for non-humanoid body manipulation.

arm, we conducted a user study to compare the efects of several mapping methods with diferent arrangements on task performance and subjective evaluations of embodiment and user preference.As a result, we identifed three important factors in mapping: "Visual and Confgurational Similarity", "Kinematics Suitability for the User", and "Correspondence with Everyday Actions."Based on these fndings, we discuss a mapping design for non-humanoid body manipulation.

INTRODUCTION
Non-humanoid bodies with diferent structures from humans are used in various felds in cooperation with the human body to achieve unique and specifc goals.In virtual reality (VR) games, players can immerse themselves in novel interactions and experiences by adopting non-humanoid avatars.For instance, they can glide through the skies as a bird or use an octopus avatar to manipulate objects with tentacles .In computer graphics (CG) animation, animators move various animals and artifcial objects such as electric lights and tableware as characters to create attractive expressions, often by capturing human movements and translating them into their actions.Additionally, in human augmentation, people can extend their bodies with additional parts, such as a third arm and tail, to improve their working capacity.Using virtual or robotic non-humanoid bodies on their own, people can access novel gaming experiences, good artistic expressiveness, and improved motor skills that are unattainable with their innate bodies.
However, for users to utilize these non-humanoid bodies as their own bodies, a signifcant challenge is to design a control scheme that enables users to manipulate them comfortably.One of the control schemes is mapping, which tracks and translates the movements of a user's body to the movements of a diferent body.If the structures of the controlled body are homologous to the user's, the mapping can naturally be designed with a high degree of operability and embodiment (the sense of feeling as one's own body); however, the structure of the non-humanoid body is diferent from that of the user, making it difcult to create useful mappings.Previous studies on mapping design proposed various approaches, such as an approach in which the operator aligns the arrangement of its body parts similar to the structure of the mapping target to compensate for structural diferences [19] and approaches that generate mappings from pairs of poses [64] [51].However, the efectiveness of these approaches may not align with the intended use of the new body, or may be limited by the physiological constraints of the human body.Jiang et al. [19] attempted to replicate avatar poses using the human body; however, there are avatars or poses that are challenging to reproduce within the range of human joint motion.The approaches of Yamane et al. [64] and Seol et al. [51] are suitable for rough animations.However, they may not provide precise mappings for manipulating specifc body parts, making them less suitable for intricate tasks.If technology allows users to embody and operate non-humanoid bodies or body parts with signifcant structural diferences from their own bodies without being limited by these diferences, it would enable more diverse interactions with others and the environment using forms that signifcantly deviate from the human shape.
To establish a design strategy for mapping that improves the manipulation experience of non-humanoid bodies, we developed an unbranched articulated virtual arm and conducted research on the impact of mapping methods on users' physical experiences.This arm, with an octopus-like appearance, is composed of 12 unbranched joints (Figure 1).Taking advantage of these multiple degrees of freedom, this arm is expected to exhibit unique interaction capabilities tied to its unique structure, such as taking on complex shapes and navigating confned spaces.To control the 12 joints of the arm, we used a one-to-one mapping approach with the 12 joints from the index fnger to the little fnger.Considering the non-independence and diferent levels of control accuracy in fnger and inter-joint movements [14,26,49] as well as human bodily perception, we hypothesized that the manner in which the order of fngers and fnger joints, namely their sequentiality, is preserved before and after the mapping process would afect the manipulation experience.To investigate the efects of mapping, we addressed the following research questions: RQ1 "How does the presence or absence of sequentiality in the mapping afect the manipulation experience of the arm?"RQ2 "Even within mappings with sequentiality, how do variations in the arrangement of the mapping afect the manipulation experience of the arm?" Building on these RQs, we conducted a comparative analysis of four mapping methods for manipulating a virtual arm in which the fnger joints were mapped to the arm joints in diferent orders (Figure 1).We prepared a baseline condition (Non-Sequential), in which the joints were arranged without a sequential order, and experimental conditions (Sequential-Index-Based, Sequential-Little-Based, and Sequential-Across), in which a sequential order was present, but the arrangements difered from each other.Our user study encompassed two motor tasks, a questionnaire, a ranking of user preferences, and interviews.We assessed each mapping condition by evaluating task performance, embodiment, Proteus Efect-related perceptual changes, and user preferences.Interviews were conducted to identify factors that infuenced the overall experience of manipulation.From the results, we identifed three factors infuencing the experience; "Visual and Confgurational Similarity", "Kinematics Suitability for the User", and "Correspondence with Everyday Actions."Based on these fndings, we discuss the implementation of a mapping design for non-humanoid bodies to achieve a superior quality of experience, even in cases where there are signifcant structural diferences between the mapped parts.

RELATED WORK
We built on previous studies in non-humanoid bodies, embodiment, mapping design, and unbranched articulated bodies.

Non-humanoid Bodies
2.1.1Fields of Non-humanoid Bodies.Non-humanoid bodies featuring structures distinct from humans, are increasingly utilized across various felds.These bodies are synchronized and employed in collaboration with human bodies.Novel gaming experiences that use animal avatars have emerged [23,50,55].These games allow players to assume the role of birds fying in the sky [50] or octopuses manipulating their surroundings with tentacles [55].What makes these experiences fascinating is the enhanced immersion in animal experiences facilitated by the visuals of animal avatars and new interactions using the unique body parts of these avatars, such as wings or tentacles, that humans lack.This trend extends to virtual reality social networking services (VRSNS), in which nonhumanoid avatars, including animals and artifcial entities, serve as a means of self-expression and special interaction [16].In computer graphics animation, animators create compelling works by animating characters that anthropomorphize animals or artifcial objects.In general, non-humanoid animation requires professionals to invest manual efort in its creation, whereas some studies have proposed techniques to animate characters in sync with human body movements [7,51,64].In telepresence, beyond the conventional use of fully humanoid avatars [13] or avatars with cameras and arm components [4], non-humanoid robotic avatars have been explored.For example, Piton [17] proposed a robotic avatar with a highly articulated snakelike body that ends with a camera.This design provided a wide feld of view owing to its exceptional postural fexibility.Additionally, the feld of human augmentation introduces a signifcant topic in which individuals incorporate machine-made body parts, such as additional fngers, arms, or tails, as integral extensions of their bodies [29,40,43,48,56,59,61,63,66].
2.1.2Classification of Non-humanoid.From a compositional perspective, non-humanoid bodies can be categorized into three types: virtual bodies, human-machine integrated bodies, and mechanical bodies.Rakita et al. [44] highlighted that virtual characters and multi-articulated robots often share common operating principles because they are composed of links and joints.We propose that this principle can be extended to human augmentation and collectively refer to these three types of bodies as "non-humanoid bodies." The defnition of a non-humanoid avatar is ambiguous.Nonhumanoid avatars can include two patterns: those with fundamentally diferent structures from the human body, and those based on a humanoid structure with an appendage, such as a tail or third arm.
Steptoe et al. [52] distinguishes the latter as "extended-humanoid" rather than non-humanoid.In this study, we defne "non-humanoid bodies/avatars" as bodies/avatars with novel body structures that are either partially or completely diferent from the human form to an extent that requires a special control scheme for manipulation, using Molnar's defnition [38] as a reference.

Embodiment
Embodiment refers to the ownership that people feel over the bodies they use, which arises from multisensory information processing [19,31,34,37] for perceptual embodiment [11].Embodiments comprise three sub-components [21]: body-ownership, agency, and self-location.According to Roth and Latoschik [46], it is "a conscious experience of self-identifcation (body-ownership), controlling one's own body movements (agency), and being located at the position of one's body in an environment (self-location), " with reference to [30,34,53].
Previous research on embodiment began with the Rubber Hand Illusion [6], in which people recognized a rubber hand as part of their own body.Subsequently, studies were extended to investigate embodiment in virtual avatars and augmented bodies.For example, users can achieve a heightened sense of body ownership from a frst-person perspective (1PP) than from a thirdperson perspective (3PP) [36,41].This is true not only for humanoid avatars but also for animal avatars [23].Multisensory stimulation and sensory-motor congruence have also been found to enhance embodiment [36,39,41,52].In addition, studies on avatar hand representations have shown that high agency can be achieved even under conditions where the texture and morphology do not resemble those of a human hand, whereas ownership is lower under conditions that lack morphological similarity, such as when fngers are missing [2].Changes in body schema and body image have also been reported when a person embodies a new body.For example, embodying avatars with diferent body shapes afects users' conscious perception of their body shape (change in body image) [42], and unconsciously infuences users' walking behavior (change in body schema) [47].For non-humanoid avatars, adopting an animal form with unique interaction methods can enhance the sense of change in bodily perception [28].
Another phenomenon related to avatar full-body embodiment is the Proteus Efect [65], in which an avatar's appearance infuences the user's cognition and behavior.For example, attractive avatar appearances increase user sociability [65], and adopting an avatar with a cheerful appearance leads to playing drums more frequently [20].Research is also beginning to explore the Proteus Efect for non-humanoid avatars and avatars with non-human appearances, such as research on the efect of the degree of human resemblance in the avatar's appearance on the fear of heights [35].While the behavioral changes resulting from the Proteus Efect are not distinctly separated from those caused by alterations in body schema, the Proteus Efect depends on the expectations and stereotypes associated with the avatar's identity [65], not the avatar's structure.
Although the efects of embodiment on humanoid bodies have been studied from various perspectives, including appearance, latency, viewpoint, and multisensory feedback, relatively limited research has been conducted on the embodiment of non-humanoid bodies.This will enable people to embody non-humanoid bodies can open novel possibilities for experiences and interactions in felds such as VR games, animation, telepresence, and human augmentation [7,15,17,19,24,32].Therefore, we investigated methods to improve the embodiment of non-humanoid avatars.

Mapping Design
For non-humanoid bodies to be useful, we must have a control scheme that allows humans to comfortably control them.Various techniques have been proposed to achieve this.The most used method is mapping (also called remapping), which translates an operator's movements into those of a new body.The most basic form of mapping is joint-to-joint mapping, in which the positions or rotational movements of the joints of the original body are mapped to the corresponding movements of the joints of the new body, thereby enabling the control of non-humanoid bodies [19,51,58,64].Joint-to-joint mappings range from simple one-to-one correspondences [58] to more complex n-m mappings [19,51,64] where combinations of multiple joints are used to control multiple joints in an avatar.The concept of mapping can be represented by the following formula: Where: y : Position or Rotation, or both, of each joint in the new body.
A : Transformation matrix.
x : Positon or Rotation, or both, of each joint in the motion source.
For more advanced mapping methods, there is an approach that prioritizes locating the end efector in some manner while controlling other parts using inverse kinematics(IK) [1,44,48].Mapping approaches are also used to control humanoid bodies in ways that difer from the real world [12,22,33,54,58], which is benefcial for less tiring VR operations in confned spaces [54], prosthetic control [22], and neurorehabilitation [12].In addition to mapping, there are approaches that control novel appendages in coordination with the innate body rather than simply "translating" the degrees of freedom of the body parts [40,59,60].This approach was used to supplement the missing degrees-of-freedom required to operate the new body.Although the combination of various techniques will improve the utilization of non-humanoid bodies, this study focuses primarily on joint-to-joint mapping as the frst step in designing a better control scheme.
Previous research on mapping design has proposed various approaches such as aligning the arrangement of the operator's body parts to be similar to the structure of the mapping target to compensate for structural diferences [19] and approaches that generate mappings from pairs of poses [51,64].However, the efectiveness of these approaches may not be appropriate for the intended use in a new body or may be limited by the physiological constraints of the human body.For example, the approaches of Jiang et al. [19] and Lockwood and Singh [33], in which human body poses replicate avatar poses, may have limitations in reproducing poses that require heightened joint range of motion than human joints.In addition, a displacement between the user and avatar position could lead to a loss of immersion and presence, making it less suitable for frstperson perspective operations.Seol et al. [51] and Yamane et al. [64] mapped full-body movements to non-humanoid characters using mappings generated from pose pairs.They are suitable for rough animation but may not be sufciently accurate for detailed tasks.Jeon et al. [18] reconstructed high-dimensional robot arm motions based on low-dimensional human motion inputs, thereby enabling intention-based control.It is intuitive but may not be suitable for scenarios that require precise and complete control of the body, such as dancing.Moreover, while some studies have shown that humans can learn non-humanoid bodies to interact with others, that is, they can adapt to new bodies [1,48,52,58], there has been limited discussion on the design of efective mappings for better interaction.Chen et al. [7] and Rhodin et al. 's [45] method of deforming meshes without using rigs is efective for animating various objects but is not optimal for scenarios where the controlled entity has a body structure composed of links and joints.Laha et al. [25] compared three control schemes using diferent motion sources to control a third arm emerging from the chest.While their work provides new insights into mapping design, they did not propose a technique for designing more efective control schemes with specifc motion input sources.The efective use of non-humanoid bodies or body parts, despite their signifcant structural diferences from the mapping source, could enhance interactions with others and the environment using these novel bodies.Therefore, in this study, we propose design factors for efective mapping of non-humanoid bodies with signifcant structural diferences to improve the manipulation experience.

Utilization of Unbranched Articulated
Bodies.
Unbranched articulated bodies such as octopus arms or snakes ofer versatility in their ability to assume various postures and effectively grasp objects of various shapes.Their application has been extended to various felds.For example, the recent introduction of the snake-like telepresence robot Piton [17] demonstrates its potential.Piton consists of a dual-camera head and a snake-like body with a high degrees of freedom.The benefts of such bodies include exceptional fexibility, allowing users to access large workspaces, efciently inspect remote environments and objects, and gain better situational awareness.In addition, Leigh and Maes presented shapeshifting supernumerary robotic limbs (SRL) that could be worn on the wrists [29].Users control the SRL via a myoelectric wristband.The SRL serves multiple purposes and can act as a joystick, extra fnger, or hook.Researchers in soft robotics explored robots inspired by octopus arms [5,27,62].In these studies, the grasping abilities of the octopus arms were harnessed using biomimetic approaches.Danielle Clode's "Vine Arm" prosthetic [8] demonstrates the potential for fashionable and aesthetically pleasing prosthetics inspired by carnivorous plants, octopus tentacles, and vertebrates.However, there has been insufcient research on how users can embody and utilize these unbranched articulated bodies.Therefore, we explored mapping methods that allow users to leverage the unique capabilities of an unbranched articulated arm inspired by octopus arms.

SYSTEM DESIGN
We designed a virtual arm with an octopus-like appearance consisting of 12 unbranched joints, each 6.3 cm long, for a total arm length of 75.6 cm (Figure 2).The distinctive structure of the arm provides unique interaction capabilities, such as taking on complex shapes and navigating confned spaces.The arm length was determined through preliminary experiments by the authors to ensure that users could visually perceive the arm up to the tip.In this study, the arm was positioned parallel to the back of the participants' right wrist (Figure 3) and the arms were controlled by mapping the movements of the 12 fnger joints of their right hand.The humanoid part of the avatar's body has an abstract appearance, and the fngers of the avatar's right hand are invisible to the operator.The rotation angles of the fnger joints were linearly mapped within a range of +/-30 degrees based on the current angle.:Minimum rotation angle of the joint corresponding to in the user's hand.
:Maximum rotation angle of the joint corresponding to in the user's hand.
Each joint can bend in both directions, allowing the arm to assume poses with multiple bends such as S-shaped poses.All the avatars used in the experiment were created in Blender, and the systems were operated in Unity.

EXPERIMENT 4.1 Experiment Overview
We conducted a user study to investigate the design factors of mapping to improve the quality of the user experience when manipulating non-humanoid bodies.We invited 24 participants to manipulate an articulated virtual arm with an octopus-like appearance under four diferent mapping conditions.They were asked to perform two motor tasks (reaching and pose imitation) and to complete subjective surveys for each mapping condition.After completing the tasks under the four mapping conditions, the participants ranked the conditions based on their preferences.Finally, interviews were conducted to gain insight into the overall experience and reasons for user preferences.From these results, we investigated efective mappings for the arm and how these four mappings afected the user experience and discussed the design implementation for nonhumanoid body manipulation.The local ethics review committee approved this study.

Experimental Conditions
We conducted a user study with four diferent mapping conditions (as shown in Figure 4) to compare their efects on task performance and subjective evaluations of embodiment and user preference.The numbers above each fnger joint in the Figure 4 indicate the mapped joint index of the virtual arm, with 1 representing the base and 12 representing the tip.In the Sequential-Index-Based condition (SI), the mapping process began with the index fnger at the root of the arm, followed sequentially by the middle, ring, and little fngers.The Sequential-Little-Based condition (SL) mapped the little fnger to the root of the arm, followed by the ring, middle, and index fngers.The Sequential-Across condition (SA) mapped the metacarpophalangeal (MCP) joints to the root of the arm, followed by the proximal interphalangeal joints and distal interphalangeal joints.The Non-Sequential condition (NS) had non-sequential mapping, where each fnger joint was discretely rearranged.
Considering the non-independence and diferent levels of control accuracy of fnger and inter-joint movements [14,26,49] and human bodily perception, this study formulated two research questions to investigate how the rearrangement of fnger joints afects the arm control experience.To investigate the efect of the presence or absence of sequentiality on the manipulation experience, we used the Non-Sequential condition, which had a non-sequential arrangement, unlike the other conditions (RQ1: How does the presence or absence of sequentiality in the mapping afect the manipulation experience of the arm?).Additionally, we prepared three diferent sequential conditions to investigate how the arrangement afects the experience (RQ2: Even within mappings with sequentiality, how do variations in the arrangement of the mapping afect the manipulation experience of the arm?).In the Sequential-Across condition, unlike the Sequential-Index-Based and Sequential-Little-Based conditions, the lateral joints were continuously mapped.This condition was designed to examine the efect of separating the joints of each fnger and the longitudinal correspondence between the virtual arm and the operator's fngers on the control experience.Additionally, the Sequential-Index-Based and Sequential-Little-Based conditions shared the continuity of the joints of each fnger before and after mapping but reversed the placement of the fngers.These two conditions were designed to examine the efects of kinematic asymmetry between the index and little sides, and body image asymmetry (e.g., the little fnger is at the tip of the body) on the control experience.
While we recognize that n-m joint mappings, often generated using machine learning approaches [19,51,64], are powerful, this study focuses primarily on one-to-one joint mapping to make the mapping comprehensible to users and to assess the fundamental impact of joint replacement on their manipulation experience.In addition, while we recognized a wide range of design possibilities for one-to-one joint mapping from the user's fngers to the arm, estimated at 12 factorial patterns, our study focused on four specifc patterns to explore the RQs.Specifcally, we selected the three sequential conditions, each of which demonstrated diferent forms of sequentiality and were considered preferable.We also included the Non-Sequential condition to represent mappings that did not follow this sequential order.Our primary focus is on the diferences between sequential mappings rather than comparing them to non-sequential mappings; therefore, we represent non-sequential mappings with only one condition.

Apparatus
The VR research platform was developed using Unity 2019 for the HTC Vive Pro 2 and operated on a gaming laptop equipped with an Intel Core i7 CPU and NVIDIA GeForce RTX 3080 GPU.Participants participated in the experiment while seated in a quiet environment.The right-hand and fnger movements were tracked using a Manus Quantum Glove and HTC Vive Tracker.

Participants
The participants in this experiment were 24 individuals (22 males and two females) with an average age of 22.33 years (SD = 2.81).Among them, three were left-handed.Five participants were frequent users of VR equipment, 12 had used it a few times, and seven were newcomers to VR experience.Each participant received a compensation of 2,700 yen at the end of the experiment.

Procedure
The experimental procedure is illustrated in Figure 5.The participants received an explanation of the experiment and signed an informed consent form.A questionnaire was administered to collect demographic information on the participant's age, sex, and VR experience.In addition, we assessed participants' pre-experiment impressions of octopuses using a 7-point Likert scale (7 = strongly  humans.Pre-Q2 The octopus's body surface is softer than that of humans.Pre-Q3 The octopus's body structure is more fexible than that of humans. agree, 1 = strongly disagree) across the three criteria, as shown in Table 1.This information was collected to explore how individual perceptions of octopus fexibility and softness might infuence the results of subjective surveys through the Proteus Efect.The participants then wore a head-mounted display (HMD) and tracking gloves to prepare for the experiment.The IPD of the HMD was adjusted according to each participant's comfort level.
In the experiment, the participants played four mapping conditions in counterbalanced order.For each mapping condition, the participants frst received a pictorial explanation of the mapping condition.They then calibrated the rotation angles of the arm joints by opening and closing their fngers to set the maximum and minimum rotation angles and engaged in a three-minute free movement phase to confrm the mapping between the fnger joints and the virtual arm joints.Subsequently, the participants performed a Reaching task and Pose Imitation task, and completed a questionnaire.The Reaching task measures the smoothness of dynamic motor performance, whereas the Pose Imitation task assesses the accuracy of precision movements.After the motor tasks, the participants removed the HMD and answered a questionnaire on subjective evaluations of embodiment and changes in bodily perception.Afterwards, the participants took a three-minute break before moving on to the next experimental condition.After completing all four experimental conditions, the participants ranked the conditions according to their preferences.Finally, participants engaged in a semi-structured interview that explored topics like their reasoning for ranking the conditions as they did, the strategies they employed to perform the motor tasks, and their overall feelings about the experiences.

Task Design and Measures
We compared each mapping condition using four diferent measures: performance on the Reaching task (time and success rate), performance on the Pose Imitation task, subjective ratings of embodiment, and perceptual changes owing to the Proteus Efect elicited by the questionnaire, and user preference.We also examined the learning efect in two motor tasks to investigate how mapping may afect adaptation [58].
4.6.1 Reaching Task.In this task, the participants were asked to use the virtual arm to touch a ball located behind obstacles over 32 trials (Figure 6).This task evaluated the smoothness of dynamic movements.There was a target, two obstacles and a wrist rest in the scene.The obstacles consisted of two semi-transparent red boxes with gaps between them, and a green ball target was placed on the opposite side of each box.A green disk wrist rest was placed near the participant, and they had to maintain their wrists at the rest while reaching the target.There were four patterns of gap width (30cm, 28cm, 26cm, and 24cm) and four patterns of ball target position (up, down, left, and right), resulting in 16 variations.Each pattern appeared once in the frst 16 trials and again in the second 16 trials, ensuring that the sets for each half contained the same elements but in a diferent order.Each trial proceeded as follows: First, participants began the trial by touching a blue box (Starter) displayed in front of their body with the virtual arm in a clenched position for one second.At the beginning of each trial, the Starter disappeared, and target, obstacles, and wrist rest appeared.Touching the target triggered a bright sound, indicating success, whereas touching the obstacles resulted in a beep, indicating failure.Regardless of the outcome, participants proceeded to the next trial.The participants were instructed to move the virtual arm as quickly as possible without touching obstacles to achieve task success.
The system recorded whether each trial was a success or failure, as well as the time elapsed from the beginning of the trial (when the target appeared) to either successful completion or failure (when the target disappeared).The number of successful trials was used for statistical analysis.In addition, we calculated the median time to completion for successful trials for each participant, each mapping 4.6.2Pose Imitation Task.In this task, participants were asked to imitate the poses of a semi-transparent arm model over 32 trials.This task evaluates the accuracy of the precision movements.The model arm was positioned at the same location as the participants' virtual arm, allowing the participants to spatially overlap their arm with the model (Figure 7).All of the model poses for the 32 trials across the four task conditions are included in the appendix (Figure 19).
In trials 1-8 and 17-24, the poses of the model were consistent across all mapping conditions (Model-Based Stages).In these trials, every set of three joints of the model arm was rotated by +30, 0, or -30 degrees.We selected eight distinct and relatively complex poses from the possible 3 4 pose variations.These eight poses were used once each in the frst (trials 1-8) and second halves (trials 17-24) of the task to ensure that the sets for each half contained the same elements in a diferent order.In trials 9-16 and 25-32, the poses of the model difered between the mapping conditions; however, they all shared the participant's hand pose when perfectly imitating the pose of the model (User-Based Stages).In these trials, every set of three joints of the model arm mapped with the specifc user's fnger (e.g., the set of joints 3, 10, and 4 for the Non-Sequential condition) rotated by +30, 0, or -30 degrees.From the 3 4 possible pose variations, we select eight poses that are not similar.These eight poses were used once each in the frst (trials 9-16) and second halves (trials 25-32) of the task to ensure that the same elements were included.To successfully mimic a tentacle pose model, we predicted two primary challenges: the cognitive challenge of discerning which fnger joints to adjust based on visual feedback and comprehension of the target hand pose, and the motor challenge of accurately replicating the pose.Accordingly, Model-Based Stages with consistent tentacle poses across the conditions were designed to measure the impact of these two aspects.By contrast, User-Based Stages with a consistent hand pose across conditions were specifcally designed to assess cognitive difculty only, removing the variable of motor difculty.Each trial proceeded as follows: Each trial lasted 16 s and consisted of four steps.The frst 6 s were for exploration, during which the participants were instructed to imitate the pose.The next 6 s were for preparation, during which participants were encouraged to continue imitating the pose but were informed of the remaining time until the recording step.The next 3 s were used for score recording, during which the participants were required to maintain the pose without moving their fngers.The fnal 1 s was a transition step for relaxation.Participants were instructed to imitate the poses as accurately as possible.
This task was evaluated using the error score, the average Euclidean distance between the corresponding joints of the participant's virtual arm and the model arm for each of the 12 joints.While metrics such as a local rotation-based error were considered, we ultimately chose this metric to assess overall postural imitation accuracy in an understandable and straightforward manner.Lower scores indicated high accuracy in this condition.The score for each trial was calculated as the average score during the 3-second score recording step.We calculated the median error score for each participant, mapping condition, stage, and for the frst and second halves to perform statistical analysis.4.6.3Qestionnaire.This questionnaire corrects for subjective evaluations of embodiment and perceptual changes owing to the Proteus Efect.The items of the questionnaire are listed in Table 2, and each item is rated on a 7-point Likert scale.Questions related to embodiment focusing on ownership(Q1-3), agency (Q4-7,9), and change (in bodily perception) (Q10-15) were based on the virtual embodiment questionnaire(VEQ) [46] but adapted for the virtual arm.Question 9 assessed the subjective manipulability of the new body structure beyond the mere presence of control, as assessed by Q5.Questions 11-13 were designed to identify where participants felt an extension of their body image when wearing virtual arms, as it was anticipated that wearing these arms might lead to a perceived extension around the hand or fnger.Questions 14 and 15 were added to understand how participants perceived changes in their body images.Questions 8, 16, and 17 were also added to assess whether the participants could acquire a sense of smoothness, softness, and fexibility in the octopus arms through the Proteus Efect.We do not calculate the factors (ownership, agency, change) by averaging the related questions as in the VEQ because we have added or customized the questions to ft the non-humanoid avatar.

RESULTS
4.6.4User Preference Ranking.After completing all four experimental conditions, participants were instructed to rank the conditions in order of preference using the scale: "best, " "good, " "bad, " and "worst." Overall, the disadvantages of the Non-Sequential condition and the diferences between the three sequential conditions were observed, supporting RQ 1 and 2.

Pre-Experiment Questionnaire
We performed a Wilcoxon signed-rank exact test on the diference from the reference value of four for each item.The results confrm that the participants signifcantly felt that the octopus had motor smoothness (Pre-Q1), skin softness (Pre-Q2), and structural fexibility (Pre-Q3) (Figure 8).

Reaching Task
We performed statistical analyses of the number of successful trials and reaching times to compare the smoothness of the dynamic movements between the diferent mapping conditions.

Pose Imitation Task
We performed a statistical analysis of the error scores to compare the accuracy of precision movements between the conditions.
For Model-Based Stages, because normality assumptions were violated (Shapiro-Wilk test, SI-f: = .337,SI-s: = .250,SL-f: = .024,SL-s: = .596,SA-f: = .001,SA-s: = .489,NS-f: = .060,NS-s: = .135),we conducted an ART and a two-way ANOVA.The results show a signifcant main efect of the condition (F (3, 69) = 42.49,p < .001, 2 = 0.65).The main efect of learning (frst and second halves) was not signifcant (F (1, 23) < 0.01, p = .97, 2 < 0.01; Figure 13).The interaction efect between the condition and learning was not signifcant (F (3, 69) = 0.68, p = .57, 2 = 0.03).Subsequent pairwise comparisons for the conditions using Wilcoxon signed-rank tests (adjusted by Holm's method) showed that the Non-Sequential condition had signifcantly higher scores than the other conditions, indicating a greater deviation from the reference model pose ( < .001; Figure 14).15).The interaction efect between the condition and learning was also not signifcant (F (3, 69) = 1.18, p = .32, 2 = 0.05).We then performed a pairwise Wilcoxon signed-rank test with Holm correction as a post hoc test for the conditions.The results show that the Sequential-Across condition resulted in signifcantly lower scores than the other conditions, suggesting a closer resemblance to the model pose (SA vs. SI, SL, NS: = .049,= .001,= .002;Figure 16).In addition, the Sequential-Index-Based condition had lower scores than the Sequential-Little-Based condition, indicating a closer resemblance to the model pose ( = .038).We conducted a questionnaire survey to assess the subjective evaluations for each mapping condition.We performed Wilcoxon signedrank tests comparing each condition to a reference score of 4, and between conditions.The latter was adjusted using Holm's method.The former aimed to assess the participants' perceptions of the questionnaire items, as diferences between conditions may have limited meaning if both are non-positive.Figure 17 presents box plots of the result of the questionnaire (Table 2).For the detailed p-values, see Table 5 in the Appendix.
Q1, Q2, and Q3 indicate that the participants in all mapping conditions felt that the arm was "my body" and "belonged to me, " but did not perceive it as a human body.
Q4, Q5, Q6, Q7, and Q9 revealed that the participants felt some degree of agency over the virtual arms in all mapping conditions.Q5 and Q6 indicated that the participants felt that they were actively controlling or causing arm movements under all conditions.Q4 showed that in the Sequential-Index-Based and Sequential-Across conditions, the participants felt that their arm movements were their own.Q7 indicated that in the Sequential-Across condition, participants felt that their arm movements were closely synchronized with their own.In addition, Q9 showed that in the Non-Sequential condition, scores were signifcantly lower than the reference score, indicating that participants did not feel that the arm was moving as they intended.In general, although there were no signifcant diferences in individual questions, the overall number of positive and negative outcome questions potentially suggests that participants felt a greater sense of agency toward the virtual arms in the following order: Sequential-Across, Sequential-Index-Based, Sequential-Little-Based, and Non-Sequential.Q10, Q11, Q12, and Q13 indicated that participants felt some extension of their fngers in the Sequential-Index-Based condition, but overall, there was no strong sense of extension of the hands or fngers.Q11 indicated that in the Non-Sequential condition, the participants felt little extension of their arms.In the Sequential-Little-Based condition, participants felt that their arms extended signifcantly more than in the Non-Sequential condition (SL vs. NS: p = .013),but no signifcant diference was observed compared to the reference value.Q12 indicated that participants in the Sequential-Little-Based condition felt a signifcant extension beyond their wrists compared to the Sequential-Across condition (SL vs. SA: p = .033),although this was not signifcant compared to the reference value.Q13 indicated that participants perceived a signifcant extension of their fngers in the Sequential-Index-Based condition.
Q14 and Q15 investigated whether the participants perceived the virtual arms as appendages or altered bodies of their right hand.However, this has not yet been confrmed.Q8, Q16, and Q17 examined whether the participants perceived a sense of motor smoothness, skin softness, and structural fexibility because of the Proteus Efect.Q8 showed no signifcant diference from the reference score under any condition, indicating that the sense of motor smoothness was not confrmed.Q16 showed that in the Sequential-Little-Based condition, there were no signifcant differences from the reference score, whereas in the other conditions, the scores were signifcantly negative, indicating that the participants did not feel an increase in the softness of their body surface.
Table 3: Spearman's Rank correlation coefcients between Q8, Q16, Q17, and the pre-survey questions.The magnitude of the correlation coefcients shows how the participants' pre-experiment impression of octopus characteristics afects the subjective scores of changes in bodily perception after using the virtual arm in each mapping condition.The values in parentheses are p-values.Q17 showed that in the Sequential-Little-Based and Non-Sequential conditions, there were no signifcant diferences from the reference score, while in the Sequential-Index-Based and Sequential-Across conditions, the scores were signifcantly negative, indicating that the participants did not experience an increase in the fexibility of the structure.We also calculated Spearman's rank correlation coeffcients and p-values for each corresponding item between Q8, Q16, Q17, and the pre-survey questions.The results show no signifcant correlations between these variables (Table 3).

User Preference
Figure 18 shows the mapping preference results ranked by the participants.Based on the number of times they were selected as the best condition, it is clear that participants tended to prefer the conditions in the following order: Sequential-Index-Based > Sequential-Across > Sequential-Little-Based > Non-Sequential.

DISCUSSION 6.1 Embodiment
The results of the questionnaires confrmed that the participants experienced a certain level of embodiment of the virtual arm in all mapping conditions.A potential diference between the conditions was observed for questions related to agency and change; Correlation Coefcients (p-value) however, almost no diferences were observed for questions related to ownership or the Proteus Efect.Regarding questions about ownership, the participants reported high levels of ownership (median scores of 5 and 5.5 for Q1 and Q3, respectively) of the virtual arm in all mapping conditions.However, they did not perceive the arm to be human-like (Q2).This difers from previous research [35], which suggests that a certain degree of morphological similarity is required to achieve high ownership.In our study, participants' fnger movements were mapped to virtual arms with varying morphologies and dynamics.Despite these diferences, participants still reported a strong sense of ownership over the arms.This suggests that if one's own body movements are visually represented on an avatar in some manner, it may be possible to establish ownership.Future research is required to examine the ownership of non-humanoid body parts, including comparisons of the non-moving condition and the asynchronous conditions.
The agency-related questions in our study indicated that participants felt a sense of control in the following order, from highest to lowest: Sequential-Across, Sequential-Index-Based, Sequential-Little-Based, and Non-Sequential.The results for Q4 showed that the Sequential-Index-Based and Sequential-Across conditions allowed participants to perceive the virtual arm's movements as their own, indicating a sense of agency.Particularly in the Sequential-Across condition, the participants perceived the arm to move in sync with their own.This may be because, in the Sequential-Across condition, the lateral joints of the fngers often moved synchronously, resulting in a general alignment between the shape of the arm and that of the participant's fngers.This allowed participants to treat the arm as an extended and enlarged version of their own fngers ("It felt like an extension of myself, with the mapping corresponding to the direction of length" [P4]; "It felt like the fngers were just/intuitively longer" [P16] [P18]).However, agency was less evident in the Sequential-Little-Based and Non-Sequential conditions, with only Q5 and Q6 showing positive results.This is likely because, in the Sequential-Little-Based condition, participants found it difcult to accurately control the ring and little fngers independently, hence, they unintentionally moved together with other fngers.
("The Sequential-Little-Based condition is similar to the Sequential-Index-Based condition, but the ring fnger mapped to near the base of the arm did not move well, and independently, therefore, it did not move as expected" [P5]).This result is consistent with a previous study that showed the low independence of the ring fnger [14].For the Non-Sequential condition, participants had difculty identifying which fnger to control, and even when they could identify it, they faced challenges in physically executing the movements due to the kinematic limitations of the hand ("The random mapping was unclear" [P8]; "The mapping around the base and tip was understood, but there were structural difculties in mimicking the model" [P5]).
There was almost no evidence of changes in bodily perception.The participants reported a sense of fnger extension only in the Sequential-Index-Based condition, although there were no significant diferences compared to the other conditions.This unique perception can be attributed to the fact that the movements of the fngers, which are mapped to the base of the arm, infuence the overall arm movement, creating a sense of fnger enlargement.Additionally, the index fnger, which is more stable in its movement compared to the other fngers, would leave a stronger impression when mapped to the base ("Because the fngers placed at the base of the arm can control the approximate position of the arm, it is benefcial if the index fnger, which is easy to move, is placed at the base" [P7]).
We also examined whether the participants perceived the arm as an additional limb or as an altered part of their right-hand fngers; however, neither was confrmed (Q14,15).Contrary to the natural expectation that the participants would view the arm as a modifed part of their fngers-especially given that the controlling fngers were invisible-this was not true.This discrepancy could be attributed to the absence of changes in bodily perception, which is thought to result from the limited duration of arm wear.
Regarding the Proteus Efect, we did not observe that the participants gained a sense of motor smoothness, skin softness, and structural fexibility associated with the impression of the octopus after the arm manipulation experience.This lack of an efect is due to the complexity of the manipulation stemming from the non-humanoid structure, which diminishes immersion in the octopus role.Unlike previous research [35], in this study, not only the appearance, but also the structure of the avatar was diferent from that of humans.For future experiences using the Proteus Efect in conjunction with the impression of non-humanoid appearance, it is suggested that maintaining humanoid body structures while changing appearance (e.g., anthropomorphized animal characters with humanoid structures) may be more appropriate.

Task Performance
We assessed the smoothness of the dynamic movements in the Reaching task and the accuracy of the precision movements in the Pose Imitation task.By integrating the results of all tasks, motor performance was ranked in the following order: Sequential-Index-Based, Sequential-Little-Based, Sequential-Across, and Non-Sequential.The sequential conditions produced higher performance than the Non-Sequential condition as a baseline.Learning efects were observed in the Reaching task and the User-Based Stages of the Pose Imitation task, but not in the Model-Based Stages.No diferences in learning efects were observed between the mapping conditions.

Mapping Conditions.
In the Reaching task, although there were no statistically signifcant diferences in the number of successful trials between the conditions, we observed diferences in reaching times.The median number of successful trials across all conditions ranged from 26 to 28 out of 32, indicating a high task success rate of approximately 85% with some individual variation.The reaching times were signifcantly shorter in the Sequential-Index-Based condition than in the Sequential-Across condition.Additionally, there was a trend toward shorter reaching times in the Sequential-Little-Based condition than in the Sequential-Across condition, although the diference was not statistically signifcant.Reaching times in the Non-Sequential condition were not confrmed to be slower than those in the other conditions.The similar success rates across all conditions can be attributed to the task pose requirements.The task required bending a portion of the virtual arm's tip in an arc, a maneuver that was feasible under all conditions with sufcient time.Furthermore, the participants heard an unpleasant sound if they failed the task, but there were no penalties for slow completion times, possibly leading them to prioritize task success over speed.The variations in reaching times were primarily attributed to the time required to form the arched arm pose and the comfort level of maintaining that pose.Specifcally, in the Sequential-Index-Based and Sequential-Little-Based conditions, the participants only had to bend a single fnger mapped to the tip, which was relatively easy to maintain.In contrast, in the Sequential-Across condition, bending only the distal joints mapped to the tip was challenging, and it was difcult to maintain the pose ("In the Sequential-Across condition, it was difcult to intentionally bend only the distal joints, and I could not control the tip of the octopus arm" [P2]).The reaching time in the Non-Sequential condition was not found to be diferent from that in the other conditions.They seemed to adopt the strategy of keeping their fngers relatively stationary and treating the virtual arm as a fxed tool like a hook rather than a fexible arm to avoid complex fnger movements.This suggests that users may resort to these strategies when dealing with complex control systems.This compromise-based operational adaptation was observed with a loss of agency, unlike the usual adaptation to a new body [10].
For the Pose Imitation task, in general, participants performed more accurately in the Sequential-Index-Based condition than in the Sequential-Little-Based condition, and less accurately in the Non-Sequential condition than in the other conditions.In the Model-Based Stages, the Non-Sequential condition performed worse than the other conditions.This is because of the difculty in identifying which fnger to control and in executing movements with the kinematic limitations of the hand.In the Sequential-Index-Based and Sequential-Little-Based conditions, the three joints in each fnger matched every three joints where the model arm bent, creating a fnger-to-segment coherence that may have afected task performance.However, because users did not specifcally mention that they noticed model arm bending at these three-joint intervals or the coherence itself, it was assumed that they were not intentionally using this coherence.In the User-Based Stages, the Sequential-Across condition performed better than the other conditions, and the Sequential-Index-Based condition performed better than the Sequential-Little-Based condition.However, in the Sequential-Across and Non-Sequential conditions, all the model poses were arc-shaped rather than more complex shapes, such as S-shaped, making it easier to imitate these poses.Considering this, the diferences between the Sequential-Index-Based and Sequential-Little-Based conditions and between the Sequential-Across and Non-sequential conditions are important.
In the User-Based Stages, the Sequential-Index-Based condition signifcantly outperformed the Sequential-Little-Based condition.
Although not statistically signifcant in the Model-Based Stages ( = 0.184) and there was individual variation, 17 out of 24 participants still showed better performance in the Sequential-Index-Based condition.This can be attributed to the diferences between the index-and little-side fngers.In particular, the index-based manipulation was more understandable based on the visual similarity ("It's easy to associate the index fnger with the thicker part at the base" [P2]), and moved more stably because the index fnger, which is commonly thought and shown in previous research [14] to be stable, is assigned to the base of the arm ("The base movements are magnifed, making it easier to manipulate when the index fnger is mapped to the base, rather than the more unstable little fnger" [P21]).
Additionally, two participants commented on their daily habits: "Since I usually grip things starting with the index fnger, the Sequential-Index-Based condition felt more natural and easier to manipulate" [P9], "My usual hand movements follow the sequence of index fnger, then middle fnger... so these actions could be adapted to the octopus arm as usual" [P24].These comments suggest that the task strategy, which involved initiating substantial movements at the base of the virtual arm and making fner adjustments at the tip, mirrored common hand movements.For example, in everyday activities, the index fnger is often the frst fnger to move.This correspondence between the user's desired body movements with the virtual arm and well-trained daily movement patterns is likely to infuence the usability.If well-established daily movement skills can be efectively translated into new motor skills of the novel body through an appropriate mapping design, the cost of operational learning could be reduced.
We planned to measure the efect of both motor and cognitive difculties on the performance between conditions in the Model-Based Stages and only cognitive difculty in the User-Based Stages.However, no efects were found that could be attributed to this diference.It is possible that even though the fnal pose of the arm was the same, the intermediate poses difered depending on the mapping, and this could have eventually afected the motor difculty in the User-Based Stages as well.Stages.This could potentially be attributed to the fact that in the User-Based Stages, the consistency of the hand poses as a goal across conditions had a positive efect, as participants could confdently reuse the hand pose they experienced in the frst and second halves.Conversely, during the Model-Based Stages, encountering the same tentacle pose repeatedly across diferent conditions might have caused confusion and adversely afected learning.In addition, the medians of the scores were lower in the User-Based Stages than in the Model-Based Stages for all conditions.This diference may be owing to variations in the pose sets for each stage, the order in which the stages were performed, and diferences in ease of learning.
A learning efect was observed in most motor tasks.However, no signifcant diferences in the learning efects were observed between the conditions.This suggests that regardless of the mapping condition, there is an improvement in both agility and control accuracy, and, at least within a few minutes to tens of minutes after starting, mapping does not have a major impact on learning efciency.

Design Factor
Based on the interviews and experimental results, we categorized the factors infuencing the task performance, embodiment, and user preferences (Table 4).
There are three factors: frst, whether there is any similarity between the mapped body parts that serve as cues to discover the corresponding joints ("Visual and Confgurational Similarity"); second, whether the user can perform the required movement to control the new body and whether the movement is efortless ("Kinematics Suitability for the User"); and third, whether the required body movements depending on the mapping correspond with the user's everyday actions ("Correspondence with Everyday Actions").
Based on the interviews, sub-factors such as "Sequentiality, " "Similarity in Visual Characteristics, " "Similarity in Arrangement, " and "Similarity in Cognitive Arrangements" were identifed as factors infuencing the user experience in the category of "Visual and Confgurational Similarity".The following are some comments from the interviewees.
• "(In the Sequential-Index-Based condition) it was easy to associate the thicker index fnger with the thicker base." [P2] • "The sequence of fngers matched between the mapped parts in the Sequential-Index-Based condition, making it easy to control." [P3] • "(In the Sequential-Across condition) I felt that the base of the fnger corresponded to the base of the octopus arm, and the tip corresponded to the tip of the octopus arm, so they matched." [P7] • "(In the Sequential-Index-Based condition) I had an image of the index fnger being at the base and the little at the tip, so it was easy to understand." [P2] "Sequentiality" refers to keeping the connected or adjacent joints adjacent before and after mapping."Similarity in Visual Characteristics" involves making the visual characteristics (such as size, thickness, or color) of the corresponding joints similar before and after mapping."Similarity in Arrangement" means arranging corresponding joints in a similar positional arrangement before and after mapping, for example, if the joints were originally located at the base of the mapping source, they should be placed at the base of the mapping target after the mapping."Similarity in Cognitive Arrangement" involves leveraging cognitive positional similarity to associate paired joints, even if there is no visible similarity in the arrangement; for example, the little fnger that is at the tip of the body should be mapped to the tip of the new body.
These factors serve as cues for associating the mapped joints between the virtual arm and the user's fngers, thereby increasing the comprehensibility (i.e., intuitiveness) of the manipulation.Indeed, numerous participants preferred conditions with more of these factors, such as the Sequential-Index-Based and Sequential-Across conditions, and commented that the matched order of the joints made the manipulation intuitive; therefore, they liked it (the number of people making such comments: SI = 9, SL = 0, SA = 9, NS = 0).This fnding suggests that intuitiveness contributes to a higher preference.From these results, we can utilize the factor "Visual and Confgurational Similarity" to improve intuitiveness and user preference.However, the intuitive conditions did not necessarily lead to better task performance, as the Reaching task performance in the Sequential-Across condition trended worse than that in the Sequential-Little-Based condition.
"Independence of Joint Movements" and "Accuracy of Joint Movements" are the sub-factors that infuence the feasibility and comfort of the required movement and the overall user experience in the category of "Kinematics Suitability for the User."The following comments highlight these factors: • "(In the Sequential-Little-Based condition) the little fnger and ring fnger tend to move along with others, so it would have been better if they were not mapped at the base." [P23] • "(In the Sequential-Across condition) it's challenging to move only the middle joints to control just the middle part of the octopus hand, even though I can control the tip.[P3] • "(In the Sequential-Across condition) I wanted to move the tip, but the base moved with it." [P21] • "(In the Non-Sequential condition) although I understood the mapped joints to the base and tip, there were tasks that were structurally and kinematically difcult for the fngers to mimic.

" [P5]
The participants often commented that the lack of independence and accuracy in joint movements prevented them from achieving their desired actions, either making them impossible or requiring signifcant efort.Conversely, the mapping of highly independent and precise fnger movements to critical joints of the virtual arm received positive feedback.Specifcally, the lack of independence and accuracy of the little fnger and ring fnger movements in the Sequential-Little-Based condition and the lack of independence of the within-fnger joints in the Sequential-Across condition were commonly cited as reasons for the low ratings (nine participants and fve participants, respectively).In addition, few participants (2 participants) rated the Sequential-Index-Based condition poorly, mainly due to unintentional movements or nervous tremors of the index fnger.The Non-Sequential condition received less feedback, likely because it was obviously challenging.These factors, which particularly afect task performance, positively favored the Sequential-Index-Based condition, while disadvantaging the Sequential-Little-Based and Sequential-Across conditions.We can consider the factor "Kinematics Suitability for the User" to improve motor performance, for example, mapping a precise and independently moving body part to the critical joint of the avatar.Despite lower task performance, the Sequential-Across condition scored higher on agency, suggesting that motor difculty may not signifcantly afect agency compared to the previously mentioned factors of intuitiveness.
Furthermore, the correspondence between fnger movements for controlling the virtual arm and everyday actions, termed "Correspondence with Everyday Actions," was also found to potentially infuence the user's experience.The following are the comments about these factors: • "(In the Sequential-Index-Based condition) since I usually grip things starting with the index fnger, the Sequential-Index-Based condition felt more natural and easier to manipulate." [P9] • "(In the Sequential-Index-Based condition) my usual hand movements follow the sequence of index fnger, then middle fnger... so these actions could be adapted to the octopus arm as usual[P24]." Diferent mappings require diferent user-fnger movements to perform the intended actions of the new body.When these fnger movements match the user's everyday actions, they are likely to enhance the user preference and ease of use.An efective mapping design has the potential to allow users to transfer their daily practiced motor skills to new motor skills with a new body, thereby facilitating faster learning of new body movements.
It is likely that more efective mapping can be designed by considering these factors.However, there are diferences in the strength of the impact of these factors on user experience and the potential trade-ofs between them.For example, while agency was high in the Sequential-Across condition and performance was high in the Sequential-Index-Based condition, designing a mapping that combines the advantages of both would be challenging within the confnes of simple one-to-one joint mappings.Designing a mapping that optimizes all parameters for experience evaluation involving user preference, performance, and embodiment is difcult.It is desired to explore trade-ofs and the degree of impact each factor has on the user experience.

LIMITATION
The results identifed three factors that infuence the user's manipulation of non-humanoids; however, we have only gained limited insight into the trade-ofs and magnitude of their efects.When designing a new control scheme for a new body, we must consider not only the design factors themselves but also the magnitude of their efects and trade-ofs.To gain a deeper understanding, detailed experiments that consider each design factor independently are required.Additionally, the factors identifed in this study were based on investigations of specifc pairs of non-humanoid avatar structures and operator body parts.Further testing with diferent avatar structures, ranging from full body to individual body parts, is required to investigate the presence of other factors.The Reaching and Pose Imitation tasks from this study can be used in such experiments.It would be desirable to customize the task to measure the unique interaction abilities associated with its unique structure, as in a previous study measuring the ability to reach distant targets with the third long arm [58]; in our study, we measured the ability to reach around obstacles using the pose fexibility of the arm.
In this study, we only conducted limited discussion on the nonindependence between fnger and inter-joint movements, as well as the diferences in control levels.With regard to the design factor "Kinematics Suitability for the User", by considering mechanisms that afect fnger manipulation as highlighted in previous research-such as mechanical connections between the fngers, the organization of multitendoned fnger muscles, and distributed neural control of the hand [14,26,49]-it will be possible to achieve better manipulation of avatars.For example, because the speed [14] and amplitude [26] of movements afect fnger independence, mapping slower or smaller fnger movements to an avatar's actions can lead to more precise manipulation.
In this experiment, we compared the outcomes of the motor tasks in both the frst and second halves and discovered that the mapping conditions did not signifcantly impact learning.However, the learning period was relatively short.Conducting comparisons over an extended period and at more intervals could potentially reveal the efect of mapping conditions on learning, which was not observed in the current study, as well as diferences in task performance after saturation.
This study confrmed diferences in task performance between diferent mapping conditions, but did not investigate the extent to which these mappings are functional or useful in everyday scenarios.Future evaluations could include common everyday situations or long-term usage scenarios with a focus on potential learning efects, like the studies conducted on prosthetics [9].
In this study, the degree of embodiment was assessed using subjective surveys.However, there are physiological methods such as the skin conductance response that can measure ownership [3].Particularly for extended body parts, examining skin conductance responses can provide insights into whether users embody the part motorically (integration within the body schema) or perceptually [11] (integration within the body image, as observed in most versions of the RHI [6,21]), which is an interesting question for the embodiment of extended appendages.
In this research, we focused on one-to-one joint mapping scenarios in which the user potentially had sufcient motion input channels to fully control the new body (although in practice, perfect control is limited by the non-independence of their joints).However, in practical scenarios involving various non-humanoid body structures, users may need to control bodies with higher degrees of freedom than the user's inputs.In these cases, extending the method beyond simple joint-to-joint mapping is necessary.Approaches such as reducing degrees of freedom through inverse kinematics (IK), supplementing degrees of freedom through cooperative movements or shared autonomous movements based on user intentions using machine learning [18], or augmenting degrees of freedom using methods such as electromyography (EMG) [56] or brainwave control can be considered.Our results ofer a basis for constructing future integrative approaches involving these approaches; for example, the identifed design factors can be used as constraints in machine learning.By advancing the research on control schemes that allow people to control bodies that are not structurally analogous to their own, we can overcome innate physical limitations, gain new forms of bodily expression, and even approach the question of the limits of bodily plasticity.

CONCLUSION
In this study, we designed an unbranched articulated arm controlled by fngers and investigated the impact of diferent mapping conditions on the user experience.From the results, we found that index-based mapping provides high operability and MCP-based mapping provides high agency, and identifed three key factors-"Visual and Confgurational Similarity," "Kinematics Suitability for the User," and "Correspondence with Everyday Actions"-that infuence the user experience when controlling non-analogous body parts compared to the operator's body.By considering these three factors, we can create efective mappings from a user's body to non-analogous body structures.This enables us to achieve a higher-quality user experience for non-humanoid manipulation and unlock interaction capabilities that were previously inaccessible to one's innate body.This study expands the design possibilities in areas such as VR avatars, human augmentation devices, and telepresence avatars, allowing us to exploit the unique capabilities of various non-humanoid bodies.

A APPENDIX
A.1 P-values of the Questionnaire results

Figure 2 :
Figure 2: Confguration and movement of the virtual arm.

Figure 3 :
Figure 3: The avatar used in the experience.
A clenched fst corresponded to +30 degrees, while an open hand position corresponded to -30 degrees.The rotation angles of the arm joints were calculated as follows:   −

Figure 4 :
Figure 4: The four mapping conditions used in the experiment.The number above each fnger joint indicates which arm joint is being mapped.

Figure 6 :
Figure 6: A participant playing the Reaching task with our system.

Figure 7 :
Figure 7: Scene of the Pose Imitation task

Figure 8 :
Figure 8: Results of pre-experiment questionnaire

Figure 9 :Figure 10 :
Figure 9: Results of number of success trials in the Reaching task compared between the frst and second halves

Figure 11 :
Figure 11: Results of the reaching time in the Reaching task compared between the frst and second halves.

Figure 12 :
Figure 12: Results of the reaching time in the Reaching task compared across four conditions.

Figure 13 :
Figure 13: Results of error scores in the Model-Based Stages of Pose Imitation task between the frst and second halves.

Figure 14 :
Figure 14: Results of error scores in the Model-Based Stages of Pose Imitation task across four conditions.

Figure 15 :
Figure 15: Results of error scores in the User-Based Stages of Pose Imitation task between the frst and second halves.

Figure 16 :
Figure 16: Results of error scores in the User-Based Stages of Pose Imitation task across four conditions.

Figure 17 :
Figure 17: Result of the questionnaire.Asterisks on each boxplot indicate values that are signifcantly diferent from the reference score of 4, as confrmed by the Wilcoxon signed-rank test

Figure 18 :
Figure 18: User preference ranking of the mapping conditions.

6. 2 . 2
Learning Efect.A learning efect was observed in the User-Based Stages of Pose Imitation task but not in the Model-Based

Figure 19 :
Figure 19: 32 Stages of the Pose Imitation task for each condition.Trials 1-8 and 17-24 were categorized as Model-Based Stages, where the poses of the model tentacle arm are consistent across conditions.Trials 9-16 and 25-32 were categorized as User-Based Stages, where the user's target hand poses are consistent across conditions.

Table 1 :
Impressions of octopus characteristics : preexperiment questionnaire IDQuestion Pre-Q1 Octopuses move more smoothly and fuidly than

Table 2 :
Embodiment Questionnaire a new body part was added while the structure of my hands and fngers remained the same.Q16 Proteus Efect I felt that a part of my body surface became softer.Q17 Proteus Efect I felt that my body structure became fexible.

Table 4 :
Factors and sub-factors infuencing the manipulation experience derived from interview and experimental results.+ and − indicate the efect of the factor with the mapping condition based on the interview comments.

Table 5 :
P-values for each item and condition compared to the reference value of 4, calculated from the questionnaire