Abstract:
The disclosure relates to a robot that has an articulated arm for moving an end in an N-dimensional space including at least N+1 motorized articulations, and a computer for controlling the movements of the motorized articulations. The computer controls a first step of prepositioning the terminal end of the articulated arm and a second step for its fine positioning.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a National Phase Entry of International Application No. PCT/FR2009/000459, filed on Apr. 17, 2009, which claims priority to French Application 08/52750, filed on Apr. 24, 2008, both of which are incorporated by reference herein. 
     TECHNICAL FIELD 
     The invention relates to the field of manipulator robots enabling the movement of a terminal end. 
     BACKGROUND 
     Manipulator robots are used for moving and positioning an object or a tool in space. They can have a serial, parallel or, less often, hybrid structure. In the case of serial structures, the various parts composing the robot are articulated with respect to each other, in series and the relative movements are obtained from actuators distributed along a kinematic chain. In the case of a parallel structure, several kinematic chains are closed and the elements constituting such chains are not necessarily all actuated. 
     The serial, hybrid or parallel manipulator robots have a certain number of degrees of robot flexibility making it possible to obtain degrees of freedom for the object to be handled. Most serial robots sold on an industrial scale are:
         either of the SCARA type, with two mobile arms in a plane and a degree of robot flexibility in a direction perpendicular to such plane (possibly completed by rotation about such latter axis) making it possible to position and orient a solid in planes parallel to a base plane   or of the anthropomorphic type, with a base, a shoulder and an arm supporting a wrist finally giving six degrees of robot flexibility (three for the position, three for the orientation).       

     A robot can be redundant if the number of degrees of robot flexibility (in relation with the number of actuators) is greater than the number of degrees of freedom obtained for the handled solid. Generally speaking, such robots are difficult to control but make it possible to avoid obstacles located in the working space or to work in hardly accessible spaces. 
     Standard ISO 9283 defines the performance criteria to be taken into account for an industrial robot, more particularly the reproducibility and the accuracy in the positioning. So far, the reproducibility of the positioning of the manipulator robots, whether serial or parallel, redundant or not, does not exceed a value close to one hundredth of a millimeter. As for the accuracy performances, they are even lower and today the best robots can guarantee only an exact positioning within 0.03 millimeters in the working space. In fields such as clock-making, where it is necessary to insert axes into holes 0.2 millimeters in diameter, or in the optoelectronic field, a reproducibility of less than 0.01 millimeters and accuracy in the positioning of the order of 0.01 millimeters are essential. 
     For some so-called singular configurations, the number of degrees of freedom of the terminal end of the robot is locally strictly lower than the number of degrees of robot flexibility. The Jacobean matrix is the matrix resulting from the differentiation of the geometric model of the robot; it is no longer revertible in singular positions. This raises a problem when, for example, the robot is controlled by a revertible differential model. Then, the terminal end of a robot is generally not positioned in areas close to the singular configurations because of the underlying control problems. 
     The document U.S. Pat. No. 4,523,100 is known in the prior art, which discloses a robot including an articulated arm supporting an articulated head for micro-movements. The articulated arm provides a rough positioning of the articulated head, and the accurate positioning is provided by linear verniers, composing the articulations of the head. Such robot has the drawback of requiring at least 6 articulations of a different nature. In so-called micro/macro devices used for accurately positioning an object in a three-dimensional space, the fine movements of the terminal ends are generally provided by an independent micrometric device fixed downstream of the kinematic chain; the assembly requires a minimum of three articulations of the supporting structure for positioning the micrometric device and the micrometric device itself includes three articulations, which means generally 6 articulations. 
     SUMMARY 
     The invention aims at remedying the drawbacks of the state of the art and more particularly at bringing an accurate positioning of the terminal end of redundant robots, which results in improved performances in accuracy (reproducibility and exact positioning) with respect to the prior art. In addition, the present invention makes it possible to work in areas close to the base or singular configurations of the robot structure. With respect to the macro/micro devices, the invention makes it possible to substantially reduce the number of articulations used for the fine positioning by providing an integrated architecture. 
     The invention relates to totally integrated and redundant robot structures for which a so-called “area of interest” exists, wherein the fine positioning of the terminal end of the robot can be obtained. The area of interest does not cover the whole working space accessible by the end of the robot, but a preferred volume of action within which the end of the robot may run along any path of motion, unlike the solution disclosed in U.S. Pat. No. 4,523,100. The invention relates to a robot including an articulated arm for the movement of an end in an N-dimensional space comprising at least N+1 motorized articulations, as well as a computer for controlling the movements of said motorized articulations, with said computer controlling a first step of prepositioning the terminal end of the articulated arm and a second step of fine positioning. 
     Said first step of prepositioning consists in engaging the end of an articulated arm in the area of interest, as close as possible to the centre of the optimum positioning area, with the centre being defined as a function of N secondary motorized articulations, with at least one of said secondary articulations being an axis of rotation. Said second step of fine positioning consists in blocking all the articulations except for said N secondary motorized articulations and in controlling the movement of the terminal end by elementary movements of at least one of the N secondary articulations. 
     In particular embodiments:
         the articulated arm for a positioning in a three-dimensional space includes at least four motorized articulations, among which at least two axes of rotation, with the first step of prepositioning consisting in bringing the terminal end of the robot in the area of interest, with said area of interest being a sub-assembly of the working space, and in that the second step of fine positioning consists in blocking all the articulations except for three secondary motorized articulations, among which said two axes of rotation, and in carrying out the final positioning through elementary movements of at least one of said secondary articulations;   the articulated arm for positioning in a three-dimensional space includes at least four motorized articulations, among which at least one axis of rotation, the first step of prepositioning consisting in bringing the terminal end of the robot to the area of interest, said area of interest being a sub-assembly of the working space and in that the second step of fine positioning consists in blocking all the articulations except for three secondary motorized articulations, among which said axis of rotation, and in executing the final positioning through elementary movements of said secondary articulations;   the articulated structure includes at least three motorized articulations among which at least two so-called secondary parallel axes of rotation, and in that the first step of prepositioning consists in bringing the terminal end of the robot to the area of interest; a second step of fine positioning consisting in blocking all the motorized articulations except for said secondary motorized axes of rotation, and in carrying out the final positioning through elementary movements by the rotation of at least one of said secondary axes;   the articulated arm for a positioning in a plane of a space includes at least three motorized articulations, among which at least one axis of rotation, with the first step of prepositioning consisting in bringing the terminal end of the robot to the area of interest, with said area of interest being a sub-assembly of the working space, and in that the second step of fine positioning consists in blocking all the articulations except for two secondary motorized articulations, among which said axis of rotation, and in executing the final positioning through elementary movements of at least one of said secondary articulations;   the articulated arm for a positioning in a three-dimensional space includes at least four serial motorized articulations, among which at least 3 so-called secondary axes of rotation, with a first step of prepositioning consisting in bringing the terminal end of the robot to an area of interest, with said area of interest being a sub-assembly of the working space, wherein the lever arms with respect to the three secondary axes of rotation have a small length and in that the second step of fine positioning consists in blocking all the articulations except for said secondary motorized axes of rotation, and in proceeding to the final positioning through elementary movements by rotation of at least one of said secondary axes;   the articulated arm includes at least three serial motorized articulations, among which at least two so-called secondary parallel axes of rotation, and in that the first step of prepositioning consists in bringing the terminal end of the robot to the area of interest, a fortiori to the optimum positioning area, with said optimum positioning area being a disc, the centre of which is the apex opposed to the hypotenuse of an isosceles right-angled triangle inscribed in a plane containing the terminal end of the handling arm and perpendicular to the secondary axes of rotation, with the hypotenuse having a first apex on the first secondary axis of rotation and a second apex on the second secondary axis of rotation; the diameter of said disc is approximately equal to the distance between the two secondary axes of rotation; the second step of fine positioning consisting in blocking all the motorized articulations except for said secondary motorized axes of rotation, and in carrying out the final positioning through elementary movements by rotation of at least one of said secondary axes;   said robot includes at least one additional articulation located upstream of the kinematic chain and an opening step enabling the definition of an area of interest through the action of such additional articulation or articulations;   the fine positioning is indirectly obtained through the reproduction of a portion of path of motion from a particular point called a point of harmonization to the target point, in order to solve the problems of dry frictions, with the harmonization point being a point located outside the dead zone linked to the target point;   the fine positioning is obtained by the processing of position exteroceptive information making it possible to deduce the distance between the position of the terminal end of the robot and the target point, and to control the robot through elementary rotations about the secondary axes;   both steps are computed prior to the execution in order to prepare a control law for a continuous movement;   both steps are calculated prior to the execution, in order to prepare a control law and a periodical re-computation during the movement;   the design of such a redundant robot for the fine positioning makes it possible to have a revertible geometric model at each step;   the control of the redundant robot for the fine positioning uses a local calibration process for a better accuracy in the positioning upon completion of the prepositioning phase;   a wrist is fixed at the end of the robot, which enables the control of the orientation of an object or a tool.       

     In other embodiments:
         the secondary axes are selected as being those which have the smallest lever arm with respect to the target point;   the distance between both secondary axes being smaller than the distance between a secondary and a third axis, as well as the distance between the third axis and the terminal point;   the angular position sensors of the secondary articulations have a resolution which is greater than the resolution of the sensors of the other articulations;   the design of the redundant robot for the fine positioning in two steps makes it possible to have an invertible geometric model at each step because of the redundancy of two consecutive parallel axes of rotation on the kinematic chain.       

     The robotic structure is composed of at least three articulated segments in serial, hybrid or parallel mode according to a redundant configuration, of proprioceptive sensors making it possible to obtain information on the actuators of the kinematic chain and a computer making it possible to control said kinematic chain. Two types of articulations are defined at the kinematic chain composing the robotic structure: the articulations for the positioning and the orientation called primary articulations (of the rotary, prismatic type or any type of articulation known to the persons skilled in the art), then among those, some rotary articulations used for a precise positioning of the terminal end of a robot so-called secondary articulations. The selection of the secondary rotary articulations in the kinematic chain depends on the configuration of the robotic structure, with some rotary articulations which can be configured as secondary articulations for a given configuration and only for primary articulations for another configuration. The selection of the secondary axes is based on the principle that the distances between the secondary axes of rotation and the terminal end of the robot are small with respect to the distances between the non secondary axes of rotation and the terminal end of the robot. 
     In alternate embodiments, some secondary motorized rotary articulations can be replaced by prismatic links in order to enable an accurate positioning in a plane or the three-dimensional space, provided that at least one motorized rotary articulation remains among the secondary articulations; thus, for a fine positioning in the three-dimensional space, the secondary articulations can result from the combination of two rotary articulations and a motorized prismatic articulation as illustrated in  FIG. 10  or a rotary articulation and two motorized prismatic articulations; for a positioning in the plane, the secondary articulations can result from the combination of one motorized rotary articulation and one motorized prismatic articulation as illustrated in FIG.  8 - e.    
     The area of interest is a restricted area of the working space which intrinsically depends on the configuration of the robotic structure and for which the following properties are checked: the terminal end of the robot may be positioned in the area of interest; the space resolution of the position obtained by controlling the secondary axes of rotation is finer than in the remainder of the working space; the elementary vectorial movements induced by the elementary rotations about the secondary axes of rotation form a family generating vectors in space, ideally an orthogonal base. For a fine positioning in the three-dimensional space, three secondary articulations will be selected from the kinematic chain. For a fine positioning in a plane, two secondary articulations will be selected from the kinematic chain. For a fine positioning on a straight line, one secondary articulation will be selected in the kinematic chain. However, in such various cases, it may be necessary to choose more secondary articulations than previously defined, since the persons skilled in the art are capable of designing a control which can manage the local redundancy resulting from the elementary movements forming a family of vectors linked in the vectorial space of the requested movements, with the principles and the advantages of the invention remaining valid. 
     Within the area of interest, an optimum positioning area can be distinguished. The centre of the optimum positioning area is a particular point in the OPA located at the same distance from the secondary axes and for which the elementary vectorial movements induced by the elementary rotations about the secondary axes of rotation form an orthogonal base of vectors in space. Not all the redundant robotic structures have necessarily an area of interest, or a fortiori an OPA. For a given robotic structure, the area of interest and the OPA depend on the configuration of the kinematic chain. However, only a part of the working space may become an area of interest. The designer of the robotic structure must be careful and define the dimensions thereof so that the OPA can exist, have a sufficient volume and be accessible by movements and configurations according to the desired application. As for the user, he or she must select from all the possible configurations, the one that will enable him or her to make the area where the fine positioning is desired and the area of interest, or a fortiori the OPA coincide. The ideal is that the fine positioning is executed in a region close to the centre of the OPA. 
     When the final positioning is carried out at the centre of the OPA, the space control of the fine positioning is uncoupled with respect to the controls of the secondary axes. When getting further from the centre of the OPA while remaining in the area of interest, a partial coupling may appear. The invention relates to the fine positioning control which can be broken down into two independent steps: the first step, also called the prepositioning step, consists in bringing the terminal end of the handling arm to the area of interest, a fortiori to the OPA; the second step consists in finely positioning the terminal end of the handling arm only using one or several secondary articulations. 
     During the step of fine positioning, the secondary axes of rotation only are activated. Because of the present structure and with an equal resolution on the angular encoders, this enables a significant and computerized improvement of the reproducibility of the positioning estimated with respect to the secondary axes of rotation. On the other hand, at the centre of the OPA, the control between the Cartesian space and the secondary articulation space is uncoupled. This small value of the reproducibility in the positioning makes it possible to locally correct position errors by strictly limiting the non linearity intrinsic in the reproducibility “sphere”. For example, a “jump” ellipsoid control can be used. 
     During the step of fine positioning, the information from the exteroceptive position sensors (mechanical, digital, optical or other micrometers, microscopes, viewing devices) can be integrated in the control system. The information from such sensors makes it possible to obtain the relative deviations between the desired final position and the position reached by the terminal end.  FIG. 1  relates to a fine assembly table illustrating such a principle. The device includes an assembling plate  10 , a first assembly formed of a North laser scanning micrometer  1  and a South laser scanning micrometer  2  associated to a laser beam  3 , and a second assembly formed by an East laser scanning micrometer  4  and a West laser scanning micrometer  5  associated to a laser beam  6 . The two (East-West, North-South) laser scanning micrometers make it possible to obtain the relative positions between a shaft  8  and a bore  9 . This deviation can then be used within a control system to obtain the final position desired. 
       FIG. 2  illustrates various methods which can be implemented to correct the deviation between the desired position  201  and the reached position. Because of dry frictions, small deviations in the position of the articulations are sometimes difficult to correct. As for the server control, a proportionate control does not exert a sufficient stress (torque or force) to overcome the stress of the dry friction in an area called a dead zone shown here by the sphere  202  wherein there is no movement generated; it is necessary to wait for the integral corrective action of the servo-control finally generating sufficient efforts to cause a movement with the risk of subsequently inducing passing phenomena related to the dynamics of the system; this is the case of the path of motion  205  which makes it possible to go from the point  203  located in the dead zone to the point  204 . Such passing may have secondary effects as regards safety and operation security. The final positioning  207  can be obtained by a direct control (for example a reverse differential control) if the origin of the path of motion  208  is outside the dead zone. If the reached position  209  is in the dead zone, it is possible obtain the fine positioning using the following process: a point of harmonization  210  is defined and located outside the dead zone obtained by the path of motion  211 . The principle then consists in reproducing a path of motion  213  starting from such a point of harmonization  210  by adjusting the final setting as a function of the deviation measured between the reached position  212  and the target  201 . The path of motion  214  is then used to go back to the point of harmonization  210 . The final setting is then slightly modified, taking into account the deviation between the point  212  and the target  201 . The path of motion  216  leads from the point of harmonization  210  to the point  215  which is the closest to the target  201 . This process can be resumed until the final point is close enough to the target  201 . 
     The accuracy of the position reached by the robot structure during the step of prepositioning remains that of a conventional manipulator robot. It can be significantly improved during the step of fine positioning in the area of interest by using a local calibration procedure. Such a procedure may, for example consist in accurately measuring the position of the terminal end with exteroceptive captors at a point of the area of interest and to deduce therefrom the variations in the position of the terminal end during the step of fine positioning by computerisation from the geometric (or differential) model, only based on the secondary axes. Other strategies can also be considered: several sensors distributed in the area of interest and coupled to various configurations making it possible to finally deduce the position of the terminal end in the area of interest while reducing the uncertainty relating to the non secondary articulations position sensors and to the errors in the geometric model on a part of the kinematics chain. Such local calibration must make it possible to reduce the importance of the errors in the geometric model related of the secondary axes by one order of magnitude. 
     It is possible to make the robot structure work as defined outside the area of interest, with the operation of the robot then being that of a conventional redundant robot without a fine positioning. The control of the articulations by the actuators is conventionally executed in closed loop using the proprioceptive information from the positions sensors (for example encoders) generally used on this type of robot. The orientation of an object or a tool fixed on the terminal end of the articulated arm can be conventionally controlled from the various articulations distributed on the kinematic chain. In an alternate embodiment, it can be considered to position a wrist on the terminal end of the robotised arm which makes it possible to control the orientation of an object or a tool fixed at the terminal end. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       Other characteristics and advantages of the invention will appear upon the reading the following description and referring to the appended figures briefly shown hereinunder: 
         FIG. 1  relates to a fine assembling table including two laser scanning micrometers making it possible to obtain the relative positions between a shaft and a bore; 
         FIG. 2  illustrates various paths of motion to correct the deviation between the desired position and the reached position; 
         FIG. 3  shows a perspective diagram of the kinematic chain of a generic embodiment for a fine positioning in the three-dimensional space; 
       FIGS.  4 - a  (perspective view),  4 - b  (top view) and  4 - c  (side view) show the diagram of a kinematic chain of a first particular embodiment for a fine positioning in the three-dimensional space; 
       FIGS.  5 - a  (side view) and  5 - b  (top view) show a diagram of the kinematic chain of a second particular embodiment for a fine positioning in the three-dimensional space; 
       FIG.  6 - a  (side view) and  6 - b  (top view) show a diagram of the kinematic chain of a third particular embodiment for fine positioning in the three-dimensional space; 
         FIG. 7  shows a kinematic chain of a generic embodiment for the accurate positioning of the terminal end in one plane of space; 
       FIGS.  8 - a  (perspective view) and  8 - b  (top view) show diagrams of a kinematic chain of a first particular embodiment for the fine positioning in the two-dimensional space, FIG.  8 - c  illustrates the improvement in the accuracy by a local calibration method; FIG.  8 - d  is an alternative for which the additional degree of robot flexibility is inserted between the two secondary axes of rotation; FIG.  8 - e  illustrates an alternate embodiment wherein a prismatic articulation is substituted for a secondary rotary articulation; 
         FIG. 9  (top view) shows a diagram of the kinematic chain of a second particular embodiment for a fine positioning in the two-dimensional space, making it possible to define the area of interest and to accurately position the terminal end of the robotized arm in this area; 
         FIG. 10  (top view) shows a diagram of the kinematic chain of a particular embodiment for a fine positioning in the three-dimensional space wherein one of the secondary articulations is prismatic; and 
         FIG. 11  (top view) shows a diagram of a kinematic chain of a particular embodiment corresponding to a hybrid robot structure for a fine positioning in a plane. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     Referring to  FIG. 3 , in a general embodiment for a fine positioning in a three-dimensional space, the robot structure is composed of three rotary articulations  302 ,  304  and  306  also called secondary articulations, in relation with, on the one hand the frame  300  through a kinematic chain  301 , and on the other hand together through the kinematic chains  303  and  305  and finally in relation with the terminal end  310  by a last kinematic chain. The global kinematic chain of the robot structure has at least one additional articulation (i.e. a fourth degree of robot flexibility) belonging to the so-called primary articulations and making it possible for the terminal end of the kinematic chain to run in a larger space than the working space related only to the secondary articulations. The fourth articulation may be inserted as desired into one of the kinematic chains  301 ,  303 ,  305  or between  306  and  310 , and here this concerns the rotary link  308 . 
     The robot structures concerned by the invention and enabling a fine positioning define, in the three-dimensional space, a so-called area of interest which corresponds to an assembly of points for which the distances with respect to the three so-called secondary axes  302 ,  304  and  306  are small but not null, and the movements induced by elementary rotations about the axes of rotation  302 ,  304  and  306  are executed along three not coplanar directions. For a particular configuration of the robot structure in this area of interest, a sub-assembly also called an optimal positioning area (OPA) is defined, the centre of which is defined as follows: this is the point of intersection  314  of three planes in space  311 ,  312  and  313  containing the axes of rotation  302 ,  304  and  306 . The distances between the point  314  and the axes of rotation  302 ,  304  and  306  are substantially of the same order of magnitude; they are not null and small with respect to the other characteristic values of the kinematic chain defining the volume of the space which can be reached by  310 . When the terminal end  310  of the robot is at point  314 , the movements induced by the elementary rotations about the axes of rotation  302 ,  304  and  306  are executed along three perpendicular directions in space. For this particular configuration, the OPA corresponds to a sphere having a centre  314  and the radius of which is approximately equal to half the minimum distance between the point  314  and the axes of rotation  302 ,  304  and  306 . 
     The structure controlling method consists in placing the terminal end  310  in the OPA using the primary degrees of robot flexibility and in blocking all the articulations except for the secondary rotation articulations  302 ,  304  and  306  which then make it possible to obtain a fine positioning in the OPA. The space resolution obtained at point  314  is then much finer than in the rest of the working space because of the small lever arms generated by the three secondary actions. In addition, the movements induced by the elementary rotations about the secondary axes are executed along three perpendicular directions in space and the control between the secondary articulation space and the Cartesian space is uncoupled. When getting further away from the centre of the OPA, the uncoupling tends to disappear but the advantages as regards the accuracy of the positioning remain within the OPA and more generally in the area called the area of interest. 
     The robot structure can also be used in a mode consisting in obtaining an accurate positioning in the three-dimensional space, whereas the three secondary axes do not exactly belong to three perpendicular planes intersecting at  314  as mentioned above, but that the previous principles of the invention are used: primary and secondary axes, small lever arms with respect to the secondary axes, movements induced by the non coplanar secondary axes. The robot structure can also be used in another embodiment consisting in obtaining a precise positioning in a plane of space using at least two axes among the secondary axes mentioned above. The robot structure can also be used in another embodiment consisting in obtaining a precise positioning on a straight line in space using at least one axis among the secondary axes mentioned above. 
     While referring to FIGS.  4 - a ,  4 - b  and  4 - c  in a particular embodiment enabling the positioning of the terminal end in the three-dimensional space with a very high precision, the robot structure is composed of two parallel axes of rotation  402  and  404  and of two parallel axes of rotation  406  and  408  which are perpendicular to the axes of rotation  402  and  404 . The plane  413  contains the axis  406  and is perpendicular to the axis  402 . The point  410  is the intersection of the plane  413  with the axis  402 . The point  411  is the intersection of the plane  413  with the axis  404 . The distance between the axes  404  and  406  is equal to the distance between the axes  402  and  404  multiplied by the ratio 0.2. The distance between the axes  406  and  408  is equal to the distance between the terminal end  310  and the axis  408  from which 0.7 times the distance between the axes  402  and  404  is deducted, so that both distances remain within the same order of amplitude. We are looking for a “length of the arm  407 /length of the arm  403 ” ratio, which must be as high as possible. According to the industrial use of such a robot arm and according to the characteristics of the working space wherein the robot arm will be used, the persons skilled in the art have to optimise the above ratio. The persons skilled in the art can arbitrarily choose a length of the arm  407  and divide it by 10 to obtain the length of the arm  403 . The distance of the axis  402  to the base of the robot  400  is not an essential criterion and will be determined as a function of the constraints within the working space.  402  may be directly fixed on the base  400  without any intermediate arm  401 . 
     The method for controlling such a structure consists in driving the axes of rotation  402 ,  406  and  408  in order to position the terminal end  310  in the area of interest close to the axes  402 ,  404  and  406 . Ideally, the persons skilled in the art will try to position the terminal end  310  close to the centre  412  of the OPA. The centre of the OPA is an apex  412  of an isosceles right-angled triangle of the plane  413 , the hypotenuse of which is the segment connecting the point  410  and the point  411 . The distance between  412  and the axis of rotation  406  is equal to the distance between  412  and  410 . Depending on the configurations of the primary articulations, the point  412  may have various positions in space. For a given configuration, the OPA corresponds to a sphere with a centre  412  and the radius of which is substantially equal to half the distance between  410  and  412 . The positioning of the terminal end in the OPA aims at minimising the lengths of the lever arms associated with the axes of rotation  402 ,  404  and  406  with respect to the terminal end  310 , but without cancelling these so that the end of the manipulator arm can be controlled in the three-dimensional space of the secondary axes. Once  310  is positioned within the OPA, the axis  408  is blocked. Then the axes  402 ,  404  and  406  are activated so as to obtain a fine positioning in space. As regards the point  412 , the elementary movements induced by the rotations of the axes  402 ,  404  and  406  are carried out in three perpendicular directions. In addition, with equal controls and resolutions on the angular sensors of the secondary axes, the position increments resulting from the elementary rotations of the secondary axes are identical in the three perpendicular directions. If the terminal end is further away from the point  412  while remaining within the OPA, the elementary movements are no longer necessarily orthogonal but remain linearly independent, and with equal control and resolutions on the angular sensors, the position increments can substantially vary. However, the advantages as regards the improvement in the accuracy of the positioning are not affected. 
     The space resolution is in relation with the digital control resolution, with the performances of the actuators control system characterized, among other things, by the covariance matrix and the proprioceptive sensors resolution and to the space configuration of the robot arm. On the modern systems, the resolution of the digital control can be considered as quasi-continuous thanks to the double precision processing by the computer. The robot structure shown makes it possible to obtain a much finer space resolution and a much better reproducibility within the OPA than in the remainder of the working space by controlling the axes  402 ,  404  and  406 . 
     Because the axes  402  and  404  are parallel, the redundancy of the robot structure causes no particular problem for the control of the mechanism during both phases of the prepositioning and the fine positioning. As a matter of fact, driving a redundant robot is always difficult since this requires integrating additional criteria in the control process (optimising the energy criterion for example). Then, during the prepositioning phase, the axes  402 ,  406  and  408  can be driven only with the only aim of bringing the terminal end in the OPA; during this phase the robot structure has a conventionally revertible geometric model. During the fine positioning phase, the axes  402 ,  404  and  406  only are actuated and the geometric model is still conventionally locally revertible. 
     While referring to FIGS.  5 - a  and  5 - b , in a particular embodiment, the robot structure for an accurate positioning of a terminal end of the robot in the three-dimensional space is composed in a reference configuration of three parallel axes  502 ,  506  and  508 , and one axis  504  perpendicular to  502 ,  506  and  508 . Except in the reference configuration, the axes  506  and  508  are always parallel but they are no longer necessarily parallel to the axis  502 . As for the dimensions of this structure, the persons skilled in the art will try to obtain a length of the arm  507 /length of the arm  505  ratio as high as possible while considering the constraints in the working space. The lengths of the arms  507  and  509  are substantially equal to each other within 10%. The length of the arm  507  is, for lack of constraints, at least 10 times longer than the distance between the axes  504  and  506 . 
     The control of such structure will be identical in every point to the previous structure, starting with the positioning of the terminal end  310  in the area of interest through the action of the axes of rotation  504 ,  506  and  508 . Then, once the end  310  is positioned, the axis  508  is blocked and the accurate positioning occurs thanks to the simultaneous actuation of  502 ,  504  and  506 . 
     While referring to FIGS.  6 - a  and  6 - b , in a particular embodiment, the robot structure for an accurate positioning of a terminal end of the robot in a three-dimensional space is composed of three parallel axes  604 ,  606  and  608  and one axis  602  perpendicular to  604 ,  606  and  608 . To size this structure, the persons skilled in the art will try to obtain a length of the arm  607 /length of the arm  605  ratio as high as possible while considering the constraints in the working space. Lengths of the arms  607  and  609  are substantially within 10%. The length of the arm  607  is, for lack of constraints, at least 10 times greater than the length of the arm  605 . 
     The control of such structure will be identical in every point to the previous structures, starting with the positioning of the terminal end  310  of the arm in the area of interest through the action of the axis of rotation  602 ,  606  and  608  (or the axes of rotation  602 ,  604  and  608 ). And once the end  310  is positioned, the axis  608  is blocked and the accurate positioning occurs thanks to the joint actuation of  602 ,  604  and  606 . 
     While referring to  FIG. 7 , in a generic embodiment enabling the positioning of the terminal end  310  and the robot structure in one plane (P) in space, the structure is composed of three kinematic chains  701 ,  703  and  705  and two axes of rotation  702 ,  704  perpendicular to the plane (P). The kinematic chain  701  connects the rotary link  702  to the support  700 ; the kinematic chain  703  connects the two rotary connections  702  and  704 ; the kinematic chain  705  connects the rotary link  704  to the terminal end  310 . An additional degree of robot flexibility in the plane (in rotation or in translation) is then integrated in at least one of the kinematic chains  701 ,  703  or  705 . This degree of robot flexibility aims at significantly widening the space which can be reached by the end  310  with respect to the space that can be reached by a robot structure of the SCARA type based on the articulations  702  and  704 . 
     The point  706  is the intersection between the plane (P) and the axis  702 . The point  708  is the intersection between the plane (P) and the axis  704 . The square of the plane (P) a diagonal of which connects the point  706  and  708  defines two new apexes  707  and  709 . In this general case and for a given configuration of the so-called secondary axes of rotation  702  and  704 , there are OPAs (indicated by OPA 1  and OPA 2 ) the centres of which are points  707  and  709 . OPAs are discs centred on  707  and  709  the radius of which is equal to half the distance between  706  and  709 . 
     The control of such structure is as follows: —Placing the end  310  in the OPA by actuating the primary articulations which include all the degrees of robot flexibility of the kinematic chains; —Blocking all the degrees of robot flexibility except for the secondary rotations along the axes  702  and  704 ; —Executing the fine positioning by actuating the axes  702  and  704 . Then, if the terminal end  310  is, for example, at  709 , the elementary movement induced by the rotations of the axes  702  and  704  are carried out along two perpendicular directions in the plane (P) from  709  to  706  and from  709  to  708 . In addition, with equal control and resolution on the angular sensors of the axes  702  and  704 , the position increments are identical in both perpendicular directions. If the terminal end  310  moves further away from the point  709  while remaining within the OPA 1 , the elementary movements are no longer necessarily perpendicular to each other but remain linearly independent and with an equal resolution on the angular sensors, the induced position increments may substantially vary. However, the advantages as regards the improvement in the accuracy of the positioning remain unaffected. 
     In a wider area than the OPA called the area of interest (ZI 1  and ZI 2 ), the short distance with the axes  702  and  704  makes it possible to obtain certain advantages during the fine positioning with performances which are indeed degraded with respect to the OPA but are often more interesting than in the remainder of the working space. Unless specific applications, the point  310  should not be positioned at the centre of the segment having ends  706  and  708 , since the elementary movements induced by the elementary rotations of the secondary axes  702  and  704  are then linearly dependent (local singularity) along the direction linking points  707  to  709 . The OPA depends on the configurations of the robot structure and also on the strategy of the positioning and moving the end of the arm and, if need be, the tool supported with respect to the part to be processed. In a previous step, it is still possible to select with some latitude the position of the centre of the OPA in the working space by acting on some primary degrees of robot flexibility. A motorized prismatic articulation along a parallel axis of articulation  702  can be added at the end of the kinematic chain  705  enabling a fine positioning in the three-dimensional space, with this principle being illustrated by the particular embodiment of  FIG. 10 . 
     While referring to FIGS.  8 - a  and  8 - b , in a particular embodiment making it possible to position the terminal end of the robot structure in a plane space, with the structure being composed of three rotary links  802 ,  804  and  806  perpendicular to the plane  811  and thus parallel to each other. The rotary connection  802  is anchored on the one hand on a support integral with space  800  by one arm  801  and on the other hand it is in relation with the rotary  804  by one arm  803 . An arm  805  supports the rotary links  804  and  806 . The rotary link  806  controls the arm  807 . The terminal end to be positioned  310  is integral with the arm  807 . The lengths of the mars  805  and  807  are substantially equal to each other with a tolerance in the order of half the length of the arm  803 . The persons skilled in the art will try to obtain a length of  805 /length of  803  ratio as high as possible while considering the constraints in the working space. Without constraint, the persons skilled in the art will consider the length of the arm  803  as at least ten times smaller than that of the arm  805 . The length of the arm  805  is selected as a function of the size of the working space desired. 
     The plane  811  contains the point  310  and is perpendicular to the axes of rotation  802 ,  804  and  806 . In this case, the centre of the OPA is the apex  810  of an isosceles right-angled triangle inscribed within the plane  811 , the ends of the hypotenuse of which are the point of intersection  808  of the plane  811  with the axis  802  and the point of intersection  809  of the plane  811  with the apex  804 . Depending on the configurations of the axes  802  and  804 , the point  810  may occupy various positions in space. For a given configuration, the area of interest corresponds to a disc with a centre  810  and the radius of which is substantially equal to half the distance between  810  and  808 . 
     The control of such structure is operated as follows: —Blocking the axis of rotation  802 ; —Placing the end  310  in the area of interest by actuating  804  and  806 ; —Blocking  806 ; —Carrying out the fine positioning by actuating  802  and  804 . Then, if the terminal end  310  is at point  810 , the elementary movements induced by the rotations of the axes  802  and  804  are carried out along two perpendicular directions in the plane  811  (from  810  to  808  and from  810  to  809 ). In addition, with equal control and resolutions on the angular sensors of the axes  802  and  804 , the position increments are identical in these two perpendicular directions. In a previous step, it is possible to select the position of the centre of the OPA by actuating axis  802 . If the terminal end  310  gets further away from the point  810  while remaining within the OPA, the elementary movements are no longer necessarily orthogonal, but remain linearly independent and with an equal resolution on the angular sensors, the induced position increments may substantially vary. However, the advantages as regards improvement and accuracy of the positioning remain unaffected. 
     While referring to FIG.  8 - c , the accuracy in the positioning may be significantly improved in the area of interest by using a local calibration process after the prepositioning phase. Two exteroceptive sensors  812  and  813 , for example digital micrometers, make it possible to know precisely the position of the terminal end  310  in the area of interest. During the step of fine positioning, with the articulation  806  blocked, the movements are carried out only from the axes  802  and  804 . The secondary geometric model connecting the angular movements of the secondary axes with the Cartesian movements in the plane can be rebuilt from the distances evaluated between  804  and  310 . Starting from the new reference in the local reference system thanks to this calibration operation, the movements on a path of motion  814  as from the position of  310  during the calibration are estimated by the secondary geometric model. Because of the small lengths of the lever arms with respect to the secondary axes, because the resolutions the sensors placed on the secondary axes are generally better than on the non secondary axes, because of the small distances between the secondary axes  802  and  804 , because of the calibration operation, the performances as regards the positioning accuracy within the area of interest are then much better than when the estimation of the position is computed from the geometric model taking into account all the primary articulations. 
     While referring to FIG.  8 - d , in a particular embodiment enabling the positioning of the terminal end of the robot structure in a plane of the space, the structure is composed of three rotary connections  802 ,  804  and  806  with  802  and  806  being secondary axes of rotation and  804  being only a primary axis of rotation. The centre  810  of the OPA is defined as mentioned above with respect to the secondary axes  802  and  806 . The control method consists in blocking  804  when the prepositioning phase is completed and in activating the secondary axes  802  and  806  only during the fine positioning phase. Unlike the previous case, it is possible to modify the position of the centre  810  of the OPA with respect to the secondary axes of rotation by acting on the distance between the axes  802  and  806 , depending on the angular setting given for the axis  804 . This makes it possible during the fine positioning phase to reduce or to improve the sensitivity of the movements along both perpendicular directions. Another advantage is that such device can be integrated on existing SCARA robots, with the terminal part composed of the arm  807  and  310  which can be considered as a tool mounted on the end of the SCARA robot having a sufficient resolution on the axis  806 . The drawbacks are that the terminal end  310  cannot be placed at the centre of the OPA only for a particular value of the angular setting given for the axis  804 . 
     In an alternative solution of the previous structure, the axes of rotation  802 ,  804  and  806  are not necessarily strictly parallel, however the movements of the terminal end during the fine positioning phase by actuating the secondary axes remain coplanar and the advantages of the structure as regards the performances in accuracy remain within an OPA which can be defined similarly to the previous case. While referring to FIG.  8 - e , in a particular embodiment making it possible to position the terminal end of the robot structure in a plane of the space, the secondary articulations are a vertical rotary link  802  and a horizontal prismatic link  816 ; the adjustment of the final position being provided by the small lever arm of the articulation  802  which gives an optimal resolution along a direction and by the prismatic articulation  816  in the perpendicular direction. Adding an additional vertical prismatic connection to provide a fine positioning in a three-dimensional space can be considered. 
     While referring to  FIG. 9 , in a particular embodiment enabling the positioning of the terminal end of the robot structure in a plane of the space (P), with the possibility of defining more widely the OPA, the structure is composed of 5 rotary connections  902 ,  904 ,  802 ,  804 ,  806  which are all parallel to each other. In this structure, the kinematic chain  902 - 903 - 904 - 905  corresponds to a robot structure of the SCARA type, whereas the kinematic chain  802 - 804 - 805 - 806 - 807 - 310  can be compared to the previously disclosed structure for a precise positioning in a plane. 
     The control of such a structure starts with a step of defining the OPA in the plane space thanks to the rotary connections  902  and  904 . The centre  810  of the OPA can thus be positioned by the persons skilled in the art in an arbitrary area of the working space of a SCARA robot composed by the kinematic chain  902 - 903 - 904 - 905 . 
     The persons skilled in the art can then go on with the accurate positioning according to the previously disclosed method after selecting the centre of the OPA thanks to  902  and  904 . The selection of the dimensions must be made so that all the areas of interest desired by the persons skilled in the art belong to the space which can be reached by the SCARA robot corresponding to the kinematic chain  902 - 903 - 904 - 905 . The distribution of the lengths between  903  and  905  is estimated by the persons skilled in the art. Lacking constraints, both arms will have identical lengths. This structure advantageously enables to carry out a fine positioning in a wider area of the working space by reproducing, if necessary, the steps of positioning the centre of the OPA, the prepositioning and the fine positioning of the terminal end of the robot arm so as to position the centre of the OPA as close as possible to the desired target. 
     While referring to  FIG. 10 , in one embodiment enabling the positioning of the terminal end of the robot structure in the three-dimensional space, the structure is composed of 3 rotary connections  802 ,  804 ,  806 , which are all parallel together and of a prismatic connection  850  along an also parallel axis, with the fine positioning being obtained by elementary movements of the secondary articulations  802 ,  804  and  850 , with the articulation  806  being blocked after the prepositioning phase. 
     While referring to  FIG. 11 , in one embodiment relating to a hybrid robot structure enabling the positioning of the terminal end in a plane, the structure is composed of three motorized rotary connections  802 ,  804  and  806 , and three passive rotary connections  825 ,  826  and  827 . The motorized rotary articulation  802  controls the angular position of the segment  822  and the rotary articulation  804  controls the angular position of the segment  824 . The segments  822 ,  823 ,  824  and the part of the segment  805  between the articulations  826  and  827  form a parallelogram, ideally a diamond. The centre  810  of the OPA is positioned on the segment  805  in a symmetrical position of the articulation  826  with respect to the articulation  827 . The control method consists in blocking  806  after the prepositioning phase and then in actuating the secondary axes  802  and  804  in the fine positioning phase only. Adding a motorized prismatic connection along an axis parallel to  802  at the end of the segment  807  so as to finely position the terminal end  310  in the three-dimensional space can be considered.