Anne Cillard

Tatiana Fuentes Rodriguez

Jean-Patrice Robin

Pierre Bize

Antoine Stier

Vincent A Viblanc
email: vincent.viblanc@iphc.cnrs.fr

Sharing your snack: unusual observation of a chick-chick feeding occurrence in colonial king penguin (Aptenodytes patagonicus)

Keywords: Allofeeding, chick feeding, food sharing, learning, parental care, penguin, seabird

King penguins (Aptenodytes patagonicus) are colonial seabirds presenting an extraordinary breeding cycle. Parents take over 14-mo to raise a single chick to independence, upon which fledglings depart at sea for more than a year. Juveniles often return to the colony within the three austral summers following departure, and before the age of first reproduction (around ca. 5-6 years old.), possibly to acquire the essential skills involved in breeding. Little to nothing is known on the acquisition of parental behavior. Here, we report an anecdotal, yet highly unusual, observation of chick-chick feeding behavior in this species. The behavior is highly unusual in that two non-sibling chicks, not yet independent, and hatched at different times (early and late) of the same breeding season were observed, the older chick feeding the younger one. Whereas alloparental feeding is known to occur in this species, this is the first reported observation of a chick-chick feeding event. This unusual behavior raises the question of whether the early social environment plays a role in the acquisition of essential parenting skills in this species.

Introduction

Allofeeding, the act of feeding another individual, is common in many bird species [START_REF] Silver | Parental Care in an Ecological Perspective: A Quantitative Analysis of Avian Subfamilies[END_REF]. Between adults, it often occurs in the context of reproduction, where food sharing between partners is suggested as a strategy allowing to strengthen the pair bond [START_REF] Lack | Courtship Feeding in Birds[END_REF][START_REF] Smith | Demand Behavior: A New Interpretation of Courtship Feeding[END_REF][START_REF] Mori | An observation of betweenmates feeding behaviour in chick-guarding chinstrap penguins[END_REF], reduce the nutritional stress of the recipient (often the female) during critical periods such as egg-laying [START_REF] Jing | Alloparenting in the Rare Sichuan Jay ( Perisoreus Internigrans )[END_REF][START_REF] Halley | Biparental incubation and allofeeding at nests of Sagebrush Brewer's Sparrows[END_REF], or allow social integration within flocks by reducing aggression in highly sociable species (e.g. Eurasian Siskins, Carduelis spinus; [START_REF] Senar | Allofeeding in Eurasian Siskins (Carduelis spinus)[END_REF]. Allofeeding also occurs in the context of parental care, where individuals might feed offspring belonging to a parent, sibling, or unrelated conspecific [START_REF] Stamps | Parent-offspring conflict in budgerigars[END_REF][START_REF] Carlisle | Helping at the nest, allofeeding and social status in immature arabian babblers[END_REF][START_REF] Jouventin | Adoption in the emperor penguin, Aptenodytes forsteri[END_REF][START_REF] Waite | Cooperative Breeding in Gray Jays: Philopatric Offspring Provision Juvenile Siblings[END_REF][START_REF] Kalishov | Allofeeding in Arabian Babblers (Turdoides squamiceps)[END_REF][START_REF] Lecomte | Alloparental feeding in the king penguin[END_REF][START_REF] Jing | Alloparenting in the Rare Sichuan Jay ( Perisoreus Internigrans )[END_REF][START_REF] Roulin | Reciprocal preening and food sharing in colour-polymorphic nestling barn owls[END_REF][START_REF] Ducouret | Elder Barn Owl Nestlings Flexibly Redistribute Parental Food according to Siblings' Need or in Return for Allopreening[END_REF][START_REF] Ogino | Drivers of alloparental provisioning of fledglings in a colonially breeding bird[END_REF]. Such behavior may be selected because of the direct and indirect fitness benefits accrued to both (often, but not always, related) recipients and donors [START_REF] Hatchwell | The evolution of cooperative breeding in birds: kinship, dispersal and life history-Philos[END_REF][START_REF] Lloyd | Females increase reproductive investment in response to helper-mediated improvements in allo-feeding, nest survival, nestling provisioning and post-fledging survival in the Karoo scrub-robin Cercotrichas coryphaeus[END_REF][START_REF] Meade | Consequences of 'loadlightening' for future indirect fitness gains by helpers in a cooperatively breeding bird[END_REF][START_REF] Ogino | Drivers of alloparental provisioning of fledglings in a colonially breeding bird[END_REF].

In this short note, we report a singular observation of chick-chick feeding in a colonial seabird species, the king penguin (Aptenodytes patagonicus). King penguins are long-lived seabirds that breed in vast colonies of several thousand of pairs on small subantarctic islands during the Austral summer [START_REF] Barbraud | Population trends of penguins in the French Southern Territories[END_REF]. Their breeding cycle is long and complex, as parents take over 14-mo to raise a single chick [START_REF] Stonehouse | The king penguin Aptenodytes pataconica of South Georgia-Sci. Reports Falkl[END_REF]Weimerskirch, Stahl, & Jouventin, 1992). Because reproduction extends for over a year, successfully breeding adults in one year are constrained to breed later in the subsequent season. Thus, breeding occurs in two waves: early breeding is initiated in November, whereas late breeding is initiated around January-February, and it is rare that late breeders succeed (Weimerskirch, Stahl, & Jouventin, 1992;[START_REF] Stier | Starting with a handicap: phenotypic differences between early-and late-born king penguin chicks and their survival correlates[END_REF]. In early November, after the molt, early breeders gather in colonies for a period of courtship and mate choice of roughly 11 days, before copulation occurs and the female lays a single egg. The egg is rapidly passed to the male, which starts incubating it on its feet, against a specialized warm skin fold devoid of feathers, called the brood pouch. During this period, the female leaves for a 300-500 km foraging trip at sea [START_REF] Bost | Foraging habitat and food intake of satellitetracked king penguins during the austral summer at Crozet Archipelago-Mar[END_REF] during which they target myctophid fish usually clustered around marine areas of high productivity such as the polar front [START_REF] Guinet | Foraging behaviour of satellite-tracked king penguins in relation to sea-surface temperatures obtained by satellite telemetry at Crozet Archipelago, a study during three austral summers-Mar[END_REF]. Male and female parents will keep alternating incubation duties, until the egg hatches some 53 days later, usually by early January. This is about the time when late breeding birds start laying their single egg that will hatch round late March [START_REF] Viblanc | Energetic adjustments in freely breeding-fasting king penguins: Does colony density matter?[END_REF]. After hatching, parents then alternate chick feeding duties at a high frequency until the start of the Austral winter in June. Adult penguins possess the unusual ability to conserve undigested, unspoiled food within their stomach, allowing to feed the chick when it hatches, or should the partner be delayed at sea [START_REF] Gauthier-Clerc | Penguin fathers preserve food for their chicks[END_REF]. During the Austral winter (June to September), chicks are then left to themselves as their parents move to more distant foraging grounds [START_REF] Bost | Exploitation of distant marginal ice zones by king penguins during winter-Mar[END_REF]. During the winter, chicks cluster into groups called "crèches" which afford them some protection against predation by giant petrels (Macronectes spp.) [START_REF] Bohec | The adaptive significance of crèches in the king penguin[END_REF] and adverse weather conditions [START_REF] Eichhorn | Heterothermy in growing king penguins[END_REF]. They are intermittently fed by their parents, and rely almost exclusively on body reserves during prolonged fasting periods to last throughout the winter [START_REF] Cherel | Ecology and Physiology of Fasting in King Penguin Chicks[END_REF][START_REF] Saraux | Chick-provisioning strategies used by king penguins to adapt to a multiseasonal breeding cycle[END_REF]. Chick feeding by the parents resume in September-October, the subsequent spring, where chicks fatten for an extra 2-3 months before molting and finally departing for their first journey at sea [START_REF] Stonehouse | The king penguin Aptenodytes pataconica of South Georgia-Sci. Reports Falkl[END_REF]Weimerskirch, Stahl, & Jouventin, 1992).

Study site and subjects

2.1.

Study site

The animals in this report were observed in the French Southern Territories (Southern Indian Ocean), on Possession Island, in the Crozet Archipelago (46°26′S, 51°52′E). Birds were monitored in the "Baie du Marin" colony, home to over 23,000 breeding pairs [START_REF] Barbraud | Population trends of penguins in the French Southern Territories[END_REF], and located close to a permanent research station.

Animals observed

During the 2019-20 breeding season, as part of various studies conducted in the framework of a long-term monitoring program on the behavior and ecophysiology of king penguin (ECONERGY 119 program of the French Polar Institute), regular behavioral scans were carried out each week between early December and early May 2020. Scan sampling was performed over 40-min periods, sampling the behavior of birds every minute, totaling over 16800 min, or 280 h, of observation. The behavioral repertoire of king penguins is described in detail elsewhere [START_REF] Stonehouse | The king penguin Aptenodytes pataconica of South Georgia-Sci. Reports Falkl[END_REF][START_REF] Côté | Aggressiveness in king penguins in relation to reproductive status and territory location[END_REF][START_REF] Viblanc | It costs to be clean and fit: Energetics of comfort behavior in breeding-fasting penguins[END_REF][START_REF] Jouventin | Why penguins communicate: the evolution of visual and vocal signals[END_REF]. Briefly, the typical behavior of adults on-land includes: sleeping and resting behavior, comfort behavior (stretching, preening, shaking, etc.), vocalizing, territorial aggression, and egg-chick care (includes turning the egg, feeding and preening the chick). In chicks, similar comfort, sleeping and resting, and vigilance behavior is observed. Vocalizing is directed mostly to the parent and consists in soliciting food. Chick behavior also includes aggressive behavior, mainly threats.

Observation and discussion

On the 16 th of March 2020, we observed (and filmed) a chick-chick feeding event in king penguins (see Online Supplementary Materials). What was singular about this observation was that an older chick hatched earlier in the breeding season (around January) was observed feeding a younger chick hatched later in the same breeding season (around March), shortly before the Austral winter. King penguins raise a single chick per reproductive attempt, so the two chicks were not siblings. During the entire observation, one adult king penguin was present in close proximity (contact with the chicks), though we had no information on whether this adult was the parent of either chick. However, following the observation, the older chick moved further away, and the adult took charge of the younger chick (AC, personal observation). The brooding pouch of the adult was markedly visible (video 0:10, 0:17, 0:25) suggesting it might indeed have been the parent of the smaller, not yet thermally independent, chick. The older chick displayed all of the typical behaviors displayed by breeding adults. Specifically, the older chick was seen (1) feeding the younger chick (video 0:00-0:07; Online Supplementary Material; [START_REF] Stonehouse | The king penguin Aptenodytes pataconica of South Georgia-Sci. Reports Falkl[END_REF][START_REF] Bohec | The adaptive significance of crèches in the king penguin[END_REF], there is to our knowledge no published record of chicks behaving parentally towards other chicks in this species. It is quite possible that the feeding attempt was a successful one: both the young and older chick showed several swallowing movements following the feeding event, which is usually observed following a successful feeding attempt (video 0:04-0:07; Online Supplementary Material; Fig 2). In addition, it is interesting to note that the older chick attempted to guide the younger chick on top of its feet after the breeding adult had done so just before.

In penguins, allofeeding is rare but found across species. Anecdotal accounts have been reported between mates in chinstrap penguins (Pygoscelis antarctica; [START_REF] Mori | An observation of betweenmates feeding behaviour in chick-guarding chinstrap penguins[END_REF], Adélie penguins (Pygoscelis adeliae; [START_REF] Yoda | A short note on an Adélie penguin feeding its own mate[END_REF] and jackass penguins (Spheniscus demersus; [START_REF] Broni | An apparent instance of courtship feeding in the jackass penguin Spheniscus demersus[END_REF]. In king penguins, allofeeding from adults to chicks is relatively common (25% of cases over 280 adult feeders observed; [START_REF] Lecomte | Alloparental feeding in the king penguin[END_REF] and is mostly attributed to failed breeders who preferentially feed chicks raised by close neighbors at during the time of brooding.

To our knowledge, allofeeding between offspring in birds has so far only been documented in between related offspring of the same clutch [START_REF] Stamps | Parent-offspring conflict in budgerigars[END_REF][START_REF] Roulin | Reciprocal preening and food sharing in colour-polymorphic nestling barn owls[END_REF][START_REF] Ducouret | Elder Barn Owl Nestlings Flexibly Redistribute Parental Food according to Siblings' Need or in Return for Allopreening[END_REF]. Most king penguins only raise a single chick every two years at best, and given that the two chicks in our observations were from the same breeding season, it seems unlikely they were closely related, though we cannot know for certain. Higher-thanexpected relatedness has been observed between neighboring breeders in king penguin colonies, though this relatedness remains weak and restricted to particular areas of the colonies such as the colony centre [START_REF] Cristofari | Spatial Heterogeneity as a Genetic Mixing Mechanism in Highly Philopatric Colonial Seabirds-PLoS One[END_REF]. Nevertheless, the fact that chick-chick feeding behavior has been observed in species with ecologies and life histories as contrasted as budgerigars (Melopsittacus undulatus; [START_REF] Stamps | Parent-offspring conflict in budgerigars[END_REF], owls (Tyto alba; [START_REF] Roulin | Reciprocal preening and food sharing in colour-polymorphic nestling barn owls[END_REF][START_REF] Ducouret | Elder Barn Owl Nestlings Flexibly Redistribute Parental Food according to Siblings' Need or in Return for Allopreening[END_REF], and penguins (this paper), suggests that (1) this unusual behavior may have evolved several times independently; and (2) relatedness may not be the only factor influencing the evolution of helping behavior in birds.

Whether such chick-chick interactions occur frequently or not in king penguins is unknown. We have been working on this species for several decades, spent every year hundreds of hours of scan-sampling observations in the field, and yet have so far never encountered such behavior before. Thus, this behavior is likely rare. Yet, penguin colonies are massive assemblages of thousands of individuals [START_REF] Barbraud | Population trends of penguins in the French Southern Territories[END_REF], and our observations were short-lived (seconds). While it is likely that such observations are usually missed, and perhaps more frequent than thought. Regardless, this observation questions the benefits and adaptiveness of such behavior. If indeed food was transferred from the older to younger chick, this behavior might appear maladaptive since any energy loss for offspring before the Austral winter is risky in the face of the strong energy constraints faced by chicks during prolonged (up to 5 months) fasting [START_REF] Cherel | Ecology and Physiology of Fasting in King Penguin Chicks[END_REF]. This would be especially the case if the donor was in poor body condition itself, since the marginal value of obtaining food depends on individual needs and/or condition. Unfortunately, we did not have information on chick body mass. However, our observation (see Online Supplementary Materials) did not suggest that the donor was in poor condition, at least visually (i.e., the donor chick did not appear to be particularly lean or emaciated). Thus, an alternative explanation may be that imitating parental behavior from a young age primes offspring for future reproduction when sexual maturity is reached. This might be especially advantageous for chicks in good condition that can afford trading-off a small surplus of food for the acquisition of a behavior critical for future lifehistory stages. Some indication that social learning might be important in king penguins comes from data on the time spent in attendance of juvenile king penguins to their natal colonies before their first breeding attempt. After having fledged, juvenile king penguin will remain at sea for at least a full year, travelling large extents of the Southern Ocean [START_REF] Orgeret | Exploration during early life: distribution, habitat and orientation preferences in juvenile king penguins[END_REF], before returning to their natal colony (most birds return after two years; [START_REF] Saraux | Effects of Individual Pre-Fledging Traits and Environmental Conditions on Return Patterns in Juvenile King Penguins-PLoS One[END_REF].

Juveniles return to their natal colonies in part for molting, however, the time they spend onland exceeds that necessary for molting only [START_REF] Saraux | Effects of Individual Pre-Fledging Traits and Environmental Conditions on Return Patterns in Juvenile King Penguins-PLoS One[END_REF]. Since first reproductive attempts are thought to occur at 3 or 4 years old at the earliest [START_REF] Barrat | Quelques aspects de la biologie et de l'écologie du manchot royal (Aptenodytes patagonicus) des îles Crozet[END_REF]) and more generally around 6 years old (Weimerskirch, Stahl, & Jouventin, 1992), it is unclear why these animals remain on-land. One suggestion is that juveniles use this time to learn the complex ritualized displays of courtship, perhaps through observation/imitation, prior to engaging into active breeding themselves [START_REF] Saraux | Effects of Individual Pre-Fledging Traits and Environmental Conditions on Return Patterns in Juvenile King Penguins-PLoS One[END_REF]. This would entail that those activities related to breeding (including courtship and potential care of the egg or offspring) could partly be under the influence of social learning in penguins.

Nonetheless, given the lack of other observations of this nature so far, it is not possible to currently conclude on the adaptive nature of this behavior. It could well be maladaptive since maladaptive behaviors should be counter selected, explaining their rare occurrence in nature.

Thus, future studies will be needed to bridge the gap between anecdote and data, allowing us to determine whether this unusual observation has any role to play (or not) in the acquisition of essential parental skills in king penguins, and more generally, in seabirds. vocalization and is a territorial threat known as bill gapping [START_REF] Côté | Aggressiveness in king penguins in relation to reproductive status and territory location[END_REF][START_REF] Viera | Active territory defence at a low energy cost in a colonial seabird[END_REF];

(C) attempting to guide the younger chick on top of its feet, the typical breeding position of adults, which brood young chicks on their feet in a specialized bare and highly vascularized skin flap called the brood pouch [START_REF] Stonehouse | The king penguin Aptenodytes pataconica of South Georgia-Sci. Reports Falkl[END_REF].

  Fig 1A); (2) behaving aggressively and territorially towards neighbors (video 0:15-0:18; Fig 1B); and (3) attempting to guide the younger chick on top of its feet, the typical breeding position of adults (video 0:26-0:33; 0:50-1:06; Fig 1C). Although older chicks are known to behave aggressively towards one another

FiguresFig

  Figures

  Fig 1. Early-born king penguin (Aptenodytes patagonicus) chick observed: (A) feeding a late-

Fig 2 .

 2 Fig 2. Swallowing sequence observed in the early-born king penguin chick, suggestive of a

Acknowledgments

We are grateful to T.S. Roth and two anonymous reviewers for helpful comments on a previous draft of this paper. This observation was recorded in the framework of the ECONERGY 119 Polar Program supported by the French Polar Institute (IPEV). We are grateful to the Terres Australes et Antarctiques Françaises for their support.


Sarah Delmas

Fabio Morbidi

Guillaume Caron

Marie Babel

François Pasteau

SpheriCol: A Driving Assistant for Power Wheelchairs based on Spherical Vision

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

SpheriCol: A Driving Assistant for Power Wheelchairs based on Spherical Vision

Sarah Delmas 1 , Fabio Morbidi 1, * , Guillaume Caron 1,2 , Marie Babel 3 , Franc ¸ois Pasteau 3 Abstract-This paper presents a new vision-based navigation assistant for power wheelchairs, called SpheriCol. Inspired by the parking assist system in cars, an omnidirectional image captured by a twin-fisheye camera is overlaid with colored distance markers from range sensors mounted on the wheelchair, to generate an augmented view of the surrounding environment. Such an image is displayed in real time to the user on a screen. To evaluate the effectiveness of the proposed system, able-bodied subjects and older adults with motor impairments have been asked to drive a consumer-grade power wheelchair equipped with SpheriCol, via a standard joystick. Our clinical trials with different obstacle courses, consistently indicate that SpheriCol is effective in improving safety and comfort, and in supporting a driver's decision during challenging but prevalent maneuvers, such as reversing out of an elevator, corridor centering, and turning on the spot.

Index Terms-Assistive robotics, smart wheelchair, omnidirectional vision, collision avoidance, safe navigation.

I. INTRODUCTION

W HEELCHAIRS maintain or improve an individual's functioning, self-confidence, and independence, thereby promoting well-being. In the absence of this assistive device, people with severe motor impairments are often excluded, isolated, and locked into poverty, thus increasing the impact of disease and disability on a person, her family, and society as a whole. In the European Union, wheelchair users comprise around 1% of the population, or 7.5 million people. In the United States, the prevalence was 2.3% or 5.5 million adults (18 years and older), in 2014 [START_REF] Taylor | Americans With Disabilities: 2014[END_REF]. According to the World Health Organization (WHO), in 2018, 75 million people worldwide needed a wheelchair, but only 5% to 15% of those in need had access to one [START_REF]Assistive Technology[END_REF].

In the last decade, assistive robotics, because of its high economic and societal value, has been at the forefront of research in robotics [START_REF] Rebsamen | A Brain Controlled Wheelchair to Navigate in Familiar Environments[END_REF], [START_REF] Carlson | Collaborative Control for a Robotic Wheelchair: Evaluation of Performance, Attention, and Workload[END_REF], [START_REF] Erdogan | The effect of robotic wheelchair control paradigm and interface on user performance, effort and preference: an experimental assessment[END_REF], [START_REF] Morales | Passenger discomfort map for autonomous navigation in a robotic wheelchair[END_REF], [START_REF] Lei | An Intention Prediction Based Shared Control System for Point-to-Point Navigation of a Robotic Wheelchair[END_REF]. However, while many individuals rely on the provision of wheelchairs, they experience driving difficulties on a daily basis [START_REF] Torkia | Power wheelchair driving challenges in the community: a users' perspective[END_REF]. In fact, even the urban spaces of modern cities fail to conform to the most basic accessibility and safety principles, and several architectural barriers still exist today for those who use mobility aids outdoors: non-adapted public transport, narrow sidewalks, absence of curb cuts [START_REF] Sundaram | Step-Climbing Power Wheelchairs: A Literature Review[END_REF], [START_REF] Podobnik | All-Terrain Wheelchair: Increasing Personal Mobility with a Powered Wheel-Track Hybrid Wheelchair[END_REF], [START_REF] Ikeda | Cooperative step-climbing strategy using an autonomous wheelchair and a robot[END_REF], [START_REF] Candiotti | Curb Negotiation With Dynamic Human-Robotic Wheelchair Collaboration[END_REF], [START_REF] Botta | Autonomous detection and ascent of a step for an electric wheelchair[END_REF]. Likewise, wheelchair users are faced with a number of challenging tasks indoors (e.g. reverse out of an elevator, doorway traversal, 1 MIS laboratory, University of Picardie Jules Verne, Amiens, France. 2 CNRS-AIST Joint Robotics Laboratory (JRL), IRL, Tsukuba, Japan. 3 Rainbow team, IRISA/Inria Rennes and INSA Rennes, France. * Corresponding author. Email: fabio.morbidi@u-picardie.fr Final manuscript submitted on February 28, 2023. turn in place, dock under a table), and they often struggle to build a mental model of the surrounding environment [START_REF] Welage | Wheelchair accessibility of public buildings: a review of the literature[END_REF], [START_REF] Sivakanthan | Minireview: Robotic wheelchair taxonomy and readiness[END_REF]. Access to good quality and affordable assistive technologies has been mandated by the Convention on the Rights of Persons with Disabilities of the United Nations for ten years, but the WHO estimates that there is still a shortage of health and rehabilitation staff with suitable knowledge and skills, to provide a wheelchair that meets the individual needs of a user in care. Moreover, wheelchair accessories tailored to suit a certain user's profile, remain expensive and are installed piecemeal.

The benefits of smart wheelchair use for older adults with cognitive impairments are well documented in the specialized literature [START_REF] How | Evaluation of an intelligent wheelchair system for older adults with cognitive impairments[END_REF], [START_REF] Viswanathan | Intelligent wheelchair control strategies for older adults with cognitive impairment: User attitudes, needs, and preferences[END_REF], [START_REF] Leblong | SWADAPT1: assessment of an electric wheelchairdriving robotic module in standardized circuits: a prospective, controlled repeated measure design pilot study[END_REF]. For instance, in [START_REF] Sorrento | Assessment of Joystick control during the performance of powered wheelchair driving tasks[END_REF], [START_REF] Gillham | Feature determination from powered wheelchair user joystick input characteristics for adapting driving assistance[END_REF], the authors report an evaluation of joystick control input during the execution of different driving tasks. Immersive technologies involving head-mounted displays have also recently garnered attention as apt training simulators for off-line learning of wheelchair control [START_REF] Zolotas | Head-Mounted Augmented Reality for Explainable Robotic Wheelchair Assistance[END_REF], [START_REF] Vailland | Vestibular Feedback on a Virtual Reality Wheelchair Driving Simulator: A Pilot Study[END_REF], [START_REF] Vailland | VR based Power Wheelchair Simulator: Usability Evaluation through a Clinically Validated Task with Regular Users[END_REF]. Several research projects [START_REF] Levine | The NavChair Assistive Wheelchair Navigation System[END_REF], [START_REF] Demeester | Wheelchair Navigation Assistance in the FP7 Project RADHAR: Objectives and Current State[END_REF], [START_REF] Morbidi | Assistive Robotic Technologies for Next-Generation Smart Wheelchairs: Codesign and Modularity to Improve Users' Quality of Life[END_REF], [START_REF] Vogel | An Ecosystem for Heterogeneous Robotic Assistants in Caregiving: Core Functionalities and Use Cases[END_REF], have addressed the problem of collision avoidance with robotic wheelchairs, by proposing solutions based on the combination of different active sensors (laser, ultrasonic or infrared sensors) for an increased data envelope. These sensors inform the user of the presence of obstacles near the wheelchair, and provide support to negotiate the environment. The main goal is to provide assistance for safe navigation and, at the same time, minimize user's intervention (thus reducing cognitive and physical workload). However, the majority of the systems developed in these projects are still early-stage technology, and though highly informative, visual feedback is often overlooked.

In recent years, cameras have been increasingly used for (semi-)autonomous localization and navigation of instrumented wheelchairs [START_REF] Leaman | A Comprehensive Review of Smart Wheelchairs: Past, Present, and Future[END_REF], [START_REF] Kutbi | Usability Studies of an Egocentric Vision-Based Robotic Wheelchair[END_REF]. In particular, multi-camera systems (three monocular cameras in [START_REF] Pasteau | A visual servoing approach for autonomous corridor following and doorway passing in a wheelchair[END_REF], a Ladybug 2 camera in [START_REF] Nguyen | Experimental Study on a Smart Wheelchair System Using a Combination of Stereoscopic and Spherical Vision[END_REF]), are gaining traction, since they are inexpensive and offer a full coverage of the surrounding environment. Nevertheless, to date, there is scant research pertaining to omnidirectional vision [START_REF] Li | Recording Gaze Trajectory of Wheelchair Users by a Spherical Camera[END_REF], and its potential for wheelchair driving assistance remains largely untapped.

In this article, we present a new vision-based decision support system, called SpheriCol (a portmanteau of "Spherical" and "Collision avoidance"), for navigation assistance of the users of electrically-powered wheelchairs (EPW). Occupational therapists and specialists in rehabilitation medicine have been consulted during the ADAPT project [START_REF] Morbidi | Assistive Robotic Technologies for Next-Generation Smart Wheelchairs: Codesign and Modularity to Improve Users' Quality of Life[END_REF], to study the applicability of this visual aid in real-life practice. The proposed system is designed to be strap-on to any commercial EPW, and its functional components have been developed atop ROS (Robot Operating System). SpheriCol relies on omnidirectional images captured by an overhead pocket-size twin-fisheye camera and range measurements from low-cost (ultrasonic or laser) sensors. The 360 • images are overlaid in real time with color-coded distance markers, to generate an augmented view with obstacle clues, of the surrounding environment. The user can select four different viewpoints via a tactile display, from which clearance around the wheelchair and thus collision risk, can be easily assessed. The driver closes the loop via a standard joystick and has full control authority over the wheelchair at all times. Extensive clinical trials in cluttered indoor environments with a Quickie Salsa M 2 EPW equipped with a ring of Time-of-Flight sensors and a Ricoh Theta S twin-fisheye camera, have shown that the proposed driving assistant offers tangible benefits in terms of risk management and control effort.

It is worth mentioning here that a system akin to ours, combining panoramic vision with laser range finders, has been recently proposed in [START_REF] Komatsu | Free viewpoint image generation system using fisheye cameras and a laser rangefinder for indoor robot teleoperation[END_REF], for robot teleoperation. Differently from our egocentric representation, the system in [START_REF] Komatsu | Free viewpoint image generation system using fisheye cameras and a laser rangefinder for indoor robot teleoperation[END_REF] generates third-person-view images from arbitrary viewpoints, but requires four fisheye cameras with a large baseline. As a consequence, it cannot be easily installed on a consumergrade EPW. Moreover, it only works in indoor corridor-like environments. A similar setup (including an Insta360 Air twin-fisheye camera), has been considered in [START_REF] Oehler | A Flexible Framework for Virtual Omnidirectional Vision to Improve Operator Situation Awareness[END_REF] to improve operator's situation awareness in hazardous environments, and it has been successfully tested on an Asterix tracked robot.

An early prototype of our driving assistant was described in our conference paper [START_REF] Delmas | SpheriCol: A Driving Assistance System for Power Wheelchairs Based on Spherical Vision and Range Measurements[END_REF]. Compared to [START_REF] Delmas | SpheriCol: A Driving Assistance System for Power Wheelchairs Based on Spherical Vision and Range Measurements[END_REF], in this article, we introduce an enhanced software architecture and data logging system, and we report the outcomes of two clinical trials which involved nineteen able-bodied subjects and older adults with mild-to-moderate motor impairments.

The rest of this paper is organized as follows. Sect. II presents the two main components of the driving assistant: the power wheelchair and the twin-fisheye camera. Sect. III describes the main functionalities of SpheriCol and the configuration/visualization interfaces. Sect. IV is devoted to the user study with a real EPW. Finally, in Sect. V, we highlight the significance of the system and its limitations, and we discuss potential directions for future of research.

II. BASIC SYSTEM COMPONENTS

A. Power wheelchair

The driving assistance system described in this article is fully compatible with the existing consumer-grade EPWs (with front-, mid-, or rear-wheel drive). The wheelchair should be equipped with a set of exteroceptive sensors located around its perimeter, 25 to 50 cm above the ground (e.g. a ring of ultrasonic sensors [START_REF]Braze Mobility, Blind Spot Sensors for Wheel Chairs & Mobility Scooters[END_REF]). The sensors (with a maximum range indoors, of 4 to 5 m), provide proximity information via range/bearing measurements to the obstacles around the wheelchair. The driving assistant also takes advantage of a tactile display (e.g. a tablet), for human-machine interaction (see Fig. 1). Besides these basic pieces of equipment, SpheriCol is hardware-agnostic, i.e. it neither requires a specific kinematic/dynamic model for the EPW, nor a particular range-sensing technology, and it can be installed as a "kit" on any power wheelchair.

B. Twin-fisheye camera

SpheriCol takes a stream of 360 • images captured by a twinfisheye camera, as input (see Fig. 2). These innovative cameras are small, lightweight, and they can record high-resolution videos with frame rates up to 30 fps. In the last decade, the compact optical design proposed by Ricoh, consisting of two fisheye lenses mounted back-to-back coupled with two lightsensitive surfaces, has gradually become mainstream and it has been adopted by other camera manufacturers (e.g. in Samsung Gear 360, LG 360 CAM, Insta360 X3, KanDao QooCam 8K and Kodak PIXPRO Orbit360).

Our driving assistant requires the twin-fisheye camera to be mounted in an elevated position on the wheelchair, to have an unobstructed view of the free space around it. To meet this requirement, a common solution in instrumented EPW [START_REF] Li | Recording Gaze Trajectory of Wheelchair Users by a Spherical Camera[END_REF], [START_REF] Erdogan | The effect of robotic wheelchair control paradigm and interface on user performance, effort and preference: An experimental assessment[END_REF] or Personal Mobility Devices [START_REF] Jayasuriya | Active Perception for Outdoor Localisation with an Omnidirectional Camera[END_REF], is to install the camera on top of a mast behind the backrest (even though design studies have shown that added sensors above the headrest might interfere with wheelchair transportation in a vehicle [START_REF] Hartman | Human-Machine Interface for a Smart Wheelchair[END_REF], [START_REF] Klinich | A Literature Review of Wheelchair Transportation Safety Relevant to Automated Vehicles[END_REF]).

It is well known that some categories of fisheye cameras are approximately equivalent to a central catadioptric system [START_REF] Ying | Can We Consider Central Catadioptric Cameras and Fisheye Cameras within a Unified Imaging Model?[END_REF]. Therefore, the unified projection model [START_REF] Geyer | A Unifying Theory for Central Panoramic Systems and Practical Implications[END_REF], [START_REF] Barreto | A unifying geometric representation for central projection systems[END_REF], can be used. We describe each fisheye lens by its own set of intrinsic parameters P cj = a uj , a vj , u 0j , v 0j , ξ j , j ∈ {1, 2}, where a uj (a vj ) is the size of unit length in horizontal (vertical) pixels, and (u 0j , v 0j ) are the coordinates of the principal point in pixels. The fifth parameter, ξ j , is the distance between the unit sphere's first projection center and the perspective second projection center of the j-th fisheye lens, as reported in [43, Fig. 2]. Following [START_REF] Caron | Spherical Visual Gyroscope for Autonomous Robots using the Mixture of Photometric Potentials[END_REF], we assume that the translation vector between the two fisheye frames F c1 and F c2 is zero, to ensure a unique projection viewpoint. Moreover, we assume that the camera frame F c coincides with F c1 (they are shown separately in Fig. 2b, for clarity). The extrinsic parameters of the twin-fisheye camera are then incorporated into the rotation matrix c2 R c1 from frame F c1 to frame F c2 .

To calibrate the twin-fisheye camera, we used a custommade calibration rig consisting of six circle patterns attached inside two half cubes, and followed the same procedure described in [START_REF] Caron | Spherical Visual Gyroscope for Autonomous Robots using the Mixture of Photometric Potentials[END_REF].

III. MAIN FUNCTIONALITIES AND INTERFACES

In this section, the main functionalities of our driving assistance system are described in detail. SpheriCol leverages the middleware ROS (Robot Operating System), for data collection and communication between the different modules, and the OpenCV library for image processing.

A. Viewpoint selection

The environment around the wheelchair can be observed from four "virtual" viewpoints (equirectangular, panoramic, spherical and bird's eye), as further elaborated below.

a) Equirectangular view: The input dual-fisheye images are mapped into equirectangular images by exploiting the estimated intrinsic parameters of the twin-fisheye camera (cf. Sect. II-B). The width of the equirectangular image corresponds to the 360 • horizontal field of view (FoV) of the twinfisheye camera. An example of dual-fisheye image (top) with its equirectangular counterpart (bottom) is shown in Fig. 3a. Because of the wide availability in twin-fisheye cameras of different manufacturers, the equirectangular view is the default view in SpheriCol, and all the others are generated from it.

b) Panoramic view: A panoramic image corresponds to half of an equirectangular image (i.e. it only covers a 180 • horizontal FoV). To synthesize a "front view", we leveraged OpenCV's Rect function to crop the left and right bands of the equirectangular image corresponding to the rear end of the wheelchair (white dashed areas in Fig. 3a,bottom). On the other hand, to generate a "rear view", we stitched the two bands together using OpenCV's hconcat function. The user is also allowed to select a specific angular sector of the panoramic image (in 5 • steps): this facilitates early detection of obstacles in the blind spots of EPW (for more details, see Sect. III-C below).

c) Spherical view: The spherical view has the advantage of clearly showing the presence of potential obstacles at ground level (see Fig. 3b). It is generated from the equirectangular view via a simple Cartesian-to-polar coordinates transformation (cf. OpenCV's linearPolar function).

d) Bird's-eye view: As the spherical view, the bird'seye view is useful to detect obstacles on the floor around the EPW, but the images have a more uniform (perspective-like) spatial resolution. To generate the bird's-eye view, we first map the m × n equirectangular image into a unit sphere, via the transformation (see Fig. 4), image I bird is obtained by projecting the point (θ, ϕ) on the unit sphere, onto a plane at point (u b , v b ) (see Fig. 4).

θ = 360 • u θ m -1 , ϕ = 90 • v ϕ (n -1)
The height h (in centimeters) of the sphere above the plane, is a parameter of the system. It depends on several factors: footprint of EPW, user's body size, seating accommodation, and type of environment (indoor or outdoor).

B. Configuration interface

The different functionalities of SpheriCol are accessible via a configuration interface. Note that differently from the visualization interface, to be presented in Sect. III-C below, the configuration interface is intended for the healthcare professionals and not for the wheelchair users. The "Options" tab in the top left corner of Fig. 5 allows to select the preferred visual/proximity information. With the remaining tabs in the same row, the user can choose one of the four viewpoints described in Sect. III-A. Infrared and ultrasonic sensors being the most popular proximity sensors in EPW, they are already available in the "Options" tab, for quick selection.

The "Points" buttons allow to display the distance measurements to the obstacles, at their corresponding locations in the images (see Fig. 7a). To project the proximity information onto the images, we leveraged the known calibration parameters of the twin-fisheye camera, and empirically estimated the rigid transformation between the camera frame F c (cf. Fig. 2) and the local frames of the range sensors. To filter out noise and ensure smooth transitions on the user's screen, a moving average filter was applied to the raw range measurements (in our experiments, see Sect. IV, we computed the mean over the last 10 measurements, which corresponds to an update rate of about 2 Hz). The user can choose how many measurements to display at the same time: if the range sensors are organized in p modules each containing q sensors, then a minimum of p and a maximum of p • q measurements, can be shown on the images.

By selecting "Lines", the distance measurements from the range sensors are interpolated using Lagrange polynomials, and superimposed on the images (see Fig. 7b and Sect. IV-A for more details). For the "Points" and "Lines" visualization modes, the following color convention was used: green, if the distance to the obstacle(s) d ∈ [START_REF] Candiotti | Curb Negotiation With Dynamic Human-Robotic Wheelchair Collaboration[END_REF][START_REF] Sivakanthan | Minireview: Robotic wheelchair taxonomy and readiness[END_REF] cm, yellow, if d ∈ [8, 12) cm, and red, if d < 8 cm.

The "Ellipses" button allows to display from 1 to 3 concentric ellipses (see Fig. 7c). The first ellipse (red) is placed at a distance d = 50 cm from the side of the wheelchair, the second (yellow) at 100 cm, and the third (green) at 150 cm. The ellipses are static, and they are not periodically refreshed using the new measurements from the range sensors.

The "Zones" button activates 12 colored bands (in four angular sectors of 90 • ) around the wheelchair: green bands for a distance d ∈ [12, 15) cm, yellow bands if d ∈ [8, 12) cm, and red bands if d < 8 cm (see Fig. 7d). To reduce visual overload, the static bands disappear when an obstacle is detected in the corresponding angular sector.

Similarly to "Ellipses", the "Indics" (Indicators) button allows to display 1 to 3 red circle arcs on the four sides of the wheelchair (see Fig. 7e). The arcs are dynamic, and they only appear when an obstacle is detected:

1 arc if d ∈ [12, 15) cm, 2 arcs if d ∈ [8, 12
) cm, and 3 arcs if d < 8 cm.

Note that the previous options are not mutually exclusive: in fact, multiple distance markers (e.g. "Points" and "Lines") can be accommodated by the configuration interface at the same time.

Since other impairments (such as low peripheral vision or visual neglect [START_REF] Iezzoni | When Walking Fails: Mobility Problems of Adults with Chronic Conditions[END_REF], [START_REF] Riddering | Keeping Older Adults with Vision Loss Safe: Chronic Conditions and Comorbidities that Influence Functional Mobility[END_REF]), may coexist with motor disabilities, auditory feedback is also available in SpheriCol. By clicking on the "Beep" and "Voice" buttons under the "Sound Warnings" tab (top right in Fig. 5), acoustic signals are generated when an obstacle is detected. Normally sighted individuals could also benefit from the auditory feedback, when their visual and haptic channels are overloaded with information [START_REF] Devigne | Power Wheelchair Navigation Assistance Using Wearable Vibrotactile Haptics[END_REF]. Finally, the "Colors", "Max Distance", and "Sound's Threshold" buttons, give access to additional configuration parameters which allow to fully customize the interface.

C. Visualization interface

The visualization interface is active during normal usage of the wheelchair. A large portion of the window is used to display the video stream from the twin-fisheye camera (see Fig. 1c). The top bar and the right menu are similar to those in the configuration interface, and they can be used to switch on/off the selected viewpoint and distance markers, respectively. With the "+" and "-" buttons, the user can either change the angular sector in the panoramic images or zoom in/zoom out the bird's-eye images, by virtually varying the height h (cf. Fig. 4).

If the user turns the auditory feedback on, either a series of beeps whose frequency is inversely proportional to the distance d to the obstacles ("Beep" option) or a voice message announcing the direction of the approaching obstacle(s) ("Voice" option), will be heard. The two options can be activated simultaneously.

IV. USER STUDY

A user study was carried out to assess the performance and viability of our driving assistant versus a conventional EPW. The hypothesis under study is that using SpheriCol improves safety and minimizes user's intervention (and thus cognitive load) during complex maneuvers. The section begins with a description of the materials (Sect. IV-A), followed by a presentation of the participants and results of two experimental campaigns (Sect. IV-B and Sect. IV-C, respectively).

A. Materials

SpheriCol has been tested with a Sunrise Medical Quickie Salsa M 2 EPW [48]. This mid-wheel drive platform has 6 wheels with independent suspensions: the 4 castor wheels have a diameter of 17.8 cm and the two drive wheels have a diameter of 33 cm. The wheelchair, which is endowed with a 7 cm curb-climbing ability, measures 61 cm at the widest point, and the 60 Ah batteries can propel it up to 10 km/h. A Ricoh Theta S camera [START_REF]Ricoh Theta S camera[END_REF] was installed overhead behind the passenger. The camera weighs 125 g and its external dimensions are 4.4 cm (W) × 13 cm (H) × 2.29 cm (D). Considering the reduced speed of an EPW in normal operation, we selected a medium video resolution of 1280 pixels × 720 pixels at 15 fps, which allowed for real-time image processing. The 48 range sensors around the wheelchair are grouped into 7 modules: 6 modules of 6 sensors are located on the left and right side, and under the footplates, and 1 module of 12 sensors is positioned behind the backrest (see Fig. 6a). The height above the floor of the modules, ranges between 13 cm (the two modules under the footplates) and 45.5 cm (the two modules installed on the mudguards). The housing of the 7 sensor modules was 3D printed at INSA Rennes. The ST VL53L1X Time-of-Flight (ToF) sensors have the following technical specifications [START_REF]STMicroelectronics: Long distance ranging Time-of-Flight sensor[END_REF]: distance measurement, up to 4 m; ranging frequency, up to 50 Hz; typical FoV, 27 • ; size, 4.9 mm × 2.5 mm × 1.56 mm.

Differently from [START_REF] Delmas | SpheriCol: A Driving Assistance System for Power Wheelchairs Based on Spherical Vision and Range Measurements[END_REF], in our current implementation, SpheriCol runs under Linux Ubuntu 18.10 on an Intel NUC mini PC [START_REF]Intel NUC mini PC[END_REF] installed on the wheelchair, and it relies on the ROS Melodic Morenia distribution and the OpenCV library (release 2.x). The camera is connected to the NUC via a USB port. To remote control the data-recording process ("rosbag" creation), we used a laptop computer connected to the NUC via SSH, a secure communication protocol. Finally, we leveraged VNC Connect [START_REF]RealVNC: Remote access software for desktop and mobile devices[END_REF], to establish a communication channel between the mini PC and a Samsung tablet (see Fig. 6b). This allows to display the images captured by the Ricoh Theta S and to transmit the data entered by the users. Fig. 7 shows different ways of augmenting the omnidirectional images captured by the Ricoh camera, with the proximity information provided by the ToF sensors (cf. Sect. III-B). Note that the curves interpolating the range measurements, provide a useful approximate representation of obstacle surfaces, and they are easier to interpret for reactive control than a sparse set of distance points. However, different contiguous obstacles cannot always be easily discriminated by using this representation. To address this issue, the lines shown in Fig. 7b are computed from data points in 90 • sectors (for example, the front line emanates from points lying within the [-45 interval, the forward direction of the wheelchair corresponding to 0 • ). Moreover, to improve readability, the lines are displayed at 10 • intervals.

B. First experimental campaign a) Participants: A convenience sample of two users with various neurologic deficits took part in the first campaign (1 male and 1 female, 60+ years old, see Fig. 6b). They are patients of Pôle Saint-Hélier, a Physical and Rehabilitation Medicine Center, in Rennes, France, and have limited driving experience with an EPW (to minimize the learning effect). Subject 1 is with right hemispatial neglect [START_REF] Parton | Hemispatial neglect[END_REF], and subject 2 is with tetraplegia due to a neurodegenerative disease. The research ethics committee approved the experimental protocol. The participants signed a consent form and they were trained on wheelchair's features.

b) Experimental setup: The campaign took place in a test circuit specifically designed at Pôle Saint-Hélier, in October 2020. The circuit included two slaloms and two simulated elevator cabins (shaded areas in Fig. 8a), and several sharp turns in narrow passageways with a clearance on either side of the wheelchair of only few centimeters (similar standardized obstacle courses have been recently considered in [START_REF] Leblong | SWADAPT1: assessment of an electric wheelchairdriving robotic module in standardized circuits: a prospective, controlled repeated measure design pilot study[END_REF]). The control inputs were provided by a standard z-axis joystick, and the participants were requested to use SpheriCol to complete the circuit as quickly and as safely as possible (i.e. with the fewest number of collisions). To compensate for the reduced awareness of stimuli on the right side of the body, the first participant tested SpheriCol with a panoramic view covering the missing area. The joystick was installed on the left side for both subjects (the side of the wheelchair where subject 1 has full-arm mobility). c) Experimental procedure and variables: The participants repeated the test circuit under the following five conditions:

• Without assistance, to familiarize themselves with the circuit (Trial I), • SpheriCol with bird's-eye view (Trial II),

• SpheriCol with bird's-eye view and line markers (Trial III), • SpheriCol with panoramic view and line markers (Trial IV), • SpheriCol (with user's preferred view and markers) in conjunction with the assistance algorithm in [START_REF] Devigne | A shared control solution for safe assisted power wheelchair navigation in an environment consisting of negative obstacles: a proof of concept[END_REF] (Trial V).

d) Experimental design and evaluation criteria:

To evaluate the effectiveness of SpheriCol, the following performance metrics were considered (cf. [START_REF] Sorrento | Assessment of Joystick control during the performance of powered wheelchair driving tasks[END_REF], [START_REF] Devigne | Power Wheelchair Navigation Assistance Using Wearable Vibrotactile Haptics[END_REF]): TABLE I: Summary of the trials in the first experimental campaign. In the 1st column, the trials in which no data were recorded (but for which the completion time and the number of collisions are available), are marked with an asterisk.

4) Variability of joystick input, 5) Information gathered from the users through a written survey. A questionnaire was handed out for completion to the participants, to assess the overall satisfaction and viewpoint preferences.

e) Collected data, experimental results and discussion: In the absence of an external motion capture system, the trajectories of EPW in each trial were estimated with OpenVSLAM [START_REF] Sumikura | OpenVSLAM: A versatile visual SLAM framework[END_REF], an accurate and flexible visual SLAM algorithm. Unfortunately, these trajectories are not aligned and they are not to scale: hence, they are not suitable for a rigorous quantitative evaluation of SpheriCol. However, we built upon the sparse 3D model of the test room generated by OpenVSLAM, to draw the accurate plan reported in Fig. 8b.

Table I summarizes the results of the experimental campaign. The last two columns of the table, report the duration of each trial and the number of collisions with the obstacles, counted by an operator visually monitoring the wheelchair. SpheriCol with the bird's-eye view and the line markers, combined with the navigation algorithm in [START_REF] Devigne | A shared control solution for safe assisted power wheelchair navigation in an environment consisting of negative obstacles: a proof of concept[END_REF], elicited the best response in the two subjects, and it is the clear winner in terms of completion time and safety (125 s and 0 collisions for subject 1; 168.5 s on average and 0 collisions for subject 2). Giving equal importance to completion time and number of collisions, the second-best option is SpheriCol with the bird'seye view only, and SpheriCol with the panoramic view and the line markers.

Fig. 9 and Fig. 10 report additional qualitative results from the same experimental campaign. Fig. 9 shows the number of ToF sensors which detected an obstacle at a distance of less than 7 cm (blue) or 2 cm (red) in six trials ("1-II" is a shorthand for trial II of subject 1). On the other hand, Fig. 10 reports the 2D histograms of the position of the joystick in the five recorded trials of subject 2, for the second simulated elevator (cf. Fig. 8a). The positions lie within a circle of radius 100, centered at the origin. To draw the histograms, 35 bins were considered. The heat map indicates how often the joystick traversed a bin (for better color rendering, the bin at the origin is set to zero, by default). By and large, the results in Fig. 9 and Fig. 10 show that SpheriCol with the bird's-eye view and the line markers, provides the best compromise between safety and variability of joystick input, during challenging maneuvers. Finally, in their questionnaires, the two subjects expressed a preference for the bird's-eye view with the line markers. In particular, subject 2 found the red line markers (which indicate that an obstacle is dangerously close to the wheelchair), very helpful during the navigation in confined spaces, like in the two simulated elevators.

In view of the encouraging results of the first experimental campaign, we decided to recruit a larger sample of able-bodied subjects and to focus on the maneuvers where SpheriCol was used the most (entering/exiting an elevator), by considering a simpler obstacle course.

C. Second experimental campaign a) Participants: In the second campaign, 17 (able-bodied experienced and non-experienced) subjects were recruited: 3 females and 14 males, 1 left-handed and 16 right-handed, average age of 30 years (range, 14-59 years). The research ethics committee approved the experimental protocol. The participants, who were trained on wheelchair's features, were asked to sign a consent form for the collection of data.

b) Experimental setup: The follow-up campaign took place in the Francis Querné hall, a gymnasium in the Beaulieu campus at INSA Rennes, in June 2021 (see Fig. 11). The test circuit is simpler than the one considered in the first campaign, and it only consists of a 4.1 m passageway and a 1 m × 1.85 m simulated elevator (top left in Fig. 11c). In fact, our previous trials revealed that these are the locations where the users are expected to benefit the most from SpheriCol. Sector 3 is more challenging than sectors 1, 2 and 4, since backward motion is required. The Ricoh Theta S camera was installed 158 cm above the ground, and 60 cm above the push handles of the wheelchair. c) Experimental procedure and variables: Each subject was requested to complete the circuit nine times in sequence, under the following conditions:

• Without assistance (three times),

• SpheriCol with bird's-eye view (three times),

• SpheriCol with bird's-eye view and line markers (three times).

We selected the three conditions above in random order, to minimize the learning effect. In this campaign, we restricted our attention to the bird's-eye view, since the wheelchair contours are clearly visible in the images (see Fig. 11b), and the free space around the wheelchair can be easily identified, to perform risk-aware maneuvers. d) Experimental design and evaluation criteria: A fivepronged approach was adopted to evaluate SpheriCol: 1) Total time required to complete the test circuit, 2) Safety of trajectory. We computed the relative pose error of the wheelchair with respect to the "safest-possible" path (i.e. the ideal path that maximizes obstacle clearance at all times), 3) Number of sensors which detected an obstacle at a distance smaller than a given threshold ("danger", d = 7 cm; "near-collision", d = 2 cm), 4) Variability of joystick input, 5) Information gathered from the volunteers through a written survey. A questionnaire was handed out for completion to the participants to assess the overall satisfaction, cognitive load, viewpoint preferences, and perceived utility of the system.

It is easy to verify that the "safest-possible" path mentioned in the 2nd item above, corresponds to the medial axis [START_REF] Siddiqi | Medial Representations: Mathematics, Algorithms and Applications[END_REF] of the test circuit. More formally, if we denote by C ⊂ R 2 the room containing the test circuit and by ∂C its boundary, the medial axis M (C) of C is defined as [57, Sect. 3.5.4] To determine the shortest path S(C) along M (C) connecting the start and end pose of the wheelchair, we used Dijkstra's algorithm [START_REF] Cormen | Introduction to Algorithms[END_REF]Ch. 22]. Note that S(C) is a planar graph whose vertices are connected by generalized edges, which are either straight-line segments or arcs (of parabolas). The path is continuous, but it contains several cusps where a real wheelchair is forced to turn in place (which is undesirable). In spite of this limitation, we chose S(C) as our ground truth in the comparative study of wheelchair's trajectories, since it is easy to compute and welldefined in environments of arbitrary shape. For the sake of illustration, the medial axis M (C) of the test room C considered in the first campaign, and the shortest path S(C) ⊂ M (C) found by Dijkstra's algorithm, are depicted in blue and red, respectively, in Fig. 8b. We computed the Root Mean Square Error (RMSE) of the translational component of the Relative Pose Error (RPE), to measure the deviation from S(C) of wheelchair's trajectories in the different runs. Following [START_REF] Sturm | A benchmark for the evaluation of RGB-D SLAM systems[END_REF], the RPE at time step i is defined as

M (C) = x ∈ C : x -x i = x -x j = min y ∈ ∂ C x -y , x i , x j ∈ ∂C, x i = x j ,
E i (Q -1 i Q i+∆ ) -1 (P -1 i P i+∆ ), (1)
where P 1 , . . . , P n ∈ SE(3) is the sequence of 3D poses from the estimated trajectory, Q 1 , . . . , Q n ∈ SE(3) is the sequence of poses from the ground-truth trajectory S(C), and ∆ is a fixed interval between two poses. From equation (1), the RMSE over all time indices of the translational component is computed as

RMSE(E 1 , . . . , E n , ∆) 1 m m k = 1 trans(E k ) 2 , (2)
where m = n -∆ is the number of individual pose errors along the sequence, and trans(E k ) is the translational component of RPE, E k . Note that since S(C) is orientationfree, we associated each sample of S(C) with a reference frame whose z-axis is aligned with the forward direction of the wheelchair. Remark 1: Note that while the RPE is widely used in the SLAM literature, it is not the only option to measure the deviation of executed wheelchair's trajectory from the reference one. For example, in [START_REF] Miller | An Analysis of Human-Robot Information Streams to Inform Dynamic Autonomy Allocation[END_REF], the authors used a discrete version of Fréchet distance [START_REF] Alt | Computing the Fréchet distance between two polygonal curves[END_REF], to compare (the projection of) human commands with the commands generated by a planner, for autonomous navigation. The Fréchet distance accounts for the velocity and ordering of points along a trajectory, a property not shared by other classical metrics, such as the Hausdorff distance (which computes the distance between two curves without explicitly considering the paths as time-indexed trajectories). However, while the discrete variant of Fréchet distance can be computed in real time (which is of practical interest for interactive assistance systems), unlike the RPE, the orientation of a rigid body along a trajectory is not taken into account. Therefore, the RPE ultimately remains the best option for the problem under investigation.

e) Collected data, experimental results and discussion: In the second campaign, we took advantage of a markerbased motion capture system (8 Qualysis Miqus cameras covering the test circuit) to precisely estimate the pose of the wheelchair. We expressed the poses of the Ricoh Theta S in the body frame of the wheelchair (whose origin is located at the mid-point of the two driving wheels), by applying a pure translation of 53 cm along the z-axis of the reference frame of the camera. Table II reports the completion time of the circuit in seconds, averaged over 3 runs per subject. We observe a fairly large inter-subject variability (which is imputable to the personal driving skills), and shorter completion times with no assistance (in fact, most of the users tried to push the limits of SpheriCol, and took more risk during the trials).

Table III reports the RMSE in centimeters, for a fixed interval ∆ = 25 (this value of ∆ has been determined empirically, and it provides the best trade-off between sensitivity to measurement noise and degree of informativeness of RMSE). To reduce the variability of results, we com-puted the averages over 3 runs per subject, under the same conditions (i.e., "Without assistance", "Bird's eye", and "Bird's eye + lines", see Fig. 11b). It is apparent from Table III that the smallest (2nd smallest) RMSE is obtained with SpheriCol 88% (70%) of the time: the smallest (2nd smallest) values are boldface (underlined). The driving assistant is thus effective in centering the EPW along the circuit and it improves user's safety, thus confirming our initial hypothesis.

As for the range measurements, in each trial, we determined how many ToF sensors detected obstacles at a distance of less than 7 cm or 2 cm. As above, we computed the average over 3 runs, under the same conditions. For a fair comparison, the results are reported in percentage: in fact, the duration of each run is different and it depends on the user's driving skills. With the 7-cm threshold, the lowest (2nd lowest) percentage of collisions is obtained 82% (59%) of the time with SpheriCol, whereas with the 2-cm threshold, the percentages are 71% (76%). This further supports the case for improved safety of our driving assistant.

To evaluate the effectiveness of SpheriCol (and user's confidence in a candidate collision-free trajectory), we also measured the variability of joystick input [START_REF] Sorrento | Assessment of Joystick control during the performance of powered wheelchair driving tasks[END_REF]. To this end, we computed the standard deviation of joystick's azimuthal angles (degrees), in sector 3 of the test circuit (see Fig. 11c). We focused on this sector rather than on sectors 1 and 4, since the user must put the wheelchair into reverse and needs more assistance from SpheriCol. Table IV reports the averages over 3 runs per subject, of the standard deviation of joystick's azimuthal angles, under the same conditions ("Without assistance", "Bird's eye", and "Bird's eye + lines"). The smallest (2nd smallest) standard deviations are obtained with SpheriCol 70% (76%) of the time, with deviations ranging from 2 From a statistical analysis of the answers to the questionnaire, SpheriCol received neutral to positive satisfaction and usability results from the large majority of participants (see Figs. 12a-12c). Fig. 12d reports the percentage of time, SpheriCol was used by the 17 subjects in the test circuit. In addition, see Fig. 12e, 44% of the users stated that the video stream is one of the major strengths of SpheriCol, and 16% of the participants appreciated the additional piece of information conveyed by the colored line markers. One out of five users deemed the system helpful for reversing the wheelchair and for risk management (collision avoidance), while 47% of the participants pointed out a time lag due to the computation of the bird's-eye view from the equirectangular image: this is potentially critical for safe navigation, especially for highspeed motions (see Fig. 12f). In our current implementation, image warping is not optimized and video latency in live streaming (on the order of tens of milliseconds) adds up to the time delay introduced by VNC Connect: hence, the average frame rate is about 5 fps. The users also reported some visualization issues: the graphical information is too rich (24% of the respondents), the elevated point of view (PoV) of the camera is hard to understand on the first try (18%), and the resolution of the image is not uniform (12%). Finally, Fig. 12g indicates that 73% of the participants opted for the driving assistant (with or without the line markers). The yellow slice (28%) in Fig. 12g, includes the subjects who expressed no preferences ("None") and those who did not answer the question ("NoA"). Note that in the pie charts in Fig. 12f and Fig. 12g, the percentages do not sum up to 100%, since some of the participants provided multiple answers and the digits after the decimal point have been omitted.

V. CONCLUSION AND FUTURE WORK

In this paper, we have presented SpheriCol, a new simple yet versatile driving assistant for the users of power wheelchairs. The system, developed atop ROS, integrates spherical vision from an overhead camera with range measurements, to support navigation in confined spaces. SpheriCol has been successfully validated on a consumer-grade wheelchair equipped with our plug-and-play system, during extensive experiments with a target audience of able-bodied volunteers and people with motor impairments. The proposed navigation system elicited the intended user's response and holds promise for achieving the next-generation robotic assistive devices. However, our clinical trials also exposed a number of limitations:

• For people who are naïve to power wheelchairs, there is not much evidence of benefit from SpheriCol in terms of task completion time, but safety and comfort are clearly improved, • With the existing visualization interface, most of the users appreciated the live video feed from the twinfisheye camera, and, to a less extent, the overlaid distance information, • The present study seems hard to generalize to any clinical population of expert wheelchair users. In fact, these individuals are highly skilled at judging distances, and they might not be willing to undertake long training sessions to embrace a new technology whose benefits become manifest only in a few complex maneuvers. In addition, the screen in front of them might obstruct a direct view of the surrounding environment, and it could be perceived as a barrier to mobility. In future works, we will adapt the shape of distance markers according to the speed of the wheelchair (as reconstructed from joystick angle), to provide more accurate visual feedback to the user. We would also like to add a social component to SpheriCol, to improve navigation among pedestrians in crowded environments [START_REF] Grzeskowiak | Crowd against the machine: A simulation-based benchmark tool to evaluate and compare robot capabilities to navigate a human crowd[END_REF]. Finally, plans are afoot to develop a purely vision-based version of SpheriCol which requires no range measurements from other sensors on the wheelchair, and which provides high dynamic range omnidirectional images for both indoor and outdoor use [START_REF] Caron | HaDROs: Omni-HDR Vision for Localization and Cartography in Environments with a Wide Range of Radiance[END_REF]. To this end, we work towards developing a system which includes two or more twin-fisheye cameras rigidly attached to the same support, as in [START_REF] Wang | 360SD-Net: 360 • Stereo Depth Estimation with Learnable Cost Volume[END_REF], [START_REF] Meuleman | Real-Time Sphere Sweeping Stereo from Multiview Fisheye Images[END_REF]. As an alternative, one could adopt a machine-learning approach inspired by [START_REF] Zioulis | OmniDepth: Dense Depth Estimation for Indoors Spherical Panoramas[END_REF], [START_REF] Jiang | UniFuse: Unidirectional Fusion for 360 • Panorama Depth Estimation[END_REF], to estimate depth from a single spherical panorama.

Supplementary material

For further details, a video featuring an EPW equipped with SpheriCol in a selection of our clinical trials, is available at the address reported at the bottom of the page 1 . In particular, the video shows the visualization interface described in Sect. III-C. 1 https://home.mis.u-picardie.fr/ ∼ fabio/Eng/Video/DelmasTMRB23.mp4

Fig. 1 :

 1 Fig. 1: Overview of system components: (a) Power wheelchair equipped with a ring of range sensors; (b) Twin-fisheye camera; (c) Visualization interface.

Fig. 2 :

 2 Fig. 2: Twin-fisheye camera: (a) Front, side, and top view of the Ricoh Theta S camera (image courtesy of Ricoh): the optical system with the two fisheye lenses, prisms and CMOS sensors is shown in the lower right corner; (b) Schematic diagram of the camera (top view): F c is the camera frame, and F c1 , F c2 are the reference frames associated with the two fisheye lenses; (c) Example of dual-fisheye image captured by the Ricoh Theta S: the circular sub-images correspond to the two fisheye lenses.

/ 2 ,Fig. 3 :

 23 Fig. 3: Viewpoint selection: [(a), top] Dual-fisheye image captured by a twin-fisheye camera, and [(a), bottom] corresponding equirectangular image; (b) Spherical view; (c) Bird's-eye view. For ease of comparison, the images in (a), (b) and (c) have been captured at the same location.

Fig. 4 :

 4 Fig. 4: Generation of bird's-eye image I bird (yellow), from the image on the unit sphere I sphere .

Fig. 5 :

 5 Fig. 5: Configuration interface of SpheriCol.

Fig. 6 :

 6 Fig. 6: (a) Location of the 48 ToF sensors on the Quickie Salsa M 2 wheelchair (top view). The seven sensor modules are depicted in green; (b) Tablet mounted on the wheelchair: the visualization interface described in Sect. III-C is activated (photo courtesy of newspaper OUEST-FRANCE).

Fig. 7 :

 7 Fig. 7: (a) Spherical view with the obstacles detected by the 48 ToF sensors: the green points indicate the free space around the wheelchair. Equirectangular view with, (b) lines obtained via Lagrange interpolation, and (c) ellipses; Spherical view with, (d) colored bands ("Zones"), and (e) circular arcs ("Indics"). In (d), the colored bands show obstacle clearance: the front wall is less than 1 m away, and the rear wall is less than 0.5 m away. The inset in (e), shows a blow-up of the six red circular arcs.

1 )Fig. 8 :

 18 Fig. 8: Experimental setup in the first campaign. (a) Test circuit (not to scale) with three photos of the two slaloms and the "nominal" path of the wheelchair (green); (b) Accurate plan of the test room obtained with OpenVSLAM [54]. The medial axis of the test room and the shortest path along it, are depicted in blue and red, respectively (see Sect. IV-C for more details).

(a) 1 -Fig. 9 :

 19 Fig.9: First experimental campaign. Number of sensors which detected an obstacle at a distance of less than 7 cm (blue) or 2 cm (red). The Arabic (Roman) numerals in the captions under each plot, refer to the subjects (trials).

(a) 2 -Fig. 10 :

 210 Fig. 10: First experimental campaign. Two-dimensional histograms of joystick position in the second simulated elevator. The Arabic (Roman) numerals in the captions under each histogram, refer to the subjects (trials).

Fig. 11 :

 11 Fig. 11: Experimental setup in the second campaign. (a) One of the volunteers about to start the test circuit; (b) Bird's-eye view with overlaid line markers: the user is reversing the wheelchair, and the red marker warns him of the presence of a wall behind him; (c) The four sectors of the test circuit. In sector 3, the user must drive the wheelchair in reverse; (d) "Nominal" path of the wheelchair in the circuit (blue) and start position.

Fig. 12 :

 12 Fig. 12: Summary of the answers to the questionnaire in the second experimental campaign. (a)-(c) Usability of SpheriCol and overall level of satisfaction; (d) Percentage of time, the 17 participants used SpheriCol in the test circuit (NA stands for "Not Available"); (e) Strengths, and (f) weaknesses of SpheriCol; (g) Preferred type of assistance (NoA stands for "No Answer").

TABLE II :

 II Summary of the trials in the second experimental campaign. The completion times in the 3rd, 5th and 7th column, are the averages over three runs per subject. The smallest (2nd smallest) values are boldface (underlined), respectively. As in TableI, the trials in which no data were recorded, are marked with an asterisk. the medial axis is the set of centers of maximal balls, i.e., of balls in C that are themselves not enclosed in another ball in C[START_REF]Handbook of Discrete and Computational Geometry[END_REF] Sect. 54.4].

TABLE III :

 III Second

	Subject	Without assistance	Bird's eye	Bird's-eye + lines
	2	132.87	146.73	148.91
	3	125.88	137.80	148.22
	4	NA	NA	127.60
	5	153.04	150.00	140.32
	6	136.94	129.60	138.66
	7	131.89	136.77	114.08
	8	137.91	134.82	145.82
	9	143.81	136.59	137.17
	10	139.00	133.90	146.96
	11	147.82	145.65	146.91
	12	151.15	143.93	137.22
	13	137.62	133.50	136.59
	14	145.30	150.75	146.96
	15	147.19	130.41	141.18
	16	140.43	150.00	142.44
	17	141.64	135.79	141.58
	18	141.35	154.18	154.24

experimental campaign. RMSE (cm) with ∆ = 25, see equation

[START_REF]Assistive Technology[END_REF]

. The reported values are the averages over 3 runs per subject (under the same conditions). The ground truth is the trajectory determined by Dijkstra's algorithm on the medial axis M (C) of the test room. The smallest (2nd smallest) values are boldface (underlined).

TABLE IV :

 IV Second experimental campaign. Standard deviation of joystick's azimuthal angles (degrees). The reported values are the averages over 3 runs per subject (under the same conditions): they have been computed in sector 3 of the test circuit (see Fig.11c). The smallest (2nd smallest) values are boldface (underlined), and NA stands for "Not Available".

to 22.6 • (mean deviation, 11.5 • ). These results mirror the findings of the first campaign, and suggest that SpheriCol contributes to smoother wheelchair trajectories.

ACKNOWLEDGMENTS

This work was carried out as part of the Interreg VA France (Channel) England ADAPT project "Assistive Devices for empowering disAbled People through robotic Technologies" (http://adapt-project.com). The Interreg FCE Programme is a European Territorial Cooperation programme that aims to fund high quality cooperation projects in the Channel border region between France and England. The Programme is funded by the European Regional Development Fund (ERDF).

The authors would like to thank Bastien Fraudet and Émilie Leblong (Pôle Saint-Hélier, Rennes), and Louise Devigne (IRISA/Inria Rennes and INSA Rennes) for their assistance during the clinical trials and for helpful discussion.