Benedicte Mittaine-Marzac
email: benedicte.mittaine-marzac@aphp.fr

Matthieu De Stampa

Emmanuel Bagaragaza

Joël Ankri

Philippe Aegerter

Impacts on health outcomes and on resource utilisation of home-based parenteral chemotherapy administration: a systematic review protocol

Introduction Despite the demonstrated feasibility and policies to enable more to receive chemotherapy at home, in a few countries, parenteral chemotherapy administration at home remains currently marginal. Of note, findings of different studies on health outcomes and resources utilisation vary, leading to conflicting results. This protocol outlines a systematic review that seeks to synthesise and critically appraise the current state of evidence on the comparison between home setting and hospital setting for parenteral chemotherapy administration within the same high standards of clinical care. Methods and analysis This protocol has been prepared following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses Protocols approach. Electronic searches will be conducted on bibliographic databases selected from the earliest available data through 15 November 2017 published in French and English languages. Additional potential papers in the selected studies and grey literature will be also included in the review. The review will include all types of studies exploring patients receiving anticancer drugs for injection at home compared with patients receiving the drugs in a hospital setting, and will assess at least one of the following criteria: patients' health outcomes, patients' or caregivers' satisfaction, resource utilisation with cost savings, and incentives and/or barriers of each admission setting according to patients' and relatives' points of view. Two reviewers will independently screen studies and extract relevant data from the included studies. Methodological quality of studies will be assessed using the 'Quality Assessment Tool for Quantitative Studies' developed by the Effective Public Health Practice Project tool, in addition to the Consolidated Health Economic Evaluation Reporting Standards statement for economic studies. Ethics and dissemination As the review is focused on the analysis of secondary data, it does not require ethics approval. The results of the study will be disseminated through articles in peer-reviewed journals and trade publications, as well as presentations at relevant conferences. PrOsPErO registration number CRD42017068164.

IntrOduCtIOn

Hospitals remain the main setting for parenteral cancer chemotherapy administration despite patients' generally positive feeling about receiving care at home. [START_REF] Leff | Satisfaction with Hospital at Home Care[END_REF] As the worldwide incidence of cancers increases, [START_REF] Fitzmaurice | Global, Regional, and National Cancer Incidence, Mortality, Years of Life Lost, Years Lived With Disability, and Disability-Adjusted Life-years for 32 Cancer Groups, 1990 to 2015: A Systematic Analysis for the Global Burden of Disease Study[END_REF] and bearing in mind that due to progress in the efficacy of treatments cancer is becoming a long-term disease, along with advances in diagnostic technology and novel targeted treatments, and due to financial constraints, it is necessary to develop alternative models of health service delivery, such as home programmes, without detrimental effects on health outcomes and costs. Despite the feasibility [START_REF] Anderson | Domiciliary chemotherapy with gemcitabine is safe and acceptable to advanced non-small-cell lung cancer patients: results of a feasibility study[END_REF][START_REF] Polinski | Home infusion: Safe, clinically effective, patient preferred, and cost saving[END_REF][START_REF] Corbett | The delivery of chemotherapy at home: an evidence synthesis[END_REF] and despite policies to enable more to receive chemotherapy at home, in a few countries, 6 7 parenteral chemotherapy administration at home remains marginal due to little evidence on improving health outcomes, patients' quality of life and cost savings. Furthermore, findings on outcomes varied, leading sometimes to conflicting results. [START_REF] Borras | Compliance, satisfaction, and quality of life of patients with colorectal cancer receiving home chemotherapy or outpatient treatment: a randomised controlled trial[END_REF] Open Access care, transportation, out-of-pocket expenses and so on) were not systematically assessed, 11 12 whereas other studies showed no significant difference in the overall costs. 9 10 Likewise, the impact on caregivers, especially the shift of the care burden from the hospital to relatives, has rarely been studied. To date, there is only one existing review of home-based chemotherapy [START_REF] Evans | A multi-method review of home-based chemotherapy[END_REF] and it ended in favour of administration at home, but this conclusion is hampered by a mix between routes of administration (parenteral and oral intake) and type of care (administration and postadministration follow-up).

Considering these facts, a systematic review will be undertaken to provide a complete overview of parenteral cancer chemotherapy administration at home to investigate whether the clinical outcomes are maintained and resource utilisation is reduced in comparison with hospitals' high standards of care.

MEthOds

This protocol has been prepared following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses Protocols (PRISMA-P) approach [START_REF] Moher | Preferred reporting items for systematic review and meta-analysis protocols (PRISMA-P) 2015 statement[END_REF] to increase confidence in the findings. It has been registered in the International Prospective Register of Systematic Reviews database (trial registration number: CRD42017068164).

types of studies

Except crossover studies, all types of studies that have investigated parenteral cancer chemotherapy home administration compared with hospital setting, such as randomised controlled or uncontrolled trials, cohort studies and parallel studies, will be included if they fulfil at least one of the following criteria: 1. Assessment of the impact of parenteral chemotherapy administration on patients' health outcomes whatever they are: survival, relapse and tolerance. 2. Assessment of the impact of parenteral chemotherapy administration on patients' or caregivers' satisfaction. 3. Assessment of the impact of parenteral chemotherapy administration on cost savings. 4. Assessment of the incentives and/or the barriers according to patients' and/or relatives' points of view. Economic evaluations of resource utilisation with costs and consequences such as cost-effectiveness, cost utility or cost-benefit, either with or without any clinical assessment, will be included.

Crossover studies will be excluded from the review; crossover studies involving oncology products or the type of hospitalisation setting could suffer from order effects, so it could be difficult to confirm statistically the lack of order effects and hence to use the results.

Participants

We will be interested in studies on participants receiving parenteral anticancer drug administration at home compared with patients receiving the drugs in a hospital setting. There will be no restriction on the type of tumour disease, age or sex of participants.

Patients and public involvement

As the review is focused on the analysis of secondary data, it does not involve patients, nor does it involve patients in the design of the study or in the dissemination of results.

Eligibility criteria

All studies exploring parenteral anticancer drug administration at home setting, mainly intravenous and subcutaneous administrations, will be selected from the earliest available data through 15 November 2017, published in French and English languages, regardless of country. The inclusion criterion defining the scope of publications included in the review will be the comparison of parenteral chemotherapy administration at home with administration in inpatients and/or outpatients wards. As our goal is to study the home-based setting as an alternative context for providing the highest standards of clinical care concerning parenteral drug delivery, we will exclude all community-based services with no anticancer drug administration at home, and studies targeting only postadministration chemotherapy monitoring, disconnection of portable diffuser, management of central venous catheter and supportive care therapy. For the same reasons, studies on oral anticancer drugs will be excluded as the oral treatment does not require hospital care; patients usually manage their pills themselves with an ambulatory follow-up and the treatment issues are deeply different (ie, chronic side effects, patients' compliance).

databases and search strategy

A detailed literature search will be conducted to identify all articles studying chemotherapy administration in a home setting for adults and paediatric patients. Published studies will be identified through searches of the Medline, Cochrane, Web of Science, Embase and Cumulative Index to Nursing and Allied Health from the earliest available date through 15 November 2017. HAH is defined as the delivery of hospital ward-level care and replaces the hospital by ensuring the continuity of care for the patient it takes care of. HAH is also known as 'hospital in the home', 'home hospitalization' and 'early supported discharge'. [START_REF] Leff | Hospital at home: feasibility and outcomes of a program to provide hospital-level care at home for acutely ill older patients[END_REF][START_REF] Stessman | Decreased hospital utilization by older adults attributable to a home hospitalization program[END_REF][START_REF] Langhorne | Early supported discharge services for stroke patients: a meta-analysis of individual patients' data[END_REF] According to Medical Subject Headings (MeSH) definition, 'Home Care Services' is a community health and nursing service providing coordinated multiple services to patients at their homes. These home care services are provided by a visiting nurse, home health agencies, hospitals or organised community groups using professional staff for care delivery. They differ from home nursing, which is provided by non-professionals, and from 'Home Care Agencies', public or private organisations, which provide home health services in patients' home either directly or through arrangements with other organisations.

Therefore, we have developed a strategy in Medline to retrieve relevant literature on the topic. The Medline Open Access search strategy will be ("Neoplasms"[Mesh] AND ("Antineoplastic Combined Chemotherapy Protocols"[Mesh] OR "Antineoplastic Agents"[Mesh])) AND ("Home Care Services"[Mesh] OR "Home Care Agencies" [Mesh]). This search strategy will be adapted in searching other databases (see search strategy in online supplementary file). The references from potentially relevant papers were manually searched for additional studies. A further research will be performed in OpenGrey, in Research Papers in Economics and in Google Scholar databases to find relevant unpublished studies in grey literature.

study selection

We will use a two-stage process to identify papers that met our inclusion criteria. The first stage accumulated all papers from two types of searches using the already mentioned databases. The first type of search will use combinations of keywords to retrieve titles of potentially relevant studies. The search output will be screened independently by two review authors (MDS, BM-M) to identify studies that potentially meet the inclusion criteria outlined above. In case of discrepancy, the abstract of the concerned study will be retrieved. If disagreements remained, a third author (EB) will arbitrate. In the second type of search, all papers citing or cited by articles that had already met our inclusion criteria will be identified, then screened as the first ones. In the second stage, the full text of these selected studies will be retrieved and independently assessed for eligibility by the same two review members. An article will be considered relevant and kept for analysis if the full text of the publication is of a comparison design assessing patients' health and/ or safety outcomes and/or patients' or relatives' satisfaction, and/or cost savings and/or the incentives and the barriers of using home as an alternative setting. Duplicates of articles will be discarded.

Any disagreement between the reviewers over the eligibility of particular studies will be resolved through a discussion with a third reviewer (EB).

data extraction

Extracted information on a standardised form will include the following: ► Study setting. ► Study population. ► Tumour type and chemotherapy regimen. ► Details of the intervention/control conditions. ► Experimental design. ► Recruitment and study completion rates. ► Patients' health outcomes including quality of life, duration of survival, progression of disease and toxicity. ► Patients' and caregivers' satisfaction and preference, and shift of burden. ► Resource utilisation with costs and consequences including cost-effectiveness, cost utility or cost-benefit analyses, and perspective of the study including provider, payer or societal and shift of costs.

► Incentives and barriers according to patients' and/or relatives' points of view. ► Information for the assessment of the risk of bias.

Data will be extracted independently by two review members; discrepancies will be identified and resolved through a discussion with a third reviewer (PA). data assessment and synthesis Quality assessment Two reviewers (MDS and BM-M) will independently assess the quality of included studies and the potential risk of bias. We will use the 'Quality Assessment Tool for Quantitative Studies' developed by the Effective Public Health Practice Project tool, [START_REF]Quality Assessment Tool for Quantitative Studies[END_REF] as it can be applied to articles of any public health topic area, assessing the components of studies (design, methods, bias). Likewise, we will use the Consolidated Health Economic Evaluation Reporting Standards statement, [START_REF] Husereau | Consolidated Health Economic Evaluation Reporting Standards (CHEERS)-explanation and elaboration: a report of the ISPOR Health Economic Evaluation Publication Guidelines Good Reporting Practices Task Force[END_REF] focusing on the design quality of the cost studies. It leads to an overall methodological rating of strong, moderate or weak. In case of disagreement, consensus will be reached through a discussion.

Data synthesis

According to the limited development of home parenteral chemotherapy administration, we anticipate methodological heterogeneity, statistical heterogeneity, heterogeneity of interventions and heterogeneity of models against a meta-analysis of the evidence base. In that case, an interpretative method should be more appropriate, leading to a description of the observed effects with peculiarities, and strengths and limits of each study, according to the quality of the study, type of study, studied population and interventions. The Grading of Recommendations Assessment, Development and Evaluation approach [START_REF] Balshem | GRADE guidelines: 3. Rating the quality of evidence[END_REF] will be used to assess the overall quality of evidence by downgrading scores in case of serious risk of bias, imprecision and study limitations, or indeed by upgrading scores of studies that traditionally have been considered to have a weak design. It would be appropriate to assess relevant studies that do not provide evidence on every outcome. Final scores on the quality of evidence will be categorised as high, moderate, low or very low, and summarised in a table. This method should be more appropriate from a holistic point of view.

Subgroup analysis

If the data are available, we will conduct subgroup analyses investigating the effects of study design, models, interventions, tumour type (haematological tumour, solid tumour) and age of the study population (children, young people <18 years old, adults, >65 years old).

A sensitivity analysis will determine the robustness of the observed outcomes facing publication language, clinical or methodological heterogeneity.

Ethics and dissemination

As the review is focused on the analysis of secondary data, it does not require ethics approval. The results of the study will be disseminated through articles in peer-reviewed Open Access journals and trade publications, as well as presentations at relevant conferences.

COnClusIOn

This review, following the PRISMA-P guidelines, will be an attempt to synthesise and to critically appraise the impact of parenteral chemotherapy administration at home for patients and their relatives compared with a hospital setting.

Other strengths of this review include the search of literature published in two languages, French and English, and the wide search from published studies in grey literature.

It is however acknowledged that the definition of home-based services including different types of interventions is confusing, which could lead to discrepancies during the analysis. Likewise, the results of the review may be limited by the diversity of study designs and present challenges in the quality assessment. These limitations will be considered in relation to the review findings.

However, this review could be useful for medical staff in choosing the best treatment setting for patients and their relatives, and could contribute to developing parenteral chemotherapy administration at home. As we anticipate great heterogeneity of the studies, mainly concerning the interventions, this review could at least highlight a definition of a realistic methodology to set up in this field.

on 13 June 2018 by guest. Protected by copyright. http://bmjopen.bmj.com/ BMJ Open: first published as 10.1136/bmjopen-2017-020594 on 9 May 2018. Downloaded from

Funding This work is supported by the Hospitalisation At Home, Assistance Publique des Hôpitaux de Paris.


Viktor Walter

Martin Saska

Antonio Franchi
email: antonio.franchi@laas.fr

Fast Mutual Relative Localization of UAVs using Ultraviolet LED Markers

This paper proposes a new methodology for outdoor mutual relative localization of UAVs equipped with active ultraviolet markers and a suitable camera with specialized bandpass filters. Mutual relative localization is a crucial tool for formation preservation, swarming and cooperative task completion in scenarios in which UAVs share working space in small relative distances. In most current systems of compact UAV swarms the localization of particular UAVs is based on the data obtained from motion capture systems for indoor experiments or on precise RTK-GNSS data outdoor. Such an external infrastructure is unavailable in most of real multi-UAV applications and often cannot be pre-installed. To account for such situations, as well as to make the system more autonomous, reliance on onboard sensors only is desirable. In the proposed approach, we rely on ultraviolet LED markers, that emit light in frequencies that are less common in nature than the visible light or infrared radiation, especially in high intensities. Additionally, common camera sensors are sensitive to ultraviolet light, making the addition of a filter the only necessary modification, keeping the platform low-cost, which is one of the key requirements on swarm systems. This also allows for a smaller size of the markers to be sufficient, without burdening the processing resources. Thus the proposed system aspires to be an enabling technology for deployment of large swarms of possibly micro-scale aerial vehicles in real world conditions and without any dependency on an external infrastructure.

I. INTRODUCTION

Mutual relative localization of flying robots is indispensable in many real-world applications that require deployment of multiple Unmanned Aerial Vehicles (UAVs) sharing the same workspace in small relative mutual distances. Using compact multi-UAV systems brings numerous benefits including cooperative task completion, extension of reach of a single robot and distribution of capabilities into independent members. Moreover, several tasks that are not solvable by a single robot do exist and some of them were successfully solved by teams of UAVs developed by the Multi-robot Systems group at CTU in Prague 3 by employing onboard visual mutual relative localization -see Fig. 1 a) andc) for examples. In this paper, we propose a novel robust method of infrastructure-independent relative localization for flights of multiple UAVs, applicable for outdoor environments, as well as the indoors. The method is based on the application of markers composed of ultraviolet LEDs on the UAVs, in addition to equipping the observer UAVs with cameras with fisheye lenses and specialized bandpass filters. The relative pose of the observed UAVs can then be retrieved easily from the image, where the markers are visible as bright spots on dark background that can be located with little processing. Our intention is to provide each swarm member with an as complete as possible information on the state of all UAVs in close proximity without any the of communication among the robots or with a base station. Fulfilling this goal requires direct sensing of mutual relative distances, information about the relative bearings and, if possible, also about their relative headings.

As can be seen in numerous examples of flocking of animals, such information can be effectively obtained through vision [START_REF] Nagy | Hierarchical group dynamics in pigeon flocks[END_REF]. In our previous works on mutual localization [START_REF] Faigl | Low-cost embedded system for relative localization in robotic swarms[END_REF], [START_REF] Krajník | A practical multirobot localization system[END_REF], passive markers in conjunction with an object detection algorithm have been used to achieve the same sensory ability. This vision-based system has been deployed in numerous indoor and outdoor experiments [START_REF] Saska | Coordination and Navigation of Heterogeneous UAVs-UGVs Teams Localized by a Hawk-Eye Approach[END_REF], [START_REF] Saska | System for deployment of groups of unmanned micro aerial vehicles in gps-denied environments using onboard visual relative localization[END_REF], [START_REF] Saska | Mav-swarms: Unmanned aerial vehicles stabilized along a given path using onboard relative localization[END_REF], where multiple drawbacks, such as strong lighting conditions dependency, large size of the markers, limited operational space and computational complexity have been identified. The most significant is the fact that the changing outdoor lighting conditions may prevent consistent recognition of the markers. The system proposed in this paper aims to alleviate these drawbacks and to further enlarge the application domain of UAV swarms. Fig. 2: Example of an image from the onboard camera with filter of a hexarotor UAV equipped with 6 markers on its arms. The picture was taken at noon, with the exposure rate set to 1000 µs. Lower left shows the same view from a conventional camera. Fig. 3: An extreme case of long range and hard to separate background. In the visible spectrum the UAV is difficult to locate even by the human eye and today's popular CNN methods [START_REF] Chaudhary | Robust real-time visual tracking using dual-frame deep comparison network integrated with correlation filters[END_REF], while in UV the three markers are clearly visible as unique peaks in brightness and can easily be detected by the proposed system.

A. State of the art and contributions

Most of the multi-UAV experiments that require localization have been realized in laboratory conditions relying on an absolute measurement by a motion capture system (Optitrack4 , VICON5 , etc.) [START_REF] Kushleyev | Towards a swarm of agile micro quadrotors[END_REF] and the relative pose measurement is emulated by calculating it from a source of absolute pose as a placeholder [START_REF] Stegagno | Ground and aerial mutual localization using anonymous relativebearing measurements[END_REF]. Outdoor cooperative flights [START_REF] Vásárhelyi | Outdoor flocking and formation flight with autonomous aerial robots[END_REF], [START_REF] Virágh | Flocking algorithm for autonomous flying robots[END_REF] tend to rely on GNSS (Global Navigation Satellite System) if a close proximity of robots is not required or on RTK-GNSS data (provided in our case by Tarsus BX305 6 ), which may achieve the precision of ±10 mm. Obviously, these approaches suffer from the necessity to pre-install an external infrastructure (motion capture cameras or RTK basestation) which precludes flights in environments that are unknown or difficult to reach by the operators themselves. Another problem is transition from outdoor to indoor environments, flight near elevated objects of larger volumebuildings, rock formations, etc. -or flight in an unknown, cluttered or inaccessible enclosed environment. Additionally, continual reception of such external information requires wireless communication, which is subject to limited range and interference both from unrelated sources and by the units themselves in the case of a large swarm. This makes the system difficult to scale up to larger number of units, which is the main idea of robotic swarms. Another challenge caused by the infrastructure dependence the task may easily be deliberately obstructed by interfering with the infrastructure, such as by introduction of artificial radio interference on key radio frequencies. In order to be reliable even in such circumstances, the units need to be able to independently avoid damage and complete their mission. If the UAVs are flying in a formation, they should be able to preserve it or keep their mutual distances within safe ranges, which is reliably enabled by the proposed approach.

Numerous principles of direct mutual localization can be found in literature. From a theoretical point of view the mutual localization problem in group of robots boils down to the (bearing) rigidity problem, see [START_REF] Michieletto | Bearing rigidity theory in SE(3)[END_REF] and reference therein for an introduction to this concept. The multi-agent mutual localization problem has been also faced in the case in which measurements do not provide the identity of the measured robot, i.e., they are anonymous [START_REF] Stegagno | Ground and aerial mutual localization using anonymous relativebearing measurements[END_REF].

Relative localization of noise-emitting objects such as UAVs was successfully tested in [START_REF] Zunino | Seeing the sound: A new multimodal imaging device for computer vision[END_REF]. This method, however, requires a large and highly specialized equipment, while providing only an approximate relative bearing of the target and being sensitive to acoustic environmental noise.

Another approach was used in [START_REF] Wang | Vision-based cooperative pose estimation for localization in multi-robot systems equipped with rgb-d cameras[END_REF], where point-clouds obtained from RGB-D cameras attached to each unit are aligned to obtain their relative poses. These sensors have severely limited range and field of view and the algorithm is computationally too complex for most onboard computers of lightweight UAVs. Similarly, [START_REF] Senthooran | A 3d line alignment method for loop closure and mutual localisation in limited resourced mavs[END_REF] used the alignment of lines detected in images of the environment of the UAVs to establish their relative positions. Such an approach can be applied efficiently in an environment with multiple straight lines, such as in streets or offices, but not in natural environments where straight lines are rare. Both of the aforementioned approaches additionally require communication between the units, at fairly high bandwidths.

Numerous experimental solutions based on vision and mutual observation of UAV and UGVs equipped with known geometrical markers were tested [START_REF] Boudjit | Detection and target tracking with a quadrotor using fuzzy logic[END_REF], [START_REF] Dhiman | Mutual localization: Two camera relative 6-dof pose estimation from reciprocal fiducial observation[END_REF]. Our previous solution uses circular visual markers [START_REF] Faigl | Low-cost embedded system for relative localization in robotic swarms[END_REF], [START_REF] Krajník | A practical multirobot localization system[END_REF] for mutual localization in small swarms of UAVs [START_REF] Saska | System for deployment of groups of unmanned micro aerial vehicles in gps-denied environments using onboard visual relative localization[END_REF], [START_REF] Saska | Mav-swarms: Unmanned aerial vehicles stabilized along a given path using onboard relative localization[END_REF] and in heterogeneous formations [START_REF] Saska | Coordination and Navigation of Heterogeneous UAVs-UGVs Teams Localized by a Hawk-Eye Approach[END_REF]. The main disadvantage of these methods is the sensitivity to light conditions, computational complexity and the physical dimensions of these markers. The large size of the markers (see fig. 1-a), needed for proper detection from reasonable distances and angle range leads to problems connected to aerodynamics and maintenance difficulties. In addition, these markers are highly susceptible to a partial occlusion that can prevent detection.

A basic and often used approach is to apply a simple, easy to segment color-based markers that work well in controlled light conditions of laboratory environments [START_REF] Tron | Vision-based formation control of aerial vehicles[END_REF], [START_REF] Rekleitis | Experiments in quadrotor formation flying using on-board relative localization[END_REF]. While in a laboratory it is easy to apply active or passive markers of a color that we ensure is not otherwise present in the environment, this is seemingly unfeasible in outdoor conditions, since in nature as well as in urban scenarios, all colors of the visible spectrum are naturally present.

The closest approach to the proposed system can be found in [START_REF] Censi | Low-latency localization by active led markers tracking using a dynamic vision sensor[END_REF], where UAV localization through infrared lights blinking in the order of kilohertz attached to helicopters is implemented. Such frequency allows for the markers tracked even with aggressive flight maneuvers. This was achieved by using an event-based camera. The solution in [START_REF] Censi | Low-latency localization by active led markers tracking using a dynamic vision sensor[END_REF] was only tested in indoor environments, with the camera being statically placed in the room, instead of onboard of a UAV. The use of a heavy and expensive specialized camera makes it unsuitable for outdoor onboard deployment. Additionally, the low resolution of contemporary event-based cameras decrease the precision and the range of detection.

The system presented here is based on the observation that while the colors of the visible spectrum, as well as a wide band of the infrared wavelengths, are present with relatively high intensity in normal sunlight, the ultraviolet light is significantly less intense. This means that in the UV spectrum the natural environments are dark and when an object bright in the ultraviolet is observed, it is likely to be artificial. Exploiting this fact does not even require a new specialized sensor, since common monochromatic digital cameras tend to be receptive to near ultraviolet frequencies, and need only be modified with a proper band-pass filter. The UV light can then be used as a robust and easy detect feature. The only false positives in detection being the sun itself and its specular reflections, while even most of artificial light sources emit little to none UV radiation.

To sum up the contribution of the paper related to the current literature, we emphasize that the proposed solution combines knowledge gained during hundreds of flights with multiple closely cooperating UAVs in realistic indoor and outdoor conditions using different state-of-the-art localization systems and a theoretical analyses of sources of disturbance that lead to false positive detections in common workspaces of UAV systems. Based on this data we propose the HW design of a system made of multiple onboard UV light sources that reliably provides the required information (distance and bearing of neighbouring vehicles) in all possible configurations of the team. In comparison with state-of-the-art solutions, our solution presents better reliability w.r.t different weather conditions and precision, while significantly reducing size and weight of the overall system and the required computational power. We provide two approaches for mutual localization using this HW setup. The first minimalistic approach uses a single camera and a single UV LED on each UAV to provide bearing information and a rough estimation of the relative distance. This method together with the work [START_REF] Brandtner | Coherent swarming of unmanned micro aerial vehicles with minimum computational and communication requirements[END_REF], where we have shown that such a sensory information (even anonymous) is sufficient for reliable coherent swarming, provides a complex solution for deployment of large swarms of micro aerial vehicles. The scalability is shown in [START_REF] Brandtner | Coherent swarming of unmanned micro aerial vehicles with minimum computational and communication requirements[END_REF] by a surprising observation that the swarm stability and coherence increases with number of swarm members even with such a limited sensory input. The second approach presented in this paper exploits possibility of using multiple LEDs onboard of UAVs to increase pre-Fig. 4: The spectrum of solar radiation in wavelengths near the visible spectrum. Notice the rapid decrease in irradiance in the UV region. 7cision of the distance measurement and operational space. In fact, this approach exploits full size of the UAVs, putting the LEDs as far apart as possible, which increases baseline used for the distance estimation, resulting in higher precision, in comparison with passive markers that are always significantly smaller that the UAV itself.

The paper is structured as follows. Section II deals with the theoretical background applied in the design of the system. Section III comprises the overview of the hardware used. Section IV explains the methodology used in estimating the mutual location of the target (neighbouring UAV) as well as the system identification. Finally, section V summarizes the results of experimental testing of the system.

II. THEORETICAL BACKGROUND

A. The ultraviolet markers and sensors

Using UV light for mutual localization is an obvious approach for deployment of swarms in real outdoor environments, as it was the case in our experiments, but not in typical laboratory experiments [START_REF] Kushleyev | Towards a swarm of agile micro quadrotors[END_REF], [START_REF] Franchi | Modeling and control of uav bearing formations with bilateral high-level steering[END_REF]. The solar radiation approximates the blackbody radiation, with peak intensity centered on the visible light (see figure 4). This means that the shape of the intensity to wavelength characteristic is asymmetric w.r.t. the wavelength. The intensity decays considerably slower with growing wavelengths than it does with diminishing wavelength. Ultraviolet parts of sunlight are therefore significantly less intense than the visible light and the infrared, even relatively close to the visible spectrum. We can exploit this observation to apply active markers that can be easily distinguished from the multicolored natural backgrounds purely based on the intensity. In the implementation, this requires physical band-pass filtering tuned to the ultraviolet wavelengths of the markers.

A gray-scale camera is more suitable for this task since it is less selective w.r.t. the wavelength than RGB cameras and is thus more sensitive to light outside of the visible spectrum. Note, that while the sun does still emit considerable amounts of UV radiation, this radiation is spread across a range of wavelengths and most of it is filtered out by the atmosphere. Additionally, it does not reflect well on solid natural surfaces. With low enough exposure rate of the camera, the only objects that will locally saturate the resulting image to white will be the markers, directly observed sun and some of its specular reflections. The appropriate exposure rate depends on the required maximal detection distance. Our tests have shown that the UV light refracted through the atmosphere and reflected from matte surfaces is normally too dim to prevent the detection. The image of the sun and its reflections should be a minor issue which can be accounted for by using knowledge of the size or other specific characteristics of the spots caused by the sun or the knowledge of sun position based on current place and time. The possibility to set the exposure so that the markers will create saturated white spots on dark background can be used to binarize the image using simple static thresholding, as opposed to the more computationally demanding adaptive thresholding needed for arbitrary lighting conditions. The image spots caused by artificial light sources will be saturated regardless of the time of the day.

In order for this system to be suitable for mutual localization of multiple UAVs, the camera has to be able to observe the surroundings in a large field of view. This can be achieved by using a fisheye lens. A potential drawback that has to be addressed is the high rate of decay of UV light in common types of glass, proportional to the specific frequency. In our tests, this has limited the wavelength of the UV light that we could use. Light sources radiating at 365 nm were suppressed to the extent that they were mostly invisible to the camera, while light sources with wavelengths of 395 nm were clearly visible. Specialized lenses permeable to high-frequency UV that also have wide FoV and are portable could not be found on the market at the current time. Moreover, the infrared filter applied to the lenses by the manufacturer also blocks out UV light. A shorter wavelength would allow for better filtering of of the sunlight. Despite this, the 395 nm light sources and filters proved to be sufficient in our experiments.

III. HARDWARE OVERVIEW

The camera used in our experiments is based on the Matrix Vision mvBlueFOX-MLC200wG sensor, equipped with the Sunnex DSL215 fisheye lens and Midopt BP365-R6 ultraviolet bandpass filter.

The mvBlueFOX-MLC200wG (figure 5-c) is a greyscale CMOS sensor with a resolution of 752 × 480 pixels, maximum frame-rate of 93 without binning and quantum efficiency at 395 nm of ≈34 % 8 In our experiments we were able to achieve a maximum frame-rate of 70 Hz with the exposure rate set to 1000 µs. The DSL215 is a fisheye lens with the maximal FoV of 185 • . This value, however only applies to the horizontal field of view with the MLC200wG sensor. 9 The BP365-R6 is a miniature interference-based optical bandpass filter for ultraviolet imaging 10 . The custom size of 6 × 6 × 1 mm allowed us to attach it between the lens and the sensor so that the whole image is covered, as seen in figure 5-b. For the markers, we have selected the ProLight PM2B-1LLE, (figure 5-d) which is a high power ultraviolet LED, with the maximum of emission centered on the wavelength of 395 nm and with Lambertian radiation pattern. 11This beacon-sensor system is small, lightweight and relatively affordable, and thus ideal for deployment with small UAVs.

IV. METHOD DESCRIPTION

A. System identification 1) Camera calibration: In order to convert the image positions of the detected spots corresponding to the markers on the UAVs into relative bearing vectors, it was necessary to perform geometric calibration of the camera. We have selected the model described in [START_REF] Scaramuzza | A flexible technique for accurate omnidirectional camera calibration and structure from motion[END_REF], suitable for cameras with wide FoV, that translates pixel positions directly into bearing vectors.

The parameters of the camera projection are affected by the different index of refraction of UV light compared to the visible light , as well as by small eccentricities of the lens mount. To account for these factors we calibrated the camera with the band-pass filter on and the lens attached in the final position. For the chessboard-type calibration pattern to be fully visible, the pattern had to be illuminated by a UV light source, with the exposure rate and threshold manually adjusted for the different angles of view, some parts of the pattern became overbright or overly dark depending on the angle of reflection. After obtaining the images, the calibration was done semi-automatically using the OCamCalib toolbox 12 . The toolbox itself provides a method of converting pixel position into a unit bearing vectors of the markers, here denoted c2w and the reverse function w2c.

The angle φ between the optical axis of the camera and an optical ray corresponding to a point in the image was modeled as a linear function of the distance r of the point from the optical center in pixels. The slope of the function was measured to be k = φ/r = 3.7673 × 10 -3 rad px -1 .

(1)

2) Spot size: An interesting imaging effect that can be exploited in this setup is the blooming effect of the camera. The markers used here are small LEDs, which with an idealized camera each LED would be projected into a single point on the sensor resulting in a single bright pixel. With real-world cameras, these markers are shown in the image as spots of sizes depending on the distance. This effect occurs due to a combination of monochromatic optical aberrations of the lens and of the finite capacity of the CMOS elements in the sensor causing excess charge being spilled over to the surrounding pixels. The exact analysis of the nature and relative impacts of these phenomena is beyond the scope of this paper.

The sizes of the spots can, however, be analyzed w.r.t. the distance of the marker (see figure 6) and thus used to give a rough estimate of the distance of the marker. Since the geometry of these spots depends on many unknown variables, and due to the finite resolution of the camera, the true position of the ray incidence within such a spot is ambiguous. The spots shrink down to the size of a single pixel at a certain distance from the camera, depending on the resolution, exposure rate, type of sensor and the radiation intensity of the marker in the direction of the camera. In order to preserve high output rate and ease of processing, we store the sizes of these spots in terms the number of pixels S after thresholding. To represent the position of the spot, we store the x and y image coordinates of the middle pixel in order of contour filling.

Since the tend to be slightly blurry around their edges, the size of the spots after binarization depends on the selected threshold.

While the estimation of distance based on such an imprecise information is not ideal, it can inform of a neighbor breaching certain safety radii or leaving the minimal mutual distance. With the algorithm presented in [START_REF] Brandtner | Coherent swarming of unmanned micro aerial vehicles with minimum computational and communication requirements[END_REF] and the proposed approach, we can achieve coherent swarming using a minimal required mutual localization setup consisting of one simple camera and LED per unit (total mass of 50g), which opens new perspectives in use of micro aerial vehicles (MAVs).

Additionally, knowing the characteristics of the spot sizes S(l) w.r.t. the distance from the camera l is useful for establishing margins of error for measurements based on the estimated bearing vectors. For this purpose, we can select a function S max (l) such that the values will lay under it. These were measured in experiments and can be seen in the next sections.

B. Directional vector estimation

Measuring the relative bearing between UAVs is one of the main requirements to let them stably fly in swarms with a predefined shape. However, it is not always necessary for each UAV to measure all the relative bearings w.r.t. all the other members. Indeed, Franchi et al. [START_REF] Franchi | Modeling and control of uav bearing formations with bilateral high-level steering[END_REF], [START_REF] Stegagno | Ground and aerial mutual localization using anonymous relativebearing measurements[END_REF] have shown that a stable, controllable swarm with a predetermined shape can be achieved by resorting only to a certain minimum number of directed observations of relative bearings between the swarm members with known identities. It was also demonstrated [START_REF] Stegagno | Mutual localization using anonymous bearing measurements[END_REF] that it is possible to reconstruct the shape of the swarm purely based on relative bearings of the unit even when the identities of the observed neighbors are unknown. With our system, such control algorithm will be applicable not only to units with limited processing and data transfer capabilities but also to outdoor applications. Since we have already calibrated the camera, we can convert a pixel position m i to the relative bearing vector v i towards a single marker as

v i = c2w(m i ). (2)
In reality the pixel position m i corresponds to a range of bearing vectors that are projected to the same CMOS element, while the vector v i corresponds to the center of that range. In the worst case, the spot is a linear chain and the true bearing vector corresponds to the farthest point of the pixel located the farthest away from the pixel we have stored to represent the spot position. The calculated relative bearing vector v i can, therefore, differ from the true bearing vector v b at most by the angle

= k S max (l) - 1 2 . (3)

C. Distance estimation based on image distance of two markers

The distance of an object in an image can be estimated based on the distance of two points M 1 and M 2 on the object (two LEDs of known relative position onboard of the UAV) and the angle α they form with the camera origin C. This requires for the camera to be calibrated, and is only applicable if we have a reasonable assumption on the angle between ←--→ M 1 M 2 and the direction towards the camera. For this method to be used for UAV localization, there needs to be at least a pair of visible markers. These two markers should not deviate too much from perpendicular alignment w.r.t. the direction towards the camera.

In order to limit the dependence of the precision of the distance estimation on the relative orientation of the observed UAV, the markers should be placed along a circle centered on the UAV local frame of reference, with equal distances between adjacent markers. Additionally, these markers should be spaced as far apart as possible, while still allowing at least a single adjacent pair to be visible from every direcion. For multirotor UAVs with a star-like layout, with the propellers attached to equally spaced arms extending from the center, the best choice is to attach these markers at the ends of these arms. In other cases, they can be attached to a protective cage or on specific additional components, to ensure radial symmetry. For a hexarotor UAV with equal arm lengths and internal angles, which is our most common use-case, the markers, composed of a single LED each, are attached to the ends of the arms. In this case a single LED per arm is sufficient, since the intensity of radiation in a Lambertian radiator (such as our chosen LEDs) at the angle of 60 • will not drop below 50 % of the intensity in the frontal direction. In a similar quadrotor UAV, the markers must be composed of symmetrically angled pair of LEDs to account for the negligible intensities of radiation in the perpendicular direction in a single LED (see figure 7 and5-e).

We recommend for the angle between these two LEDs to be 120 • in order to get approximately the same radiation intensity in the direction away from the center as with a single centered LED (see figure 8).

For a hexarotor with such markers we can estimate the distance in a range defined by two borderline assumptions:

1) The observed pair is in perpendicular alignment w.r.t. the direction towards the camera -camera in position C A in figure 9; 2) One marker of the pair is on the connecting line of the hexagonal frame -camera in position C B in figure 9. Which situation is currently closer to being the case unknown. While hexarotor is used as an example, similar borderline assumptions can be defined for quadrotors, octarotors, etc.

Depending on whether we need to check for UAVs being too close or too far away, we can select either calculation.

In the case 1) the UAV is more likely to be closer than estimated, while in the case 2) it is more likely to be further away. In a swarming algorithm such as [START_REF] Brandtner | Coherent swarming of unmanned micro aerial vehicles with minimum computational and communication requirements[END_REF] the UAVs need to compare the distances of neighbors with two margins, the far limit and the near limit, between which the distance should be kept. In order to make such swarming more reliable, it makes sense to calculate with case 1) for the far limit and with case 2) for the near limit. This is also applicable for tasks such as cooperative carrying of large objects (see figure 1-a), where these limits are connected with the level of control over the object, collision avoidance and energy conservation.

The distance can be calculated from the triangle formed by the camera C and the two markers M 1 and M 2 . The parameter d is distance between M 1 and M 2 and α is M 1 CM 2 . The relative bearing vectors from the camera towards points M 1 and M 2 are denoted v 1 and v 2 .

α = arccos (v 1 • v 2 ) = arccos (c2w(m 1 ) • c2w (m 2 )) (4)
In the case 1), the distance l A to the UAV center can be expressed as

l A = d 2 cot α 2 + v, (5)
while in case 2), the distance l B can be expressed as

l B = v cot (α) + d 2 . ( 6
)
The symbol v here stands for the height of an equilateral triangle with side d.

The intensity of radiation in a Lambertian light source, such as the one we are using is roughly proportional to the cosine of the angle from the axis. It therefore is more common to see only two of the six markers than three or four.

To establish error margins for the two cases at ground truth distance l, we take the assumption that the wrong case was presumed, so that while calculating for case 1), the real situation corresponded to case 2) and vice-versa. If in the case 2) the calculation for the case 1) was used, the relation of the estimated distance to the real distance would be

l aerr = d 2 cot arctan v l -d 2 /2 + v. (7)
In the converse case, the erroneous selection of calculation results in the estimate

l berr = v cot 2 arctan d 2 l -v + d 2 . (8)
These margins should be additionally expanded by the effects of finite resolution and spot size. Due to foreshortening, as the UAV retreats away from the camera, the change of mutual distance of the two markers in the image becomes less and less pronounced. This is more significant when the mutual distance of the images of the markers becomes comparable with the size of a pixel. As was the case in the directional vector estimation, the maximum angular error in the direction of the vector v 1 is equal to k(S max (l) - 1 2 ) The final maximal value of distance estimation in the first case is then:

l amax = d 2 cot   arctan v l-d 2 -k (S max (l) -1 2 ) 2   +v (9)
The minimal value for this case is:

l amin = d 2 cot arctan d 2 l -v + k (S max (l) - 1 2
) +v (10) In the other case, where we presume that one of the spots in the observed pair corresponds to a marker on the line connecting the camera and the center of the UAV, the maxima and minima of the estimation can be expressed similarly:

l bmax = v cot arctan v l -d 2 -k (S max (l) - 1 2 ) + d 2 (11)
l bmin = v cot 2 arctan d 2 l -v + k (S max (l) - 1 2 ) + d 2 (12)

D. Full pose estimation

For a more precise position estimation of a neighbor UAV that is more suitable for 3D environments and returns orientation as well, we might consider using a Perspectiven-Point method. This may prove quite challenging in implementation, due to the anonymity of the observed points and due to the diminished visibility of the markers not facing the camera. Additionally, these methods are computationally more complex, which may reduce the output rate. One way to increase the number simutaneously of visible points is to increase the number of the LEDs on the UAV. This may be done in two possible ways:

1) by composing each marker out of multiple LEDs, as can be seen in figure 5-e 2) by adding more single-LED markers for denser coverage. Care should be taken with such a modification, since if the distribution of the markers is too dense then they will tend merging in the image into a single spot. The problem of anonymity can also be addressed this way, by constructing patterns that can be matched with a known template without ambiguity.

Another potentially effective approach under consideration is to encode information such as individual ID of a marker into blinking patterns.

V. EXPERIMENTS

A. Distance estimation based on spot size

To evaluate the relationship between the mutual distance and the size of the bright spot an Optitrack motion-capture system was used to record the ground-truth distance between the camera and a single LED in its view, while the size of the spot was being recorded simultaneously. This procedure was repeated for multiple exposure rates. The binarization threshold used for segmentation of the bright spots was set to 200 out of 255, or 78.42% of the saturated brightness (for the characteristics, see figure 10). These tests seem to indicate, that the best exposure rate for detecting whether the neighbors are within a reasonable distance with this setup is 1000 ms, when the spot shrank consistently to the size of a single pixel at 6.62 m while still sufficiently filtering out the ambient UV illumination. Therefore, a very simple and low-cost approach (only one camera and one LED is required) can be used for an effective collision avoidance as it provides sufficient safety distance. For example the safety distance used in Multi-robot Systems group in [START_REF] Loianno | Localization, grasping, and transportation of magnetic objects by a team of mavs in challenging desert like environments[END_REF] was 5 m. Within the range from 3.14 m to 6.62 m the occurence of spots with the size of 1 pixel become common. For distances smaller than 3.14 m the non-linear the characteristic can be used for a rough, but quantitative distance estimation in applications, where the UAVs have to operate within very close mutual distances. From the characteristic for the 1000 µs exposure rate (figure 11) we have derived the parameters of an approximating equation [START_REF] Zunino | Seeing the sound: A new multimodal imaging device for computer vision[END_REF] in the form of a quadratic-hyperbolic function rounded to the nearest integer.

S max = 1.3398 + 31.4704

(x -0.0154) 2 . (13)
A quadratic-hyperbolic function was selected because the number of saturated pixels from a single ray depends roughly on the overall energy that has been received by the sensor from the marker, which in turn is governed by the inverse square law.

A different exposure rate can be selected for tasks where closer or greater mutual distances are required (note the different single-pixel thresholds in figure 10 in applications where very tight formations of micro aerial vehicles are needed we can select short exposure rate to reach a higher precision in distance estimation at short distances, in addition to better selectivity w.r.t. other light sources.

If the margins used in a swarming algorithm are derived from the spot sizes, then we can expand or shrink a formation simply by changing the exposure rate. This can even be done dynamically based on the circumstances, altering the swarm parameters on-the-fly (for instance by changing the constants in a Boids model [START_REF] Saska | Swarms of Micro Aerial Vehicles Stabilized Under a Visual Relative Localization[END_REF] we can change the swarm size and thus adjust the working area).

Using a high exposition rate presents a trade-off, since it allows for detection and quantitative distance estimation in larger mutual distances, but has the side-effect of lower selectivity w.r.t. other light sources and thus lower robustness.

B. Bearing vector estimation precision

In order to verify the precision of the relative bearing vector estimation and the distance estimation based on the mutual distance of two spots in an image, we have equipped a hexarotor frame with an arm length of 0.4 m with UV light sources on the end of each arm. Precision and relia- Lines connecting the camera with the potentially visible markers were calculated from the ground truth poses of the camera and the hexarotor frame. Relative bearing vectors were estimated from the bright spots in the image. The bearing vectors and connecting lines were compared and the angles between the closest found matches were stored. Figure 12 shows, that the predicted maximal error in the estimation according to equation (3) holds.

C. Neighbor distance from mutual distance of points

In the same dataset as used previously, the pair of adjacent spots with the greatest mutual distance in the image was used as the basis for the distance estimation. The distance of the frame center from the camera was calculated both according to equation 5 and equation 6. The estimated distances compared to the ground truth obtained from the OptiTrack system can be seen in figure 13, together with plots of the predicted margins of error based on the previously obtained function S max (l). Note, that in the first case most estimates are greater than the ground-truth, while in the other case the opposite is true.

Figure 14 shows the relative errors in estimations in both cases.

Within the tested range the error increases roughly linearly with the distance. This is conforms to the expectations and is of no concern in forming a swarm, since the precision is only low outside of collision range.

The precision is decreased by the randomized angle of the observed pair of markers so that the results would be consistent with real-world situations.

For comparison, the precision listed in [START_REF] Faigl | Low-cost embedded system for relative localization in robotic swarms[END_REF] was measured in ideal laboratory conditions with all variables accounted for. In such unrealistic conditions our system will exhibit higher precision, due to the larger baseline.

D. Outdoor experiments of mutual localization of two UAVs

To verify the selectivity of the sensor, as well as the range and precision in an outdoor environment, which is the ground truth distance of the object (m) primary intended use-case, we have performed a flight with a pair of our outdoor UAV platforms. The platform itself is a DJI 550 frame, equipped with a Pixhawk controller an Intel NUC computer, described in detail in [START_REF] Loianno | Localization, grasping, and transportation of magnetic objects by a team of mavs in challenging desert like environments[END_REF]. The sensory equipment comprises a range sensor for altitude measurements, RTK-GNSS antenna for ground truth measurement, the UV camera described in this paper and a color camera for a conventional video recording. The target UAV was equipped with six ultraviolet LED markers as described above. The exposure rate of the camera was set to 1000 µs. The markers could still be detected at 15 m and after that there were spurious drop-offs. Compare the table III in [START_REF] Faigl | Low-cost embedded system for relative localization in robotic swarms[END_REF], where the maximum range is 5.5 m for the highest resolution. Indeed, since the camera FoV listed in the paper is only 42 • while our system uses a FoV of 180 • , our system can be meaningfully compared with their system being used with less than the smallest listed resolution, where the maximum range was only 3.2 m.

An example of the image obtained by the ultraviolet- The two estimates according to equations (5) -case A and ( 6) -case B tend to be greater and smaller than the ground truth respectively. The spurious pattern around 60 s and 110 s is the result of the observed UAV spinning in place, leading to the two equations rapidly exchanging their validity. sensitive camera can be seen in the figure 2. We have attempted to measure the precision of the ultraviolet markerbased localization by using the RTK-GNSS data inertial measurement unit and built-in compass as ground truth. As is shown in figures 15 and 16, the distance estimations according to equations ( 5) and (6 resulted in upper and lower margins, enclosing the ground truth. While the position retrieved by RTK-GNSS was sufficiently precise, the orientation estimate was burdened by a severe drift (see figure 17below), causing misalignment in the bearing vector returned by our UV sensor. This hints at an alternative application of our system as a precise orientation sensor if the position of two or more mutually unoccluded UAVs is known from RTK-GNSS data, since the observed relative bearing does not drift.

VI. CONCLUSION

In this paper we have proposed a novel system for outdoor and indoor mutual relative localization using ultraviolet LED makers. The main intended use-case of this method is in swarm control and stabilization of formations of light-weight helicopter UAVs in arbitrary environments. The proposed Fig. 17: Selected frames from the video output of the camera and visualization of the mutual state estimation procedure. The blue star and white square represent the ground truth of the observed UAV. The thick red line shows the range of possible positions computed by our system. This can be seen in a video found at http:// mrs.felk.cvut.cz/uvdd1. approach enables significantly higher detection range, robustness to light conditions and surrounding environment (background of images) in comparison with state-of-the-art methods, while having low computational intensity, small size and weight and providing sufficient precision. The error in the relative bearing vector towards a single ultraviolet marker is in operational distances below 0.02 rad in distances above 3 m, and thus allows direct applicability of the method using most of the current swarming and formation stabilization approaches. Two algorithms for estimating the mutual distance were developed to satisfy requirements of known multi-UAV stabilization techniques. The first relies on the size of the detected spot in the image, while the second is based on the diminishing apparent internal distance between a pair of retreating markers with known true mutual distance. The system was tested in outdoor environment and was shown to be robust with respect to outdoor lighting conditions as predicted. The theoretical predictions, as well as the experimental data presented here, show a lot of promise for deployment in swarm robotics.

Fig. 1 :

 1 Fig. 1: Examples of applications of mutual relative localization developed by our group. a) Cooperative carrying of large objects, b) simultaneous flight through forest-like environments using bioinspired swarming rules, c) mapping of historical buildings by a formation of camera-carrying UAV and spotlight-carrying UAVs to obtain footage with fixed illumination angle d) heterogeneous formation of self-stabilised UAV-UGV.

Fig. 5 :

 5 Fig. 5: Summary of the proposed system components. The UAV (a) is equipped by a mvBlueFOX-MLC200wG camera sensor (c) with DSL215 lens with BP365-R6 bandpass filter that allows it to observe and localize ultraviolet LED-based markers (d) or (e)

Fig. 6 :

 6 Fig. 6: Relative difference in sizes of spots generated by markers attached to quadrotor UAVs approximately 2 m (lower triplet) and 5 m (upper triplet) away from the camera.

Fig. 7 : 8 :

 78 Fig.7: Allignments of LED markers for a hexarotor, and a quadrotor. In the center layout, only a single marker would be visible from some directions, as opposed to the rightmost layout, with markers consisting of two LEDs at the mutual angle of 120 • .

Fig. 9 :

 9 Fig. 9: Schematic of the two borderline algnments of a hexarotor and the camera. With the camera in position CA, the observed pair is in perpendicular alignment w.r.t. the camera. In position CB the points are in the 30 • alignment w.r.t. the camera.

Fig. 10 :

 10 Fig. 10: Distance dependence of the bright spot size for multiple exposure rates. The vertical lines denote distances beyond which the spots are consistently reduced to a single pixel.

Fig. 11 :

 11 Fig.11:The spot size to distance characteristic for the exposure rate of 1000 µs. The green line denotes the distance where the spot becomes a single pixel. The magenta line denotes the shortest distance, where spots with the size of 1 px appear. The red curve is the approximating function of the maximum possible spot size.

Fig. 12 :

 12 Fig. 12: Angles between the estimated bearing vectors based on the image and the true bearing vectors. The red line denotes the expected maximal errors based on equation 3

Fig. 13 :

 13 Fig.13: The precision of estimation of the distance while presuming the orthogonal alignment (upper plot) and the 30 • alignment (lower plot) of the observed points.

Fig. 14 :

 14 Fig.14: Relative errors δ la and δ lb of the estimated distances in case of presuming the orthogonal alignment (upper plot) and the 30 • alignment (lower plot) respectively. The red line denotes predicted maximal relative error.

Fig. 15 :

 15 Fig.15: UAV distance estimates compared with the ground truth. The two estimates according to equations (5) -case A and (6) -case B tend to be greater and smaller than the ground truth respectively. The spurious pattern around 60 s and 110 s is the result of the observed UAV spinning in place, leading to the two equations rapidly exchanging their validity.

Fig. 16 :

 16 Fig.16: The same estimates as in figure15with the angle α expanded by k(S(l) -1 2 ).

  ). For example,

		100
	bright spot area (px)	20 60 80 40	2.12 m 2.12 m	3.23 m 3.23 m	5.06 m 5.06 m	6.62 m 6.62 m	8.34 m 8.34 m		100 µs 200 µs 500 µs 1000 µs 2000 µs 5000 µs 10000 µs	14.16 m 14.16 m
		0
		0	2.5	5		7.5	10	12.5	15
						distance (m)

http://optitrack.com/

https://www.vicon.com/motion-capture/engineering

https://cdn.shopify.com/s/files/1/0928/6900/ files/\\Datasheet\_BX305\_Kit\_433\_915\_EN\_0913. pdf

Preprint version, final version at http://ieeexplore.ieee.org/ 2

Preprint version, final version at http://ieeexplore.ieee.org/ 3 2018 IEEE ICUAS

https://www.matrix-vision.com/\\USB2. 0-single-board-camera-mvbluefox-mlc.html

http://www.optics-online.com/OOL/dsl/dsl215.pdf

http://midopt.com/filters/bp365/

http://datasheet.octopart.com/\\ PM2B-1LLE-Prolight-datasheet-41916849.pdf

https://sites.google.com/site/scarabotix/ ocamcalib-toolbox,[START_REF] Scaramuzza | Ocamcalib: Omnidirectional camera calibration toolbox for matlab[END_REF] Preprint version, final version at http://ieeexplore.ieee.org/ 4 2018 IEEE ICUAS

Preprint version, final version at http://ieeexplore.ieee.org/ 5

Preprint version, final version at http://ieeexplore.ieee.org/ 6 2018 IEEE ICUAS

Preprint version, final version at http://ieeexplore.ieee.org/ 7

Preprint version, final version at http://ieeexplore.ieee.org/ 8

Preprint version, final version at http://ieeexplore.ieee.org/ 9 2018 IEEE ICUAS

This research was partially supported by the ANR, Project ANR-17-CE33-0007 MuRoPhen and by CTU grant no. SGS17/187/OHK3/3T/13, the Grant Agency of the Czech Republic under grant no. 17-16900Y

3 https://mrs.felk.cvut.cz


Jean-Patrick Francoia

Jean-Christophe Rossi

Gerald Monard
email: gerald.monard@univ-lorraine.fr

Laurent Vial
email: laurent.vial@univ-lyon1.fr

Digitizing Poly-L-lysine Dendrigrafts: from Experimental Data to Molecular Dynamics Simulations

Despite of a growing use of the poly-L-lysine dendrigrafts in biomedical applications, a deeper understanding of the molecular level properties of these macromolecules is missing. Herein, we report a simple methodology for the construction of threedimensional structures of poly-L-lysine dendrigrafts, and the subsequent investigation of their structural features using microsecond molecular dynamics simulations. This methodology relies on the encoding of the polymers-experimental characterizations (i.e. composition, degrees of polymerization, branching ratios, charges) into alphanumeric strings that are readable by the Amber simulation package. Such an original approach opens avenues toward the in silico exploration of dendrigrafts and hyperbranched polymers.

Introduction

Dendrigrafts of poly-L-lysine (DGLs) recently complemented the family of polycationic dendritic macromolecules that include the prominent polyamidoamine (PAMAM) and polyethylenimine (PEI) polymers (Figure 1). [START_REF] Collet | An Expeditious Multigram-Scale Synthesis of Lysine Dendrigraft (DGL) Polymers by Aqueous N-Carboxyanhydride Polycondensation[END_REF] Because their iterative synthesis in aqueous conditions is thermodynamically controlled by precipitation and kinetically controlled by steric hindrance, DGLs share features with both PAMAM dendrimers (i.e. generation-based growth and narrow molecular weight distribution), and hyperbranched PEI (i.e. broad number of regioisomers and rapid increase in molecular weight per generation). In contrast to PAMAM and PEI, DGLs are biodegradable, 2 exhibit low cellular toxicities, [START_REF] Tang | Harnessing the PEG-Cleavable Strategy to Balance Cytotoxicity, Intracellular Release and the Therapeutic Effect of Dendrigraft Poly-L-Lysine for Cancer Gene Therapy[END_REF] and turned out to be non-immunogenic. [START_REF] Romestand | Dendrigraft Poly-L-Lysine: A Non-Immunogenic Synthetic Carrier for Antibody Production[END_REF] As a consequence, DGLs have recently gained a huge interest in the biomedical field during the last quinquennium, with numerous applications in drug and gene delivery, 2,3,5-18 biomaterials and tissue engineering, [START_REF] Kojima | Dendrigraft Polylysine Coated-poly(glycolic acid) Fibrous Scaffolds for Hippocampal Neurons[END_REF][START_REF] Lorion | Biosynthetic Support Based on Dendritic Poly-L-Lysine Improves Human Skin Fibroblasts Attachment[END_REF][START_REF] Eap | Nanofibers Implant Functionalized by Neural Growth Factor as a Strategy to Innervate a Bioengineered Tooth[END_REF][START_REF] Eap | Collagen Implants Equipped with 'Fish Scale'-like Nanoreservoirs of Growth Factors for Bone Regeneration[END_REF][START_REF] Cadiere | Assessment of Poly-L-Lysine Dendrigrafts for Virus Concentration in Water: Use of MS2 Bacteriophage as Proof of Concept[END_REF][START_REF] Mendoza-Palomares | Smart Hybrid Materials Equipped by Nanoreservoirs of Therapeutics[END_REF][START_REF] Fioretti | Nanostructured Assemblies for Dental Application[END_REF] bio-imaging [START_REF] Han | Tumor Cell Membranetargeting pH-dependent Electron Donor-Acceptor Fluorescence Systems with Low Background Signals[END_REF][START_REF] Li | A Choline Derivate-modified Nanoprobe for Glioma Diagnosis using MRI[END_REF][START_REF] Liu | Targeted Imaging of Activated Caspase-3 in the Central Nervous System by a Dual Functional Nano-Device[END_REF][START_REF] Huang | Chlorotoxin-modified Macromolecular Contrast Agent for MRI Tumor Diagnosis[END_REF][START_REF] Theodossiou | A Novel Mitotropic Oligolysine Nanocarrier: Targeted Delivery of Covalently Bound D-Luciferin to Cell Mitochondria[END_REF][START_REF] Kojima | Dendrimer-based MRI Contrast Agents: The Effects of PEGylation on Relaxivity and Pharmacokinetics[END_REF] and biosensing. [START_REF] Francoia | Monitoring Clinical Levels of Heparin in Human Blood Samples with an Indicator-Displacement Assay[END_REF][START_REF] Francoia | A KISS (keep it simple, sensor) Array for Glycosaminoglycans[END_REF][START_REF] Couturaud | Grafting of Poly-L-Lysine Dendrigrafts onto Polypropylene Surface Using Plasma Activation for ATP Immobilization -Nanomaterial for Potential Applications in Biotechnology[END_REF] Despite this growing use of DGLs, a deeper understanding of the molecular level properties of these macromolecules is missing. In this context, we decided to explore the possibility to construct DGLs in silico and subsequently perform molecular dynamics (MD) simulations.

Results and Discussion

Experimental Data

As DGLs are only made of L-lysine amino acids, one could assimilate them to proteins. However, some of the residues are linked to each other through isopeptidic bonds (i.e. amide linkages that involve the nitrogen atom of the lateral chain of lysine residues). From the data that were previousy collected in our group, [START_REF] Collet | An Expeditious Multigram-Scale Synthesis of Lysine Dendrigraft (DGL) Polymers by Aqueous N-Carboxyanhydride Polycondensation[END_REF] we extracted the degree of polymerization obtained from size exclusion chromatography (DP) and the mean branching ratio obtained from 1 H NMR spectroscopy (BR, defined as the ratio of the number of -branched Lysine residues over the total number of residues DP), which allowed us to calculate the number of peptidic and isopeptidic bonds, as well as the number of free α-and free -amine functions for each dendrigraft generation G1-G4 (Table 1). Also, determining the protonation state at physiological pH of each generation of DGL was obviously required in order to perform accurate modeling experiments. When a molecule bears several acidic functions, the protonation state of each of them influences the intrinsic acidity of the other ones, resulting in a shift of the functions' pKa. This phenomenon is called the polyelectrolyte effect. [START_REF] Koper | Proton Binding by Linear, Branched, and Hyperbranched Polyelectrolytes[END_REF] Moreover, these pKa are also influenced by several other parameters, such as the solvent exposition of the acidic functions, or their capacity to form hydrogen bonds. While the pKa of the α-amine in an isolated lysine residue is 9.16, the literature reports an average value of 7.7 for proteins' N-termini, with a low value of 6.8. [START_REF] Thurlkill | pK Values of the Ionizable Groups of Proteins[END_REF][START_REF] Pace | Protein Ionizable Groups: pK Values and their Contribution to Protein Stability and Solubility[END_REF] We performed pH-metric titrations on DGLs (with trifluoroacetate TFA as counterions) in deionized water. The samples were fully acidified with 0.5 mL of 1M nitric acid, and then submitted to incremental additions of 0.5M sodium hydroxide using a 702 SM Titrino automatic titrator. The resulting titration curves are shown in figure 2. One would expect the pH to be stable below 1 mL of added NaOH since it was the required volume to neutralize the amount of nitric acid used to acidify the samples. However all the titration curves displayed a "lack" of nitric acid. This gap could be explained by the fact that not all the amine functions were protonated in the commercial powders. 38 Thus, we made the hypothesis that a part of the nitric acid added in a first place was consumed by the protonation of these neutral amino groups. The second peaks of the derivatives allowed us to calculate the number of α-amino groups in the samples, except for DGLs G1 since the presence of a unique α-amino group did not result in a mesurable signal by potentiometry.

Due to the polyelectrolyte effect, the third peaks of the derivatives -corresponding to the pKa of the -amines -were barely visible. The deprotonation of these functions takes place on a wide range of pH, making it impossible to determine the number of -amines, which was therefore calculated from the ratio α (see table 1). The electroneutrality equation was then used to calculate the protonation fraction Θ (equation 1), where C a is the concentration of added acid, C b the concentration of added base, C T F A the missing concentration of TFA, C p the total concentration of amino groups, and C H + and C OH -the concentration of free H + and free OH -, respectively.

Θ = C a -C b -C T F A -C H + + C OH - C p (1)
Θ = C a -C b -C T F A -10 -pH + 10 -pKw 10 -pH C p (2)
Equation 1 could also be expressed as a function of the pH, leading to equation 2. Applied on the experimental titration data, equation 2 gave the protonation degree of DGLs G1-G4 at a physological pH of 7.8, which was selected since all the reported applications for DGLs are in the biomedical field (Table 2). It turned out that this percentage of non-protonated amine functions are in excellent agreement with the percentage of α-amine functions in the DGLs. This suggested that only the -amines were protonated at pH 7.8.

Encoding

From these experimental parameters, a manual approach toward an initial set of threedimensional (3D) structures for DGLs may suffer from several flaws: i) it is highly timeconsuming to manually edit starting structures that contain all atoms and residues with a correct naming in a coherent order, as well as no crossing nor bumping between the branches, ii) it is very much error-prone since the fourth-generation G4 consists of 365 residues, iii) it is likely to be biased toward an homogeneous distribution of the residues and unlikely to be representative of the experimental characteristics of the polymers. For these reasons, a new and automated method has been designed for the construction of 3D structures of DGLs. As a first step, the macromolecules G1-G4 have been deconvoluted into six discrete building blocks, which encompass all the possible arrangements (i.e. peptidic or isopeptidic bonds, charged or neutral nitrogen atoms) of the L-lysine residues within the dendrigrafts (Figure 3). Each building block was subsequently labeled with a one-letter code that unambiguously identifies it. DGL G1 could be written as the following alphanumeric string: ACCCCCCh (from C-terminal to N-terminal). It should be highlighted that DGLs were analogously synthetized in silico and at the bench, with the growth of the chains from C-terminal to the N-terminal using N -protected-L-lysine residues. Moving to a higher generation required the deprotection of the lysines-side chains, and elongation/branching/termination events from the free nitrogen atoms. [START_REF] Collet | An Expeditious Multigram-Scale Synthesis of Lysine Dendrigraft (DGL) Polymers by Aqueous N-Carboxyanhydride Polycondensation[END_REF] For the higher generation G2-G4, numbers have been introduced within the strings, which addressed the locations of the residues where branched chains were growing from (starting from the C-terminal amino acid). For instance, a possible representation of a G2 polymer using these molecular descriptors would be an alphanumeric string of 48 letters, and 6 discrete numbers (Figure 4, Top). As a result, these alphanumeric strings encoded not only the position of every L-Lysine residues in the macromolecules, but also their connections and protonation states (Figure 4, Bottom). The algorithm that built this sequence works as follows (Figure 5). Starting from a single monomer, the chain was elongated through the iterative formation of peptidic bonds until the DP (= 8) of DGL G1 was reached.

Then, 6 (= DP × BR) residues were randomly branched to G1 in order to respect the experimental number of isopeptidic bonds. A loop was subsequently used to randomly grow the polymer through peptidic bonds until the DP ( = 48) of DGL G2 was reached. Finally, the algorithm walked through the tree and translated it into the following alphanumeric string BCDCDDDDCCh8CCCCCh7CCCCCCCCCh6CCCCCh5CCCCh3CCCCh1CCCCh, which encodes one possible structure of DGL G2. Using this algorithm, a homemade python script 39 allowed us to generate eight random -but respecting the initial experimental parameters (i.e. DP, BR, and net charge) -sequences for each generation of DGL G2 to G4

(see ESI †). Within a set, each new generation of DGL was grown from the corresponding lower one.

The coded polymers could then be converted to candidate 3D structures by using a customized Nucleic Acid Builder (NAB) program [START_REF] Macke | Molecular Modeling of Nucleic Acids[END_REF] from the Amber simulation package. 39,[START_REF] Case | University of California[END_REF] To put it simply, each one-letter coded residue was sequentially read by the program (from C-terminal to N-terminal), translated to a three-letter equivalent in order to satisfy the PDB three-letter conventional naming of the residues required by AMBER preparatory tools (see Figure 3), converted to its corresponding 3D molecular building block, and finally added at the right position to the growing dendrigraft. Preparatory ab initio quantum mechanics calculations (Hartree-Fock method, at the 6-31G level) were performed in order to assign atomic partial charges for the six building blocks A-h by using the Antechamber module of the Amber simulation Package. After each addition, the positions of all current atoms were optimized using a short conjugated gradient minimization (cut-off of 15 Å, with a maximum of 100 iterations) in order to ensure that no bond or atom overlapping was caused.

Molecular Dynamics

We performed an investigation on the structural features of DGLs by using MD simulations on the full set of 3D structures of the dendrigrafts that were generated previously (1 structure for DGL G1, 8 structures for each upper generation, 25 polymers in total). All-atom classical MD simulations were run on NVIDIA graphics processing units and included the generalized Born solvation model, which previously proved to yield the best agreement between calculated and experimental structures for proteins. [START_REF] Nguyen | Folding Simulations for Proteins with Diverse Topologies Are Accessible in Days with a Physics-Based Force Field and Implicit Solvent[END_REF] Also, the method of hydrogen mass repartitioning was applied for further accelerating the simulations. [START_REF] Hopkins | Long-Time-Step Molecular Dynamics through Hydrogen Mass Repartitioning[END_REF] Using this setup, trajectories of 10 microseconds for first-and second-generation DGLs, and of 1 microsecond for third-and fourth-generation DGLs could be obtained within reasonable calculation time scales. The mean calculation times (with simulation times in parentheses) on NVIDIA K20 Via the Flory theory approach, we obtained the scaling relation Rg ∼ N 0.41 , where Rg is the radius of gyration and N the number of residues of the dendrigrafts. [START_REF] Flory | The Configuration of Real Polymer Chains[END_REF] The exponent of the power law lies in between the calculated values at physiological pH of 0.34 and 0.57 for poly-L-lysine dendrimers and linear poly-L-lysines, respectively. [START_REF] Falkovich | Are Structural Properties of Dendrimers Sensitive to the Symmetry of Branching? Computer Simulation of Lysine Dendrimers[END_REF][START_REF] Jin | Investigating the Influence of Phosphate Ions on Poly(L-lysine ) Conformations by Taylor Dispersion Analysis[END_REF][START_REF]The theoretical values of the Flory exponent are 0.33 and 0.59[END_REF] This suggests that the dendrigrafts adopt intermediate morphologies, which may remind those of unfolded and intrinsically disordered proteins. 48 This conformational flexibility was further supported by the 2D root-mean-square deviations of selected residues 49 (see ESI †) and the Ramachandran plots of all possible residues (data not shown) along the MD trajectories, from which it was clear that no folded structure was clearly identifiable for any of the 4 generations of dendrigraft G1-G4.

In order to assess the shape of the dendrigrafts, the asphericity parameter (∆) and shape parameter (S) can be evaluated from the inertial tensor 50 described in equation 3, where M is the total mass, m i and r i are the mass and position of the i th residue, and α, β = x, y, z.

T α,β = 1 2M 2 N N j m i m j (r iα -r jα )(r iβ -r jβ ) (3)
The squares of the three principal radii of gyration-R G -are calculated from the trace of the matrix-T (α, β), which amounts to the sum of its eigenvaluesλ 1 ,λ 2 andλ 3 (equation 4).

R 2 G = trT = 3 i=1 λ i (4)
These eigenvalues are used to calculate ∆, which measures the average deviation from spherical symmetry (equation 5).

∆ = 3 2 3 i=1 (λ i -λ) 2 (trT ) 2 (5)
Where

λ = 3 i=1 λ i 3 (6)
On the other hand, S further describes the ellipticities of the polymers. In three dimensions, S can be calculated from equation 7.

S = 27 3 i=1 (λ i -λ) (trT ) 3 (7)
When applied to our trajectories, these treatments gave almost null ∆ and S values (see ESI † for full set of values). While the theoretical lowest value of ∆ is zero (i.e. characterizing a sphere) and the highest value is one (i.e. characterizing a rod), the values of S are theoretically bounded following the inequality -1 4 ≤S≤ 2, with negative and positive values indicating oblate and prolate objects, respectively. When applied to our trajectories, the calculated values actually establish that our dendrigrafts are mostly globular, as they previously were represented in the literature (Table 3), with the exception of the first-generation G1 that slightly tends toward a disc-shaped rod due to its linear topology. Insights into the spatial occupancy of the macromolecules were gained by combining the atomic coordinates of each frame -captured every nanosecond for G1 and G2, and every 100 picoseconds for G3 and G4 -over the entire MD trajectory. The resulting volumetric maps showed that the DGLs tend to occupy a large amount of the available space as a result of the flexibility of their branches (Figure 6). Table 3: Averages and standard deviations of the asphericity (∆) and shape (S) parameters for first-to fourth-generation DGLs G1 to G4.

G1 G2 G3 G4

∆ 0.107 ± 0.034 0.029 ± 0.014 0.023 ± 0.007 0.008 ± 0.002 S -0.069 ± 0.032 -0.003 ± 0.006 -0.004 ± 0.003 -0.001 ± 0.001

Then, we plotted both the normalized atomic and cationic densities as a function of their distances from the center of mass of the polymers (Figure 7). 51 Such an analysis revealed that: i) the atomic density shifts from the core toward the outside of the dendrigrafts with increasing generation, and ii) the cationic charges are mainly found on the outer shell layer of the dendrigrafts. The distribution of the positive charges, as well as the bulk density of the dendrigrafts, can also be appreciated from snapshots taken after 1 µs of the trajectories (Figure 8). Finally, we measured the distance between all adjacent charged nitrogen atoms (NZ) using the pair correlation function (Figure 9). It turned out that all DGLsindependently to their generation -displayed adjacent NZ separated by a similar average distance of 8.0 Å (first peak of the curves). This latter observation relates to the synthetic route towards DGLs, 1 which implies a N -protected lysine derivative and therefore excludes an impact of the electrostatic repulsion on the ionizable nitrogen atoms' distribution. By being able to generate accurate 3D structures of four generations of poly-L-lysines dendrigrafts with respect to their experimental characteristics (i.e. composition, degrees of polymerization, branching ratios, number of charges at physiological pH), and to determine their molecular properties (i.e. topology, shape, flexibility), one should now be able to study at the molecular level their interactions with biologically relevant partners such as drugs, metabolites, biopolymers, genetic materials, proteins, or cells. These computational studies may not only provide important information to apprehend their unique features such as biocompatibility, [START_REF] Tang | Harnessing the PEG-Cleavable Strategy to Balance Cytotoxicity, Intracellular Release and the Therapeutic Effect of Dendrigraft Poly-L-Lysine for Cancer Gene Therapy[END_REF][START_REF] Romestand | Dendrigraft Poly-L-Lysine: A Non-Immunogenic Synthetic Carrier for Antibody Production[END_REF][START_REF] Hofman | In Vitro Transfection Mediated by Dendrigraft Poly-L-lysines: The Effect of Structure and Molecule Size[END_REF] membrane translocation ability, [START_REF] Hofman | In Vitro Transfection Mediated by Dendrigraft Poly-L-lysines: The Effect of Structure and Molecule Size[END_REF] and highly efficient electrostatic binding property, 32 but consequently also lead to the development of DGLs for real-world applications in nanomedicine.

Computational Details

Residues were prepared with the antechamber module of AmberTools. [START_REF] Case | University of California[END_REF] Atomic charges were generated from RESP charges extracted from HF/6-31G* optimized geometries of capped residues. Initial structures were built using the Nucleic Acid Builder (NAB) program [START_REF] Macke | Molecular Modeling of Nucleic Acids[END_REF] and the LEaP module of AmberTools. From the primary sequence of one dendrimer, new residues were added one by one and, at each new addition, a minimization of the full system was performed for 100 steps. All molecular dynamics simulations were carried out using the GPU implementation 53 of the pmemd program in Amber15 41 with the combination of GB-Neck2 model, 54 mbondi3 radii, [START_REF] Nguyen | Improved Generalized Born Solvent Model Parameters for Protein Simulations[END_REF] and ff14SB. [START_REF] Maier | Improving The Accuracy of Protein Side Chain and Backbone Parameters from ff99SB[END_REF] No cutoff was applied for computing the nonbonded interactions. A time step of 4 fs was used with hydrogen mass repartitioning. [START_REF] Hopkins | Long-Time-Step Molecular Dynamics through Hydrogen Mass Repartitioning[END_REF] Bonds involving hydrogen were constrained by the SHAKE algorithm. [START_REF] Ryckaert | Numerical Integration of the Cartesian[END_REF] Temperature was controlled with a Langevin thermostat at 300 K with a collision frequency γ = 1.0 ps -1 .

Conclusions

In conclusion, microsecond molecular dynamics simulations on second-to fourth-generation poly-L-lysine dendrigrafts revealed a myriad of conformational states accessible to them without folded states. This conformational plasticity (i.e. this ability to adaptably display positive charges to make ion pairs) may explain why DGLs are such efficient binders for anionic ligands even in the most competitive media. In addition, the generated structures can now be exploited for in-depth analyses of the interactions between these macromolecules and biologically relevant partners for future biomedical applications. More broadly, this work provides to the community a general approach toward the construction of dendrigrafts -but also hyperbranched polymers -in silico. We are therefore confident that molecular dynamics will become a pervasive tool to explore the structural features of large dendrigrafts and hyperbranched polymers at the molecular level.

Figure 1 :

 1 Figure 1: Schematic representation of the first-to fourth-generation DGLs G1-G4 (each dot represents a L-lysine residue, pending free amino groups are not represented).

Figure 2 :

 2 Figure 2: pH-metric titrations of DGLs G1-G4 in deionized water. Error bars are calculated from the standard deviation of each pH measurement.

Figure 3 :

 3 Figure 3: All possible L-Lysine buildings blocks A-h (and their corresponding three-letter codes in brackets) involved in the construction of DGLs G1-G4.

Figure 4 :

 4 Figure 4: The alphanumeric description of a second-generation dendrigraft G2 (Top), and the corresponding arrangement of the residues (Bottom). Residues in blue indicate the mother DGL G1. Peptidic and isopeptidic bonds are depicted as black line and grey lines, respectively.

Figure 5 :

 5 Figure 5: Flowchart toward the encoding of one possible strucure of DGL G2, which respects its experimental characteristics.

Figure 6 :

 6 Figure 6: Volumetric maps of first-to fourth-generation DGLs G1-G4 at 1 microsecond with 99% probability boundary surfaces. All images are to the same scale. Images were generated with VMD (ref. 52).

Figure 7 :

 7 Figure 7: Normalized atomic (in grey) and cationic (in blue) density profiles of first-to fourth-generation DGLs G1-G4 (ref. 51).

Figure 8 :

 8 Figure 8: Snapshots of the first-to fourth-generation DGLs G1 to G4 taken after 1 microsecond at T = 300 K. Blue dots highlight the positively charged nitrogen atoms at pH 7.8. All images are to the same scale.

Figure 9 :

 9 Figure 9: Radial Distribution Function (RDF) of the charged nitrogen atoms (NZ) for the first-to fourth-generation G1 to G4.

Table 1 :

 1 Selected properties of DGLs G1-G4. DP: degree of polymerization; BR: branching ratio.

	DGL DP BR	Free α-amino	Free -amino	Isopeptidic bonds Peptidic bonds
	(%)	groups	groups
	G1 8 0	1	8	0	7
	G2 48 12	7	42	6	41
	G3 123 24	31	93	30	92
	G4 365 23	85	281	84	280

Table 2 :

 2

	DGL Θ (%)	+ α	(%) Net charge
	G1 N/A	N/A	+7
	G2	86	86		+41
	G3	79	75		+92
	G4	79	78		+280

Protonation state of DGLs G1-G4 at pH 7.8. Θ: protonation fraction; : number of free -amino groups; α: number of free α-amino groups. We assumed that, as for DGLs G2-G4, only the -amino groups of DGL G1 were protonated.

  GPUs were 207.6 h (10 µs) for G1, 362.6 h (10 µs) for G2, 78.4 h (1 µs) for G3, and 432.2

h (1 µs) for G4. At this point, it should be noted that -albeit each dendrigraft within a same generation displays a unique topology -the analyses of the trajectories did not revealed divergent dynamic behaviours. As a consequence, the post-calculation analyses for only one dendrigraft per generation are shown in the manuscript (for the full set, see ESI †).

Acknowledgement

This work was supported by the Centre National de la Recherche Scientifique (CNRS), the Université de Lorraine, and the Université de Montpellier. GPU resources were allocated by the Centre de Calcul ROMEO of the Université de Reims Champagne-Ardenne. DGLs were supplied by the COLCOM company (Montpellier, France).

Supporting Information Available

The following files are available free of charge.

Alphanumeric strings, 2D root-mean-square deviations, asphericity and shape parameters, normalized atomic and cationic densities, radial distribution function, and volumetric maps of all polymers (PDF).

analyzed during the trajectories. The behavior of these amino acids within a polymer was considered to be representative of the whole macromolecule's behavior.