Catherine Lejeune
email: catherine.lejeune@u-bourgogne.fr.

Christine Binquet

Franck Bonnetain

Amel Mahboubi

Michal Abrahamowicz

Thierry Moreau

Maria Raikou

Laurent Bedenne

Catherine Quantin

Claire Bonithon-Kopp

ESTIMATING THE COST RELATED TO THE SURVEILLANCE OF COLORECTAL CANCER IN A FRENCH POPULATION

Keywords: economic evaluation, cost prediction, colorectal cancer, recurrence, surveillance JEL CODES: C1 -Econometric and Statistical

Little is known about costs related to the surveillance of patients that have undergone curative resection of colorectal cancer. The aim of this study was to calculate the observed surveillance costs for 385 patients followed-up over a 3-year period, to estimate surveillance costs if French guidelines are respected, and to identify the determinants related to surveillance costs to derive a global estimation for France, using a linear mixed model. The observed mean surveillance cost was € 713. If French recommendations were strictly applied, the estimated mean cost would vary between € 680 and € 1 069 according to the frequency of abdominal ultrasound. The predicted determinants of the cost were: age, recurrence, duration of surveillance since diagnosis, and adjuvant treatments. For France, the surveillance cost represented 4.4% of the cost of colorectal cancer management. The cost of surveillance should now be balanced with its effectiveness and compared with surveillance alternatives.

Introduction

Colorectal cancer is a major health problem. It is one of the most frequent cancers in both sexes in France with approximately 37,500 new cases in 2005 [START_REF] Bouvier | Mass screening for colorectal cancer in France[END_REF]. Data collected by the Burgundy Registry of Digestive Cancers in the administrative area of Côte d'Or between 1976 and 1995 indicate that about 80% of the patients undergo primary resection for cure.

Nonetheless, about 9% of these patients will develop a loco-regional recurrence, and 21% of patients will develop metastases following their initial surgical resection. Almost 80% of these recurrences will appear within the first three years after surgery [START_REF] Manfredi | Incidence and patterns of recurrence after resection for cure of colonic cancer in a well defined population[END_REF].

Current French guidelines for post-surgery management of colorectal cancer issued following the 1998 French Consensus Conference [START_REF] Bonithon-Kopp | Prevention, screening and management of the colonic cancers[END_REF] are:

• clinical examination every 3 months for the first 2 years, every 6 months for the next 3 years;

• abdominal ultrasound every 3 to 6 months for the first 3 years, then yearly for 2 years;

• chest x-ray yearly for 5 years;

• colonoscopy after three years, or, if the initial colonoscopy detected at least three adenomas with one >1 cm diameter or presenting a villous component, a colonoscopy performed after 1 year.

In contrast with economic burden associated with the diagnosis and the initial therapeutic management of colorectal cancer, little is known about the costs related to the long-term surveillance of this cancer and their possible variation depending on whether guidelines are respected or not. A recent study performed on a data set of the Burgundy Registry of Digestive Cancers revealed that adherence to French guidelines for surveillance was relatively poor with a large proportion of patients followed-up below the recommendations (47%), and smaller proportions followed-up either in respect of (24%) or above the guidelines (29%) [START_REF] Boulin | Patterns of surveillance practices after curative surgery for colorectal cancer in a French population[END_REF].

Therefore, due to the variability of surveillance patterns, there is uncertainty on the cost associated with surveillance practices. The possibility of a difference between the observed cost and the expected cost of surveillance if guidelines were respected can thus be questioned.

The estimation of surveillance cost is of great interest for the French health care insurance system, which reimburses, in a context of scare resources, all medical procedures performed during the surveillance period. Moreover, better knowledge of the cost of surveillance may contribute to the discussion between decision makers and the scientific community on the need to reconsider the content of guidelines, or if the diffusion of these guidelines should be improved.

Therefore, the aim of our population-based study was to determine the cost of surveillance patterns and to compare it with the expected cost of surveillance if French guidelines had been respected. The secondary objective was to identify cost determinants in order to derive a global estimation of surveillance costs for France, and determine what proportion of the total cost of colorectal cancer management is taken up by surveillance.

Materials and methods

Study population

This study included all patients living in two French administrative areas (Côte d'Or and Saône-et-Loire), with a total population of 1,631,100 according to the 2005 census, who were diagnosed with a first colorectal cancer between January and December 1998.

Inclusion criteria

All patients diagnosed with TNM I, II and III colorectal cancer which could be resected with curative intent were included. In addition, patients with curatively treated stage IV tumours with a surgically removed single liver metastasis were also eligible. Finally 473 patients matched these inclusion criteria.

Exclusion criteria

Patients with evidence of progressive second cancer (n=3), and patients followed for less than 6 months because of recurrence or death after initial surgery (n=63) were excluded. Twenty-two patients with incomplete information on the management of their surveillance were also excluded, leading to a final study population of 385 patients (Figure 1).

Data collection

Demographic and clinical data

Most initial data were extracted from the registry database. Demographic data included: age, gender, administrative area. Place of residence was also recorded: patients living in towns with more than 2,000 inhabitants were considered as urban residents. Those living in towns with less than 2,000 inhabitants were considered as rural residents. Tumours were characterized according to TNM stage (I, II, III, IV) and location (rectum, colon) defined according the International Classification of diseases, 9 th Revision. Clinical modifications (ICD-9-CM), and adjuvant treatment (radiotherapy, chemotherapy) were also extracted. The registry database did not provide any information on other clinical baseline data such as comorbidities defined by the Charlson index [START_REF] Charlson | A new method of classifying prognostic comorbidity in longitudinal studies: development and validation[END_REF], preoperative complications (occlusion and perforation), recurrence and date of recurrence of the primary tumour, and on surveillance procedures. We thus collected data from all of the physicians involved in the diagnosis and management of patients during the three first years after curative surgery. The names of surgeons, gastroenterologists, general practitioners were first identified from the registry database. Their medical records were systematically reviewed in order to collect information about surveillance procedures and to identify other physicians (oncologists or other specialists) involved in the surveillance of patients through correspondence and radiological, ultrasound, biological and endoscopic reports.

Data on geographical access to medical care were also recorded. These data referred to the distance that a patient had to travel from his/her place of residence to consult a general practitioner or a gastroenterologist. Distances are expressed in kilometres. Calculations were computed using 'Michelin road network tables' [START_REF]Michelin road network tables[END_REF]. When a patient's medical record contained no names of general practitioners or gastroenterologists, a theoretical distance was computed from the patient's residence to the nearest general practitioner and gastroenterologist (distance was zero when there was a practice in the patient's town). The decision to include distance to the general practitioner and gastroenterologist was justified by the fact that these doctors performed most of the routine clinical examinations for surveillance [START_REF] Coriat | How do gastroenterologists follow patients with colorectal cancer after curative surgical resection? A three-year population-based study[END_REF].

Surveillance data

The medical records from the physicians were systematically searched for information on all surveillance procedures recommended by the 1998 French Consensus Conference for management after curative colic surgery [START_REF] Bonithon-Kopp | Prevention, screening and management of the colonic cancers[END_REF]. These surveillance procedures were: clinical examination, abdominal ultrasound, chest x-ray, and colonoscopy. All other surveillance tests were also recorded: tumour markers such as carcinoembryonic antigen (CEA) and cancer antigen 19-9 (CA19-9), other blood tests (cell blood count, liver enzymes, gammaglutamyltranspeptidase, bilibirubin, lactate dehydrogenase, alcaline phosphatase, glutamic-oxaloacetic transaminase, ionogram and creatinine), and other radiographic or endoscopic examinations such as computed tomography, magnetic resonance imaging, scintigraphy and endorectal ultrasonography.

For each patient, all of the surveillance procedures were collected for every quarter (i.e. every 3 months) during the period related to the surveillance. The surveillance period started at the date of curative surgery and ended at the date of the procedure showing the first sign of recurrence, or at the end of the 3-year surveillance period if no recurrence occurred.

Economic analysis

Economic data

The economic analysis was performed from the French national health insurance perspective.

Only direct medical costs, expressed in Euros (€) were included. Reimbursement prices were used as a proxy of costs. These prices were obtained from three fixed-price scales commonly used in France. Until 2005, the only way to calculate the cost of examinations reimbursed by the French national health insurance system was to use the "Nomenclature Générale des Actes Professionnels" (NGAP), and the "Nomenclature des Actes de Biologie Médicale" (NABM), two price scales of medical and biological procedures. In 2005, a new price scale was introduced: the "Classification Commune des Actes Médicaux" (CCAM), which should take the place of the NGAP and NABM. At the moment however, three scales are used simultaneously.

In this study, the most recent versions of the NGAP, NABM and CCAM were used, the NGAP for the year 2005 to estimate the cost of clinical examinations, the NABM for the year 2005 to estimate the cost of tumour markers, and the CCAM for the year 2007 to estimate the cost of all radiographic and endoscopic examinations. All reimbursement prices used in the cost analysis are given in Table 1. The cost of biological tests was not taken into account in the analysis because 75% of this cost was found among patients treated by chemotherapy. Thus it was assumed that it was related to the specific follow-up of chemotherapy patients, and could therefore not be included in surveillance costs related to colorectal cancer.

Observed costs

Observed surveillance costs were calculated by summing up, quarter by quarter, the costs of all of the recorded medical procedures performed (consultations, radiographic and endoscopic examinations, and tumour markers).

Expected costs of surveillance according to the French guidelines

The expected surveillance costs were estimated for each patient, quarter by quarter, taking into account the duration of the surveillance period and the French Conference Consensus guidelines (medical procedures recommended and intervals between medical procedures). First, the expected number of clinical examinations, abdominal ultrasounds, chest x-rays, and colonoscopies as recommended by the Conference Consensus was estimated for each patient according to the duration of the surveillance (until recurrence or until the end of the three-year surveillance period if no recurrence was detected). Then the expected cost of surveillance was calculated using the NGAP, NABM and CCAM for each patient and for each quarter of their surveillance period. Because abdominal ultrasound could be performed either every 3 or every 6 months according to the French guidelines, two expected surveillance costs were estimated. The first corresponded to the situation where abdominal ultrasound was performed every 3 months; the second corresponded to the situation where abdominal ultrasound was performed every 6 months.

Discounting was not be applied because observed surveillance costs and expected surveillance costs were estimated over the same period of time, ie 3 years.

Statistical analysis

The z-test was used to determine the statistical difference between the observed surveillance cost and the two estimated surveillance costs. The difference between surveillance costs was considered significant when the p value was lower than 0.05.

In order to identify independent determinants of the observed surveillance cost, a multivariable linear mixed model analysis of variance for repeated data was used [START_REF] Laird | Random-effects models for longitudinal data[END_REF]. The cost related to the surveillance, log-transformed to reduce its skewness, was used as the dependent variable.

Variables introduced into the model were: the quarter, defined as a time variable from 1 to 12 and assumed to have a linear effect on the cost; recurrence categorised into three categories: absence of recurrence, recurrence detected during a medical visit for symptoms, recurrence detected during a routine medical visit; age categorised as: <65, 65-74, ≥75; gender; administrative area (Saône-et-Loire, Côte d'Or); urban or rural area of residence; tumour location (rectum, colon); TNM stage at diagnosis (I, II, III+IV), preoperative complications (No, Yes), comorbidities (No,Yes); adjuvant chemotherapy (No, Yes); adjuvant radiotherapy (No, Yes), distance to general practitioner (0 kilometers, > 0 kilometers) and distance to the gastroenterologist (<15 kilometers, ≥ 15 kilometers). A coefficient above 0 for a given dummy indicator meant that the surveillance cost was higher for a subgroup compared to the reference subgroup.

In the multivariable linear mixed model analysis of variance for repeated data, we stipulated Y i as the n i dimensional cost vector for subject i, 1≤i≤N, N being the number of subjects.

Therefore the linear mixed-effects model with serial correlation could be written as: X i and Z i were (n i x p) and (n i x q) known design matrices, β was the p-dimensional vector containing the fixed effects and b i ~ N(0,D) was the q-dimensional vector containing the random effects. ε i ~N(0, σ 2 In i ) was a n i -dimensional vector of measurement error components  . Serial correlation was captured by using a Gaussian stochastic process, W i , which is assumed to follow an N(0, τ 2 H i ) law. The serial covariance matrix Hi only depends on i through the number ni of observations and through the time points t ij at which measurements are taken. The fixed-effects parameters captured the influence of explanatory variables on the mean structure, exactly as in the standard linear model. However, the occurrence of random effects and a structured covariance matrix distinguished the linear mixed model from the standard linear model by taking into account repeated measurements of the same experimental unit, with spatially correlated data. Part of the covariance structure arises from so-called ''random effects'' (i.e., additional covariate effects with random parameters). These are effects that arise from the characteristics of individual subjects. A compound symmetry covariance structure and an autoregressive variance structure were tested. The choice of the covariance structure was based on the Akaike information criteria.

The analysis was conducted using SAS package version 9.1.

Model validation

The model was validated by comparing the observed average cost per patient to the predicted average surveillance cost for nine hypothetical patient profiles with different age (<65, 65-74, ≥75), and TNM stage of the tumour (I, II, III+IV). The "smearing estimator" developed by Duan, et al, was used to back-transform the log of cost in order to allow cost predictions [START_REF] Duan | Smearing estimate: A nonparametric retransformation method[END_REF].

Stratification of the surveillance cost according to the age and the TNM stage distribution was justified by the fact that stage is known to be a major prognostic factor. Moreover, age and stage are two basic parameters characterizing the clinical status of the patient at the time of diagnosis and may strongly influence the intensity of surveillance.

Results

Sample characteristics

Overall, 385 patients were included in this study. Among them, 98 (25%) presented a recurrence before the end of the 3-year period. The remaining 287 patients were followed until the end of the 3-year period. (Table 2). Characteristics of the study population are detailed in Table 3. The mean age was 70.4 years (standard deviation 11.3 years). Sixty-three percent of patients were living in a rural area (n=242). The tumour was located in the colon for 255 patients (66%). Only 17% patients were diagnosed with stage I cancer (n=65). Most of the patients had neither comorbidities (n=273), nor preoperative complications (n=344).

Adjuvant chemotherapy and radiotherapy was given to 105 (27%) and 58 (15%) patients respectively.

Observed and expected cost of surveillance

Observed cost

The total observed cost of the 3 years of surveillance was € 274,421 for the 385 patients included in the study (Table 4). The average cost per patient was thus € 713. Eighty-six percent of the total surveillance cost was associated with medical procedures recommended by French guidelines (€ 235,976). The cost of recommended procedures was mostly composed of clinical consultations and abdominal ultrasounds. Fourteen percent of the total cost of the 3 years of surveillance was associated with medical procedures that were not recommended by French guidelines (€ 38,445), mainly analyses for tumour markers.

Expected cost

The two expected costs of the surveillance period were estimated according to intervals for abdominal ultrasound recommended by French guidelines. They were compared to the observed surveillance cost (table 5). Results showed that the observed surveillance cost was close to the expected cost if abdominal ultrasound was performed every 6 months (respectively € 713 and € 680 on average per patient (p=0.04)). If abdominal ultrasound was performed every 3 months, the expected cost was clearly higher than the observed cost (respectively € 713 and € 1,069 on average per patient (p<0.001)).

Independent factors associated with the observed cost of 3 years of surveillance

The model was finally based on an autoregressive structure. Results of the multivariable analysis are shown in Table 6. After adjusting for the other covariates, adjuvant treatments, age, recurrence, and quarter were found to be significant determinants of surveillance costs.

Both chemotherapy and radiotherapy were associated with higher surveillance costs compared to the absence of adjuvant treatment (p<0.0001 and p=0.03 respectively) even after adjustment for stage at diagnosis and after exclusion of costs of biological tests, which were assumed to be related to specific post-chemotherapy follow-up. Patients whose recurrence was detected during either a medical visit due to symptoms or during routine medical visit, were found to have a higher mean surveillance cost than patients with no recurrence during the 3-year period (p=0.005 and p<0.0001 respectively). Age was also related to surveillance costs: patients aged over 75 years had a lower cost than patients less than 65 years (p=0.007). Time since diagnosis was also found to be a determinant of surveillance costs. The longer the surveillance period, the lower the mean surveillance cost (p<0.0001).

Validation of the model

The model was validated by comparing the average observed surveillance cost to the average predicted surveillance cost for patients with colorectal cancer, alternative combinations of age category (<65, 65-74, ≥75) and stage at diagnosis (I, II, III+IV). Comparisons between predicted costs and observed costs are illustrated in Figure 2. This comparison is represented by the difference between observed and predicted cost quarter by quarter over the 3-year period related to the surveillance. Globally, predicted and observed costs are relatively concordant, even though a greater difference can be noticed among patients with stage III or IV cancer and those younger than 65 years. Patients younger than 65 years had predicted surveillance costs of € 642, € 1,140 and € 2,646, respectively, depending on the stage (I, II, III+IV). The corresponding observed costs were € 617, € 883 and € 996, respectively. For patients aged 65-74, average predicted costs were € 523, € 921 and € 1,574 respectively, while the observed costs were € 568, € 774 and € 847. For patients over 75 years old, predicted costs were € 489, € 604 and € 867, versus mean observed costs of € 660, € 526 and € 606, respectively.

Estimation of the economic burden of colorectal cancer surveillance in France

In order to assess surveillance costs in France, average age-and TNM stage-specific costs predicted by the linear mixed model were applied to the 36,000 new cases of colorectal cancer diagnosed in France in 2000 [START_REF] Remontet | Cancer incidence and mortality in France over the period 1978-2000[END_REF]. The distribution of these 36,000 colorectal cancers according to age and TNM stage at diagnosis was estimated using data from the Association of French Cancer Registries (Francim network), which covers 12 areas in France and provides French national estimations of cancer incidence and mortality from data of all French cancer registries [START_REF]Francim network[END_REF]. As indicated in Table 7, the cost of surveillance in France was estimated to be € 42,357,068. To assess the economic burden of colorectal cancer surveillance in France, the surveillance cost was related to the total cost of treatment for colorectal cancer in France, estimated from the 36,000 new cases diagnosed in 2000, and the average costs of treatment of colorectal cancer per patient according to TNM stage, estimated with the database of the Burgundy Cancer Registry [START_REF] Clerc | Cost of care of colorectal cancers according to health care patterns and stage at diagnosis in France[END_REF]. The cost of treatment of colorectal cancer in France was estimated at € 930,828,696. Therefore, the estimated cost of surveillance in France accounts for 4.4% of the total management cost for colorectal cancer (i.e. treatment cost and surveillance).

Discussion

The first originality of this work lied in the estimation of the economic burden of observed surveillance practices compared to recommended surveillance guidelines. The study showed that the observed surveillance cost was near to the lowest boundary of the expected surveillance cost if French guidelines were respected. This result can be explained by the fact that almost two thirds of patients underused or respected the guidelines [START_REF] Boulin | Patterns of surveillance practices after curative surgery for colorectal cancer in a French population[END_REF] As far as we know, most of previously published international studies on the topic of colorectal cancer surveillance only assessed adherence to recommended guidelines. These studies showed that most of the time recommendations were not strictly followed, and suggested either that the content of existing guidelines be reconsidered or that practitioner should receive further training [START_REF] Elston Lafata | Routine surveillance care after cancer treatment with curative intent[END_REF][START_REF] Giordano | Strategies of follow-up for colorectal cancer: a survey of the American Society of Colon and Rectal Surgeons[END_REF][START_REF] Grossmann | Results of a national survey among Dutch surgeons treating patients with colorectal carcinoma. Current opinion about follow-up, treatment of metastasis, and reasons to revise follow-up practice[END_REF][START_REF] Cheung | Adherence to surveillance guidelines after curative resection for stage II/III colorectal cancer[END_REF][START_REF] Cooper | Receipt of guideline-recommended follow-up in older colorectal cancer survivors : a population-based analysis[END_REF][START_REF] Harewood | Assessment of adherence to published surveillance guidelines--opportunity to enhance efficiency of endoscopic practice[END_REF][START_REF] Mulder | A nationwide survey evaluating adherence to guidelines for follow-up after polypectomy or treatment for colorectal cancer[END_REF][START_REF] Spratlin | Community compliance with carcinoembryonic antigen: follow-up of patients with colorectal cancer[END_REF]. However, none of them compared the observed cost of surveillance with the expected costs if guidelines had been respected. To our knowledge, the only study that could be really compared to our work is French. This study estimated the cost of a surveillance period following curative resection for colorectal cancer using data from the Herault Tumor Registry [START_REF] Borie | Surveillance du cancer colorectal opéré à visée curative dans le département de l'Hérault : Etude médico-économique[END_REF][START_REF] Borie | Cost and effectiveness of follow-up examinations in patients with colorectal cancer resected for cure in a French population-based study[END_REF]. Their results showed that the cost of the examinations not recommended by the Consensus Conference accounted for 30% of the total observed surveillance expenditures. The average cost per patient was estimated to be € 843 over a 5-year period. Our study showed some different results: the cost of nonrecommended surveillance procedures accounted for 14% of the total cost of surveillance, and the average cost per patient was estimated to be € 713. This difference can be explained by the choice of the surveillance period (5 years versus 3 years in our study). The choice of a 3-year period in our study was justified by the fact that 80% of recurrences appear within the first three years after surgery [START_REF] Manfredi | Incidence and patterns of recurrence after resection for cure of colonic cancer in a well defined population[END_REF]. The difference can also be explained by the exclusion of the costs of biological tests from the calculation of the observed surveillance cost. We estimated that three-quarters of the cost of biological tests was related to patients treated with chemotherapy. Therefore this cost could not really be considered as the cost related to the surveillance of colorectal cancer after curative surgery. One last explanation could be that our study was performed after the Consensus Conference whereas the Herault' study was performed before. Indeed, patients included in the Herault' study underwent a potentially curative resection of colorectal cancer in 1992.

Another original contribution of our work was the identification of the determinants of costs using a mixed model analysis of variance for repeated measurements. This model is known to manage repeated data. It was appropriate for our study because the history of individual costs was available at each quarter of the 3-year period. The other main advantage of the model is to allow meaningful interpretation of coefficients. This is not the case for other methods such as the Cox model [START_REF] Cox | Regression models and life tables[END_REF]. The Cox model requires no specific assumptions on the distribution of costs and allows cost-to-event to be taken into-account. However, hazard ratios provided by the Cox model are difficult to interpret in practice when applied to costs. Our model was validated by comparing the observed and the expected cost of profiles of patients differing by their age and the TNM stage at diagnosis of their colorectal tumour. The results showed a relatively close concordance, except for the youngest patients and those with stage III or IV cancer. This could be explained by the small size of these groups of patients.

The model showed that surveillance costs were higher among patients treated with chemotherapy or radiotherapy than among patients without adjuvant treatment. These results could suggest that patients undergoing adjuvant treatment are followed more closely than patients without adjuvant treatment, even after exclusion of costs of biological tests performed during the surveillance period. Certain sociological and psychological factors may also influence the intensity of follow-up. Another important result was the influence of age on surveillance costs. A more advanced age (i.e patients over 74) was associated with a lower surveillance cost than that for younger patients. Low costs can be due to either quantitative factors (smaller number of consultations and radiographic and endoscopic examinations), and/or monetary factors (low cost examinations). A previous analysis on the same population comes in support of the finding in our study, and showed that inclusion in the intensive follow-up pattern rather than in the minimal follow-up pattern was independently predicted by age < 65 years, advanced tumour stage, chemotherapy and, with a borderline significance level, by radiation therapy [START_REF] Boulin | Patterns of surveillance practices after curative surgery for colorectal cancer in a French population[END_REF].

One last original contribution of our study was to use determinants of the costs in order to derive a global estimation of surveillance costs for France as a whole. We showed that surveillance costs represented less than 5% of the total cost of colorectal cancer management.

Although we can not rule out possible variations in surveillance costs across geographical areas, we have reasons to believe that our cost estimation is relevant for the whole of France, even though registry data set covers only two geographical areas. This estimation was based on an unselected population from two districts that may be considered representative of France as a whole because their colorectal cancer incidence and mortality rates, as well as their public and private cancer care facilities are comparable to the national average.

Moreover, age and TNM stage distribution of cancer cases were close to those observed in all

French districts covered by the Association of French cancer registries [START_REF]Francim network[END_REF], which covers about 16% of the French population. Our global estimation, however, could be criticized because it was based on two parameters only: the age and TNM stage distribution. Even though they can be considered major parameters to characterize the status of the patient at the time of diagnosis, other variables such as tumour location or adjuvant treatment could have been included. This work can be considered as a cost-of-illness study. This approach has often been criticized because the only information it provides is a global cost and an average cost per patient associated with a health care strategy [START_REF] Byford | Economic note: cost of illness studies[END_REF]. Therefore, despite the originality of the topic, our results are not sufficient to suggest reconsidering the content of French guidelines.

In this context, a cost-effectiveness analysis comparing a conventional surveillance program as recommended by French guidelines with an intensive surveillance program based on the use of computed tomography, abdominal ultrasound and colonoscopy as suggested by the American Society of Clinical Oncology in 2005 [START_REF] Desch | Colorectal cancer surveillance: 2005 update of an American Society of Clinical Oncology practice guideline[END_REF] could be of interest and help in decision making. As far as we know, no cost-effectiveness analysis has been undertaken in the French context yet. Our work could provide a framework by providing economic data required by such an analysis.

In conclusion, this population-based study showed that despite imperfect adherence to French guidelines, surveillance cost accounted for a small part of the total cost of management of colorectal cancer. Moreover surveillance costs were close to the expected costs if guidelines had been respected. The decision to reconsider the content of guidelines now depends on either new medical evidence, or medico-economic information. a Reimbursement prices were used as a proxy of costs b SD = standard deviation ; c a p-value lower than 5% showed significant results.

  These patients were identified by the Burgundy Registry of Digestive Cancer which has recorded all digestive tract cancers occurring in Côte d'Or and Saône-et-Loire since 1976. Cancers were classified according to the TNM classification, T indicating the size or direct extent of the primary tumour, N indicating the degree of spread to regional lymph nodes and M indicating the presence of metastases. TNM stages I, II, III and IV correspond respectively to stages 1 to 4 of the Dukes classification [25].

Figure 1 .a

 1 Figure 1. Flow chart

Figure 2 .

 2 Figure 2. Difference between predicted and observed surveillance costs quarter by quarter over the

Table 2 .

 2 Vital status of the study population during the 3-year surveillance period (n=385)

	Status

Table 3 .

 3 Initial characteristics of the study population (n=385)

	Characteristic

Table 3

 3 (continuation). Initial characteristics of the study population (n=385)

	TNM stage at diagnosis
	I	65	17%
	II	204	53%
	III + IV	116	30%
	Preoperative complications
	No	344	89%
	Yes	41	11%
	Comorbidities
	None	273	71%
	At least one	112	29%
	Adjuvant chemotherapy
	No	280	73%
	Yes	105	27%
	Radiotherapy
	No	327	85%
	Yes	58	15%
	Distance to the general practitioner
	0 kilometers	244	63%
	> 0 kilometers	141	37%
	Distance to the gastroenterologist
	< 15 kilometers	208	54%
	≥ 15 kilometers	177	46%

Table 4 .

 4 Cost a of recommended and non recommended medical procedures performed during

	the surveillance period (n=385)
	Procedures	Observed total	Relative cost of
		cost (€)	medical procedures
	Recommended procedures
	Clinical examination	92,878	39%
	General Practitioner	36,620	35%
	Specialist b	56 258	65%
	Abdominal ultrasound	91,382	39%
	Chest X-ray	14,939	6%
	Colonoscopy	36,778	16%
	Total cost of recommended procedures	235,976	86%
	Non recommended procedures
	CT scans	10,709	17%
	MRI	918	1%
	Scintigraphy	773	1%
	Endorectal ultrasound	1,930	3%
	Carcinoembryonic antigen (CEA)	16,348	25%
	Cancer antigen 19-9 (CA19-9)	7,768	12%
	Total cost of non recommended procedures	38,445	14%
	Total surveillance cost	274,421
	Average surveillance cost	713
	per patient

a Reimbursement prices were used as a proxy of costs b Specialist included gastroenterologists, oncologists, surgeons and other specialists

Table 5 .

 5 Estimation of the total expected surveillance cost a if French guidelines are respected

		Observed cost related to	Expected cost related to the surveillance (€)
		the surveillance (€)
			6-months abdominal ultrasound	3-months abdominal ultrasound
	Recommended procedures
	Clinical consultations	92,878	76,521
	Abdominal ultrasound	91,382	146,286	296,125
	Chest X-ray	14,939	19,876
	Colonoscopy	36,778	19,134
	Non recommended procedures	38,445	-	-
	Total surveillance cost	274,421	261,817 (p=0.04) b	411,656 (p<0.001) b
	Average surveillance cost	713	680	1,069
	a Reimbursement prices were used as a proxy of costs
	b Comparison between the observed surveillance cost and the estimated surveillance cost was performed using a z-test at a significance level of
	0.05.

Table 6 .

 6 Independent predictors of the observed surveillance cost a . Multivariate analysis.

	Coeff	SD b	p-value c

Table 7 .

 7 Estimation of surveillance costs a of colorectal cancer in France over a 3-year period according to age and TNM stage Reimbursement prices were used as a proxy of costs b Francim data (The Association of the French Cancer Registries)

		Age-and stage-specific	Distribution of the 36 000 new	Predicted surveillance cost per	Annual surveillance cost
		distribution of colorectal	cases of colorectal cancers in	patient according to age and	in France
		cancers in 12 areas in	France according to age-and stage	stage	(36 000 colorectal
		France b	for the year 2000	(mixed model)	cancers)
	Stage I
	< 65 years	6.4%	2 312	642 €	1 484 110 €
	65-74 years	6.7%	2 424	523 €	1 267 835 €
	> 74 years	6.3%	2 274	489 €	1 112 089 €
	Stage II
	< 65 years	7.7%	2 787	1 140 €	3 176 647 €
	65-74 years	9.1%	3 261	921 €	3 003 720 €
	> 74 years	12.3%	4 423	604 €	2 671 772 €
	Stage III + IV
	< 65 years	14%	5 198	2 646 €	13 754 424 €
	65-74 years	17%	6 135	1 574 €	9 657 072 €
	> 74 years	20%	7 185	867 €	6 229 400 €
	Total	100%	36 000	-	42 357 068 €

a

Acknowledgments:

The authors would like to thank: Dr F.Sassi (London School of Economics) for his methodological help ; N.Thomas, E.Couturier, D.Carel, E.Naudet, and E.Monnet for providing data on geographic access to medical care.

Funding: This work has been funded by a SNFGE grants (Société Nationale Française de Gastroentérologie).

Conflict of interest: none


The Errors in Russian Agreement and Case Government made by French-speaking Students Ekaterina Uetova Independent Scholar, Moscow, Russia st u dy 1 st u dy 2 the acquisition of Russian agreement and government, we conducted studies: 1. the study of the errors in agreement case government in Russian. 2. of errors in the endings of nouns taking into account the correct forms. Moreover, we compare errors made by French students with errors of Russian-speaking monolingual children.

b st r ac t

The working corpus includes aged 17 to 26. This corpus is collected the Russian Learner (RLC, http://www.web-corpora.net/RLC/).

CO R P U S

Though study relies on the RLC's error annotation we modified for and comfortable analysis of data.

N N OTATI O N

We would like to thank the National University Higher School of Economics (Moscow, Russia) and the University Cote d'Azur -CNRS (Nice, France) for their permanent support in our research.

Ac k n l e d g e m e ts

During work, we have a lot of questions and for further research. Firstly, it would be interesting to mark up a larger corpus of texts and to conduct a full-fledged of balanced corpora equally distributed by levels of proficiency in in order to be able to find trends in the acquisition of Russian a foreign language conduct statistical analysis of the influence of various factors on language acquisition. Secondly, we would like to look at the number of correct forms and incorrect ones in larger corpus. For example, to find whether there actually more words of the first declension of the feminine than the masculine in the corpus. Thirdly, it is necessary to mark up errors for their sources (interference, the influence of context, etc.) and by the semantics of to see with which verbs, in constructions students most often make mistakes. would allow us to obtain more accurate data that would show trends in the of the Russian language by Francophone students at various levels.

F u t u r e P l a n

1. There are fewer errors in agreement than in government. 2. are errors in gender and number than in case person .

3. Errors person are made only at the A1 level . 4. Errors in gender are more often made adjectives, and in number case in nouns .

5. Students in more than half of the . 6. Students often confuse the accusative and locative in constructions of direction place . 7. Students' case errors, as in case of Russian monolingual children, are caused by an incorrectly chosen gender or declension of noun.

8. The distribution of correct forms becomes similar to the distribution from The Russian National Corpus.

9. The number of in cases is decreasing. 10. The dative is the most case for our experimental group. This is probably due to the that it used often and therefore is not practiced in the classroom. Chart 1. of errors by type of agreement.

Chart Distribution of errors in government with preposition.

Chart 2. Distribution in government without preposition.

  CO N C L U S I O N Chart 4. Distribution of the correct use cases and errors. PF -incorrectly used nominative -incorrect (not nominative) Correct -correct case 5. Distribution of errors in each case (the proportion of incorrectly used cases all uses).


Mohamed Djeha
email: mohamed.djeha@lirmm.fr

Antonin Dallard

Ahmed Zermane

Pierre Gergondet

Fellow, IEEE Abderrahmane Kheddar

Human-Robot Handovers using Task-Space Quadratic Programming

Bidirectional object handover between a human and a robot enables an important functionality skill in robotic human-centered manufacturing or services. The problem in achieving this skill lies in the capacity of any solution to deal with three important aspects: (i) synchronized timing for the handing over phases; (ii) the handling of object pose constraints; and (iii) understanding the haptic exchanging to seamlessly achieve some steps of the (i). We propose a new approach for (i) and (ii) consisting in explicitly formulating the handover process as constraints in a task-space quadratic programming control framework to achieve implicit time and trajectory encounters. Our method is implemented on Panda robotic arm taking objects from a human operator.

I. INTRODUCTION

Human-centered robotics trends aim at close contact interactions in different areas: hospitals, industry, malls, homes, restaurants, etc. This cohabitation implies a large taxonomy of human-robot interactions. Among the most challenging one, seamlessly exchanging objects between a human and robot as giver and receiver agents through (bi-directional) handovers. Indeed, handing objects between humans is a very frequent daily form of interaction in almost all domains [START_REF] Ortenzi | Object handovers: A review for robotics[END_REF]. Therefore, embedding human-centered robotic systems in automation and services with handovers capabilities, is a key enabler for rich cognitive interaction [START_REF] Ajoudani | Progress and prospects of the human-robot collaboration[END_REF], [START_REF] Billard | Trends and challenges in robot manipulation[END_REF]. Although human-human handover is an intuitive behavior, it is a result of complex and sophisticated learned social-cognitive communication channels [START_REF] Strabala | Toward seamless human-robot handovers[END_REF]. Grasping such a complexity in an equivalently robot control formulation strategy is not a trivial problem.

Indeed, how to codify the human-robot handover process has been thoroughly addressed in the research community. The state-of-the-art studies split the handover process in two main phases: the pre-grasping phase [START_REF] Shibata | Experimental analysis of handing over[END_REF]- [START_REF] Bdiwi | Handing-over model-free objects to human hand with the help of vision/force robot control[END_REF] and the grasping phase [START_REF] Nagata | Delivery by hand between human and robot based on fingertip force-torque information[END_REF]- [START_REF] Costanzo | Handover control for human-robot and robot-robot collaboration[END_REF]. Such a breakdown is simply chronological: the former focuses on detecting the object, estimating/predicting the human movement and planning the robot reaching motion toward the meeting point, whereas the latter consists of understanding the interaction forces (haptics) applied at the object by the two handing over agents during the exchange such that to ensure a stable grasping. In [START_REF] Medina | A humaninspired controller for fluid human-robot handovers[END_REF] a retraction phase is considered, which describes how the giver and receiver move away after the latter gets the full control of the object. Yet, for an exhaustive handover survey, please refer to the excellent recent review in [START_REF] Ortenzi | Object handovers: A review for robotics[END_REF]. Despite the huge amount of works addressing human-robot handover, one issue remains open: how to ensure/codify an adaptive behavior of the robot w.r.t to a human versatile intention on where to exchange the object, aka HandOver Location (HOL), with the robot, and in which configuration (orientation). A large amount of existing works required the knowledge of the HOL as a precondition either for motion planning or control formulations of the pre-grasping phase. In particular, the HOL is often considered either as fixed (the robot moves systematically to a fixed spot to pick-up the object) or pre-planned (real-time detection and estimation of the object fixed-location) [1, Tables 12]. There are works that provide HOL estimation and on-line prediction methods [START_REF] Medina | A humaninspired controller for fluid human-robot handovers[END_REF], [START_REF] Prada | Implementation and experimental validation of dynamic movement primitives for object handover[END_REF]- [START_REF] Nemlekar | Object transfer point estimation for fluent human-robot handovers[END_REF]. However, such existing approaches have at least one of the following shortcomings:

• Collecting data sets to train motion prediction models;

• Time-consuming computations leading to a hashed or a slow handover; • Magic-numbers of meta-parameters to be tuned;

• Conservatism in the HOL prediction policy;

• Non-systematic success of the handover performance;

• The object orientation at the HOL is often kept the same during the experiments; • Knowledge of the HOL is very often required. In this work, we formulate the premises of a generic robot control-strategy that ensures high fidelity and reliability of reaching motion for bi-directional handover scenarios and guarantees adaptability w.r.t the HOL and object orientation (Fig. 1). Particularly, our control formulation gathers the advantages from both methods in [START_REF] Medina | A humaninspired controller for fluid human-robot handovers[END_REF], [START_REF] Costanzo | Handover control for human-robot and robot-robot collaboration[END_REF]. Indeed, our method is HOL knowledge free. We only assume that the object structural properties and dimensions are known, and there exists a sensor that provides the pose (Cartesian position and orientation) of the object of interest, e.g. [START_REF] Paolillo | Interlinked visual tracking and robotic manipulation of articulated objects[END_REF]. Conversely to [START_REF] Costanzo | Handover control for human-robot and robot-robot collaboration[END_REF], our method ensures/codifies a real-time proactive and adaptive robot motion w.r.t to the human versatile intention on where to exchange the object with the robot and in which configuration (orientation) without the need of offline acquired data. Our aim is to build on our existing multi-objective task-space optimization Quadratic-Programming (QP) framework [START_REF] Bouyarmane | On weight-prioritized multitask control of humanoid robots[END_REF], [START_REF] Bouyarmane | Quadratic programming for multirobot and task-space force control[END_REF] that prove to be very powerful in an industrial context [START_REF] Kheddar | Humanoid robots in aircraft manufacturing: The airbus use cases[END_REF] and a humanassistance context [START_REF] Bolotnikova | Task-space control interface for softbank humanoid robots and its human-robot interaction applications[END_REF]. In particular, our proposed idea relies on the concept of coupled tasks where the state of one task is forwarded as the reference for another task. More precisely, we formulate an observation task that estimates either human hand or object full-state in terms of pose, velocity and acceleration which are then forwarded as references for a trajectory-tracking task for the robot end-effector to track. Leveraging multi-objective QP control paradigm, these two tasks run concurrently in a leaderfollower fashion: the object (leader) moves and converges to the HOL while the robot end-effector (follower) moves proactively toward the object while adjusting its orientation accordingly. From this standpoint, our approach is similar to the coupled Dynamical Systems (DS) in [START_REF] Medina | A humaninspired controller for fluid human-robot handovers[END_REF]. Except that our approach is computationally cheap and does not require the estimation of the HOL nor to separately learn human and robot DS models. To sum-up, our contributions to coupled task-space observer-controller are as follows:

• Systematic approach (no conservative policy of HOL prediction) with less parameter to tune (task gains only); • No need for planning and time consuming processes of collecting data and model training; • Requires no time-consuming computations resulting in a smooth (fluid) and seamless handover motion; • Codifies rich behaviors with multi-objective QP control paradigm: proactive position and orientation control while accounting for safety constraints (collision avoidance, joint and actuation limits, etc.); • Generalizes to bi-directional human-robot handovers;

• Needs only a sensor or estimator that provides the object pose, e.g. [START_REF] Paolillo | Interlinked visual tracking and robotic manipulation of articulated objects[END_REF], [START_REF] Rana | Wearable sensors for real-time kinematics analysis in sports: A review[END_REF], [START_REF] Jongeneel | Model-Based Visual Object Tracking with Impact Collision Models[END_REF].

Notations: x ∈ R 3 is expressed in frame R . R ∈ SO(3) denotes the rotation matrix of the frame R w.r.t R . If R = R w , the world-frame, then R = R . ω× = skew(ω)
denotes the skew-symmetric matrix associated with the vector ω ∈ R 3 . α x denotes the velocity of x ∈ X . If X is an Euclidean space then α x = ẋ. q T = q q ∈ R 4 is the unit quaternion representation of R where q ∈ R and q ∈ R 3 with q = 1, and q -1 T = q -q . The vector part of the quaternion product q ⊗ q is denoted as q q = q q + q q + q × q ∈ R 3 . If q = q -1 then q q = 0. P ∈ R 3 denotes the Cartesian coordinates of R origin. Ṗ , P ∈ R 3 are is linear velocity and acceleration. The angular velocity and acceleration of R frame are ω , ω ∈ R 3 , respectively.

II. HANDOVER PARADIGM A. Handover Control Problem

In order to perform object handover efficiently, the robot reaching-motion toward the HOL shall be synchronized with the object's motion to achieve a one-shot continuous and smooth motion. If the HOL is known in advance, the control formulation resumes to perform simply a set-point reaching task for the end-effector. Nevertheless, the HOL and its timing as well as the object orientation are highly versatile: they may change during the handover motion or between two successive processes depending on the human intention and her/his posture. Handing over an object can even be aborted on the human decision while moving. Hence, planning the robot motion is likely to fail in such conditions. Alternatively, a reactive control method is more suitable for its ability to adjust the robot motion in real-time. We denote by end-effector the robot terminal link used to pick-up the object. It encompasses two-finger grippers, multi-finger hand and even a non-human like devices as a suction-cup or an electromagnetic gripper [START_REF] Pan | Exploration of geometry and forces occurring within human-to-robot handovers[END_REF].

Our approach is to tackle the human-robot handover problem from a reactive closed-loop control perspective. We shall explain our approach when the human is the giver, then we show how it applies when s/he is the receiver. The HOL can be seen as an attractor toward which the object is converging (steered by the human). Since the HOL is not known a priori, the robot end-effector can track the object trajectory leading to a proactive motion such that when the object converges to the HOL, its trajectory becomes a point to which the endeffector converges. The same reasoning can be applied for the orientation. The remaining question is how to obtain the object trajectory in terms of pose X obj ∈ R 7 , linear and angular velocity α X obj ∈ R 6 and linear and angular acceleration αX obj ∈ R 6 ? These terms are encompassed as the object full-state

s obj =   X obj α X obj αX obj   ∈ R 19 . (1)
Often, s obj cannot be directly obtained by the sensors as generally they provide only X obj . Hence, an estimation of s obj needs to be constructed from X obj and it is denoted as

s obs =   X obs α X obs αX obs   ∈ R 19 . (2)
To this end, the observation task is formulated as a PD controller that drives X obs toward X obj , e.g., [START_REF] Paolillo | Interlinked visual tracking and robotic manipulation of articulated objects[END_REF]. While converging, the observation task outputs also α X obs and αX obs , e.g. [START_REF] Pham | Handobject contact force estimation from markerless visual tracking[END_REF]. s obs terms are then used as references for the trajectory-tracking task formulated for the end-effector. Note that the observation task allows to generate trajectories for the orientation tracking without the need for offline planning methods [START_REF] Sciavicco | Modelling and Control of Robot Manipulators[END_REF]. The same approach can be adapted if the human is a receiver. In such case, the end-effector already holds the object and its full-state known by forward kinematics. Instead, the observation task constructs the fullstate of the human hand [START_REF] Pham | Handobject contact force estimation from markerless visual tracking[END_REF].

Multi-objective task-space QP control has been extensively used as it enables to specify various tasks objectives while explicitly accounting for a set of convex constraints [START_REF] Bolotnikova | Autonomous initiation of human physical assistance by a humanoid[END_REF].

In [START_REF] Bouyarmane | Quadratic programming for multirobot and task-space force control[END_REF], one single QP controller can be formulated for multirobots systems either decoupled or interacting with each other using contact forces. In particular, the pre-grasping handover phase can be suitably formulated using the multirobots QP by considering the robotic arm and the object as two decoupled robots where the former is a redundant multibody system where all the joints are actuated, and the latter as a floating-base rigid-body system. Moreover, the observation task is formulated for the object to compute s obs and the trajectory-tracking task is formulated for the end-effector. The following subsections explicit in details our approach.

B. Background

Consider a n degree-of-freedom redundant robotic arm such that its joint configuration is defined by q ∈ R n . The robot is governed by the following equation of motion:

M (q)q + N (q, q) = τ + J T c f, (3)
where M (q) ∈ R n×n is the inertia matrix, N (q, q) ∈ R n encompasses Coriolis, centrifugal and gravity torques, τ ∈ R n is the joint-torque, J c ∈ R 6×n is the Jacobian at the contact point and f ∈ R 6 is the contact wrench. Let us consider the frame R ee rigidly attached to the end-effector and which pose is

X ee = P ee q ee ∈ R 7 . (4)
Its velocity and acceleration are given as

α Xee = Ṗee ω ee = J ee q ∈ R 6 , (5)
αXee = Pee ωee = J ee q + Jee q ∈ R 6 ,

where J ee ∈ R 6×n is the end-effector Jacobian. Let us consider the object as a one-rigid-link robot with 6 DoF to which a frame R obj is rigidly attached and which pose is

X obj = P obj q obj ∈ R 7 , (7)
where X obj is assumed to be provided by a sensor. Its velocity and acceleration are given as

α X obj = Ṗobj ω obj ∈ R 6 , αX obj = Pobj ωobj ∈ R 6 . (8)
The object structural and dimension properties are known.

C. Observation Task

Let us consider an observed object to which a frame R obs is rigidly attached which pose is

X obs = P obs q obs ∈ R 7 . (9)
Assuming that the object (linear and angular) velocity and acceleration [START_REF] Huber | Humanrobot interaction in handing-over tasks[END_REF] are not provided by the sensor (which is likely the case), the observation task aims at constructing these non-measured states by estimating s obs in (2). This is achieved by the observation task that steers X obs toward X obj by keeping the observation error e obs as small as possible such that e obs = P obs -P obj qobs q-1 obj ∈ R 6 .

The observation error velocity and acceleration are given as α e obs = α X obs , αe obs = αX obs .

The observation task state is defined as

η obs = e obs α e obs ∈ R 12 . (12)
Thus, the observation task is formulated as follows

ηobs = 0 I 0 0 η obs + 0 I µ obs , µ obs = αX obs (13)
Choosing µ obs in (13) a linear state feedback

µ obs = -[K s obs K d obs ] η obs = -K obs η obs , (14)
with K s obs , K d obs ∈ R 6×6 are diagonal positive-definite matrices denoting the stiffness and damping gains; it yields to the observation-task closed-loop dynamics

ηobs = A obs η obs , A obs = 0 I -K s obs -K d obs , (15)
with A obs Hurwitz [START_REF] Khalil | Nonlinear systems; 3rd ed[END_REF]. Note that η obs only converges asymptotically to zero if the object is static (X obs constant). However, choosing high gain values typically enables a fast convergence and keeps e obs sufficiently small. The benefits of the observation task are three folds: (i) allows a bounded estimation of s obs in (2) given ( 13)-( 15); (ii) X obj is low-pass filtered by the closed-loop observation task dynamics (15); (iii) enables an online generation of a smooth twice-differentiable trajectory 1 for the Cartesian and orientation coordinates of R obs without the needs of an offline planning methods [START_REF] Sciavicco | Modelling and Control of Robot Manipulators[END_REF]. The latter advantage is the core idea presented in this paper: the observation task outputs trajectory references required by the trajectory-tracking task in order to achieve a proactive handover process. More importantly, theses two tasks are integrated in the multiobjective QP controller as shown in Section II-F.

Once having s obs , we can compute the full-state for any other frame R attached to the object (for which the local pose X obs is known) by simply applying the classical kinematic relations for position, velocity and acceleration:

P = P obs + R obs P obs , ( 16
) Ṗ = Ṗobs + ω obs × R obs P obs , ( 17
) P = Pobs + ωobs × R obs P obs + ω obs × 2 R obs P obs , (18) R = R obs R obs . ( 19
)
Note that the rigid body assumption implies that Ṗ obs = 0, Ṙobs = 0, ω = ω obs and ω = ωobs .

D. Trajectory-Tracking Task

Let R grasp be the grasping frame rigidly attached to the object and which pose is defined as

X grasp = P grasp q obs ∈ R 7 , (20)
such that P grasp ∈ R 3 denotes the coordinates of the point where the end-effector grasps the object and is computed from ( 16), and q obs is obtained from R grasp in [START_REF] Vahrenkamp | Workspace analysis for planning humanrobot interaction tasks[END_REF]. R grasp velocity and acceleration are computed as

α Xgrasp = Ṗgrasp ω obs ∈ R 6 , αXgrasp = Pgrasp ωobs ∈ R 6 . ( 21
)
Let us define the trajectory-tracking task error as

e tt = P ee -P grasp qee q-1 grasp ∈ R 6 , (22)
and which derivative is given as

α ett = Ṗee -Ṗgrasp ω ee -ω obs = α Xee -α Xgrasp ∈ R 6 . ( 23
)
Let us denote the trajectory-tracking task state

η tt = e tt α ett ∈ R 12 . (24)
Hence, the trajectory-tracking task dynamics is formulated

ηtt = 0 I 0 0 η tt + 0 I µ tt , (25)
µ tt = αXee -αXgrasp = J ee q + Jee q -αXgrasp .

Then, choosing µ tt in [START_REF] Kheddar | Humanoid robots in aircraft manufacturing: The airbus use cases[END_REF] as

µ tt = -[K stt K dtt ] η tt = -K tt η tt , (27)
with K stt , K dtt ∈ R 6×6 are diagonal positive-definite matrices denoting the stiffness and damping gains; it yields to the following trajectory-tracking task closed-loop dynamics

ηtt = A tt η tt , A tt = 0 I -K stt -K dtt . ( 28
)
where A tt is Hurwitz. This enables a global asymptotic convergence of η tt to the origin [START_REF] Khalil | Nonlinear systems; 3rd ed[END_REF]. Commonly, the trajectory is planned such that the initial reference trajectory pose is as close as possible to the current end-effector pose X ee (t 0 ) which indeed ensures that the tracking error e tt (t 0 ) is small and thereby enforces the end-effector pose to stick on trajectory forward in time. However, when the trajectory starts far from the initial end-effector pose, the latter converges to the trajectory with an asymptotic decay of the tracking error η tt . This property enables the anticipatory motion of the end-effector which moves proactively toward the object grasping position (see Fig. 2).

E. Posture Task

The posture task is mainly intended to solve the remaining redundant states (q, q) and keep them bounded. Let q ref ∈ R n be a given reference posture designed generally to represent a suitable robot posture (e.g., elbow up). Let us define the posture task state as

η pos = e pos ėpos = q -q ref q . ( 29
)
The posture task dynamics is thereby

ηpos = 0 I 0 0 η pos + 0 I µ pos , µ pos = q. (30)
Choosing µ pos in [START_REF] Pan | Exploration of geometry and forces occurring within human-to-robot handovers[END_REF] as

µ pos = -K spos K dpos η pos = -K pos , (31)
leads to the posture task closed-loop dynamics

ηpos = A pos η pos , A pos = 0 I -K spos -K dpos , (32)
where A pos is Hurwitz given that the stiffness and damping gains K spos , K dpos are diagonal positive-definite. Eq. ( 32) yields asymptotic convergence of η pos to the origin. However, this is only the case when the posture task is not in conflict with the other tasks and constraints among which the posture task has the lowest priority. Alternatively, e pos is only ensured to be uniformly ultimately bounded [START_REF] Bouyarmane | On weight-prioritized multitask control of humanoid robots[END_REF].

F. Multi-Tasks QP Formulation

Let us denote χ T = qT αT obs f T ∈ R n+6+3 the vector encompassing the linear and angular acceleration of the observed rigid-body object, the joint-acceleration of the robotic arm, and the contact force. Given the affinity of (13) w.r.t αX obs , that of (26)(30) w.r.t q and that of (3) w.r.t q and f , then we can combine all the tasks and constraint in a single weighted-prioritized QP formulation

min χ i w i E i χ χ + F i χ 2 (33a) S.t: C χ χ ≤ d χ (33b)
where w i > 0 is the associated weight to each task i. QP formulation [START_REF] Bolotnikova | Autonomous initiation of human physical assistance by a humanoid[END_REF] enables to: (i) combine the different competing tasks in (33a) by settling a soft prioritization scheme; (ii) account for unilateral constraints (33b) that embed limitations like joint-position, velocity, acceleration and torque limits, as well as safety aspects like (self)collision avoidance to ensure safe grasping [START_REF] Djeha | Adaptive-gains enforcing constraints in closed-loop qp control[END_REF]; (iii) find optimal q that generates the robotic arm motion that achieve at best all the tasks while fulfilling all the constraints; and (iv) handle multi-robot control where the robotic arm and the object are considered as two distinct robots entities which opens the possibility to add other robots to achieve the handover (e.g., bi-arm handover) while still using one compact formulation [START_REF] Bouyarmane | Quadratic programming for multirobot and task-space force control[END_REF].

III. EXPERIMENTAL RESULT

For demonstration, we implemented our approach on the open-source code implementation of the QP controller interface mc rtc 2 . Based on the embedded sensors data, mc rtc builds and solves the QP problem at each control cycle (1 ms). Experiments are conducted using 7-DoF robotic arm Panda. Perception Neuron 3 sensor-suit has been used for the pose measurement (Fig. 3). An API provides the hand pose in an arbitrarily fixed-frame at a frequency of 60 Hz. A calibration step is necessary to correctly coincides the sensor frame with R w . The calibration process is repeated at the beginning of each handover experiment to avoid drifting. When the human is a giver, the object is assumed to be rigidly attached to the hand, and thereby its pose can be computed based on the hand's one. Several handover scenarios have been performed where the robot starts from different configurations. In addition, multiple HOLs have been tried (Fig. 4). The observation task gains have been set to high values K s obs = 1500I, K d obs = 2 K s obs to ensure an accurate object pose estimation s obj (1). Fig. 5 shows how X obs tracks X obj . The high observation task gains allow an accurate pose tracking. Concurrently, it allows obtaining a good estimation of α X obj and αX obj by computing α X obs and αX obs from [START_REF] Medina | A humaninspired controller for fluid human-robot handovers[END_REF]. s obj is then forwarded to the trajectorytracking task where the gains of the orientation part have been chosen twice bigger than those of the translation to ensure that end-effector reaches the object while its orientation has already converged to the target. The stiffness of the translation part is fixed at I and the corresponding 2 https://jrl-umi3218.github.io/mc_rtc/index.html 3 https://neuronmocap.com/ I. From Fig. 6, the object and the end-effector meet seamlessly and smoothly at the HOL without being specified a priori, see Fig. 7. Furthermore, the end-effector adapts reactively to the variation of the grasping point as shown in the attached video.

IV. CONCLUSION

We propose an original new approach for human-robot handovers formulated using task-space optimization controller. The core idea is based on a novel implementation of tasks interdependency, which consists in providing the state of a task (of estimation nature) as an input to another task so that both meet at the HOL without explicit time or object configuration specification. Our experimental results confirmed very promising performances of simple handovers focusing mainly on the reaching phase. This new approach raised very promising novel features of the task-space optimization control schemes. Extension in terms of functionalities and theoretical investigation on how observer-tasks can Fig. 6. Position (left) and orientation (right with RPY angles) of the frames Rgrasp (dashed) and Ree (solid) obtained by the trajectory-tracking task. The sudden variation in the yaw angle is sound because the angle is bounded between -π and π. This does not induce any singularity issue since the orientation is implemented using unit quaternions. be embedded in a unified task-space observer/control framework through task interdependencies and constraints between task errors opens perspectives in embedding scheduling in the task-space control formalism. Our on-going and future research is focusing on this issue together with completephases and more complex handovers considering force cues.

Fig. 1 .

 1 Fig. 1. Proposed seamless handover process executed without any prior knowledge about the HOL and final object orientation.

Fig. 2 .

 2 Fig. 2. Illustrative scheme showing the frames Rw, Ree, R obj , R obs and Rgrasp. The observed object is tracking the actual object giving the data from sensor thanks to the observation task. The end-effector tracks the observation task state yielding an anticipatory motion toward the HOL where it ultimately meets the object. The colored unit vectors in Ree track their corresponding in Rgrasp. For instance, if the object is cylindrical, only the yellow unit vectors must be aligned.

Fig. 3 .

 3 Fig. 3. Perception Neuron motion capture sensor-suit used for the handover experiments and mounted on the left arm. Three IMUs (highlighted in colored squares) mounted on the left hand are used to provide an estimation of the hand pose (the orange square).

Fig. 4 .Fig. 5 .

 45 Fig. 4. Different HOLs (red) desired by the human operator. The object is a black cylindrical container. The transparent robots represent the initial configuration.

Fig. 7 .

 7 Fig. 7. 3D trajectories of Rgrasp (blue) and Ree (orange). The initial and terminal points are denoted with a square and a circle, respectively.

This is also known as a reference model-based approach for trajectory references generation[START_REF] Khalil | Nonlinear systems; 3rd ed[END_REF] Chapter 13]. In addition, the trajectory feedforward terms are generated in real-time since the observation task is updated at the same frequency of QP no matter the sampling-frequency of the sensor.