Pauline Maurice
email: pauline.maurice@polytechnique.org

Meghan E Huber
email: mehuber@mit.edu

Neville Hogan
email: neville@mit.edu

Dagmar Sternad

Evelyn E Newman

Velocity-curvature patterns limit human-robot physical interaction

teaching and research institutions in France or abroad, or from public or private research centers.

Velocity-curvature patterns limit human-robot physical interaction

Pauline Maurice 1 , Meghan E. Huber 2 , Neville Hogan 2 , and Dagmar Sternad 3

Abstract-Physical human-robot collaboration is becoming more common, both in industrial and service robotics. Cooperative execution of a task requires intuitive and efficient interaction between both actors. For humans, this means being able to predict and adapt to robot movements. Given that natural human movement exhibits several robust features, we examined whether human-robot physical interaction is facilitated when these features are considered in robot control. The present study investigated how humans adapt to biological and nonbiological velocity patterns in robot movements. Participants held the end-effector of a robot that traced an elliptic path with either biological (two-thirds power law) or non-biological velocity profiles. Participants were instructed to minimize the force applied on the robot end-effector. Results showed that the applied force was significantly lower when the robot moved with a biological velocity pattern. With extensive practice and enhanced feedback, participants were able to decrease their force when following a non-biological velocity pattern, but never reached forces below those obtained with the 2/3 power law profile. These results suggest that some robust features observed in natural human movements are also a strong preference in guided movements. Therefore, such features should be considered in human-robot physical collaboration.

Index Terms-Physical Human-Robot Interaction; Human Factors and Human-in-the-Loop; Human-Centered Robotics

I. INTRODUCTION

T HE physical separation between humans and robots is starting to disappear, as robots move from a purely secluded industrial context into the human world. Not only is the workspace shared, but direct physical interaction -where a human and a robot cooperatively work on a common task, e.g. transporting a bulky or heavy object -is also becoming more common. In the workplace, collaborative robots are Boston, MA 02115, USA. d.sternad@northeastern.edu Digital Object Identifier (DOI): see top of this page. used to extend human abilities by providing movement guidance, weight compensation or strength enhancement, thereby improving the accuracy of the gesture and/or reducing the physical load on the worker [START_REF] Colgate | Intelligent assist devices in industrial applications: a review[END_REF]. Robots acting as human partners also receive a lot of attention, both in industrial robotics, e.g. coworkers such as the Baxter robot (Rethink Robotics, Boston, MA, USA), and in service robotics, e.g. robotic caregivers for elderly persons.

In human-robot co-manipulation tasks, physical interaction is crucial both for task achievement and for the comfort of the human. This raises the question of how to control the robot to make the interaction efficient and intuitive. Lynch et al. presented a framework to design passive guides for joint load manipulation that optimize the human-robot cooperation [START_REF] Lynch | Motion guides for assisted manipulation[END_REF]. However, the optimality criterion was an assumption and was not itself evaluated. For instance, when designing a robotic guide for an arm movement, they used a principle of unconstrained human movement to evaluate the optimality of the interaction. While they were successful in proving the optimality of their guide with respect to the chosen criterion, the validity of the criterion per-se in the context of constrained movement was left unaddressed.

In unconstrained situations, human arm movements show several features that have remarkable robustness, such as a speed-accuracy trade-off (Fitts' law) [START_REF] Fitts | The information capacity of the human motor system in controlling the amplitude of movement[END_REF] and a speed-curvature relation, the so-called two-thirds power law [START_REF] Lacquaniti | The law relating the kinematic and figural aspects of drawing movements[END_REF], [START_REF] Viviani | A developmental study of the relationship between geometry and kinematics in drawing movements[END_REF], [START_REF] Schaal | Origins and violations of the 2/3 power law in rhythmic three-dimensional arm movements[END_REF]. Several optimality principles have been proposed to generate these features [START_REF] Engelbrecht | Minimum principles in motor control[END_REF], such as minimum jerk [START_REF] Flash | The coordination of arm movements: an experimentally confirmed mathematical model[END_REF], minimum endpoint variance [START_REF] Harris | Signal-dependent noise determines motor planning[END_REF], and minimum torque change [START_REF] Uno | Formation and control of optimal trajectory in human multijoint arm movement[END_REF]. Some of these features have also been observed in visual perception tasks [START_REF] Viviani | Biological movements look uniform: evidence of motor-perceptual interactions[END_REF]. In human-human co-manipulation, Noohi et al. showed that the minimum jerk principle also applied [START_REF] Noohi | Computational model for dyadic and bimanual reaching movements[END_REF]. However, it is not clear whether these principles in unconstrained movements still hold when humans interact with a robot. Indeed, Reed and Peshkin demonstrated that humans behaved differently in human-robot and human-human physical interaction, even if the robot moved in human-like patterns [START_REF] Reed | Physical collaboration of human-human and human-robot teams[END_REF]. This raises the question whether programming robots according to biological principles of movement can make the human-robot interaction more successful.

Several studies have investigated how humans interpret robot motion when observing a robot moving. Huber et al. compared biological (minimum jerk of the end-effector) and non-biological (trapezoidal profile in joint space) velocity profiles for a robot handing over objects to a human. They showed that the reaction time of the human was significantly shorter when the biological velocity profile was used [START_REF] Huber | Humanrobot interaction in handing-over tasks[END_REF]. Further, participants felt safer with the biological velocity profile. De Momi et al. conducted a similar experiment and showed that humans were able to distinguish between biological and nonbiological profiles in robot motion [START_REF] Momi | a neural network-based approach for trajectory planning in robot-human handover tasks[END_REF]. Bisio et al. demonstrated that humans understood robot intentions as long as the robot moves according to biological movement patterns [START_REF] Bisio | Motor contagion during human-human and human-robot interaction[END_REF]. Kupferberg et al. showed that human-like velocity profiles facilitated the perception of a humanoid robot as an interaction partner [START_REF] Kupferberg | Biological movement increases acceptance of humanoid robots as human partners in motor interaction[END_REF]. Dragan and Srinivasa reported that, even after familiarization, humans could not interpret "unnatural" movements of a robot as easily as "natural" ones [START_REF] Dragan | Familiarization to robot motion[END_REF]. While these studies suggest that using biological movement patterns increases the efficiency of the human-robot cooperation, they examined only visually-mediated interaction; there was noor very limited -physical interaction. When information is provided continuously through haptic contact, consequences might arise because sensory-motor delays are significantly shorter (∼ 30 ms) than delays in visuo-motor coordination (∼ 250 ms).

In physical human-robot cooperation, many studies have focused on humans leading -or at least deciding -the movement. In such cases, detection of human intention is the primary concern so that the robot can select the best assistance (e.g. [START_REF] Dumora | Robot assistance selection for large object manipulation with a human[END_REF], [START_REF] Noohi | A model for human-human collaborative object manipulation and its application to human-robot interaction[END_REF], [START_REF] Corteville | Human-inspired robot assistant for fast point-to-point movements[END_REF]). However, there are other situations that also require the robot to lead the movement. Thus, it is important to understand how humans interpret and adapt to robot movements when in physical contact with the robot. Evrard and Kheddar observed that, in human-robot shared object manipulation with obstacle avoidance, humans did not trust the robot when it was leading the movement [START_REF] Evrard | Homotopy switching model for dyad haptic interaction in physical collaborative tasks[END_REF]. They suggested that this could be caused by the nonbiological trajectories of the robot. To address this issue, Corteville et al. compared three velocity profiles (minimum jerk, triangular and rectangular) for the movement of a robot assisting fast point-to-point movements [START_REF] Corteville | Human-inspired robot assistant for fast point-to-point movements[END_REF]. They reported that participants were able to move along with the minimum jerk and triangular profiles, but that only the minimum jerk profile felt natural. While interesting, this study was rather qualitative, and participants could deviate from the robot's velocity profile.

This paper investigates quantitatively whether humans can adapt to non-biological patterns in robot movements. We focus on the case where the robot alone leads the movement, and the human has to move along with the robot to the best of his/her ability. We evaluate the physical interaction through the human-robot interaction force. Specifically, we examine the effect of different velocity patterns along a curved path traced by a robot. In unconstrained movements the hand velocity is related to the curvature of the path by the 2/3 power law. If humans are unable to adapt to non-biological, velocity patterns when the human only has to follow the robot, it will demonstrate an important limitation to human adaptation in human-robot physical interaction.

II. METHOD

A. Two-thirds Power Law

In natural drawing movements, numerous studies have shown a systematic relation between the kinematics of the hand motion and the geometric properties of the path [START_REF] Lacquaniti | The law relating the kinematic and figural aspects of drawing movements[END_REF], [START_REF] Viviani | A developmental study of the relationship between geometry and kinematics in drawing movements[END_REF], [START_REF] Schaal | Origins and violations of the 2/3 power law in rhythmic three-dimensional arm movements[END_REF]. This principle of human movement, referred to as the twothirds power law, is described by the equation

v(t) = K r(t) 1 + α r(t) β (1)
where v is the tangential hand velocity, r the radius of curvature of the path, K the velocity gain factor which depends on the general tempo of the movement and on the length of the segment, α a parameter ranging from 0 to 1, and β = 1/3. When the trajectory has no inflection points, α = 0, the relation can be simplified to

v(t) = K r(t) β (2)
This power law describes the observation that the hand velocity along the path decreases when the path becomes more curved, and increases when the path becomes straighter. The initial formulation of the 2/3 power law used curvature instead of radius of curvature, and angular velocity instead of tangential velocity, with an exponent 2/3. Formulations with the radius of curvature and tangential velocity are identical but the exponent changes to 1/3. Even though the latter formulation is more commonly used, the name 2/3 power law persisted. To avoid confusion, we refer to this principle only as the power law in the remaining paper.

B. Experimental Set-up

The study comprised two sets of experiments: Experiment 1 examined whether non-biological vs. biological velocity patterns affected the human-robot interaction in a movement executed jointly by a human and a robot; Experiment 2 examined whether humans were able to learn non-biological velocity patterns with extensive practice when executing a movement jointly with a robot. The two experiments only differed in their design while the task and apparatus were identical. Both experiments were divided into 2 sub-experiments with slightly different experimental conditions described hereafter (Exp. 1.A and 1.B; Exp. 2.A and 2B).

1) Task: Participants were asked to trace a planar ellipse in a horizontal plane jointly with a robotic arm which moved with an imposed velocity profile. The elliptic path with its variable curvature is a suitable test-bed since the power law robustly describes velocity changes in natural human movement along such a path by Eq. 2. Importantly, the movements of the participants had no effect on the robot trajectory. Participants held the end-effector of the robot, and were instructed to move along with the robot in order to exert as little force as possible on it. They were explicitly told to actively move with the robot and not to passively let it drag their arm. With active movement, participants had to compensate for their own arm inertia. No visual display of the path was provided for tracking, although participants saw the robot moving. Hence, they had to rely on their proprioceptive and haptic sensation of the robot motion. 2) Apparatus (Fig. 1): The robot was the HapticMaster R , a 3 DoFs robotic manipulandum (Moog, Nieuw-Vennep, The Netherlands) [START_REF] Van Der Linde | Hapticmaster-a generic force controlled robot for human interaction[END_REF] (the horizontal planar motion only used 2 DoFs). Participants stood and held the robot with a power grip, through a knob-shaped user handle mounted on the endeffector (Experiments 1.A, 2.A and 2.B). In Experiment 1.B, participants held the robot through a vertical handle which had a pivot joint around its vertical axis; thereby the robot end-effector orientation and the participant's wrist orientation were decoupled. For each participant, the height of the robot was adapted such that their forearm was approximately horizontal when holding the handle at rest. Participants chose a comfortable distance to the robot and were instructed not to move their feet during a trial.

The robot traced out an elliptic path (major axis = 30 cm, minor axis = 10 cm) in the horizontal plane. Each trial lasted 12 s where the robot drew the ellipse in counter-clockwise direction, 4 times without stopping. 4 consecutive cycles rendered sufficient data to afford elimination of initial and terminal transients, while being short enough to limit fatigue within a trial. The beginning of each trial was signaled by 3 short sounds, after which the robot started to move. The end of the trial was marked by one short sound.

The force applied by participants on the user handle was measured with a 3 DoFs force sensor mounted at the tip of the robot arm. The participants' force and the trajectory of the robot end-effector were recorded at 700 Hz. The robot was controlled in position with a function of the Haptic Master API equivalent to a Cartesian PD controller [START_REF] Van Der Linde | Hapticmaster-a generic force controlled robot for human interaction[END_REF]. The desired position of the robot was updated at 700 Hz, and an internal control loop ran at 2 kHz. velocity pattern (4 levels) and the orientation of the ellipse (2 levels).

The velocity pattern defined the velocity profile of the robot along the elliptic path, based on the relation between tangential velocity and curvature according to Eq. 2. Four different conditions were created with different values of β (Fig. 2). In the standard condition, β = 1/3, the robot moved according to the power law observed in voluntary human movements (biological condition). In the exaggerated condition, β = 2/3, the robot moved even faster -compared to the standard condition -when the curvature was small (the path was almost straight), and even slower when the curvature was high. In the reverse condition, β = -1/3, the robot moved faster when the path was curved and slower when the path was almost straight. The constant condition corresponded to β = 0, i.e. a constant tangential velocity along the whole path. In these 4 conditions, only one varying parameter β created biological (standard), weakly non-biological (constant, exaggerated) and strongly non-biological (reverse) patterns. The velocity gain factor K (Eq. 2) was modified for each velocity pattern condition to keep the ellipse period constant across conditions and avoid confounding with overall movement speed (when the length of the path is fixed, K determines the duration of the full trajectory). Details of the calculation of K can be found in [START_REF] Viviani | Biological movements look uniform: evidence of motor-perceptual interactions[END_REF]. The duration of a single ellipse cycle was 3 s, which corresponded to an average velocity close to the preferred velocity of humans determined in pilot tests.

The orientation of the ellipse was defined by the direction of the major axis: it was either aligned with the participant's frontal axis (X) or with his/her sagittal axis (Y) (Fig. 1).

Each participant performed 10 successive trials per condition, for all 8 conditions. Each condition started with an example trial in which the participant only observed the robot to familiarize him/herself with the specific movement pattern. Trials within a block of the same condition were separated by a 5 s break; blocks were separated by a several-minute break to avoid physical or mental fatigue. The order of the 8 conditions was counterbalanced across participants. The In Exp. 1.A, participants held the robot with the knobshaped handle. Exp. 1.B was a control experiment to test the effect of the constrained wrist orientation imposed by the knob-shaped handle. As the robot had only 2 DoFs in the horizontal plane, the orientation of its end-effector, and of the knob, changed with the position along the path. This imposed a varying wrist orientation that might have affected participants' performance. Therefore, in Exp. 1.B, participants held the robot with the vertical rotating handle that permitted free rotation of their wrist (Fig. 1 right).

5) Design of Experiment 2:

The two learning experiments (Exp. 2.A and 2.B) tested only one condition where the velocity along the path was constant and the major axis of the ellipse was aligned with the X (frontal) axis. The constant velocity condition was chosen because it is non-biological and a plausible scenario for a robot control law. At the same time, this pattern was not too challenging and biomechanical limitations during high accelerations were less likely than in the reverse case.

In both experiments, each participant performed a total of 200 trials, presented in blocks of 20 trials, separated by short breaks. The entire session lasted about 1.5 hour per participant.

In Exp. 2.A, participants received no feedback on their performance, as in Exp. 1.A and 1.B. In Exp. 2.B, participants received online visual feedback of the force applied on the robot (Fig. 3). A red bar moving vertically on a black screen represented the magnitude of the force in the horizontal plane (averaged over 80 ms); participants were instructed to keep the bar as low as possible on the screen. To encourage participants, a success zone was indicated by a white rectangle. The rectangle height was scaled for each participant based on his/her average RMS force in the standard condition. This baseline force level was measured in 10 standard trials performed at the beginning of the practice session, without any visual feedback.

C. Data Analysis 1) Dependent Variable:

The efficiency of the human-robot interaction was assessed by the force applied by participants on the user handle of the robot in the horizontal plane

F = f 2
x + f 2 y , where f x and f y are the components of the force along the X and Y (see Fig. 1 for the definition of the axes). Higher forces meant that the participant did not anticipate or was unable to follow the robot movement. Thus higher forces indicated a less intuitive interaction that entailed more effort from the participant.

Performance in each trial was quantified by the root mean square force over the trial F RM S . The first half of the first ellipse and last half of the last ellipse were excluded from the computation of F RM S to eliminate transients.

2) Statistical Analysis Experiment 1: A three-way repeatedmeasures analysis of variance (within-subject ANOVA) was conducted on the data of Exp. 1.A, with 3 fixed factors: velocity pattern, orientation of the ellipse, and trial number. Participants were entered as a random factor. Pairwise multiple comparison post-hoc tests with Bonferroni corrections were also conducted between the different velocity patterns. Exp. 1.B was analyzed with a four-way repeated-measures ANOVA on the data of both Exp. 1.A and 1.B, with the same 3 fixed factors, plus handle as between-subject factor.

3) Statistical Analysis Experiment 2: In order to assess whether performance improved with practice in Exp. 2, a linear regression was fitted over the 200 trials of each participant, and the slopes of the linear function were estimated. To assess the level of performance at the end of the practice session in Exp. 2.B, a pairwise-t-test was performed to compare the last 10 constant (non-biological) trials of all participants with their 10 standard (biological) trials executed at the beginning of the experiment. Note that visual feedback of the force was provided in the constant trials but not in the standard trials.

III. RESULTS

A. Experiment 1 1) Force Profiles Exp. 1.A: Fig. 4 shows the within-trial evolution of the force applied by participants on the robot, in both X and Y direction, for the 4 different velocity patterns. Despite small variations, especially in magnitude, the force pattern within each of the 4 velocity conditions was consistent across participants 1 . In contrast, the force patterns across velocity conditions were very different, indicating that the velocity modulations of the robot along the path had a nonnegligible effect on human-robot interaction. The force profile appeared smoothest and least variable across the cycle in the standard (biological) condition, which suggests that participants better anticipated and followed the robot's movement in this condition. Sharp peaks in the force profile of the three other conditions happened when the robot accelerated or decelerated rapidly.

2) Statistical Results Exp. 1.A: Submitting the RMS force to the ANOVA revealed a significant effect of velocity pattern (F (3, 27) = 65.99, p < 0.001). This supports that the modulation of the robot velocity affected the human-robot interaction, independently from any other factors. The difference between participants was also significant (F (1, 9) = 76.24, p < 0.001) due to different baseline levels of force, as shown by each participant's average force profile in Fig. 4. One participant's force profile clearly lay outside the standard deviation area, Only the second and third ellipse traversals are displayed since the first and last ellipses were affected by transients (one trial consists of four continuous ellipses). Note that, for the sake of legibility, the force scale is different in the reverse condition. Right column: Force vector along the elliptic path. Blue lines represent the across-trials and across-participants average force vectors during the third ellipse (sampling rate: 5 ms). The red line represents the elliptic path of the robot. The green dot marks the starting point on the ellipse (t = 6 s). The black arrow indicates the direction of counter-clockwise motion. For legibility, the length of the displayed force vector is divided by 20 in all conditions. both in the biological and non-biological conditions. The ANOVA did not detect effects of orientation or trial number, nor any interactions. If the pattern differences were only due to biomechanical constraints, the two ellipse orientations might have revealed differences (though this does not rule out all biomechanical constraints). Finally, the absence of differences across trials suggests that there was no learning of the movement over the course of the 10 trials.

Post-hoc pairwise comparisons revealed that the RMS force of the standard velocity pattern differed significantly from the 3 other velocity patterns (adjusted p-values: p = 0.014 for standard vs. exaggerated, p = 0.003 for standard vs. constant, p < 0.001 for standard vs. reverse). More specifically, Table I shows that the force applied in the standard condition was smaller than in any other conditions. The force magnitude in the standard condition was 26 % (SD = 14 %) than in the constant condition, 25 % (SD = 15 %) smaller that in the exaggerated condition and 57 % (SD = 12 %) smaller than in the reverse condition (average values computed across all trials/participants/orientations).

3) Statistical Results Exp. 1.A and 1.B: To assess the effect of the handle in Exp. 1.B, the RMS force of both experiments (1.A and 1.B) was submitted to a four-way ANOVA including handle as between-subject factor. The analysis did not detect any effect between the two handle conditions. The level of force applied by participants with the different velocity patterns was similar with both handles (Table I). This suggests that the results of Exp. 1.A were not a consequence of the participant's wrist constrained by the robot end-effector orientation. All other results were similar to those of Exp. 1.A. Specifically, the significant effect of velocity pattern was still observed (F (3, 42) = 86.90, p < 0.001), and the p-values in post-hoc pairwise comparisons were smaller than in Exp.1.A given the larger number of participants.

B. Experiment 2

1) Performance Improvements: Fig. 5 displays the evolution of the RMS force across the 200 trials for each participant, both with and without visual feedback, together with the fitted regression lines. Table II summarizes the regression slopes, as well as the 95 % confidence interval for the slope. Among the five participants who did not receive visual feedback (Exp. 2.A), only one showed a decrease in RMS force across trials (Participant 3). The four other participants showed an increase (not significant for Participant 5 since the 95 % CI included the zero slope). Conversely, the four participants who received visual feedback (Exp. 2.B) did show a significant decrease in RMS force across trials (zero slope not included in the 95 % CI). These results suggest that participants were able to learn the non-biological movement, but only when visual feedback about their force applied on the robot was provided.

2) Performance of the Non-Biological Profile after Practice: In Exp. 2.B (with visual feedback), pairwise t-test comparisons between the RMS force of the standard condition before practice and the constant condition after practice did not render any significant difference (p = 0.54). This suggests that although participants improved their performance in the non-biological profile with practice when guided with visual feedback, they did not surpass their performance with the biological profile, even without practice or feedback.

IV. DISCUSSION

The results of this study suggest that humans are better at moving along with a robot that follows a biological velocity pattern, compared to a non-biological one. The experiments also show that humans are able to learn a non-biological velocity pattern, but only with extensive practice and additional visual feedback. In addition, the observed improvement is limited as the performance never surpasses that obtained with a biological velocity pattern. This preference for biological movement patterns in human-robot interaction had only been demonstrated previously in visual interaction [START_REF] Huber | Humanrobot interaction in handing-over tasks[END_REF], [START_REF] Momi | a neural network-based approach for trajectory planning in robot-human handover tasks[END_REF], [START_REF] Bisio | Motor contagion during human-human and human-robot interaction[END_REF], [START_REF] Kupferberg | Biological movement increases acceptance of humanoid robots as human partners in motor interaction[END_REF], [START_REF] Dragan | Familiarization to robot motion[END_REF]. Physical interaction was only investigated by Corteville et al. but with a less quantitative approach and without examining changes with practice [START_REF] Corteville | Human-inspired robot assistant for fast point-to-point movements[END_REF]. Our results nevertheless raise some questions that are discussed hereafter.

Effects of Arm Inertia: It may be argued that similar differences in applied forces between the different velocity patterns have been obtained if participants had been completely passive and only dragged by the robot. The RMS force would be smallest with the biological profile because it resulted in smoother movements and, hence, smaller inertial force. To avoid this confound from passive movements, participants were explicitly told to actively move along with the robot. To verify whether participants followed this instruction, 3 participants were asked after the end of Exp. 1 to perform 5 trials of each condition in a totally passive manner. For each condition, we performed pairwise correlations between the continuous force profiles of active and passive trials. As expected, the correlations between 2 active trials or 2 passive trials were very good (0.83 ± 0.09 for active trials and 0.82 ± 0.14 for passive trials). In contrast, the correlations between active and passive trials were low (0.15 ± 0.35). This finding shows that at least these 3 participants adopted different strategies when they were instructed to actively move along vs. to be passive and compliant. This suggests that in our experimental trials, participants were not completely passive and the observed results were produced by active movements.

Practice, Learning and Retention: The difference in the evolution of the applied force with practice in Exp. 2.A vs. 2.B suggests that the haptic and proprioceptive sensation of the applied force was not sufficient, or not sufficiently salient given the low level of force, to induce learning. Participants needed visual feedback to assess and guide their performance. This is consistent with earlier findings on motor learning which showed that when intrinsic feedback or knowledge of results did not suffice to assess performance, failure to provide augmented feedback led to degraded motor learning [START_REF] Salmoni | Knowledge of results and motor learning: a review and critical reappraisal[END_REF].

The improvement with practice observed in Exp. 2.B is consistent with the general ability of humans to adapt to a wide range of scenarios [START_REF] Shadmehr | Adaptive representation of dynamics during learning of a motor task[END_REF]. In human-robot interaction specifically, Dragan and Srinivasa observed a similar adaptation with visual interaction (i.e. observation of the robot movement) [START_REF] Dragan | Familiarization to robot motion[END_REF]. In their study, participants significantly improved their ability to interpret unnatural movement patterns in a robot after familiarization. Hence, the superior performance with biological velocity patterns in Exp. 1 does not imply that less biological patterns present a hard limit to human performance. However, improvement in Exp. 2.B required extensive practice and performance also did not reach a plateau in the 1.5 hour-long practice. In addition, the same level of performance was reached without any practice with a biological velocity pattern. Given the long duration of Exp. 2, physiological and/or psychological fatigue might have limited the improvement. Fatigue could also explain the increase in RMS force observed in Participant 1, 2 and 4 of Exp. 2.A. Yet, as improvement required long practice, fatigue, both mental and physical, was an inevitable confound. An additional critical issue is retention, i.e. does improvement persist and transfer to other scenarios after practice? In order to be used and useful, robots interacting with humans should be controlled in a way that makes the interaction intuitive and immediately successful, without requiring any practice. Therefore, biological movement patterns should be given preference.

Predictability and Effort: The forces at play in the experiment presented are small and one may argue that the differences in force between the non-biological and biological conditions are not physically meaningful. However, there are important arenas of robotic applications where sensitivity to small forces is of high importance, such as in surgical applications. Furthermore, the current measure only includes the net external force applied by participants on the robot. Yet, it is likely that non-biological movements also cause an increase in antagonist muscle co-contraction, as the human prepares him/herself for expected perturbations. Hence, future work should also measure muscle activation to evaluate joint stiffness or impedance under different velocity patterns. Finally, even if not physically tiring, the incompatible and possibly unpredictable changes in velocities lead to discomfort and cognitive fatigue. A recent study showed that in complex object control, predictability of the object dynamics was a major determinant for human movement generation that outweighed the minimization of force [START_REF] Nasseroleslami | Rhythmic manipulation of objects with complex dynamics: predictability over chaos[END_REF]. Hence, complex interactions may introduce additional costs that are absent in unconstrained movements.

Generalization to Other Movements: The present evaluation of biological movement features in their effect on humanrobot physical interaction has only considered one specific ex-ample: the 2/3 power law in elliptical shapes. Future work will be directed towards showing our results also in more complex movements patterns, such as Lissajous figures or cloverleaf patterns, both in 2D and in 3D [START_REF] Maoz | Complex unconstrained threedimensional hand movement and constant equi-affine speed[END_REF], [START_REF] Flash | Affine differential geometry analysis of human arm movements[END_REF]. Further, other robust features have described different aspects of movements, such as minimum jerk or speed-accuracy trade-off [START_REF] Flash | The coordination of arm movements: an experimentally confirmed mathematical model[END_REF], [START_REF] Fitts | The information capacity of the human motor system in controlling the amplitude of movement[END_REF]. Similar tests should be performed to assess whether violation of these principles in human-robot interaction also present obstacles to successful co-manipulation.

V. CONCLUSION This study aimed to assess whether humans can adapt to non-biological patterns in robot movements when physically interacting with a robot. Specifically, we focused on the ability of humans to move along with a robot that followed either the 2/3 power law (biological pattern) or non-biological velocity profiles during an elliptic movement. Experiment 1 showed that humans performed with significantly smaller force against the robot when the robot's trajectory followed the 2/3 power law. Despite individual variations in baseline performance, all participants exhibited the same trends across the different velocity patterns. Importantly, this was observed for both orientations of the ellipse and both types of robot handles. Experiment 2 showed that with extensive practice humans were able to lower the force applied when the robot moved with a non-biological (constant) velocity pattern, but only when visual feedback of the applied force was provided. Importantly though, even after extensive practice, the performance in the non-biological pattern did not surpass the performance obtained without any practice with the biological pattern. The results of these two sets of experiments suggest that principles of unconstrained human movement can give important insight for physically guided movements.

It needs to be kept in mind that this study examined humanrobot collaboration in a limit case, where the robot was in full control of the movement. This differs from most robotics applications where the human at least partially controls the movement. Evidently, collaboration aims to capitalize on the human's perceptive and cognitive abilities to enhance the combined action. Nevertheless, even when the human can influence the robot motion, robotic assistance often relies on a pre-defined model of the movement [START_REF] Lynch | Motion guides for assisted manipulation[END_REF], [START_REF] Corteville | Human-inspired robot assistant for fast point-to-point movements[END_REF]. As movements that are optimal for humans might not be optimal for robots (due to differences in actuators and sensors), understanding the limitations of human adaptive abilities is important to facilitate human-robot physical interaction.

Fig. 1 .

 1 Fig. 1. Experimental set-up. Left: Top-down schematic view. The elliptic path is displayed on the figure for clarity, but participants did not see any visual display. Center: Participant performing the task. Right: Handle used in Exp. 1.B to decouple wrist and end-effector orientations.

3 )

 3 Participants: 10 young healthy adults participated in Exp. 1.A, and 6 others participated in Exp. 1.B. 5 young healthy adults participated in Exp. 2.A and 4 others participated in Exp. 2.B. All participants performed the task with their right dominant hand. Participants (10 females and 8 males, aged 19-33) were biology and engineering college students with no background in human-robot interaction. Participants were naive to the purpose of the study and signed an informed consent form approved by Northeastern University Institutional Review Board prior to the experiment. 4) Design of Experiment 1: Each subject performed 8 different movement conditions, defined by 2 parameters: the

Fig. 2 .

 2 Fig. 2. Magnitude of the tangential velocity along the elliptic path for the four velocity patterns. β is the exponent in the velocity-curvature relation in Eq. 2. The color scale is based on the minimum and maximum values of the velocity across all four conditions.

Fig. 3 .

 3 Fig. 3. Online visual feedback of the force applied on the robot provided to participants of Exp. 2.B. The red bar moved vertically. F is the current magnitude of the applied force, averaged over 80 ms. F standard RM Sis the average RMS force applied by the participant over 10 trials of the standard (biological) condition. The success zone (white rectangle) was smaller than F standard RM S so that participants would not be tempted to plateau when they reached the level of F standard RM S .

Fig. 4 .

 4 Fig.4. Within-trial evolution of the force applied by participants on the robot in Exp. 1.A for the four velocity patterns and for frontal axis (X) ellipse orientation. Left column: Time-series of the force component along the frontal (X) axis. Middle column: Force component along the sagittal (Y ) axis. The blue line and pink shaded zone represent the average force and standard deviation across all 10 trials and all participants. The gray lines represent individual participant averages across all 10 trials. Only the second and third ellipse traversals are displayed since the first and last ellipses were affected by transients (one trial consists of four continuous ellipses). Note that, for the sake of legibility, the force scale is different in the reverse condition. Right column: Force vector along the elliptic path. Blue lines represent the across-trials and across-participants average force vectors during the third ellipse (sampling rate: 5 ms). The red line represents the elliptic path of the robot. The green dot marks the starting point on the ellipse (t = 6 s). The black arrow indicates the direction of counter-clockwise motion. For legibility, the length of the displayed force vector is divided by 20 in all conditions.

Fig. 5 .

 5 Fig. 5. Evolution across trials of the RMS force for each participant in Exp. 2.A (upper row) and 2.B (lower row). The blue dots represent the individual trials, and the red line is the fitted linear regression. Participants 1 to 5 did not receive visual feedback (Exp. 2.A) whereas Participants 6 to 9 received online visual feedback of the force they applied on the robot (Exp. 2.B).

TABLE I RMS

 I FORCE APPLIED BY PARTICIPANTS ON THE ROBOT FOR THE FOUR VELOCITY PATTERNS OF EXPERIMENT 1.

		Exp. 1.A	Exp. 1.B
		F RM S (N )	F RM S (N )
	Condition	Mean	Std	Mean	Std
	standard	1.42	0.70	1.55	0.80
	constant	1.96	0.89	2.07	0.93
	exaggerated	1.94	0.91	1.96	1.10
	reverse	3.29	1.03	3.28	1.14

TABLE II PER

 II -PARTICIPANT SLOPE AND ITS 95 % CONFIDENCE INTERVAL OF THE LINEAR FUNCTION FITTED ACROSS ALL 200 TRIALS OF EXP. 2.A AND B

	No visual feedback	(Exp. 2.A)	Participant Slope (10 -3 N/trial) CI upper bound (10 -3 N/trial) CI lower bound (10 -3 N/trial)	1 3.0 4.1 1.9	2 0.6 0.8 0.3	3 -2.4 -1.8 -2.9	4 2.4 3.0 1.8	5 0.3 1.0 -0.3
	With visual feedback	(Exp. 2.B)	Participant Slope (10 -3 N/trial) CI upper bound (10 -3 N/trial) CI lower bound (10 -3 N/trial)	6 -2.1 -1.7 -2.4	7 -1.4 -0.8 -2.1	8 -8.6 -4.5 -10.0	9 -5.8 -4.9 -6.7

The figure only displays the frontal axis ellipse orientation, but a similar consistency is observed for the sagittal axis orientation, although with different force profiles.

This paper was recommended for publication by Editor Yasuyoshi Yokokohji upon evaluation of the Associate Editor and Reviewers' comments. This work was supported in part by NIH-R01-HD087089, NSF-NRI 1637854 and 1637824, NSF-EAGER 1548514 and 1548501 and by the Eric P. and Evelyn E. Newman Fund. Pauline Maurice is supported in part by the European Union's Horizon 2020 Research and Innovation Program under Grant Agreement No. 731540


Tomás López Jiménez

Cooperation among Institutions of the Soviet Union and Cuba: Accomplishments between 1972 and 1990

Keywords: Computing in Cuba, Soviet Union, COMECOM, CMEA

This work provides a landscape on the manner in which Cuba and the Soviet Union had cooperated in the computing field between 1972 and 1990. It highlights some of the important milestones between the two nations including Cuban membership on the Council for Mutual Economic Assistance, the COMECOM, and its activities in the Coordinating Committee for Multilateral Export Controls. It also addresses Cuba's relationship with the Former Soviet Union after 1990.

Introduction

The SoRuCom.2006 Conference has offered a unique opportunity to exchange information on contributions to electronic computing (EC) from the Former Soviet Union (FSU). These facts, both worthy and significant for students, professors, and professionals of its disciplines worldwide, need further documentation by the history of computing. This conference occurs sixty years after the public demonstration of the ENIAC computer, immediately after World War II and three years before the establishment of the Council for Mutual Economic Assistance (CMEA) in 1949, under the leadership of the FSU. The intermingling of causes and effects among these events, their true motivations, and their usefulness for humanity are still partially and barely researched or informed. In fact, the effects induced in the CMEA countries by the multilateral collaboration constitute part of the history of the scientific development of the EC promoted by the FSU, which dedicated special efforts to this collaboration; thus, empowering it with the creation in 1969 of the Intergovernmental Commission for Collaboration in the field of EC (ICCEC). Therefore, part of the accomplishments of the joint works is also part of Soviet and Russian computing history.

Cuba became a member of CMEA in 1972, three years after the institution of the ICCEC, over twelve years from the beginning of bilateral relations with the FSU. This paper discloses some elements of this bilateral history on EC. First, we explore its principal landmarks in Cuba since 1972; then we also reflect on some of the main achievements from the rich and friendly Cuban-Soviet collaboration in this field.

Development of the EC in Cuba before its Admission to COMECOM

2.1

Computing in Cuba before 1 January 1959

When the Cuban Revolution triumphed on 1 January in 1959, the knowledge of EC did not exist in a practical sense in the country. This was the status even though there was a vast tradition using tabulating and accounting machines for data processing, including the use of some electronic ones since 1957 that included two IBM 407 machines and a UNIVAC 120. Actually, some private schools, mostly Cuban, prepared specialists for their use. By the end of 1958, the first electronic computer appeared in Cuba; it was a first generation IBM RAMAC 305 with the first magnetic discs in the world, when they still constituted a world novelty [START_REF]See IEEE Santa Clara Valley Section[END_REF]. One should note that in 1927 IBM opened a business office in Cuba, the 27 th outside the borders of the USA; in fact, it placed in the 16 th position among its main landmarks of foreign business concerning the installation of tabulators in Havana in 1927. Cuba was the thirteenth country to which they exported their equipment [2]. The Cuban government confiscated IBM Cuba in 1961. These facts are evidence that in 1959 there were in Cuba some advanced components of EC. In addition, the minimum necessary conditions for starting its development were already in operation and the country exerted a certain attraction for IBM [START_REF] Barquin | The State of Computation in Cuba -DATAMATION[END_REF]. When the United States government broke its diplomatic relations with the Cuban government in 1961, it imposed a ferocious blockade on the country that started in February of 1962, thereby making access to their technology on the island very hard or almost impossible.

First steps: The 1959-1967 period

In 1959, a deep educational reform started in the country. In January of 1960, Commander-in-Chief Fidel Castro stated, "The future of our country has to be necessarily a future of scientific men, a future of thinking men." Later on in March of 1962, the Minister of Industries, Commander Ernesto Che Guevara pointed toward electronics as one of the four important lines for the development of the country. That same year the government organized the Automation and Electronics Division with the mission of developing research and working experiences in electronics, cybernetics, automation, and computing [START_REF] Sáenz | Ciencia y tecnología en Cuba[END_REF].

In 1964, the National Calculus Center (CNC) at the University of Havana (UH) acquired the British second-generation computerthe Elliott 803B; the university completed its installation in 1965. The School of Mathematics and other areas of the university, in collaboration with the Department of Applied Mathematics of the Central Planning Board (JUCEPLAN), as well as other institutions, developed applications for the optimization of transportation, diets optimization and management of chicken plants, numerical weather forecasts, and other areas that benefited the country.

The sugar industry developed important applications for the period as part of its perspective plan to produce ten million tons of sugar in 1970. It all started with the RAMAC and until 1966, it progressively used the Elliot 803B in applications with regression and linear programming models in order to optimize the harvest period and the composition of sugar cane varieties per plant, the operational control, as well as the optimization of the transportation of the sugar cane among other areas.

2.3

The essential conditions were created: The 1968-1971 period

Between 1968 and 1976, the following parallel and complementary paths directed the Cuban development of the EC:

1. Under the responsibility of the JUCEPLAN, the board fostered planning and statistical centralized control over the country plans and programs and the 1970 population and housing census. The National Calculus Plan (PNC) was created for this program, based on the importation of technology and technical assistance. In 1969, the Electronic Calculus Division was also organized. 2. The second path foresaw empowering the scientific and technological national development. Personally conceived and encouraged by Commander-in-Chief Fidel Castro by the end of 1968, it was assigned to the UH, with an immediate objective of developing the first Cuban computer, a real challenge for a very young scientific policy [START_REF] López | Cubans have got a special gift for mastering the computing[END_REF]. 3. The third path was under the responsibility of the national defense and security organisms; it also included a tight collaboration with the other two.

The PNC reached agreements in 1968 with the French government in 1970 for the supply of two second-generation SEA 4000 computers. From 1972 on, there were other supplies of two mainframes IRIS 50 and some minicomputers IRIS 10, both were third-generation models. Some of the minis were remote satellite terminals, three of them were destined to universities and the rest to specialized organizations, mainly places which were already using the Cuban minis CID 201A and B by the time they received the French minis.

On April 1969, the UH created the Digital Research Center (CID) with the mission of developing the Cuban computer. On 18 April of 1970, the first Cuban minicomputer, the CID 201, became operational. It was a third-generation model, with DTL integrated circuits, a 4K memory with 12-bit ferrite core words. Its architecture did not follow a full line of compatibility with the PDP 8. They connected a teletype to it with a paper tape I/O system at 33 bits/sec. In October of 1970, they also connected to it an audio compact cassette tape recorder at 300 bauds, ten times faster than the paper tape, and in addition, an auxiliary memory of up to 64K words by which its applicability, productivity, and reliability were largely increased [6]. This achievement occurred five years before reports of the first standards for similar use in microcomputers; it became an alternative for the expensive flexible disk units in use by then [7]. Eighteen units of the CID 201 were manufactured and delivered between the end of 1970 and 1972, under the name of CID 201A, a technological variant whose only difference relied on the casing.

The fact that the original DEC systems were inaccessible for Cuba and the lack of compatibility between the CID 201A and PDP 8 programs became an extraordinary challenge for the CID researchers. By the end of 1970, the local software of the CID 201 included a basic binary and octal input/output system, an arithmetic package of integer and floating point, a LEAL 201 compiler (Algorithmic Languageauto code of indigenous design in polish and symbolic notation, which followed some of the concepts of Autocode Elliot 803B). By 1972, they added an interpretive compiler of a simplified FORTRAN and some other programs. Additionally in 1972, the experimental CID 202 minicomputer went into service with its research objectives. It had a 16K ferrite memory, with 16 bits words, an original architecture with the novelty of running two simultaneous programs with their respective operators.

By the end of 1972 Cuba saw the completion of the new family of minicomputer CID 201B; however, it was not wholly compatible with the PDP 8. It doubled the 201A speed, with a memory unit of up to 32K words through 4K modules, eight auto index registers by module over the first eight address of each zero page, interruption system for the I/O devices and a bus for direct access magnetic disks and tapes. The computer accommodated various software packages that included an original powerful FORTRAN IV compiler. In October 1972 witnessed the definition of the next generation of minicomputers, the CID 300; it would be wholly compatible in software with the PDP 11, following DEC's more innovative tendencies.

In 1973, CID started a minicomputers factory in the industrial area of the V. I. Lenín Vocational School based on its own indigenous expertise. Students had full participation in the production lines as part of their training and vocational development. This practice proved fruitful for them as they continued their higher education studies as engineers or mathematicians with early deep and advanced theoretical and practical knowledge on computing.

To summarize, therefore, in 1970 UH launched its Computing Commission with a national reach. It strengthened and diversified its research program, incorporating others for the industrial development as well as the applications and fast development of the teaching of the computing disciplines in the national education system. In 1970 the degree in the Computing Sciences began at the School of Mathematics of the UH and at the Central University; numerous faculties and colleges introduced the subjects of FORTRAN IV Programming and Analysis. By 1971 the UH introduced the area of computing engineering for students who had finished their fourth year in telecommunication or in automatic controls. The CID strengthened its academic department as it created courses on operation, programming, and applications, starting a master degree program in digital systems in 1971, in conjunction with Canadian universities.

Main characteristics and accomplishments of cooperation work in EC between the institutions of the FSU and Cuba (1972-1990)

EC tendencies at the beginning of the socialist collaboration

In 1969 the CMEA adopted the agreement to create the socialist central computers (CC -mainframes), five years after the IBM 360 generation of computers appeared. The conclusion of agreements for minicomputers occurred in 1974, nine and four years after the launching of the PDP 8 and PDP 11 respectively, when the microprocessor and integrated memories market had just been born, with a fast incorporation to EC. Local tendencies and needs reinforced the popularization and massive use of computing because it provided greater power at lesser costs. It was already an extraordinary challenge to reach the world upper levels; to stay abreast and to keep a reasonable follow-up and to prevent the relative backwardness from increasing was a very difficult goal.

First steps in the EC collaboration between the FSU and Cuba

Cuba joined the CMEA three years after the agreement to develop the CC systems of the Unified Systems of Electronic Computer Machines. The Cubans already had some essential scientific and industrial knowledge in order to consider higher-level objectives in EC, independently of its economy, which did not yet surpass the characteristics of a poor developing country. That is the reason the world classified Cuba as one of the least developed countries of the signing members.

In 1974 when they reached agreement for the development of the System of Mini Electronic Computer Machines (SM MCE), Cuba, represented by CID as a national head organization, was one of its founding countries [START_REF] Egorov | Detailed Scheme[END_REF]. That is how the collaboration with the Soviet INEUM started, the leading multilateral organization of the project SM.

With the creation of the National Institute of Automated Systems and Computing Techniques in 1976, a member of the Council of Ministers, the Cuban-FSU collaboration in EC was prioritized at a high national level, thereby strengthening and intensifying the relations and compromise among institutions and peoples of both countries [START_REF] Nitusov | Computing Technique of the CMEA countries[END_REF]. The FSU signed the Cuban specialization in central processors, video terminals, keyboards for video terminals and microcomputers, as well as software products for the SM systems.

Main projects and joint outcomes

The Cuban-Soviet projects were part of the minicomputer generation of the SM second architecture, because it included among its guidelines the full compatibility of programs with the PDP 11 family of computers [START_REF] Filinov | System mini ECM (SM MCE)[END_REF]. This would facilitate a more effective contribution to Cubans, due to their experience and knowledge of the DEC lines. This accomplishment occurred despite the fact that the economic blockade, to which they added the CoCoM regulations among others, impeded the access to original products and documentation [START_REF]CoCom: Coordinating Committee for Multilateral Export Controls. CoCom was established during the Cold War to put an embargo on Western exports to East Bloc countries[END_REF].

The CID participated in the SM 3 and SM 4 development, including the joint startup of the first prototypes of the SM 3 in 1976, carried out by INEUM. The Cuban variant of the SM 3, the CID 300/10, reached a conclusion in 1976; its national tests began in 1977 and in the international essay, they codified it as SM 2301, which was in serial production between 1977 and 1988 with a total amount of 410 systems. In addition, they created a Cuban prototype of the SM 4 called the CID 300/20. They also developed the decimal arithmetic processor for CID 2201 (SM 50/02).

From 1974 to 1990, Cuba developed numerous alphanumeric and graphic video terminals, supplying more than 12,000 units to Soviet institutions in addition to satisfying the Cuban needs [START_REF]The XXX Anniversary of the creation of the first Cuban computer, the CID 201[END_REF]. Among the main objectives stated was the gathering of experience with the raster-scan technique, incorporated to the CID 702 (SM 7203) in 1975-1976. They used advanced controllers through analogs from Intel 8275 and 8279. The functional analogy with the most advanced models of leading marks, with solutions and their own resources constituted key objectives. The CID 7205 (SM 7213) emulated the DEC VT 52 and they incorporated a graphic regimen to this model. Other terminals emulated were the VT 100 and the VT 240 [13].

Between 1984 and 1990, various models of keyboards were developed and manufactured, fulfilling the SM standards and guaranteeing the functional analogy with those of IBM PC, VT 100, VT 240, and others. They used in abundance the contact key by electrically conductive rubber; Soviet institutions received dozens of thousands of keyboards from Cuba. The Cuban and Soviet specialists, who jointly developed these projects, reached a favored place among the keyboard and terminal video designers for SM.

With the software for SM, they obtained important results, among them the COBOL CID 300 compiler, tested for the SM in 1979, and widely used with Soviet minicomputers. Some other software products were the management system GES300, the multi terminal SMT300, the dBASE300, the UNIX tools and the COMUNIX CID300-IBM.

Conclusion

Nowadays, both the organizations and the Cuban specialists that worked closely together for more than eighteen years with their Soviet siblings are devoted to other development and application of modern informatics, where by some ways many of the results of that long and fruitful collaboration remain. In the 1980s, the ICID began a gradual redirection towards the development and production of high-level medical equipment and applications for diagnosis, intensive care, rehabilitation, and reaching a very high prestige and quality in that specialty. These equipment and applications are used profusely in the national health system and are exported to several countries. A similar process happened with complex automation, now specializing in applications for the sugar industry, the medical and the pharmaceutical industries, and the tourist facilities as well. Certain factors, beyond the objectives of the current work, caused the advance and the level of the results of the socialist CE to lag behind in respect to the advance of leader countries at world levels. Nevertheless, in that period the collaborative work made unquestionable and everlasting contributions to human development. Among them are the contributions to scientific knowledge and the graduation of a great mass of highly qualified specialists, that were in those moments placed at the disposal of countless and diverse institutions. It is an irrefutable fact that as a result of this bilateral collaboration, at least modest contributions were added to those objectives, along with the friendship and mutual knowledge achieved among Cubans and formerly Soviet citizens, forever Russian citizens. The history stated here and much more are part of the history of computing of these countries.


Ksenia Tatarchenko
email: ktatarch@princeton.edu

"Lions -Marchuk": The Soviet-French Cooperation in Computing

Keywords: Computers, Soviet Union, France, Cold War

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

Introduction

Two common assumptions dominate the perception of the history of Soviet computing: Soviet computers were few and not very good; levels of secrecy were extremely high, causing isolation from the international community. [START_REF] Bariéty | Le voyage de de Gaulle à Moscou en 1966 et la «question allemande» (D'après les documents des Archives de ministère français des Affaires Etrangères)[END_REF] This paper demonstrates that although these notions are not entirely incorrect, there is a case demonstrating that the development of Soviet computer science was on par with the international level, and that East-West cooperation in computing did exist. The case under investigation is the so-called "Lions-Marchuk" collaboration under the umbrella of the Soviet-French bilateral agreement of 1966. I attempt to answer the question: How did such cooperation become possible politically, institutionally and scientifically?

The three parts of the paper articulate the beginnings of Soviet-French cooperation in the following order. First, I introduce a vertical framework for the Lions-Marchuk relation, which is the Soviet-French Bilateral Agreement in Science and Technology. I argue that the agreement should be read in the context of the pivotal role that science and technology played in transatlantic hegemonic relations. In the second part, I examine the horizontal level of cooperation: How did the peculiarities of the development of computer technology and science in France and the USSR create the institutional bases and motivations for cooperation in computing? Finally, I study the realities of the so-called "Lions-Marchuk" cooperation.

«Détente, entente et coopération»

In March 1966, France left the leadership of the NATO, and, three months later, General de Gaulle undertook a triumphant official visit to the Soviet Union. This visit was, no doubt, a great event for the Soviet diplomacy. From the 20 th to the 28 th of June de Gaulle visited Moscow State University, Novosibirsk and its Akademgorodok, Leningrad, Kiev and Volgograd. The results of the visit are still a historical controversy. Some diplomatic historians assert that Soviets were left almost empty-handed: an invitation to visit Paris and a couple of scientific exchange agreements. The main issue of the day, the so-called "German Question," was left without any resolution. [1, 2] For some others, the French-Soviet Agreement signed on the 30 th of June 1966 marked the French-Soviet détente and served as a model for the subsequent relations between the Soviet Union and Western countries. [13] I believe that the scientific agreements between France and the USSR should be read in the context of John Krige's conclusion that basic science was the key node articulating American hegemony with the post-war reconstruction of science in Europe. [9] The French pursuit of nuclear capacity is the best-known element of the European resistance to American scientific and technological leadership. According to French technocrats the wartime defeat was to be overcome through technological development; the future of the French nation was at stake. [6] In this light, the agreements of the 30 th June were more than a gesture and should be inscribed in a longer political movement of establishing French science and technology as independent from United States' influence. [START_REF] Belousova | K vizitu generala de Gollia v Sovetskiy Soiuz v 1966 godu (Na osnove arkhivov Ministerstva Mezhdunarodnykh Del Rossii)[END_REF] Whereas informatique, the French term for computer science, became international, early French computing history is sometimes told as a "history of technology transfer." [START_REF] Carr | A Visit to the Computation Centers in the Soviet Union[END_REF] In fact, the French name for computerordinateur,was invented in 1955 to better promote IBM machines on the French market. Furthermore, in 1964, the General was faced with a somewhat unanticipated set of problems. Bull, the only French company that specialized in computers for management, lost its majority holdings and became dominated by the American General Electrics Company. France had an effective nuclear force de frappe, the ultimate demonstration of the triumph of De Gaulle's independent line; yet the failure to retain a native computing industry was significant. When in 1966 the USA put an embargo for a delivery of a big scientific computer (CDC 6600) ordered by France for its "bombe H" calculations, it triggered important governmental interventions in the affairs of French computing industry and science.

In the second half of 1960s, the new ambition of the French government was to challenge the American domination of the French computing market. The special inter-ministry commission created in 1965 rated informatics of "equal importance to atomic energy, civil aviation, and space." [START_REF] Dahan-Dalmedico | Un Mathématicien d'exception entre recherche, industrie et politique[END_REF] Within the Soviet Union the situation in the field of computing was rather complicated: a great deal of secrecy and contention split Soviet computing between the military and academia. [7, 12] The military benefited from a better material supply; meanwhile academia counter-balanced its scare resources with a relative openness. In October 1955, the existence of Soviet computers was revealed to the world at the now famous Darmstadt Conference, prior to being officially declassified for the Soviet Union's own citizens. [START_REF] Gerovitch | From Newspeak to Cyberspeak[END_REF] After this date there were rare visits and contacts between Soviet and Western computer scientists under the inter-academies exchange agreements and under the auspices of the International Federation for Information Processing (IFIP). [3] High level scholars connected with computing, such as academician Dorodnitsyn, were looking for every possibility of international contacts, and advanced the following reasons when arguing at the governmental level: to access easy sources for information collection; but also to prevent negative propaganda of the USSR's technological underdevelopment, provoked by insufficient demonstration of the Soviet achievements in computing. [START_REF] Hecht | The Radiance of Franc: Nuclear Power and National Identity after World War II[END_REF] When in 1966 the French-Soviet Agreement provided a rare opportunity for cooperation, it was able to satisfy several Soviet interests: to grant the Soviets information on the French "state of the art" in computing, but also to provide a platform to access American know-how, since Americans were dominating the French market and French researchers had extensive connections with American scientists. Ironically, Akademgorodok, a center situated far away from Soviet Western frontiers, became the main beneficiary of this new possibility for cooperation. In 1958, academicians Lavrentiev, Sobolev and Khristianovitch acquired the support and funds from the Khrushchev government for the construction of a Siberian city of science. Designed as an alternative to the secret research centers working for the military (the infamous "boxes"), the new Akademgorodok was created to stimulate Siberian civil research, its connections with industry, and the exploitation of Siberian natural resources. Using his position at the head of a newly created Siberian branch of the Academy of Sciences and personal connections at the "top," Lavrentiev promised young talented researchers fast promotions and some cold but free air far from Moscow's sight. [8] These conditions rapidly made the scientific town an international center of great fame.

The context unfolded here can explain French and Soviet official willingness to cooperate in the field of computer science, endowing the agreement with some real content of "mutual interest." The international treaties that followed the visit of General de Gaulle to the USSR in 1966 provided the administrative and financial framework for cooperation. Cooperation between Soviet and French computer scientists functioned and developed according to these structures throughout the following decades up until 1993.

Akademgorodok CC -INRIA

INRIA, as a pilot institution for computer science, was responsible for Soviet-French cooperation in this field and represented France in all negotiations at the level of the working group in computing. Institutes specialized in computing under the auspices of the Academy of Sciences participated on the Soviet side. The Akademgorodok Computing Center (CC) became the main interlocutor of INRIA due to a constellation of circumstances: the official civilian character of the research done in Akademgorodok, the important role of computers as scientific tools for Akademgorodok sciences, and the human factor. Academicians Sobolev and Lavrentiev are known for their personal involvement with the early development of Soviet computing; unsurprisingly, they launched an initiative for the creation of a special CC in Akademgorodok. [START_REF] Ichikawa | Strela-1, the First Soviet Computer: Political Success and Technological Failure[END_REF] Lavrentiev personally invited a young applied mathematician, Guriy Marchuk, to direct it. In 1964, the CC became independent from Sobolev's Institute of Mathematics and existed until the troubled times of nineties, when it was divided into several institutes.

The best account on the early history of Soviet computing under the umbrella of cybernetics is From Newspeak to Cyberspeak: A History of Soviet Cybernetics by Slava Gerovitch. The focus of the book is the complex relation between Soviet science and politics, which was responsible for the checkered nature and destiny of Soviet cybernetics. [5] Akademgorodok became home for Alexey Liapunov and Sergei Sobolev, two of three authors of the famous article-manifesto "Essential Characteristics of Cybernetics" [Osnovye cherty kibernetiki], which appeared in Questions of Philosophy [Voprosy Filosofii] in 1955 and marked a turning point in favor of cybernetics, previously publicly abused as pseudo-science. [14] Moreover, some new generation computer scientists, like Andrey Ershov, a talented pupil of Liapunov, gathered in Siberia at the very moment when Soviet cybernetics was gaining in power. Located at the periphery of the cybernetic movement, these scientists were involved with a different kind of computing, distinct from the interdisciplinary cybernetics. According to my interpretation the young Akademgorodok CC (newly created and staffed with a very young team) was implementing the principle "enough philosophy, lets get to work," and was intentionally seeking international contacts in order to build its reputation on a national scale. The quest for machines, budgets, buildings, and human resources was closely connected to the issues of scientific authority and fame.

The conditions in which the French INRIA had found itself were not entirely dissimilar. French scholars labeled the early period of INRIA's existence as "badly guided" -"Institut malmené." [START_REF] Josephson | New Atlantis Revisited: Akademgorodok, the Siberian City of Science[END_REF] The challenges left to the young institute by the government, research for the French industry and education, were very difficult to realize in the conditions of insufficient and unqualified personnel, lack of machines, and a constant threat of decentralization. In addition, the heterogeneous administration constantly fought over the distribution of the tight budget. In order to assert its own identity, INRIA sought partners at home and abroad.

The first reports published by INRIA underlined its success in developing international connections. INRIA was responsible for education in computer science and distributed international fellowships, which helped a lot to establish initial contacts with the most prominent centers in the United States. [START_REF] Krige | American Hegemony and the Postwar Reconstruction of Science in Europe[END_REF] These first reports also revealed the role of INRIA in Soviet-French cooperation. The first president of the institute, Michel Laudet, traveled to Moscow to participate in French-Soviet working groups and set up the procedures for exchanges. [START_REF]Méthodes Mathématique de l'Informatique -4, Sur les méthodes numérique en sciences physiques et économiques Marchouk[END_REF] However, most interesting for us are the summary descriptions of the cooperation between the department of numerical computing directed by Lions and the Akademgorodok CC, directed by Marchuk. This line of collaboration became nicknamed "Lions-Marchuk cooperation," reflecting the importance of the personal relationship between the two scientists.

Lions -Marchuk Cooperation

In Marchuk's published memoirs, an almost legendary story tells us that, during his visit to Akademgorodok, General de Gaulle personally delivered J-L Lions' invitation to Marchuk to visit his laboratory in Paris. [START_REF]Méthodes Mathématique de l'Informatique -7[END_REF] The invitation in question was more likely made by Gaston Palewski, the Minister of Science and Technology from 1962 to 1965, during a different visit to Akademgorodok. However, the metamorphosis captured in the memoirs (published in 2002) transforms the Marchuk of 1966 into a hero with a historical mission and underlines the important political aspect of the beginning of the Lions-Marchuk cooperation.

Documents show that at first Marchuk visited Lions at the Institut de Blaise Pascal, part of the Sorbonne, in 1966. Soon Lions became the director of the department of Numerical Informatics, later renamed Laboria, the research unit at the heart of INRIA. Surrounded by the talented young people, so-called "lionceaux" ("lions' cubs" in French), Lions succeed in developing a powerful school of applied mathematics, and expanded considerably its field of operations. [4] I was told by Alain Bensoussan, one of the "lionceaux" who replaced Lions as head of INRIA, that long before any official cooperation Lions was particularly interested in Siberian splitting up methods and encouraged Bensoussan to employ them in his PhD research. [START_REF] Malinovskii | Istoriia vycheslitel'noi tekhniki v litzakh[END_REF] Marchuk also recalls being surprised by Lions' deep knowledge of his works; Lions read scientific Russian but couldn't speak it. [START_REF] Rey | La Tentation du rapprochement: France et URSS à l'heure de la détente, 1964-1974[END_REF] Apparently linguistic issues did not cause any trouble to establishment of mutual sympathy based on the commonality of research interests, but also on several less tangible factors, such as the tradition of collaboration between Russian and French mathematicians and common traits in personalities.

It is important to highlight that the collaboration worked out not only for Lions and Marchuk themselves: in fact, they also made their teams cooperate. The INRIA reports describe three principal themes of cooperation: 1) Techniques of decomposition, decentralization and parallelization (cooperation on the splitting up methods by N. Yanenko and R. Temam); 2) Identification of systems; 3) Optimization. [START_REF] Sobolev | Osnovnue cherty kibernetiki[END_REF] In brief, almost all of the most influential "lionceaux" participated in collaborations with Soviet scientists from Novosibirsk. Important personal links on the lower levels of the network were formed. 15 Such cooperation involved making their students work on adjacent topics and sharing their results. It was cumbersome to organize a long visit for a student or researcher, because of a difficult bureaucratic procedure, the request for a place from the so-called "long-stay" quotas. However, the government sponsored the short-term visits and annual meetings. From the end of the 1960s and during the 1970s, short visits were routine, and the so-called "Lions-Marchuk" colloquium took place every year, alternating between Akademgorodok 11 G. I. Marchuk, O. N. Marchuk, Neizvestnye stranitzy iz zhizni nekotorykh uchionykh (Moskva: Nauka, 2002), pp. 137-38. [START_REF] Malinovskii | Istoriia vycheslitel'noi tekhniki v litzakh[END_REF] Alain Benssoussan, personal communication to the author. [START_REF] Rey | La Tentation du rapprochement: France et URSS à l'heure de la détente, 1964-1974[END_REF] Guriy Marchuk, personal communication to the author. [START_REF] Sobolev | Osnovnue cherty kibernetiki[END_REF] and Paris. The main visible results of these meetings were publications, such as the following volumes: Sur les méthodes numériques en sciences physiques et économiques; Étude numériques des Grandes systèmes. [10, 11] The contents of these collections reflect 1970s tendencies within numerical analysis. The main topics of research were: principles of organization of software systems for the resolution of partial differential equations by finite elements; modeling and optimization of complex systems; and technical aspects of implementation of methods of approximation using supercomputers.

One important factor that both Lions and Marchuk had to deal with was the wellknown problem of the lack of machines. They were interested in developing numerical techniques allowing optimization of machine power. INRIA and Akademgorodok CC researchers had to proceed with a different philosophy compared to the American approach when resolving scientific problems. There is a direct statement disclosing these differences of practices in Lions' letter to Harold Agnew, director of the Los Alamos Laboratory from 1970 to 1979. Lions explains: "We have to work in advantage on the models and mathematical aspects before going to the computer. From this point of view (and only from this one!) we work more like the Russians." 16 The oral history interviews I conducted with Lions' collaborators transmitted a very similar message, but without the parenthetical note.17 Two schools of numerical analysis, the French and the Siberian, had at least two characteristics in common: they had "to think more" (than Americans) and they relied heavily on personal networks, structured around the father figures of the school-founders.

Although neither Marchuk nor Lions are computer scientists, properly speaking, they played crucial roles in promoting the use of computers as scientific instruments and in creating the administrative basis for the development of computer science. Both Lions and Marchuk were sought-after and successful advisers, keeping links with their former students and actively helping them to acquire positions, so that the "Lions-Marchuk cooperation" acquired the character of "networks in cooperation." Both Lions and Marchuk not only frequently crossed national frontiers, but also circulated with ease in the different spheres: science, politics and industry. From the middle of the 1970's and during the following years the careers of these two men underwent a dramatic rise. They became powerful administrators of the "big science" at the highest levels. 18 A consequence was a change in the nature of their involvement in cooperation matters.

Conclusion

We saw that for the cooperation between the French and Soviet computer scientists to exist, an accumulation of political, institutional, and personal willpower and interest was indispensable. The French government wanted to cooperate in order to build up a computer industry and research independently of American efforts. The Soviets were trying to access the Western computing world. Both INRIA and Akademgorodok CC were young institutions and used international contacts to create their own identity and to establish their authority within the national context. Finally, Lions and Marchuk were the human engines of the cooperation. They used the political agenda to realize their scientific and career ambitions, generating transnational links at the different levels of their personal networks.

The Lions-Marchuk cooperation demonstrates that Soviet -West cooperation in computing did exist under certain political circumstances, and that the well-known Soviet shortage of machine power contributed to the development of numerical techniques of great interest to Western researchers. Finally, this paper reveals the potential promise of looking beyond the Soviet-American antagonism.

  On July 19 th , 1966 General de Gaulle signed the "Plan Calcul" which prompted the creation of a new private computer company and a public research institute: CII (Compagnie Internationale pour l'Informatique) and INRIA (Institut National de Recherche en Informatique et Automatique). Symbolically, the newly created INRIA was attributed the location in Rocquencourt, a NATO military camp recently liberated from its occupants. Researches moved into the military caserns.

  Rapport d'activité de l'INRIA, 1969, p. 51. 15 One of the favored examples of INRIA staff is a romantic story between a French researcher from INRIA, A. Morocco, and an interpreter from Akademgorodok. The love story grew into the marriage, witnessed by numerous documents in INRIA Archives. Morocco and his wife asked for research travel to Akademgorodok. Here is one quote from the correspondence between Lions and Marchuk: "…you already know him. He would go with his wife, who is from Novosibirsk (the best example of collaboration!!!)" January 10, 1978, INRIA Archives, box 83.06.035.

For an earlier example of such a movement, see how the USSR adapted the French standard for its television: Walter Kaiser, "The PAL-SECAM Color Television Controversy," History of Technology, vol. 20 (1998), no.1: 1-16.

Pierre Mounier-Kuhn, "History of computing in France," IEEE Annals of the History ofComputing, vol. 11 (1989), no.

4: 237-240, p. 237. The whole volume is dedicated to the history of computing in France.

Henri Boucher, "Informatics in the Defense Industry," IEEE Annals of the History of Computing, Vol.12 (1990), no. 4: 227-240, p. 238.

Unfortunately, the history of the Darmstadt is relatively understudied, see: Slava Gerovitch, From Newspeak to Cyberspeak: A History of Soviet Cybernetics, (Cambridge, Mass.: MIT Press, 2002), pp. 155-58; Herman Goldstine, The Compute from Pascal to von Neumann (Princeton, NJ: Princeton University Press, 1972), pp. 349-62. For published sources see: "Darmstadt Conference Proceedings," Nachrichtentechnische Fachberichte (Braunschweig), vol. 4 (1956), no. 1; and Alston Housholder, "Digital Computers in Eastern Europe," Computers and Automation, no. 12:4 (1955), p. 8.

A. A. Dorodnitsyn, "Justification of the USSR AS need to join IFIP", October 9, 1959 in Ershov Archive, see: http://ershov.iis.nsk.su/archive/eaimage.asp?lang=2&did=28&fileid=78246

Notes on the conversation about the history of Soviet Computing with M. A. Lavrentiev by A. P. Ershov in Ershov Archve, see: http://ershov.iis.nsk.su/archive/eaindex.asp?pplid=799&did=17909

Alain Beltran and Pascal Griset, Histoire d'un pionnier de l'informatique (Paris: EDP Sciences, coll. Sciences & Histoire, 2007), p. 17.

Rapport d'Activité de l'IRIA, 1972, p. 73.

Rapport d'Activité de l'IRIA, 1970, p. 59.

J-L Lions to Harold Agnew, letter quoted in Dahan-Dalmedico, Jacques-Louis Lions, pp. 183-84.

George Nissen, personal communication to the author.

Marchuk is best known as the last president of the Soviet Academy of Sciences and Lions left INRIA to preside over the French national center for space studies (CNES).

Acknowledgments

This paper is based on my master thesis defended at the Sorbonne in June 2005, INRIA -Akademgorodok, a history of French-Soviet Cooperation in Computer Science, 1966Science, -1993. I would like to thank the people who granted me interviews and supplied other information, particularly G. I. Marchouk, A. S. Alexeev, V. P. Orechenko, A. B. Ugolinokov, A. Bensoussan, G. Nissen, and P. Nepomyastchy.