Marija Tomić

Christine Chevallereau

Kosta Jovanović

Veljko Potkonjak

Aleksandar Rodić

Human to humanoid motion conversion for dual-arm manipulation tasks

Keywords: Motion capture system, dual arm manipulation, imitation algorithms, humanoid robot, motion planning

A conversion process for the imitation of human dual-arm motion by a humanoid robot is presented. The conversion process consists of an imitation algorithm and an algorithm for generating human-like motion of the humanoid. The desired motions in Cartesian and joint spaces, obtained from the imitation algorithm, are used to generate the human-like motion of the humanoid. The proposed conversion process improves existing techniques and is developed with the aim to enable imitating of human motion with a humanoid robot, to perform a task with and/or without contact between hands and equipment. A comparative analysis shows that our algorithm, which takes into account the situation of marker frames and the position of joint frames, ensures more precise imitation than previously proposed methods. The results of our conversion algorithm are tested on the robot ROMEO through a complex "open/close drawer" task.

Introduction

The imitation process is an interesting and fast method for teaching robots new motion skills. The motion learning process is based on the repetition of observed motions. Once a human observes a task being carried out for the first time, they are usually capable of immediately performing the same action. In robotics, this process is more complex and can be interpreted in different ways, such as: the imitation learning process and the motion imitation process [START_REF] Do | Imitation of human motion on a humanoid robot using non-linear optimization[END_REF]. The imitation learning process is aimed at understanding the characteristics of human motions, based on data collected from multiple observations of the demonstrated action. On the other hand, the motion imitation process is based on the imitation of human movements without any analysis of the characteristics of the human motion. In this paper we consider the latter approach and propose an algorithm based on how the robot imitates human motion, by utilizing recorded data obtained from a marker-based motion capture system. Today, there are numerous techniques for recording and analyzing human motions. Human motions can be tracked by a number of different motion capture systems, such as inertial, optical, magnetic, acoustic or mechanical. The type of motion capture system used depends on the volume of measurements taken, the required resolution, the characteristics of the motion recorded and the environment in which the motion is performed. Acoustic [START_REF] Vlasic | Practical motion capture in everyday surroundings[END_REF], inertial [START_REF] Miller | Motion capture from inertial sensing for untethered humanoid teleoperation[END_REF] and magnetic [START_REF] Aloui | A new approach for motion capture using magnetic field: models, algorithms and first results[END_REF] motion capture systems are able to record outdoor and indoor human motions. The most commonly used techniques for recording human movement are marker-based and marker-less motion capture systems. Comparative analyses of different motion capture systems are given in references [START_REF] Ceseracciu | Comparison of markerless and marker-based motion capture technologies through simultaneous data collection during gait: proof of concept[END_REF][START_REF] Zhou | Human motion tracking for rehabilitation-A survey[END_REF][START_REF] Gómez | Analysis and comparison of motion capture systems for human walking[END_REF]. In order to record a 3D model of human motion, including the position and orientation of the required segments and joints, in this research we used an ART marker-based motion capture system.

The imitation process can be defined in Cartesian space and/or joint space [START_REF] Billard | Discovering optimal imitation strategies[END_REF]. In Cartesian space, the motions of the hands, head, or feet are recorded and a geometric inverse model of the humanoid can be used to achieve the task. In joint space, the objective is to enable the robot to replicate joint motions of the human, following the human configuration. This last objective is conventionally used for the imitation constraints and dynamic stability. Jamisola et al. [START_REF] Jamisola | Task-space modular dynamics for dual-arms expressed through a relative Jacobian[END_REF] show modular task-space dynamic formulations for a dual arm controlled as a single manipulator. They used existing kinematic and dynamics models of each of the stand-alone manipulators to arrive at the overall dynamics of the single end-effector dual-arm. The treatment of a dual-arm as a single end-effector manipulator through the use of the relative Jacobian affords a drastic increase in the null-space dimension and lesser constraints in the task space. This approach was tested for dual-arm manipulation tasks which did and did not require coordination between hands.

The human motion imitation problem is addressed at the kinematic level by Ude et al. [START_REF] Ude | Programming full-body movements for humanoid robots by observation[END_REF][START_REF] Ude | Automatic Generation of Kinematic Models for the Conversion of Human Motion Capture Data into Humanoid Robot Motion[END_REF]. They propose a method for transforming the recorded 3D position of the markers into high dimensional trajectories of the humanoid robot joints based on twist representation. The human body was modeled as a scaled model of the humanoid robot. They established relationships between the motion of the robot's joints and the motion of the markers by using B-spline wavelets and large-scale optimization techniques.

The method was applied offline to a humanoid robot called DB. Ayusawa et al. [START_REF] Ayusawa | Simultaneous global inverse kinematics and geometric parameter identification of human skeletal model from motion capture data[END_REF][START_REF] Ayusawa | Motion retargeting for humanoid robots based on identification to preserve and reproduce human motion features[END_REF] propose a gradient-based method for simultaneous identification of the geometric parameters of a human skeletal model and calculation of inverse kinematics by using information about the recorded positions of markers.

In order to define the geometric parameters, as segment lengths, and the positions of the markers relative to the robot segments, they introduced virtual translation of joints. In the present research, the problem of human motion imitation was studied at the kinematic level.

According to the state of the art of the imitation process, we additionally explored:

• Imitation of the upper-body human motion by the humanoid, where the motion consists of phases without and/or with hand contact with the environment and a transition strategy between these two types of motion.

• An analytical imitation algorithm based on the Jacobian matrix (instead of the standard optimization algorithm presented in our previous research [START_REF] Tomić | Arm Motions of a Humanoid Inspired by Human Motion[END_REF]), which is capable of real time extraction of Cartesian motions and joint motions that can be used by the humanoid.

In the present research, human-to-humanoid motion conversion is divided into two parts. In the first part, we used the information provided by the motion capture system and analytically defined the imitation algorithm to acquire the desired motion of the humanoid in the task and joint spaces. The algorithm is based on the markers positioned on a scaled model of the humanoid (virtual markers), which follow the motion of markers (real markers) placed on the human. The intermediate use of a scaled model of the humanoid presented by Ude et al. [START_REF] Ude | Automatic Generation of Kinematic Models for the Conversion of Human Motion Capture Data into Humanoid Robot Motion[END_REF] permits the size of the robot to be adapted to the size of the human that has accomplished the task and thus to record the coherent joint and Cartesian motions. Since the task of the imitation algorithm proposed in the present paper is to generate a motion where the hands and the environment are in contact, precise imitation of the hand motions is important. This imitation algorithm incorporated not only marker motion but also joint motion measurement, in order to increase the robot's imitation accuracy. Instead of twists in our kinematic model, the modified Denavit and Hartenberg (DH) convention was used to simplify modeling [START_REF] Khalil | A new geometric notation for open and closed-loop robots[END_REF]. The imitation algorithm is based on the kinematic structure of the humanoid and can be used in real time.

In the second part of the conversion, the motion imitation of the scaled robot model was used to generate a human-like motion on the robot ROMEO in its real size (1.40 m tall) and in the same environments. The strategy differed depending on whether a contact with the environment did or did not exist during the studied phase of motion. When there was contact with the environment, the hand motions were defined to achieve the contact and the robot hand motions had to be the same as those of the human. During the phase without contact, priority was given to motion that appeared visually close to human motion and was based on similar joint motions of the humanoid robot with respect to the human. Hand motions can be modified since they are not constrained by equipment. As such, if contact motion is observed, hand motion in Cartesian space is perceived as a constraint while joint positions in joint space are the object of the optimization process. Contrarily, if contact free motion is observed, the optimization process focuses on both hand motion in Cartesian space and joint positions in joint space, and different priorities can be set.

The approach exploited in this research is elaborated in Section 4. Conversion from human to humanoid motion is analyzed for a complex task that consists of both types of motion. A transition strategy for motion with and without contact is introduced. Since the task is motion imitation with contact between hands and equipment, the technique proposed by Ude is unable to generate these types of motions for the robot. The advantage of the proposed conversion algorithm over existing algorithms is precise imitation of the position and orientation of human hand motions, which is necessary to perform the task. The results of the conversion algorithm were tested on the ROMEO robot in the same environment as that of the human.

The following paragraphs present kinematic parameters and their correlations for each model instance in the conversation process (human and graphical/digital representation -avatar, scaled model of the humanoid, and ROMEO). An overview of the entire human-to-humanoid motion conversion process is provided in Section 2. Each step of the conversion process is explained in detail. The conversion process for human-to-humanoid motion imitation is directly related to the transformation process from kinematic human parameters to those of the humanoid. To that end, three kinematic models were used: kinematic model of the human graphical/digital representation (avatar), scaled kinematic model of the ROMEO robot, and kinematic model of the real-size ROMEO robot (see Fig. 1). These models were represented by their parameters in Cartesian space and joint space, as indicated in Fig. 1. The conversion process started with the kinematic model of the human body, which was automatically generated by the motion capture system. This digital/graphical representation of the human body was denoted as the avatar model. The avatar model contained twenty spherical joints (60 degrees of freedom (DoFs) in total), to define its kinematic model. The avatar segment sizes which corresponded to those of the human were estimated by the motion capture system. To enable human motion imitation by a humanoid robot, ROMEO was selected because it is a humanoid with 37 DoFs, but its segment sizes differ from those of a human. In order to make a connection between the avatar and the humanoid kinematic model, an intermediate model, called a scaled model of the humanoid, was defined. The scaled model of the humanoid had the same kinematic structure as ROMEO (37 DoFs) and the same segment sizes as those in the avatar model.

The conversion from the avatar to the model of the humanoid in Cartesian and joint spaces was described by equations, to facilitate understanding of the scaling process. Considering the avatar model, Eq. [START_REF] Do | Imitation of human motion on a humanoid robot using non-linear optimization[END_REF] relates generalized joint coordinates ( h q ) and hand position and orientation in Cartesian space:

h h h X J q = (1)
For dual-arm manipulation, h X represents the position and orientation of both human hands, and h J is the Jacobian matrix of the avatar model. The dimension of vector h q contains 60 elements that correspond to the avatar's 60 DoFs. However, to enable conversion from the recorded human motion to the generated ROMEO robot motion, the scaled kinematic model of ROMEO was used to represent the human body model. To that end, the scaled robot model had 37 DoFs and segment dimensions equal to human. The imitation algorithm, based on the scaled model of the humanoid, was defined with the ultimate goal of generating human-like motion of the humanoid in joint space. The marker trajectories and the joint positions in Cartesian space obtained for the avatar model were translated to the scaled model of the humanoid. Consequently, this information was input into the imitation algorithm to obtain the human motion in joint space sr q . Accordingly, the human hand motions in Cartesian space generated by the scaled model of ROMEO were calculated from the equation:

h sr sr X J q = (2)
where sr J is the Jacobian matrix of the scaled model of ROMEO. For humanoid robot control, the joint motion sr q is useful but the motions of the hand, which are in contact with the environment, are mandatory. Since this information was not directly measured by instrumentation, it was defined via Eq.

(2) based on the joint motion resulting from the imitation process and the Jacobian matrix sr J . To arrive at human motion of the humanoid robot ROMEO, joint motion sr q can be played on the robot. However, the motion of the robot's hands in Cartesian space, resulting from joint motion sr q , was defined by the equation:

robot robot sr X J q = (3)
where robot J is the Jacobian matrix of the ROMEO model and robot X is the position and orientation of ROMEO's hands in Cartesian space. The scaling factors between models of different segment sizes were integrated through the Jacobian matrices robot J and sr J . The motion of the robot's hands in Cartesian space ( robot X ) was different from the motion of human hands h X since the segment sizes of the human and the robot were not the same. Therefore, the motion of the robot's hands generated in this manner can only be used for a motion without contact between hands and equipment. If the motion involves such a contact, the motion of the robot's hands has to be the same as that of the human in Cartesian space:

robot h X X = (4)
Thus, in contact tasks where the motion of the robot's hands has to be the same as of human hands in Cartesian space, and where, additionally, human motion needs to be imitated in joint space, the generalized robot coordinates ( robot q ) can be defined by the inverse kinematic algorithm [START_REF] Ceseracciu | Comparison of markerless and marker-based motion capture technologies through simultaneous data collection during gait: proof of concept[END_REF]. The inverse kinematic algorithm is the object of optimization, as explained in Section 4.

( )

robot robot h robot robot sr q J X I J J q

+ + = + - (5)
Here, robot J + represents the pseudo-inverse of the matrix robot J and I is the identity matrix.

The paper is organized as follows. Section 2 presents the conversion steps from human to humanoid motion and the basic characteristics of the robot and the capture motion system. Section 3 proposes our imitation algorithm that converts data obtained from the capture motion system into joint trajectories of the scaled robot model. The imitation process starts with the definition of the humanoid robot kinematic model. The motion generation algorithm for the real robot ROMEO, which takes into account the output from the imitation algorithm, is given in Section 4. The conversion process was tested for the dual arm "open/close drawer" task and the results are presented in Section 5.

Conversion Steps from Human to Humanoid Motion

Regardless of the motion capture system, the conversion from human to humanoid motion can be represented in four steps: the first step is recording of human motion; in the second, a digital/graphical representation of the human body (avatar) is defined according to the data acquired by the motion capture system; in the third step a human-size kinematic model of the robot (scaled humanoid model) is defined and the imitation algorithm used to obtain motions in the joint and Cartesian spaces of the humanoid; and the fourth step concerns the generation of ROMEO's motion (with and without contact), using the output from the imitation algorithm. An overview of the conversion from human to humanoid motion is given in Fig.

2.

Fig. 2. The process of conversion from human to humanoid motion

The motion capture system is able to recognize and find relations between the actor's body segments in consecutive frames and provide a graphical representation of the actor (avatar) in a virtual environment [START_REF] Gmbh | System user manual ARTtrack[END_REF] (see Fig. 2, step 1). The kinematic model of the avatar graphically represented the human body and included 60 DoFs (20 joints with 3 DoFs per joint). Since the kinematic model of the humanoid, which was used in the imitation process, had 37 DoFs in total (fewer DoFs than the avatar), the model of the avatar could not be used directly and a reduced model that enabled human to humanoid motion replication had to be adopted.

An adult human body has 206 bones linked by different types of joints, which can be flexible. The imitation process needs to be based on the effective kinematic model of the humanoid robot, consistent with its joint mobility and size. Many humanoid robots of a size close to that of a human have several DoFs, e.g. at least 7 DoFs per arm and 6 DoFs per leg (see Fig. 3). A humanoid robot with these characteristics, such as the humanoid robot ROMEO, can be used for accurate human motion imitation.

The closer the kinematic model of the humanoid is to the model of a human as regards the size, joint limits and kinematic model, the better the imitation.

The transformation of the kinematic model of the avatar to the model of ROMEO is described on two levels. At the first level, the simplification of the kinematic model was taken into account, so the kinematic model of the avatar (which had 60 DoFs) was reduced to the model of the robot ROMEO (37 DoFs). This kinematic model, which had the same segment size as that of the avatar model and the number of DoFs equal to those of ROMEO, was defined as a scaled model of ROMEO. Therefore, the scaled model of ROMEO was used in the imitation algorithm to define human motion in joint space. The output of the imitation algorithm was coherent motions in joint space and Cartesian space for the scaled model of ROMEO. At the second level, the difference in body segments between the human and ROMEO was taken into account in order to imitate human motion with the real model of ROMEO. Imitation was implemented with the algorithm for human-like motion generation. At this level, the motion defined in joint and Cartesian spaces provided by the imitation algorithm was non-coherent (using the real size of ROMEO) and the algorithm favored the motion defined in joint or Cartesian space depending on whether the task did or did not involve contact with the environment.

Robot ROMEO

The humanoid robot ROMEO has been developed by Aldebaran Robotics (see Fig.

ART Motion Capture System

The ART motion capture system consists of a hybrid suit of 17 sets of markers relative to the feet, shins, thighs, shoulders, upper arms, forearms, hands, head, hip, back, and torso (see Fig. 2). A set of 8 infrared (IR) cameras is used to record markers motions. The motion capture hardware is supported by DTrack software and ART Human software is used for tracking and reproducing the motion of the actor in a virtual environment. DTrack software acquires 2D marker positions using information from each IR camera and provides the transformation matrices of each marker (position and orientation of the marker) relative to different local frames attached to the body parts with respect to the global reference frame. ART Human software uses the information provided by DTrack and provides a direct link between motion of the human subject and motion of the 3D graphical model of the human (avatar) in real-time. ART Human estimates the locations of the human joint frames and the human segment size using marker information. The digital human representation, the avatar model, is created in this manner [START_REF] Gmbh | System user manual ARTtrack[END_REF]. The flowchart showing how the motion capture system works is depicted in Fig. 2, step 2. The sampling frequency for data acquisition is set to 100Hz.

The Imitation Process

The information provided by the motion capture system can be used to define the characteristics of the human body and its motion in the task space. In the previous decades, the focus of some research papers has been on estimating a kinematic model of the human body using data obtained by the motion capture systems [START_REF] Kӧhler | Automatic Human Model Parametrization from 3D Marker Data for Motion Recognition[END_REF][START_REF] Kirk | Skeletal Parameter Estimation from Optical Motion Capture Data[END_REF]. In this research, we used data obtained by the ART motion capture system to scale the kinematic model of the robot ROMEO to the characteristics of the actor. The position of the real marker relative to the corresponding proximal frame of the actor's joint and the dimensions of the segments were calculated and assumed constant in the scaled model of the humanoid. In reality, this quantity varies during motion of the actor due to unmodeled joints of the human and motion of the skin. The unmodeled joints in the shoulders are responsible for vertical displacement of the shoulders and the real markers attached to the shoulders (see Fig. 5). Although the markers are firmly attached to the body segments, the distance between a real marker and its proximal joint is not constant due to the motion of the skin. This phenomenon is the most obvious in the case of hand and shoulder markers. An error occurs and a perfect imitation of human motion by the scaled kinematic model of the humanoid is not possible. Virtual marker fames were defined according to real marker frames in the initial configuration, during the initialization process. Details about the calculation of virtual markers frames are provided in the Appendix. The imitation algorithm was used to calculate the joint configuration of the scaled model of ROMEO, in order to minimize the matching error between the virtual and real markers and the matching error between the joint positions of the human to the joint positions of the scaled model of ROMEO.

Imitation algorithm for the scaled model of the robot

In this section, an analytical imitation algorithm based on the Jacobian matrix capable of real time extraction of Cartesian motions and joint motions is introduced. The imitation algorithm was formulated as an optimization algorithm [START_REF] Zhou | Human motion tracking for rehabilitation-A survey[END_REF], which calculated the generalized coordinates of the joints (t ) imitation i q for the scaled model of ROMEO, for each time sample i t , with [ ]

1 i N ∈
, where N is the number of time samples of the recorded motion.

( )

( ) min imitation i q q t = ζ (6)
The criterion function ζ , which should be minimized, was comprised of the error between the position of the frames attached to the actor joint aj P and those of the scaled model of the humanoid rj P ; the error between the position of the real marker frames rm P and virtual marker frames vm P ; and the error in orientation between the real marker frames rm R and virtual marker frames vm R in the way proposed in Eqs. ( 7) and [START_REF] Billard | Discovering optimal imitation strategies[END_REF]. Since the precision of orientation measurement was lower than that of position measurement, and the orientations of the proximal segments were implicitly taken into account via their effect on distal joint positions and markers, the orientations of the proximal frames were disregarded in the minimization criterion. Only the orientations of the distal segments were included.

The optimization criterion is:

2 ( , ) i t q ζ = ε (7)
where P t P q e t q t q e t q P t P q

( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( , ) ( , ) ( , ) ( ) ( ) ( ) (
P t P q ⎡ ⎤ α - ⎢ ⎥ ⎢ ⎥ β - ⎢ ⎥ ⎢ ⎥ γ Δ ⎢ ⎥ ⎢ ⎥ ε = ⎢ ⎥ γ Δ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ δ - ⎢ ⎥ ⎢ ⎥ δ - ⎢ ⎥ ⎣ ⎦ (8)
where α , β , γ and δ are the weighting factors for the errors in marker positions, joint positions, hand marker orientations, and hand joint positions, respectively;

( ) q (which express the real and virtual marker orientations of the left hand, respectively), can be rewritten in terms of quaternions as

rm
⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ( ) ( ) ( ) ; ( ) ; ( ) ( ) ( ) ( ) ( ) ( )
⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ( ) ( ) ( ) ( ) RightShoulder LeftElbow RightElbow rj rj rj q P q P q P q ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ (
1 2 3 4 ( ) ( ) ( ) ( ) LeftHand LeftHand LeftHand LeftHand LeftHand rm rm i rm i rm i rm i Q Q t Q t Q t Q t ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦ and 1 2 3 4 ( ) ( ) ( ) ( ) l L e f t H a n d L e f t H a n d L e f t H a n d L e f t H a n d vm vm i vm i vm i vm i Q Q t Q t Q t Q t ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦
, respectively where

1 ( ) rm LeftHand LeftHand rm i Q t η = , 2 3 4 ( ) ( ) ( )
rm LeftHand LeftHand LeftHand LeftHand T rm i rm i rm i e Q t Q t Q t ⎡ ⎤ = ⎣ ⎦ , 1 ( ) vm LeftHand LeftHand vm Q q η =
, and

2 3 4 ( ) ( ) ( ) vm LeftHand LeftHand LeftHand LeftHand T vm vm vm e Q q Q q Q q ⎡ ⎤ = ⎣ ⎦ .

The orientation error

LeftHand rvm e Δ was calculated using Eq. [START_REF] Kirk | Skeletal Parameter Estimation from Optical Motion Capture Data[END_REF]:

( , ) ( ) ( ) ( ) ( ) ( (
Δ = η ⋅ - η ⋅ - ⋅ (9)
where ( ) S ⋅ is the skew-symmetric operator of the vector.

The orientation error of the right hand

RightHand rvm e Δ was calculated in the same way.

20

The minimization criterion is quadratic. The configuration at time sample i t can be expressed as the configuration at time 1 i tplus the change in configuration q Δ . Thus, the criterion can be expressed as a function of q Δ :

1 1 1 ( , ) ( , ( ) ) ( , ( )) ( , ( ))
i i i m i t a t i o n i i i m i t a t i o n i i i m i t a t i o n i t q t q t q t q t t q t q - α - β - ε =ε +Δ =ε +ε Δ (10)
where vector

( , ( ))

i imitation i t q t α -ε can be evaluated based on Eq. ( 8), and matrix

( , ( ))

i imitation i t q t β -ε based on its derivative. The analytical expression for q Δ is deduced for the optimality condition

( ) 2 1
( , ( ) ) 0

i imitation i t q t q q q - ∂ ε + Δ ∂ζ = = ∂Δ ∂Δ
, so that:

1 1 ( , ( )) ( , ( ))
i imitation i i imitation i q t q t t q t + β - α - Δ = -ε ⋅ε (11) where 1 ( , ( ))
i imitation i t q t + β - ε
represents the pseudo inverse of the matrix 1 ( , ( ))

i imitation i t q t β - ε . More details about vectors 1 ( , ( ))
i imitation i t q t α -ε and matrix

i imitation i t q t β -ε are provided in the Appendix.

Factors α , β , γ and δ in the imitation algorithm assigned different desired levels of precision for joint and marker tracking. The values of the weighting factors were set heuristically. Since contact tasks require high precision of the hand positions and orientations in Cartesian space, weighting factors δ (hand position weighting factor) and γ (hand marker orientation) had significantly higher values than other factors.

However, the weighting factor γ should be set to slightly less than δ, since orientation measurement precision is lower than that of position measurement. The positions of proximal (shoulder and elbow) joints in Cartesian space is less important than the Cartesian position of the hand joints, but they still have a significant effect on the similarity between recorded human motion and generated humanoid motion.

The associated weighting factor was β. The similarity between the recorded human motion and the generated humanoid motion was depicted by marker position as well, but with the aim of reducing the effect of skin motion (which directly influences the motion of the markers), weighting factor α had to be set to the lowest value. Accordingly, the weighting factors were selected as follows: α =1, β =2, 10 γ = and δ=20.

The actor motion in Cartesian space h X was re-calculated using (t ) imitation i q and the direct geometric scaled model of the ROMEO robot. Furthermore, the orientation of the hands' joints, which was unknown from the data obtained by the motion capture system, was also calculated in this manner. A comparative analysis of the recorded hand positions and the position calculated by the imitation algorithm is given in Section 5.

From Imitation Results to Motion of Robot ROMEO

The motion obtained with the previously described imitation algorithm could not be used directly by the humanoid robot ROMEO because joint limitations had not been taken into account. If joint motion ( ) imitation q t is used directly by ROMEO, the motion in Cartesian space will not be preserved and thus contact with the environment will not be achieved. On the other hand, if Cartesian motion is used, human skill will not be preserved. Therefore, we propose different strategies depending of the existence of contact with the environment or not. A contact with the environment is assumed to exist via the hands of the robot. The case of contact with another body part may be considered in a similar way. A transition strategy will also be proposed between the contact and no contact phases.

During a motion with contact, the motion of the actor's hands was constrained by the characteristics of the equipment. In [START_REF] Jovanović | Dynamic modeling of an anthropomimetic robot in contact tasks[END_REF], we elaborated the types of contact constraints and the corresponding mathematical representations. Here we studied the case in which the robot should do the task in the same environment as that of humans, with the same type of contact. The moment when the robot's hands established contact with the equipment was calculated using the hand positions of the scaled model of the robot and the known position of the equipment. To that end, the hand coordinates of the scaled robot model and the equipment coordinates were represented in the same referent frame. For the phase of contact, the robot's hands should be able to follow the same motion in Cartesian space as the actor's hands. A necessary condition for performing the task by the robot is that the trajectories of the actor's hands (for the phase of contact) are within the workspace of the robot. The workspace of ROMEO was defined according to the robot segment size and the joint limits as proposed in [START_REF] Bagheri | Kinematic analysis and design considerations for optimal base frame arrangement of humanoid shoulders[END_REF][START_REF] Wenger | Performance Analysis of Robots[END_REF]. If this condition is satisfied, when the robot is initially in the same place as the actor, the actor's motion will be easily achieved by ROMEO. Otherwise, a new initial position and orientation of the robot need to be calculated for the task to become feasible. In the latter case, the transformation matrix that describes the displacement of the robot is taken into account, in order to modify the desired motion of the robot's hands accordingly.

Inverse kinematic algorithm as a tool for human-like motion generation

The human motion imitation process requires the robot to be able to perform a task like a human. Since the structure of ROMEO is designed with redundant features, the same motion as that of human hands can be obtained for different arm configurations. By using the inverse kinematic algorithm, the recorded human joint motion can be imitated by ROMEO. The minimized difference between the current joint trajectories ( ) robot q t and joint trajectories ( ) imitation q t obtained with the imitation algorithm for the scaled robot model

( ) ( )

robot imitation q t q t was included in the inverse kinematic algorithm as an additional criterion:

1 1 ( ) ( ) ( )( ( ) ( )) ( ) ( ) ( ) robot i robot i robot robot robot i imitation i robot i robot i robot i dq t J dX t I J J q t q t q t q t dq t λ + + - - = -- - = + ( 12
)
where robot J λ + is the damped least-square inverse of the Jacobian matrix robot J and damping factor 0.003 λ = (see [START_REF] Wampler | Manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods[END_REF]), which was introduced with the aim of solving the discontinuity problem of the pseudoinverse solution for a singular configuration; robot J + is the pseudo-inverse of the Jacobian matrix robot J of ROMEO, calculated for the robot size; I is the identity matrix; and c robot robot i X q t -, calculated by the direct geometric model using the real size of the robot:

1 ( ) ( ) ( ( )) d c i r o b o t i r o b o t r o b o t i dX t X t X q t - = - (13)
The desired trajectories of the robot's hands d robot X have to be the same as the motion of human hands in Cartesian space h X . The joint limits were included in the inverse kinematic algorithm by using the internal clamping loop that checked and removed the joints that reached their upper or lower joint limits min robot q and max robot q , respectively. If a joint reached the limit, the joint value was clamped to the limit value. The elements of the Jacobian matrix J and identity matrix I related to the clamped joint were set to zero. In this manner, any further motion of the clamped joint is prevented. The inverse kinematic algorithm continues to initiate other joints in order to reach the desired values for the hands. The inverse kinematic algorithm with a clamping loop is explained in detail in Baerlocher et al. [START_REF] Baerlocher | An inverse kinematics architecture enforcing an arbitrary number of strict priority levels[END_REF].

The primary task of the inverse kinematic algorithm was to follow the desired hand trajectories ( )

d robot i X t .
If motion involved contact between hands and equipment, the robot needed to use the same equipment and manipulate it in the same way as a human. The desired motions of the robot's hands were defined in the imitation algorithm, calculating the hand position and orientation using ( ) imitation q t and the direct geometric model of the scaled ROMEO. However, it is important to note that ( ) imitation q t was defined for a scaled model of the robot and that Jacobian matrix J used here was calculated for the real size of ROMEO. Parameters ( ) imitation q t and ( )

d robot i X t
were not consistent, thus the secondary task was not achieved and

( ) robot q t differed from ( ) imitation q t .

Motion of robot hands without contact

A robot is not able to simultaneously follow recorded hand and joint motions since the robot size and joint limits and those of a human are not the same. When there is no contact with the environment, it may be preferable to follow human joint motions rather than human Cartesian motions, in order to express human skills.

However, to keep the same control approach with and without contact with the environment, and to take into account the joint limits, we used a slightly modified Eq. ( 12):

( )

c c i r o b o t i m i t a t i o n M o d i f i r o b o t r o b o t i dX t X q t X q t - = - 1 ( ) ( ) ( ( ))
where ( ) imitationModif i q t is the modified value of ( ) imitation q t , since the value of ( ) imitation q t can be outside the robot's joint limits. The modification was implemented using the algorithm proposed by Safonova et al. [START_REF] Safonova | Optimizing human motion for the control of a humanoid robot[END_REF]. In this manner, ( )

( ) c robot imitation Modif i X q
t was inside the workspace of the robot and the desired motion in the joint and Cartesian spaces was coherent and consistent with the dimensions of the humanoid robot.

The joint limits were also taken into account.

Transition strategy connecting motions with and without contact

For a motion with or without contact of the hands with the environment, we proposed the algorithm given by Eqs. ( 12) and [START_REF] Ude | Automatic Generation of Kinematic Models for the Conversion of Human Motion Capture Data into Humanoid Robot Motion[END_REF]. The difference between the two cases is in the manner used to define the desired Cartesian motion. As a consequence, we propose a transition strategy based on rescaling the size of the robot to the size of the actor. The transition strategy starts during the motion without contact, if the position of the robot's hands relative to the object to be contacted reaches a prescribed vicinity. Here we assumed the prescribed vicinity was a sphere of 0.1 m radius. During transition, the sizes of the robot segments on the model were linearly modified to reach the sizes of the actor. The hand trajectories were calculated for the incrementally rescaled model of the robot by using the value of ( )

imitationModif i q t , which
corresponds to this part of the motion. The transition strategy was over when the size of the rescaled model of the robot was the same as that of the actor and the value of ( ) imitationModif i q t was the same as that corresponding to the sample when the contact between the actor's hands and the equipment was achieved.

A connection between the hands and the equipment was therefore made.

The desired trajectories of the robot's hands can be processed further. In order to smooth trajectories of the robot's hands, we applied the Savitzky-Golay filter which is based on fitting consecutive sub-sets of adjacent data points with a low-degree polynomial by the linear least squares method [START_REF] Orfanidis | Introduction to Signal Processing[END_REF].

Handling collision

This research also addressed dual-arm motions performed by actors. Any actor naturally avoids collision with equipment and self-collision. Since we used data generated by the imitation algorithm, which characterize human skills, to generate motion of the robot it is expected that the robot, similarly to the actor, will avoid self-collision. Also, the trajectories of the robot's hands during the contact phase of the motion were the same as those of a human, thus collision with the equipment was eliminated. Collisions did not occur in the tested motion. In other cases, collision avoidance could be included in the generation of humanoid motion using the techniques developed in [START_REF] Mühlig | Interactive imitation learning of object movement skills[END_REF][START_REF] Dariush | Online transfer of human motion to humanoids[END_REF][START_REF] Ruchanurucks | Humanoid robot upper body motion generation using B-spline-based functions[END_REF]. The vision-based path planning method for dual-arm end-effector features proposed by Qu et al. [START_REF] Qu | Multi-cameras visual servoing for dual-arm coordinated manipulation[END_REF] is also a useful tool for precise pose alignment of two objects, which is the position and orientation of the hands and equipment in our case.

Results

In this section we will analyze the results of the imitation algorithm and the conversion process for the "open/close drawer" task. "Open/close drawer" is a complex motion which consists of motions with and without contact. Initially, the motion was without contact until the actor touched the drawer. The task continued with a motion with contact, during which the actor performed the drawer opening and closing functions. In order to show the general characteristics of the imitation algorithm, we tested it on a set of 7 different dual-arm tasks, each performed by 19 actors, and present the corresponding results. The results obtained with the imitation algorithm are compared with those of the numerical algorithm proposed by Ude [START_REF] Ude | Programming full-body movements for humanoid robots by observation[END_REF][START_REF] Ude | Automatic Generation of Kinematic Models for the Conversion of Human Motion Capture Data into Humanoid Robot Motion[END_REF]. The imitation algorithm proposed by Ude is a numerical optimization approach based on following the 3D position of markers physically attached to the human body, with markers placed on the scaled robot model. That imitation algorithm has been developed for imitating free human motion (motion without contact) and, consequently, precise imitation of the hand joints was not required.

Simulation results of the imitation algorithm

The imitation algorithm proposed in this paper was designed to give the highest priority to hand position and orientation tracking, to ensure that the task was properly done. According to the results for the "open/close drawer" task presented here (see Fig. 6, color blue), our imitation algorithm produced the same motion of the actor's hands as the scaled model of the ROMEO robot. The highest normed errors in following the actor's hand trajectories were about 4 mm. Since the robot model had enough DoFs, the imitation algorithm performed well when following hand orientations. Bigger errors in following the shoulder and elbow joint motions (larger amplitude around 25 mm) were the results of simplifying the kinematic model of the human by using the model of the robot ROMEO. To highlight the performance of the proposed imitation algorithm, the results are compared with the numerical algorithm proposed by Ude et al. [START_REF] Ude | Programming full-body movements for humanoid robots by observation[END_REF][START_REF] Ude | Automatic Generation of Kinematic Models for the Conversion of Human Motion Capture Data into Humanoid Robot Motion[END_REF] and shown in Fig. 6, red scale. Since Ude's numerical algorithm is based on following 3D marker positions, the errors in following the joint position and orientation are bigger compared to our imitation algorithm (see Fig. 6). In [START_REF] Ude | Automatic Generation of Kinematic Models for the Conversion of Human Motion Capture Data into Humanoid Robot Motion[END_REF], big errors in following hand joint position and orientation would not allow ROMEO to achieve contact between hands and equipment and the task would not be accomplished. On the other hand, errors in following the position of the real marker with the virtual marker obtained with the algorithm proposed by Ude are smaller compared with the results of our imitation algorithm, since hand position tracking is of the highest priority in our algorithm (see Fig. 7). Fig. 7. Normed position errors in following real marker rm P with virtual marker vm P obtained with our (analytical) imitation algorithm (blue scale) and the numerical imitation algorithm proposed by Ude [START_REF] Ude | Programming full-body movements for humanoid robots by observation[END_REF] (red scale), in meters.

Although the algorithm proposed by Ude ensures a small error when the 3D position of the markers is followed, precise following of the position and orientation of the hand joints is not guaranteed. The reasons are the calculation of the transformation matrix between real markers and the closest proximal joint, which is not so precise, and the fact that this transformation matrix may change due to skin motion.

It is apparent that our algorithm allows better tracking of the hand motion compared with the algorithm proposed by Ude and also ensures correct tracking to the pose of the shoulder and elbow that characterize the shape of the arm (i.e. its configuration).

Summing up, the hand trajectories generated through our imitation algorithm can be used as a desired robot motion in the conversion process, in the inverse kinematic algorithm for the task with and without contact between hands and equipment.

The imitation algorithm was tested on a set of different dual-arm motions ("rotation of valves", "rotation of canoe paddles", "inflating a mattress with a pump", "open/close drawer", "rotation of a steering wheel", "cutting with knife" and "grating food"), each performed by 19 actors. The quality of imitation of one motion was represented as The results show that our imitation algorithm has average errors in following the desired hand positions of about 3 mm for most actors. For some actors, these errors are somewhat bigger, about 5 mm. The reason is a large disparity between the simplified human model represented by ROMEO and the kinematic model of the real actor (confidence in the distance between joints).

ROMEO robot motion simulation and experimental results

The conversion process is based on the results obtained from the imitation algorithm, which are applied in the algorithm for humanoid motion generation. The trajectories of the hand motions obtained for the scaled robot model by using the imitation algorithm are shown in Fig. 9(b). Since the size of the robot was not equivalent to the size of the actor, the desired hand trajectories during the motion without contact were outside the robot's workspace and the robot was unable to perform the motion. Therefore, the hand motions generated with the imitation algorithm had to be additionally modified according to the robot's characteristics, as proposed in our algorithm for humanoid motion. The generated trajectories of the robot's hands during the motion with and without contact, as well as the transition strategy, are shown in The trajectories depicted in cyan are the motions without contact with equipment, obtained as proposed in Section 4.2; the trajectories in magenta represent the motions obtained with the transition strategy when the contact between the hands and equipment was calculated according to the algorithm proposed in Section 4.3; and dark blue represents the trajectories of the actor's hands during motion with contact. The desired trajectories of the robot's hands are based on the results of the actor's motion from the imitation algorithm and/or the motion of the robot's arms imitating human motion. Therefore, the robot's hand motion was free of both collision with equipment and self-collision, like the recorded human motion. The experimental results of the actor's "open/close drawer" motion and the same motion performed by ROMEO are shown in Fig. 10. The robot and the actor performed the task in the same environment. The height of the robot was less that the height of the actor. Consequently, the robot performed the task at the level of its chest, whereas the actor did so at waist level. ROMEO had conventional hands with flexible fingers, which were not actuated and the robot was required to just open and close hands. This was the reason why the drawer was ajar at the beginning of the experiment. With a robot that has complex hands with actuated joints, the contact between the hands and the drawer would have been possible with the drawer closed, exactly in the same manner as the actor performed the task.

Conclusion

A conversion process for the imitation of dual-arm human motion, utilizing the upper body, has been presented. It consists of an imitation algorithm and an algorithm for humanoid motion generation. The imitation algorithm, defined for a scaled model of the robot ROMEO, is based on virtual markers which follow real marker motions and incorporates additionally recorded joint motions. The imitation algorithm is based on the analytical expression of Jacobian matrices and is able to define the expected motion of the scaled robot in real time. Compared to existing algorithms, our imitation algorithm provides better accuracy of motion imitation in Cartesian space. Precise imitation of hand motion in Cartesian space is essential for a task where the hands come into contact with the environment. The algorithm for humanoid motion generation is based on an inverse kinematic algorithm whose objective is to follow the desired robot hand motions and, at same time, ensure that the motion of the humanoid resembles human motion behavior. Since our task involved motion which included phases with and without contact between hands and equipment, we additionally defined an algorithm for the transition between the phases. Therefore, by way of an important contribution of this work, the proposed conversion algorithm is suitable for human motion imitation by a humanoid for a task with and without contact, as well as complex tasks that involve both types of motion, which other imitation algorithms are not. The results of our conversion process were experimentally tested on the real robot ROMEO. Ultimately, one can say that the proposed conversion methodology can be used as a universal and robust algorithm for human-to-humanoid motion conversion, regardless of the type of dual-arm motion or the characteristics of the actor. th k proximal robot joint, calculated analytically with SYMORO+ software [START_REF] Khalil | SYMORO+: a system for the symbolic modelling of robots[END_REF]. The current position of the th l virtual marker is calculated from the equation

Q qt Q q t J q t q - - = + Δ. ( ) LeftHand Qvm J
q is the Jacobian matrix of the left-hand virtual marker represented in terms of quaternion and calculated using equation

3 3 3 3 4 3 ( ) ( ) ( ) LeftHand LeftHand x x Qvm vm x I O J q J q O q ⎡ ⎤ = ⎢ ⎥ Ω ⎣ ⎦
, where

Q q Q q Q q Q q Q q Q q q Q q Q q Q q Q q Q q Q q ⎡ ⎤ - - - ⎢ - ⎢ Ω = ⎢ - ⎢ ⎢ - ⎢ ⎣ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
Q Q q Q q Q q Q q ⎡ ⎤ = ⎣ ⎦ .
The current orientation of the virtual marker on the right hand is calculated in the same way.

According to the previous equations, vector

Fig. 1 .

 1 Fig. 1. Models in the human-to-humanoid motion conversation process and related parameters

Fig. 3 .

 3 Fig. 3. Robot ROMEO and its kinematic model

  The motion capture system always automatically generates the avatar model as a 3D graphical representation of the human. Each avatar joint is represented as spherical. Therefore, the avatar model has 60 DoFs to represent human motion. The kinematic model of ROMEO was used to imitate human motion in joint space. Therefore, the kinematic representation of the human body was reduced from the avatar model to the kinematic model of ROMEO. Since the information obtained from the motion capture system (such as the position and orientation of real markers and the position of joints) is defined according to the model of the human-size avatar performing the recorded action, the kinematic model of ROMEO was scaled to the size of the human. In that manner it was possible to calculate human motion in joint space.An initialization process was introduced with the aim of defining the initial configuration of the actor and to scale the size of ROMEO to the size of the actor and attach virtual markers to the scaled model of ROMEO. The initial configuration of ROMEO (see Fig.4(a)) is proposed as the initial configuration of the actors (arms horizontally extended forward, with palms facing the floor (see Fig.4(b))), because it is well defined and easily achievable.

Figure 4 .

 4 Figure 4. The scaling process: (a) extended kinematic model of the robot ROMEO in its basic configuration; (b) extended kinematic model of ROMEO scaled to the dimensions of a human in the initial configuration, with markers and marker frames Since the kinematic model of ROMEO was taken as the kinematic model of a human, the size of the

Figure 5 .

 5 Figure 5. Displacement of the shoulders and real markers attached to the shoulders during motion.

t

  are the positions of the left and right actor hand joints at time sample i t , of the left and right robot hand joints in the current joint configuration q ; and the orientation errors between the real and virtual markers attached to the left and right hands (distal markers) at time sample i t and in joint configuration q , respectively. The orientation errors were represented in terms of quaternions. The rotation matrices,

1 (

 1 the position and orientation variation between the desired trajectories of the robot's hands ( )d robot iX t and the current position and orientation of the robot's hands

Figure 6 .

 6 Figure 6. Orientation and position errors between the recorded motion and the motion generated by our (analytical) imitation algorithm (blue scale) and the numerical imitation algorithm proposed by Ude [13] (red scale): (a) normed orientation errors RightHand rvm e Δ

,

  the mean value of the Euclidian distance between the recorded positions of the hand joints hand a P and those obtained with our imitation algorithm hand r P for all samples of the motion. In order to present the general performance of the imitation algorithm for each actor, we calculated ( ) E µ and the mean value of E for all the motions performed by each actor. The general characteristics of our imitation algorithm for each actor expressed by ( ) E µ and the imitation algorithm proposed by Ude are shown in Fig. 8.

Figure 8 .

 8 Figure 8. Quality of imitations of right and left hand motions of 19 actors, expressed by ( ) E µ , obtained by

Fig. 9 (

 9 Fig. 9(c).

Figure 9 .

 9 Figure 9. "Open/close drawer" task performed by the actor and the robot: (a) Actor during the task: simulation model of the robot and calculated trajectories of the robot's hands, (b) in the imitation algorithm, and c) in the algorithm for humanoid motion generation.

Fig 10 .

 10 Fig 10. Snapshot of the "open/close drawer" motion performed by: (a) the actor; (b) and the robot

  )

			P	rm	i t	P	vm	q
				aj		i	rj
			LeftHand rvm	i
	i
			rvm	RightHand	i
	aj	LeftHand		i	rj	LeftHand
	aj	RightHand		i	rj	RightHand

  ⎦

													and
	LeftHand vm	1 vm LeftHand	( )	2	LeftHand vm	( )	3	LeftHand vm	( )	4	LeftHand vm	( )	T

Acknowledgements

The research leading to these results has received funding from the Ministry of Education, Science and Technological Development of the Republic of Serbia, under contract TR-35003, and the Equipex Robotex project funded by CNRS under grant agreement No. ANR-10-EQPX-44-01.

Appendix

The imitation algorithm proposed in this paper addresses an optimization problem which has an analytical solution for the value ( ) imitation i q t at each time sample i t , minimizing the criterion function given by Eq. [START_REF] Gómez | Analysis and comparison of motion capture systems for human walking[END_REF]. Since the initial configuration of the robot, init q , is calculated in the initialization process and the initial positions of the robot's joints and virtual markers are known, the current value ( ) imitation i q t can be calculated incrementally by using 1 ( )

+Δ .Therefore, the criterion function, ( ( )) i q t ε , can be expressed as a function of q Δ :

) t q t t q t q P t P q t q P t P q t q e t q t q e t q t q P

and LeftHand

The current position of the th k robot joint is represented by the relation

where

where

is the vector of the Jacobian matrices for all virtual markers and rj J is the vector of the Jacobian matrices for all the proximal robot joints. q Δ is calculated according to Eqs. ( 11), (A4), and (A5). The initial guess for the imitation algorithm at the first sample is taken to be the initial configuration, init q , of the scaled model of the robot. In future samples of the imitation algorithm, the solution from the previous sample 1 ( ) imitation i q tis used as the initial guess for the current iteration in the optimization algorithm. The values of the cost function cannot be zero due to large differences between the kinematic models of the human and the humanoid.

The position and orientation of the virtual markers are defined from the scaled model of the robot in the initial configuration. The virtual marker frame (with transformation matrix


Duo Wei

Antoine Bruneau-Voisine

Dmitry A Valyaev

Noël Lugan

Jean-Baptiste Sortais
email: jean-baptiste.sortais@lcc-toulouse.fr

Manganese catalyzed reductive amination of aldehydes using hydrogen as a reductant

come

A one-pot two-steps procedure was developed for the alkylation of amines via reductive amination of aldehydes using molecular dihydrogen as reductant in the presence of manganese pyridinylphosphine complex as pre-catalyst. After the initial condensation step, the reduction of the imines formed in situ is applied under mild conditions (50-100 °C) with 2 mol% of catalyst and 5 mol% of tBuOK under 50 bar of hydrogen. Excellent yields (> 90%) were obtained for a large combination of aldehydes and amines (38 examples), including aliphatic aldehydes and amino-alcohols.

In the last two years, the use of manganese as a sustainable alternative to precious transition metals in hydrogenation and hydrogen borrowing reactions has achieved an impressive explosion. 1 Starting from the hydrogenation of aldehydes, ketones and nitriles, 2 the scope of reducible functional group was rapidly enlarged to esters, 2d, 3 amides, 3c, 4 and CO2. 5 Soon after, hydrogen transfer reactions using isopropanol as reductant 6 and asymmetric reduction 2d, 7 have been disclosed. In the field of hydrogen borrowing reactions, the first manganese-catalyzed dehydrogenative coupling of alcohols and amines to form imines 8 was rapidly complemented by the synthesis of esters 9 from alcohols, and amides 10 from alcohols and amines. In the field of C-C bond formation reactions, alkylation of ketones with alcohols, 11 and olefination of nitriles 12 were also achieved. Interestingly, the upgrading of ethanol in butanol, 13 the dehydrogenation of methanol 14 to H2 and CO2, or the deoxygenation of alcohols 15 were also found to be catalyzed by manganese complexes. Finally, the access to various higher amine derivatives using alcohols as alkylating reagents was developed, 16 including the N-monomethylation of amines, [16][17] aminomethylation of [hetero]arenes with methanol/amines, 18 and multi-component synthesis of quinolines, 19 pyrroles 20 and pyrimidines. 21 Reductive amination 22 is one of the chemical reaction in the chemist tool-box for the preparation of amines. 23 It relies on the in situ condensation of a ketone or aldehyde with an amine to form the corresponding imine, which is subsequently reduced to the desired amine. When using molecular hydrogen as reductant, it appears that the key step in the reaction sequence is the hydrogenation of the intermediate imine.

In line with our previous work on manganese catalyzed reactions [START_REF] Zheng | [END_REF] and catalytic amines synthesis using first-row transition metals complexes, 25 we report thereafter the first alkylation of amines via reductive amination of aldehydes using molecular hydrogen as reductant and well-defined manganese complexes as pre-catalysts. We have selected complexes 1-4 as candidates for this study (Scheme 1) as we recently demonstrated that manganese (I) bromo-tricarbonyl complexes bearing bidendate pyridinylphosphine ligands were good catalysts for the hydrogenation of carbonyl derivatives, and especially complex 2 featuring diphenyl-(2-aminopyridinyl)-phosphine ligand. 26 Scheme 1. Manganese complexes used in this study.

We initially focused on the direct hydrogenation of Nbenzylideneaniline c1 as model substrate, using catalyst 2 and a base, under 50 bar of H2, based on previously optimized conditions for the hydrogenation of ketones. First, we found that alcohols, and notably ethanol, were suitable solvents for the hydrogenation step (See Table S1 in S.I.) as a green solvent alternative to toluene. It then appeared that the nature of the base had little influence on the reaction, NaOtBu, KOtBu, KHMDS, or Cs2CO3 leading to satisfactory conversions (2 (1 R e v i s e d m a n u s c r i t p t mol%), base (2 mol%), 100 °C, EtOH, 22h, 41% to 64% yield, see Table S2 in S.I.). The activity of complexes 1-4 was compared at 80 °C with 1 mol% catalyst and 2 mol% of tBuOK (Table 1, entries 1-4) and complex 2 appeared to be the most active one. Increasing the catalyst loading to 2 mol% led to a full conversion (entry 5). Interestingly, the temperature could be decreased to 50 °C without any detrimental effect on activity (entry 6), and even to 30 °C where a decent conversion still occurred (76%, entry 7).

Table 1. Optimization of the reactions conditions of the hydrogenation of benzylideneaniline c1 with manganese catalysts 1-4.

Entry [a] Catalyst (mol%) Temperature (°C) Time (h) Yield (%) [c] 1 [a] 1 (1) 80 19 40

2 [a] 2 (1) 80 24 74

3 [a] 3 (1) 80 19 17

4 [a] 4 (1) 80 19 1

5 [b] 2 (2) 80 17 > 98

6 [b] 2 (2) 50 17 > 98

7 [b] 2 (2) 30 24 76

[a] Conditions: an autoclave was charged in a glovebox with, in this order, c1 (181 mg, 1.0 mmol), EtOH (4.0 Mn-complex (1 mol%), tBuOK (2.2 mg, 2 mol%), and then pressurized with H2 (50 bar) and heated. [b] c1 (91 mg, 0.5 mmol), EtOH (2.0 mL), 2 (5.0 mg, 2 mol%), tBuOK (2.8 mg, 5 mol%).

[c] Yield was determined by 1 H NMR spectroscopy and GC on the crude mixture.

In terms of practical and economical synthesis, direct reductive amination of aldehydes is more desirable than hydrogenation of corresponding isolated imines. Hence, we turned our attention towards the direct synthesis of benzylaniline d1 from benzaldehyde a1 and aniline b1. In a first attempt, all the components, i.e. 2, a1, b1, tBuOK, and H2, were introduced in an autoclave being heated at 80 °C overnight (Scheme 2, conditions A). Disappointingly, a mixture of benzylalcohol e1 (44%), imine c1 (38%), and the desired amine d1 (18%) was obtained, showing that the hydrogenation of benzaldehyde occurred faster than the condensation with aniline. In a second strategy, the condensation step was carried out in the presence of the catalyst and the base at 80 °C for 5 h, then the reaction mixture was pressurized under H2 and stirred at 80 °C overnight (conditions B). Unfortunately, the main products were again alcohol e1 (61%) and imine c1 (29%). Finally, we decided to perform first the condensation of the aldehyde with the amine in EtOH, imine c1 being formed in 90% yield after 24 h at 100 °C, and then to add the precatalyst, the base, and H2 to the crude imine before heating under stirring at 80 °C overnight (Conditions C). To our delight, under these conditions, the desired N-benzylaniline d1 was obtained in high yield (87%).

Here after, 1.2 equivalent of amines b were used to ensure the full conversion of the aldehyde a into the imines c before the hydrogenation step (Table 2). We next probe the scope of this first manganese catalyzed reductive amination system thus defined.

Scheme 2. Optimization of the procedure for reductive amination of benzaldehyde with aniline under the catalysis of manganese complex 2. See main text for conditions definition and SI Table S4 for experimental details.

In general, as far as the formation of the imines is not a limiting step, [START_REF]For benzaldehydes derivatives with anilines, the condensation may be carried out at r.t. in 1 h[END_REF] the subsequent hydrogenation proceeds well for a wide variety of aldehydes and amines (Table 2). First, benzaldehydes derivatives bearing either electron donating or electron withdrawing groups both react with anilines to afford in fine the corresponding amines in good yield (entries 1-16). Noticeably, halogen substituents (d6-d10), including iodo substituent, were well tolerated with less than 10% deiodination in the cases of d9 and d10. Esters and amides moieties were not reduced under these conditions (d12-d13). Interestingly, starting from 4formylacetophenone a14 in the presence of 2 equivalent of aniline b1, only the aldimine moieties was reduced in the transient di-imine intermediate c14 affording the corresponding amino-ketimine d14, [START_REF]Ketimines are not reduced under these conditions[END_REF] while in the presence of 1 equivalent of b1, amino-ketone d15 was obtained in good yield.

In the same vein, the reductive amination of benzaldehyde a1 with 4-acetyl-aniline b16 led selectively to the corresponding 4-acetylamine d16 leaving the ketone functionality untouched. Organometalllic ferrocenylaldehyde a17 was also suitable for this protocol. Several heterocycles, including pyrrole, furane, pyridine, thiophene, and thiazole were well tolerated by the catalytic system (entries 18-23). It is noteworthy that this reductive amination protocol is not limited to aniline derivatives, as sulfonylamide b24 as well as aliphatic primary b25-b27 and secondary amines b28-b30 were also successfully coupled. Ethylenediamine b31 afforded the N,N'dibenzylethylenediamine d31, without formation of imidazolines. [START_REF] Ishihara | [END_REF] Remarkably, the amino-alcohols b32-b34 were alkylated to afford selectively the corresponding hydroxyamines, the pending hydroxy group not entering into a potentially competitive N-alkylation process. 16 To complete the series of amines amenable for this transformation, -aminoesters b35-b36 were alkylated with success. A series of aliphalic aldehydes (a37-a40), including butanal (a37), readily available by hydroformylation or bio-sourced aldehydes such cinnamaldehyde (a40), were also successfully engaged in the present reductive amination protocol. Non-conjugated C=C were typically not reduced in the course of the reaction, while conjugated C=C bonds were reduced under harsher conditions, 30 which is in line with the selectivity observed for the reduction of ,-unsatured ketones. 26

R e v i s e d m a n u s c r i t p t

Table 2. Scope of the reductive amination of aldehydes with amines in presence of 2 as precatalyst. [a] ([a] Typical reaction conditions: a solution of aldehyde a (0.5 mmol), amine b (0.6 mmol) and anhydrous EtOH (2.0 mL) was stirred at 100 °C for 24h, then transferred to a 20 mL autoclave followed by 2 (5.0 mg, 2 mol%) and tBuOK (2.8 mg, 5 mol%). The autoclave was subsequently charged with H2 (50 bar) and heated. [b] Isolated yield after purification. Finally, it has to be noted that a few functional groups such as terminal alkyne, nitro group, or unprotected pyrrole were not tolerated.

R e v i s e d m a n u s c r i t p t

In conclusion, we have shown that a well-defined manganese pre-catalyst featuring a readily available bidendate diphenyl-(2aminopyridinyl)-phosphine ligand catalyzes efficiently the reductive amination of aldehydes using H2 as reductant with a wide functional group tolerance. This higher amines synthesis protocol significantly enlarges the scope of reactions catalyzed by manganese complexes and nicely complements a previous approach based on alkylation of amines with alcohols.

  Duo Wei, a Antoine Bruneau-Voisine, a,b Dmitry A. Valyaev, b Noël Lugan b and Jean-Baptiste Sortais* b,c

  [c] a1(4.3 mmol), condensation: 2 h, r.t.[d] c.a. 10% of deiodination product.[e] b1 (100 L, 1.1 mmol).[f] a1 (122 L, 1.2 mmol). [g] 2 (5 %mol), tBuOK (10 mol%).

Conflicts of interest

There are no conflicts to declare.

Notes and references


Naouel Boukrina Makouf

Hénia Bouzidi Mousser

André Darchen

Abdelhamid Mousser

Carbon monoxide substitutions by trimethyl phosphite in diiron dithiolate complex: Fe-Fe bond cleavage, selectivity of the substitutions, crystal structures and electrochemical studies

Keywords: [FeFe] hydrogenase, Carbon monoxide substitution, Diiron hexacarbonyl complex, Thermal activation, Electron transfer catalysis, Single-crystal X-ray study

    Carbon monoxide substitutions by trimethyl phosphite in diiron dithiolate complex Fe-Fe bond cleavage, selectivity of the substitutions, crystal structures and electrochemical studies N.B. Makouf, H.B. Mousser, A. Darchen, A.

Introduction

Among vital hydrogenase enzymes, [FeFe] hydrogenases are receiving a special attention, due to their unusual structures and their catalytic power in production of hydrogen. The crystal structure of the [FeFe] hydrogenase was first reported in 1998 by Peters et al. [1] and later by Nicolet et al [START_REF] Nicolet | Fontecilla-Camps[END_REF]. The binuclear complexes of iron whose structures are close to those of the [FeFe] hydrogenase complexes have been known for more than 80 years [3]. Since [FeFe] hydrogenase crystal structure publication [1], some complexes containing a Fe2S2 core have attracted the interest of chemists [4][5][6][7][8]. These complexes are easily synthesized and have been studied as structural and functional mimics of enzyme active site [9]. The catalytic properties for hydrogen generation by models of [FeFe] hydrogenases can be modified by substitution of one or two (CO) by more donor ligands in order to increase the electron density at the iron atoms enhancing its basicity. This substitution reactions can be carried out under thermal activation [10,11], photochemical activation [12,13] and Electron Transfer Catalysis (ETC) or electrochemical activation [14,15] and is of major importance in organometallic and coordination chemistry in connection with catalytic processes.

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The carbon monoxide substitution by a ligand L more donor than (CO) has been largely investigated in iron polynuclear complexes [16][17][18][19][20][21][22][23][24][25][26][27]. Binuclear compounds (µ-η 2 -ROCS)(µ-SMe)Fe 2 (CO) 6 [16] and [(µ-RS) 2 Fe 2 (CO) 6 ] [25] reacted with P(OMe) 3 under ETC activation to afford monosubstituted compounds firstly and then the disubstituted products [17,18,28].

The results are apparently consistent with the empirical rule that one (CO) substitution occurs at each metal centre [29]. However kinetic studies [30] and sequential use of P(OMe) 3 and P(OCD 3 ) 3 [31] have revealed that the participation of bridging ligands does not be neglected and the second (CO) substitution may be not exclusively on the unsubstituted metal center.

Under thermal activation, Lagadec et al. [32] studied the (CO) substitution in the binuclear complexes [R1C(S)SR2]Fe 2 (CO) 6 and established that, with ligands such as L = P(OMe) 3 , CNR or PHPh 2 , monosubstituted products were exclusively obtained. For all carbon monoxide substitutions by trimethyl phosphate in diiron hexacarbonyl complexes carried out under thermal or electron transfer catalysis activations [23], the same monosubstitution regioselectivity was observed in each case. Binuclear iron complexes with sulfured organic bridges are generally stable during their thermal reaction with ligands more donor than (CO) [27,33] . Surprisingly, we have observed an unusual Fe-Fe bond cleavage in the complex (µη 2 PhC(S)=C(S)Ph)Fe 2 (CO) 6 1 [34] during its thermal reaction with P(OMe) 3 .

This work is a part of aiming to perform substitution reactions of (CO) by ligands more donor in iron complexes having close resemblance to the diiron unit of the [FeFe] hydrogenase under thermal and ETC activations. In complex 1 when P(OMe) 3 was used in substitution under thermal activation two complexes 2 and 3 were obtained (Scheme 1). The X-ray studies show that the two P(OMe) 3 are in apical positions in trans of the iron -iron bound in complex 2 and in equatorial positions in complex 3. However the ETC substitution reaction led to the monosubstituted compound 4 (Scheme 1) according with spectroscopy and electrochemical

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 4
analysis. In order to understand these exchange ligand reactions, the electrochemical behavior of complexes 1, 2, 3 and 4 was investigated and the results are reported here.

Scheme 1

Experimental

Physical measurements

1 H NMR spectra were recorded at 89.55 MHz, in CDCl 3 with TMS as internal standard. Mass spectra were recorded with a Varian MAT 311 spectrophotometer at 70 eV at CRMPO (Rennes, France). Elemental analyses were carried out by Service Central d'Analyse (Vernaison, France). The electrochemical experiments were carried out in a three -electrode thermostated cell with a PAR 362 potentiostat coupled to a Kipp and Zonem XY recorder. Pt micro disc and a saturated calomel electrode (SCE) were used as working and reference electrodes, respectively. Diffraction measurements of single crystals of complexes 2 and 3 were made at 293 K on a Kappa CCD diffractometer (Bruker AXS BV, 1997BV, -2004) ) equipped with a graphite monochromatic using Mo Kα radiation (λ = 0.71073 Ǻ). Crystal data collection reduction and refinement were accomplished with COLLECCT (Nonius, 1998), SCALEPACK and DENZO [START_REF] Otwinowski | Methods in Enzymology. Macromolecular Crystallography. Part A[END_REF] programs. The structure was solved by SIR 2002 [START_REF] Burla | [END_REF] and refined by using SHELXL-97 [START_REF] Sheldrick | SHELXL-97, Programs for Crystal Structure Analysis (Release 97-2[END_REF]. The hydrogen atoms were located in Fourier maps but introduced in calculated positions and treated as riding on their parent C atom, with 0.95 (aromatic) and with Uiso(H) = 1.2 Ueq (aromatic C atoms). The molecular graphical was showed with ORTEP -3 [START_REF] Burnette | ORTEP III[END_REF] program and material for publication was prepared with WinGX 1.7 software [START_REF] Farrugia | [END_REF]40].

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 5 2.

Reagents

The supporting electrolyte Bu 4 NBF 4 (Fluka, Purum) was recrystallized in a mixture of methanol and water (1/1), dried at 120°C and used at 0. Diiron hexacarbonyl compound 1 was prepared according to the literature [34]. P(OMe) 3 (5 mmol) was added to compound 1 (1.5 mmol) in dry toluene (20 ml). The mixture, in the dark and under nitrogen, was heated at 45°C for 1 h. The progress of the reaction was followed by thin layer chromatography. The reaction products were separated by chromatography on thin layer of silica gel and elution with petroleum ether. The isolated complexes were: 2 (30%) and 3 (25%). They were purified by crystallization from ethanol solution. All yields are based on (Ph(CS) 2 Ph)Fe 2 (CO) 6 . (25 ml), in the dark and under nitrogen. The electrolysis was carried out by holding the potential at -0.85 V versus SCE and was stopped when the electrolyzing current dropped sharply and the change in current reached minimal. After filtration, evaporation of the solvent and chromatography on silica gel the complex 4 (70%) was isolated and was purified by crystallization from ethanol solution.

2.3.

Results and discussion

Thermal reaction of 1 with P(OMe) 3

Under thermal activation an excess of P(OMe) 3 reacted with Ph(CS) 2 PhFe 2 (CO) 6 1 and afforded two colored compounds: 2 (30 %) and 3 (25 %). Spectroscopic (Mass, 1 HNMR, IR) analysis showed that complex 2 was a disubstituted binuclear compound. The IR spectrum of 2 on KBr pellet displayed intense bands between 1920 and 2020 cm -1 which were assigned to the terminal carbonyl coordinated to iron atoms. Mass spectrometry confirmed the presence of two P(OMe) 3 in the compound 2. The aromatic proton resonance was assigned to the complex

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7 multiplet centered at δ 7.2 ppm. Compound 3 was a mononuclear complex carrying two P(OMe) 3 ligands. The formation of complex 3 involves the occurrence of a fragmentation on the iron carbonyl complex 1 during its thermal reaction with P(OMe) 3 . In order to understand this reaction, we investigated the cyclic voltammetry of complex 1 in the presence of P(OMe) 3 ligand. and the of complex 1 was performed.

Reaction of 1 with P(OMe) 3 under ETC

Cyclic voltammetry of complex 1

In CH 2 Cl 2 , at room temperature, complex 1 underwent one two-electron reversible reduction step and the reduction potential was observed at -0.99 V versus SCE (Fig. 1). However, the lability of 1 may be disclosed in the presence of a donor ligand. When a ligand P(OMe) 3 was added into solution of 1, the cyclic voltammogram (Fig. 1) showed the typical behavior of a (CO) substitution by P(OMe) 3 catalyzed by electron transfer occurring at the cathode surface [41,42]. The cathodic peak C1 (Epc = -0.90 V versus SCE) of 1 decreased while a peak C2, corresponding to the superposition of two peaks, appeared at more negative potential (Epc = -1.30 V versus SCE) and indicated the formation of mono and disubstituted complexes.

Electrolysis of complex 1 in the presence of P(OMe) 3

The addition of an excess of P(OMe) 3 to a solution of 1 under ETC led to the monosubstituted No fragmentation of the iron carbonyl complex 1 was observed and the expected monosubstituted complex 4 (70%) was isolated.

Voltammetric studies

To understand the mechanism substitution reaction, voltammetric studies of the complexes 2, 3 and 4 were performed.

a. Cyclic voltammetry of complex 2

Under N 2 atmosphere complex 2 was reduced in CH 2 Cl 2 solution in a single chemically reversible two-electron step (C 1 /A 1 ) at -1.5 V versus SCE (Fig. 2). These observations indicate that the bielectronic reduction of complex 2 is made according to a mechanism ECE where the chemical step may be the Fe-S bond cleavage leading to the anion 2 2-according to the described reduction of (µ 2 -SPhS-)Fe 2 (CO) 6 with 2 equiv of electrons [43]. The chemical step of this mechanism is also reversible.

Under CO atmosphere, the dianion 2 2-is not stable. The coordination of (CO) induced replacement of the two P(OMe) 3 ligands and at the reverse scan, voltammogram revealed the formation of the hexacarbonyl complex 1 (Fig. 2, system C 2 /A 2 ). At more negative potentials an insertion of (CO) on the dianion 2 2-can lead, after Fe-Fe bond cleavage, to an heptacarbonyl complex 5 (Scheme 2) whose oxidation is observed at -0.5 V versus SCE (peak A 3 ) according to an ECEC mechanism. Under N 2 atmosphere complex 3 was reduced in CH 2 Cl 2 solution in a single chemically reversible two-electron step (Fig. 3, system C 1 /A 1 ) at -1.25 V versus SCE in comparison with the intensity of the reduction current of the complex 1. The obtained dianion 3 2-was also stable and involved an ECE mechanism with a reversible chemical step where the chemical step may be the Fe-S bond cleavage leading to the anion 3 2-.

Under CO atmosphere, the voltammogram shows a high reactivity of the dianion 3 2-. Indeed, during the first potential scan a new reversible system C 2 /A 2 appeared at -0.9 V versus SCE assigned to tricarbonyl mononuclear complex 6 (Scheme 3) which oxidizes around -0.5 V versus SCE (Fig. 3, peak A 3 ) according to an ECEC mechanism. Under N 2 atmosphere the binuclear compound 4 was reduced in CH 2 Cl 2 solution in a single chemically reversible two-electron step (Fig. 4, peaks C 1 and A 1 ) observed at -1.15 V versus SCE (Fig. 4) in comparison with the intensity of the reduction current of the complex 1. These observations indicate that the dianion 4 2-was stable and involved an ECE mechanism with a reversible chemical step where the chemical step may be the Fe-S bond cleavage.

The difference between the reduction potentials of complexes 1 and 4 is about of 300 mV and is in agreement with a monosubstitution of (CO) by P(OMe) 3 .

Under CO atmosphere the voltammogram of 4 (Fig. 4) showed that P(OMe) 3 can be replaced by (CO) after reduction of complex 4 into dianion 4 2-. During the reverse scan, two reversible systems A 2 /C 2 and A 3 /C 3 were observed at -0.9 V and -0.5 versus SCE, respectively. A 2 /C 2 was attributed to 1/1 2-system and A 3 /C 3 may be assigned to the system 5/5 2-oxidation and reduction, according to the hypothesis that we have already formulated during the study of precedent complexes studies under CO atmosphere (Scheme 2).

Fig. 4

The structures of 2 and 3 were not clearly specified and an X-ray determination was needed to prove the proposed formulas in order to follow all the discussions on our results. However,

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11 the crystal structure of complex 4 could not be determined because of the poor quality of the relevant crystals.

X -Ray crystal analysis

X -Ray crystal analysis of compound 2

Crystals of complex 2 were triclinic with space group P-1. The X -Ray study of 2 established that it was a binuclear disubstituted complex. As expected, the molecular geometry of complex 2 is analogous to that of its parent arene dithiolate diiron complex 1. The molecular structure (Fig. 5) shows that one CO substitution occurs on each metal center, according to the empirical rule [29]. The two P(OMe) 3 are in apical positions in trans of the iron -iron bound (Fig. 5). The Fe-Fe bound length [2.4797(1) Ǻ] is in accordance with that observed in [Fe 2 (µbtdt)(CO) 4 (P(OEt) 3 ) 2 ] complex [33] and is slightly shorter than that observed in the starting complex 1 [34]. The average Fe-P distances and Fe-Fe-P angles are 2.1703 Å and 150.275°, respectively and are comparable to those observed for the selenium analogous complexes [44]. The average Fe-S-Fe angle and C-O distances of 65.94° and 1.1469 Ǻ, respectively are in the same ranges of similar complexes [33]. The Fe-S bonds in 2 are slightly longer (ca. 0.0137 Å) than that in the unsubstituted compound 1 due to the stronger σ-donor properties of phosphite ligands compared to carbonyl groups [34]. Crystal data collection parameters and some of selected bond lengths and bond angles were given in Tables 1 and2, respectively. In the crystal packing, the components of the structure are linked via intermolecular C-H….O and C-H….S hydrogen bonds (Table 3) to form a zigzag chain along the a-axis (Fig. 6). Collection parameters are shown in Table 1, and selected bond distances and angles are tabulated in Table 2.

M A N U S C R I P T A C C E P T E D

Table 1

Fig. 6 Table 2 3.3.2. X -ray crystal analysis of compound 3

Crystals of complex 3 were orthorhombic with space group P cab . The X -Ray study of 3 established that it was a mononuclear disubstituted iron complex with trigonal-bipyramidal geometry. The [C 6 H 5 CS] 2 group was coordinated to the iron atom through the two Fe -S bounds. The Fe -S bond lengths 2.1932( 14) Å and 2.1523(13) Å are comparable to those observed for sulfur analogues [45] and were shorter than those obtained in complexes 1 [34] and 2. The dithio diphenylethylene groups were coordinated to the single iron with the two similar -S-C(Ph) and the mean (1.7315 Å) of the -S-C(Ph) bond lengths was shorter than that observed in complexes 1 [34] 16)°]. The Fe-CO bond (1.740(5) Å) is slightly shorter than that observed in the complex 1 [34] and can be due to the π back-donation of the iron atom towards the carbonyl [23]. O2 and C2 atoms of P(OMe) 3 group present a severe disorder. The refined model using constraints corresponds to a distribution of these two atoms with 0.70 and 0.60 for O2 and C2 respectively (Fig. 7). Its crystal and collection parameters are shown in Table 1, and selected bond distances and angles are tabulated in Table 2. In the molecular stacking up of the complex 3, every two molecules are interpenetrated and linked via intermolecular C-H….O hydrogen bond (Table 3), forming a zigzag chain along the b axis at c = 0 or c = 1/2 (Fig. 8). The double bond PhC(S)=C(S)Ph (C5=C6 of 1.3273 (5) Å) in complex 2 is shorter than that observed in complex 3 (C8=C9 of 1.364 (6) Å) and can be explained by a greater steric consideration in the complex 2. Fig. 7 Fig. 8 Table 3 3.4.

Proposed mechanism for the formation of complexes 2, 3 and 4

The formation of 2, 3 and 4 are summarized in the scheme 4. However the mechanism of the reaction of complex 1 with an excess of P(OMe) 3 could proceed according to a system M A N U S C R I P T

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composed of consecutive and competitive reactions. Thus the monosubstituted complex 4 is firstly formed, whatever the thermal [33] or E.T.C [46] activation. Starting from an excess of the P(OMe) 3 , under thermal activation, complex 4 could be involved in two competitive substitution reactions (Scheme 5). The first one would be a (CO) exchange reaction consistent with the empirical rule that one (CO) substitution occurs at each metal center [29] leading to the complex 2. The second (CO) substitution could occur on the same already substituted iron atom of 2 or 4 leading to a fragmentation resulting from the important steric effect and the resulting high charge density on this iron leading to the complex 3. Fe(CO) 4 2-fragment could be formed as decomposition product of complexes 2 or 4.

Scheme 4

Scheme 5

Conclusion

In this study, we have reported that exchange carbonyl reactions by P(OMe) 3 in complex (µ-

Molecular formula

Formula weight (g mol

2. 3 . 2 . 1 .

 321 Complex 4. (µ-PhC(S)=C(S)Ph)Fe 2 (CO) 5 P(OMe) 3, m.p. 101°C. 1 H NMR δ: 7.2(m) ppm. IR(C 2 Cl 4 ): ν CO = 1950; 1990; 2000; 2060 cm -1 . Mass spectrum: M + found 589.90017; M + calc. 589.90084.

Fig. 1

 1 Fig.1

complex 4 .

 4 The electrolysis(45 min) was carried out at -0.85 V versus SCE, in the dark and under nitrogen atmosphere. The mixture was treated and separated by chromatography on

  Fig.2

Fig. 3 Scheme 3 M

 33 Fig.3

Fig. 5

 5 Fig. 5

and 2 . 13 complexes [ 45 ]

 21345 The P atoms were coordinated in an equatorial position with Fe-P bond lengths [2.1452(14) Å and 2.1220(14) Å] and S-Fe-P angles [117.74(5)°, 144.05(5)°, 89.04(5)°and 95.87(5)°] are in accordance with those observed in similar . The coordination of the metal center was completed by one carbonyl in apical position [170.56(

η 2

 2 PhC(S)=C(S)Ph)Fe 2 (CO) 6 1 lead to three complexes, depending on the used activation. A binuclear disubstituted complex (µ-PhC(S)=C(S)Ph)Fe 2 (CO) 4 [P(OMe) 3 ] 2 and a mononuclear iron disubstituted complex (η 2 PhC(S)=C(S)Ph)Fe(CO)[P(OMe) 3 ] 2 were obtained under thermal activation. When using electron transfer catalysis the monosubstituted compound (µ-PhC(S)=C(S)Ph)Fe 2 (CO) 5 [P(OMe) 3 ] was obtained. All the synthetized complexes were characterized by spectroscopic analysis (Mass, 1 H NMR, IR). Cyclic volammetry of complexes 1-4 were carried out and showed that they underwent in a single chemically reversible two-electron reduction step. Exchange of CO by P(OMe) 3 induced by electron transfer were observed in the complex (µ-η 2 PhC(S)=C(S)Ph)Fe 2 (CO) 6 . Under CO atmosphere

Table 2 Table 3 3 DFig. 1 .

 2331 Fig.1. Cyclic voltammetry of 2 mM of complex 1 in CH 2 Cl 2 0.1 M Bu 4 N + BF 4 -; Pt electrode; scan rate 0.1 Vs -1 . Complex 1 alone; -------and ……. First and second scan in the presence of an excess of P(OMe) 3 .

Fig. 2 .Fig. 3 .

 23 Fig.2. Cyclic voltammetry of 2 mM of complex 2 in CH 2 Cl 2 0.1 M Bu 4 N + BF 4 -; Pt electrode; scan rate 0.2 V s -1 . Complex 2 under N 2 atmosphere; -------Complex 2 under CO atmosphere. …... Complex 1 (2 mM) under N 2 atmosphere.

Fig. 4 .Fig. 5 .

 45 Fig.4. Cyclic voltammetry of 2 mM of complex 4 in CH 2 Cl 2 0.1 M Bu 4 N + BF 4 -; Pt electrode; scan rate 0.2 Vs -1 . Complex 4 under N 2 atmosphere; …… Complex 4 under CO atmosphere.

Fig. 6 .Fig. 7 .

 67 Fig.6. The crystal packing viewed along axis c. Dashed lines indicate intermolecular C-H….O and C-H….S hydrogen bonds which join molecules into endless chains along the a-axis direction.

Fig. 8 .

 8 Fig.8. The crystal packing viewed along axis a. Dashed lines indicate C-H….O intermolecular hydrogen bond, forming a zigzag chain along the b axis at c = 0 and c = 1/2.

  CO = 1950 cm -1 . Mass spectrum: M + found 574.0071; M + calc. 574.0100.

	2.3.2. Reaction of (µ-η 2 PhC(S)=C(S)Ph)Fe 2 (CO) 6 1 with P(OMe) 3 under ETC
	P(OMe) 3 (5 mmol) was added to complex diiron hexacarbonyl 1 [34] (0.38 mmol) in CH 2 Cl 2
	0.1 M	Bu	4	N	+	-4 BF

1.1. Complex 2. (µ-PhC(S)=C(S)Ph)Fe 2 (CO) 4 [P(OMe) 3 ] 2 , m.p. 137°C. 1 H NMR δ: 7.2(m) ppm. IR(KBr): ν CO = 1920; 1930; 1950; 2020 cm -1 . Mass spectrum: M + found 685.9329; M + calc. 685.9348. M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 6 2.3.1.2. Complex 3. (η 2 PhC(S)=C(S)Ph)Fe(CO)[P(OMe) 3 ] 2 , m.p. 148°C. 1 H NMR δ: 7.2(m) ppm. IR(KBr): ν

Table 1

 1 Crystal data and refinement details for X-ray structure determination of complexes 2 and 3

	Complex 2	Complex 3

Acknowledgements

The authors express their thanks to the Algerian « Ministère de l'Enseignement Supérieur et de la Recherche Scientifique » and the Algerian « Direction Générale de la Recherche Scientifique et du Développement Technologique » for financial support.

P(OMe) 3 were replaced by CO ligand in a chemical reversible step. The X-ray studies of (µ-PhC(S)=C(S)Ph)Fe 2 (CO) 4 [P(OMe) 3 ] 2 and (η 2 PhC(S)=C(S)Ph)Fe(CO)[P(OMe) 3 ] 2 were established and showed that the P(OMe) 3 are in apical positions in the binuclear disubstituted complex and are in equatorial positions in the mononuclear iron disubstituted complex.

Finally the exchange reaction of carbonyl by P(OMe) 3 in the complex (µη 2 PhC(S)=C(S)Ph)Fe 2 (CO) 6 is not selective and the two ways (thermal activation and electron transfer catalysis) did not lead to the same compounds.

Formatting of funding sources

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Angles (°)