Control of a surgical device for eye surgery

Abstract

The invention relates to a surgical device (10) comprising at least two robots (11, 12), each robot (11, 12) comprising an articulated arm (21, 22) mounted on a base (31, 32), a tool (41, 42) being attached to the end (E1, E2) of the arm (21, 22), each tool comprising a distal end (I1, I2) suitable for being inserted into an insertion point (T1, T2) of an eye, the device comprising a control unit (7) configured to move the end (E1, E2) of the arm of each robot so as to rotate the eye in its orbit to improve the visibility and accessibility of the eye during surgery.

Description

[0001] Control of a surgical device for eye surgeryTECHNICAL FIELD This application generally concerns surgical devices, in particular those using a remotely operable surgical robot, and finds application in eye surgery. STATE OF THE ART Eye surgery is a delicate procedure. In particular, vitreoretinal surgery is a surgical procedure that aims to remove the vitreous humor (the transparent gel that fills the eye) and to treat conditions that the retina may have, such as diabetic retinopathy, retinal detachment or age-related macular degeneration. This surgery is performed under local or general anesthesia, and is done via cannulas called trocars that are inserted into the sclera. Trocars allow surgeons to reach the inside of the eye with surgical tools (vitreotome, diathermy probe, laser, forceps,etc.) to remove the vitreous humor and treat underlying conditions. To perform this procedure, the surgeon sits at the head of the lying patient, and to visualize what is happening, he uses an ophthalmic microscope. Vitreoretinal surgery requires extremely stable and precise surgical gestures, at the limit of the motor capabilities and dexterity of surgeons. To overcome these limits, surgeons use robotic assistance, which allows these types of gestures to be performed with greater stability and precision, for an improved surgical result and increased patient safety. In particular, a device as described in document WO 2020 / 115249 is used. Such a device comprises a pilot station from which a surgeon remotely pilots at least two surgical tools, each carried by a robotic arm. Although offering many advantages,such a device has limited accessibility to the entire eyeball. DISCLOSURE OF THE INVENTION The invention proposes to overcome at least one of these drawbacks. To this end, the invention proposes, according to a first aspect, a surgical device comprising at least two robots, each robot comprising an articulated arm mounted on a base, a tool being fixed to the end of the arm, each tool comprising a distal end adapted to be inserted into an insertion point of an eye, the device comprising a control unit configured to move the end of the arm of each robot, the control unit being configured to implement the following steps for each robot: a) Receiving a position instruction for the end of the tool expressed in a reference frame linked to the insertion point, the tool being inserted into the eyeball of the eye,the eyeball being by anatomical mobile in rotation relative to its orbit which is fixed relative to the base of the robots; b) Reception of an orientation instruction of the eyeball in the orbit; c) Configuration of a model of a geometric scene defined by each robot and the eye, the geometric model making it possible to locate any point in a reference frame associated with an element of the scene, said configuration taking into account the position instructions received and the orientation instruction received; d) calculation from the configured model of the transformation of each robot defining the position and the orientation of the end of each arm positioning the tools so as to obtain a globe oriented according to the orientation instruction received and placing the end of the tools according to the position instructions received; e) piloting each robot to position each arm according to the calculated transformation. The invention is advantageously completed by the following characteristics,taken alone or in any of their technically possible combinations: - the control unit is configured to implement a repetition of steps a) to c) to continuously position each arm according to the positions and orientation received in steps a) and b). - the geometric model of the scene is defined for each robot by a first known transformation between a reference frame linked to the insertion point of the tool in the eye and a reference frame linked to the center of the eyeball; a second transformation defined only by a rotation between a reference frame linked to the center of the eyeball and a fixed reference frame linked to the center of the orbit, said rotation corresponding to the received orientation; a third known transformation between the reference frame linked to the center of the orbit and a fixed reference frame linked to the base; a transformation of a robot between a reference frame linked to the end of the arm and the reference frame linked to the base, said transformation defining the position of the end of the arm in the linked reference frame, au base ;a fourth known transformation between the frame linked to the end of the arm and the frame linked to the end of the tool. -step d) comprises the following substeps for each robot:d1) determining the coordinates of a vector between the insertion point and the end of the tool in the frame linked to the end of the arm from the position of the insertion point in the frame linked to the end of the arm obtained from the received position and the fourth known transformation d2) determining the coordinates of the vector between the insertion point and the end of the tool in the frame linked to the base from the position of the insertion point in the frame linked to the base obtained from the second and third transformations and the received position d3) calculating the transformation of the robot from the coordinates of the vector obtained in steps d1) and d2).-the position of the insertion point in the coordinate system linked to the end of the tool depends on the position of the end of the tool in the coordinate system linked to the insertion point, the end of the arm, the end of the tool and the insertion point being aligned. -the coordinate systems linked to the end of the tool and to the end of the arm are oriented in the same way, the fourth transformation being a single translation along the axis of the tool. -the control unit is configured to implement a determination of the position of the center of the eye in the coordinate system linked to the insertion point of the tool.-the position of the center of the eye in the reference frame linked to the insertion point of the tool is determined by means of a model of the eye defined by -an axial length AL which is the distance between the top of the cornea and the fovea- an anterior chamber depth ACD distance between the top of the cornea and the top of the lens -a white-to-white distance WW: horizontal diameter of the cornea- a limbus-trocar distance LT: this is the distance separating the limbus, i.e. the edge of the iris, from the insertion point of the trocar, measured radially relative to the iris- the opening angle of the trocar α: this is the angle formed by the line OT and the longitudinal axis of the patient from head to toe, projected onto the plane (x^⃗ Oy^⃗ ) of the reference frame R. ^ ^ ^^^ , model in which -the radius of the eyeball R is worth R = OT = (AL − ACD)- the limbus belongs to the surface of the eyeball, its distance from O is equal to R;- the two reference points of the distance LT and the vertical axis z are coplanar the position of point O in the reference frames linked to the eye noted R ^ ^^^^^ ^ ^^^^ and R ^ étant donnée par : -the device comprises an imaging system configured to acquire at least one image of the eye, a control system being configured to specify a movement of the eye in combination with the acquired image of the eye and thus define a desired position of the eyeball to define the orientation of the eyeball in its orbit. -the control system comprises a touch control screen or a trackball so as to define the desired rotation of the eye. The invention relates according to a second aspect to a computer-implemented method for controlling a surgical device according to the first aspect of the invention. The invention makes it possible to control a robot comprising two arms in order to obtain a rotation of the eye during robotic eye surgery, using the synchronization of the movement of at least two surgical tools mounted on robotic mobile arms and passing through trocars. Thus, during robotic vitreoretinal surgery,it becomes possible to apply a lateral force to the trocars by leveraging the tools. This makes it possible to rotate the eyeball in its orbit and, consequently, to visualize the peripheral areas of the retina and to access them more easily. The invention makes it possible to position the robotic arms in such a way that the ends of the tools are each at a desired position in the eye while ensuring that the eyeball is positioned in its orbit in a desired orientation. The robot is controlled based on a geometric model of the operating scene defined by the patient's eye and the robotic arms. At the eye, or more precisely the eyeball, two insertion points for the respective surgical instrument are defined. The insertion points correspond to the center of the circle formed by the intersection of the trocar cannula with the sclera of the eye,surface of the eyeball. The insertion points are fixed relative to the sclera and therefore relative to the eyeball. Each eyeball is mobile in an eye socket which is assumed to be fixed in the reference frame of the operating scene. In addition, the eye has a center which is both that of the orbit and that of the eyeball. The position of the center of the eye in the reference frame of the operating scene is known and determined prior to the operation, by configuring a model of the eye. The model of the eye is advantageously used to determine geometric transformations within the operating scene, in order to locate any point in one of the reference frames associated with each element of the scene. PRESENTATION OF THE FIGURES Other characteristics, aims and advantages of the invention will emerge from the description which follows, which is purely illustrative and non-limiting,and which must be read in conjunction with the appended drawings in which:- Figure 1a illustrates a surgical scene comprising a surgical device according to an embodiment of the invention - Figure 1b illustrates a geometric model corresponding to the surgical scene of Figure 1a;- Figure 2 illustrates geometric parameters of the eye used to estimate a position of the center of the eye;- Figure 3 illustrates steps for controlling the surgical device according to the invention implemented by a control unit of a surgical device according to the invention; - Figure 4 illustrates steps implemented by the control unit of a surgical device according to the invention;- Figure 5 illustrates the muscular structure of an eye;- Figure 6 illustrates a touch display for specifying a rotation of the eye;- Figure 7 illustrates a trackball type controller (in English,"trackball") to specify an eye rotation; - Figure 8 illustrates an interactor for specifying an eye rotation; - Figure 9 illustrates images of a retina to specify an eye rotation. In all figures, similar elements have identical references. DETAILED DESCRIPTION Presentation A method for controlling a surgical device to modify an eye orientation will be described. Such a method is based on a geometric model of the operating scene during robotic bimanual vitreoretinal surgery. We first describe the surgical device, then the construction of the scene and its use for geometry calculations. We will then assign input and output parameters to it. Finally, we will describe how the assembly can be used to position the surgical tools while generating an eye rotation during the control process. Finally,will be described different means for defining a rotation of the eye. Device Figure 1a illustrates an operating scene So in which a surgical device 10 for eye surgery is used. Such a device comprises two robots 1, 2. Each robot comprises a robotic arm 21, 22 mounted on a base 31, 32 (here the base is mobile but this is not necessarily always the case). A tool 41, 42 is mounted at the end E1, E2 of each arm 21, 22. The tools 41, 42 are inserted into the operated eye 5 via a trocar T1, T2 (or insertion point). The tool 41, 42 is rectilinear and is modeled as an axis 411, 421 which extends from the end E1, E2 of each arm 21, 22 towards a free end of the axis, free end inserted into the trocar and which corresponds to the effector of the instrument (clamp, laser, etc.). A control station 6 allows the surgeon to control the positioning of the tools 41,42. Such a control station 6 is for example described in document WO2022 / 106457 A1. In addition, a control unit 7 makes it possible to translate the surgeon's commands into control instructions for each robotic arm 21, 22 so that the end E1, E2 of each arm 21, 22 moves according to the instructions from the control station 6. Also, an imaging system 8 allows the surgeon from the control station 6 to view the eye and the manipulated tools. Such an imaging system is for example an ophthalmic microscope. Each robotic arm 21, 22 is equipped with actuators making it possible to move the tool 41, 42 in space according to at least six degrees of freedom (three translation axes and three rotation axes) in order to comply with the positioning commands from the control station 6. Such an actuator architecture for a robotic arm 21, 22, allocating six degrees of freedom to the tool 41, 42 mounted thereon,allows in particular to move it so that its axis constantly passes through its Instantaneous Center of Rotation (CIR). The position of this center is not imposed mechanically, it can: ^be defined software at the exact location of the trocar T1, T2 through which the tool 41, 42 passes, so that its movements do not create constraints on the sclera of the eye 5;^ be moved during surgery, for example to follow the movements of the patient as described in document WO 2022 / 106457A1. In order to allow better visibility of the eye during surgery, a control method which will be described will make it possible to determine a movement of the arms to allow rotation of the eye during surgery. In what follows the method is described with the use of two surgical tools, and therefore two robotic arms,but it can be applied to a larger number without in any way modifying its principle. Model of the operating scene The control of the surgical device 10 is based on a geometric model of the operating scene So defined by the eye and the robots 1, 2 of figure 1a whose geometric model Mso is illustrated in figure 1b. The operating scene So comprises several elements:^ the two tools 41, 42 used for the surgery;^ the two robots 1, 2, each consisting of:o a robotic arm 21, 22 on which the tool 41, 42 is mounted;o the base 31, 32 possibly mobile in order to move the robot in the operating room but which remains fixed during the surgery.An eye 5 comprising an eyeball 51, for which two points 52, 53 for insertion of a tool 41, 42 are defined, the eyeball 51 and therefore the insertion points 52, 53 being mobile in an orbit 54. In this scene, the eyeball 51 is mobile in the orbit 54 which is fixed relative to the base 31,32. In addition, the eye 5 has a center O which is both that of the orbit 54 and that of the eyeball 51. Its position relative to the base 31,32 is known and determined during an initialization phase (we will come back to this). Each of the elements of the scene is assimilated to a body which transforms a spatial geometric reference frame R ^^^^^^ ^ into another reference frame R ^^^^^^ ^ . Each reference frame has an origin O, ^^^^^ and a direct orthonormal vector basis ^^x^^^^^^^^^^^^^^^⃗ ,^ y^^^^^^^^^^^^^^^⃗ ,^ z^^^^^^^^^^^^^^⃗ ^. For a given field, a unique transformation of the space ^ ^^^^^ allows you to transform your reference point R ^^^^^ ^ into your reference point R ^^^^^ ^^^^^ ^ . Such a transformation consists of a translation T which moves the origin of R ^^^^^ onto the origin of R ^^^^^ and a rotation ^^^^^ ^^^^^ ^ ^ Ω which applied to R ^ changes its orientation to that of R ^^^^^ ^: The transformation of a body is unique at each moment. It can either: ^remain constant over time. This is the case for non-deformable solids, such as bases that are not moved during surgery, but also for tools whose flexibility is considered negligible in this model. ^vary over time. This is particularly the case for robotic arms, whose purpose is to change the position and orientation of the tools relative to the base. In relation to Figure 1b, to constitute the model of the operating scene Mso, the bodies are assimilated to links of geometric chains SG1, SG2. Two mechanically linked bodies follow one another in a chain, and reference points are assigned to them so that the reference point R^ of a body coincides with the reference point R^ of the previous one. Taking into account two surgical tools held by two independent robotic mobile elements, as illustrated in Figure 1b, the model is made up of two geometric chains SG1, SG2.These chains SG2, SG2, however, have a common link corresponding to the orbit 54 of the eye 5. It is thanks to this link that the movements of the two chains SG1, SG2 can be synchronized in order to generate a rotation of the eye. In Figure 1b, the body chain models the operating scene So geometrically by a geometric model Mso of the operating scene within the framework of the invention and makes it possible to move from one reference point of a body to another reference point of another body. According to this body chain, the links between each body within the scene are thus defined. Within the framework of the invention, we therefore have the following bodies: eye / insertion point 52, 53,; orbit 54, base 31, 32, robot 21, 22 and tool 41, 42 and as visible in figure 1 to a body is associated two references R^^^^^ ^^^^^ ^ and R. ^. The table below lists the different bodies / elements of the scene as well as the associated references. In the reference column, the references R^^^^^ ^^^^^ ^ and R are used ^without referring to the geometric chain considered, the two being identical. We will specify the chain 1 or 2 if necessary. It will be noted, in this respect, that the eye 5 comprises two bodies eye1 and eye2 each associated with an insertion point 52, 53 of a tool 41, 42 in the eye 5. We note that for each chain similar reference points are therefore defined. Body Description of the body Reference Reference Description This reference point is the one in which the position commands of the tool are expressed, as retrieved from the insertion point 52, 53 in the surgeon via the pilot station. eyeball 51 of the patient. Its origin T1, T2 corresponds to the center of the circle formed by the intersection of the cannula of the trocar with the sclera of the eye which is expressed the R^^^^ ^ surface of the eyeball. This involves positioning the tool at each insertion point 52, 53 of the tool with a reference centered in the eyeball 51.insertion point 52, 53. Its orientation is such that when the transformation of this body is known and fixed during surgery, it is identical to that of the eye, it is identical to that of the reference R ^^^^^^. ^ = R ^ ^ ^^^ . R ^ ^ ^^^ The positioning of this marker is fixed relative to the R marker ^ ^ ^^^ and their orientations are identical. This body corresponds toIts origin O is in theory the center of the orbit 52 in which the R^^^^^^ ^ the ball joint connection which exists between the eye and the eyeball 51 is mobile. It allows to model the orientation of the eye 5, and is estimated during the process. Orbit consists of only one This reference frame is a fixed reference frame in the rotation block Ω ^^^^^^ which reorients the operative, the patient and the bed on which the R marker ^ ^ ^^^associated with the R^^^^^^^ ^ it is elongated being considered as center of the eye 5 to obtain immobile. a fixed reference point relative toIts origin O is identical to that of the patient's head. reference point R ^^^^ ^ = R ^ ^ ^^^^^ and corresponds to the Base R ^^^^ ^center of the eye. This body corresponds to the base Its orientation is such that its x axis, which is mobile if necessary, is parallel to the transverse axis of the patient (from ear to ear) and its z axis is vertical. The transformation of this body ^^ robot as defined by its system of R ^^ is known and fixed during ^steering, the one in which its Cartesian positions and instructions are expressed during surgery. For example, in the case of a serial robotic arm, the origin of this reference frame is generally located at the center of its first axis. This body corresponds to any This reference frame is also fixed in the operating room, the base being static actuators, which allows the robot to move the tool in space during surgery. Its positioning relative to the reference frame according to its six degrees of R ^^^^^^ ^ = R ^ ^ ^^^ is considered freedom. known, its determination, via a referencing method which is not the subject of this presentation. R ^ ^ ^^^^ This reference point is that of the end E1, E2 of the arm, its positioning in relation to the reference point R ^^^^ ^ = R ^ ^ ^^^^depends on the instruction given to the robot and evolves during surgery. This body corresponds to the surgical tool ^^ mounted on the robot R ^^^ ^Its z axis corresponds to the longitudinal axis of the tool (its origin is arbitrarily placed on it), and its x and y axes are arbitrarily oriented. The transformation of this body is known and fixed during surgery. The origin I1, I2 of this reference frame corresponds to the tool ^^ nd à of u ^^^ ^ the end of the tool (in closed position for clampable tools) and its orientation is identical to that of the R mark ^^^^^ ^ = R ^ ^ ^^^^ This reference is the one that allows the tool position commands to be materialized, by specifying the position of I in relation to the reference R ^ ^ ^^^. Thanks to the geometric model thus defined, it is possible to determine in any frame the expression of a point or a vector as long as its expression in another frame is known.Eye model – Determination of the center O of the eyeThe eye is a particular body since it depends on the patient and the way in which the trocar of the tool is placed. The body eye1 transforms the frame R ^ ^ ^^^^ , of origin T1 and in which the tool positioning command is expressed, in a reference R ^^^^^ ^ , whose origin O corresponds to the center of the ball joint that exists between the eye and its orbit. Also, the body eye2 transforms the reference R ^ ^ ^^^^ , of origin T2 and in which the tool positioning command is expressed, in a reference R ^^^^^^ , whose origin O corresponds to the center of the ball joint which exists between the eyeball and its orbit. Its transformation is a simple translation, defined by the position of point O in the reference frame R ^^^^^ ^ , R ^ ^ ^^^^. Point O is defined theoretically, but in practice no means of measurement allows it to be located. A model of the eye is therefore set up to estimate this position. For this, the following quantities in relation to figure 2 are introduced: 1. the axial length AL: this is the distance between the top of the cornea and the fovea. This is a common biometric data measurable during a preoperative examination. In the absence of measurement, an average estimate of 23.8 mm is used, an estimate which can be made more precise by taking into account the gender, age, origin and possible eye pathologies of the patient (see [Marilou Thesis]). 2. the anterior chamber depth ACD: this is the distance between the top of the cornea and the top of the lens. This is a common biometric data measurable during a preoperative examination. In its absence, an average estimate of 3.17mm can be retained, a value that can be refined according to the patient's characteristics (see [Marilou Thesis]). 3. the white-to-white distance WW: this distance represents the horizontal diameter of the cornea. It is a common biometric data measurable during a preoperative examination. In its absence, an average estimate of 11.80mm can be retained, a value that can be refined according to the patient's characteristics (see [Hashemi]). 4. the limbus-trocar distance LT: this is the distance separating the limbus (edge ​​of the iris) from the insertion point of the trocar, measured radially relative to the iris. Vitreoretinal surgery trocars are supplied with a gauge allowing a predefined distance to be precisely respected, which, depending on the supplier, can vary between 3mm and 4mm (see [Kourous]). 5. the opening angle of the trocar α: this is the angle formed by the line (OT) and the longitudinal axis of the patient (from the feet to the head), projected onto the plane (x^⃗ Oy^⃗ ) of the R reference point.^ ^ ^^^ . This angle depends mainly on the surgeon's habits. It can be easily measured once the trocars are inserted, by the surgeon directly or by processing the images acquired by the microscope. In the absence of measurement, the current value of 60 degrees can be used. The following hypotheses or approximations are also made: - the diameter of the eyeball is equal to the difference between the axial length and the depth of the anterior chamber, and therefore its radius R is R = OT = (AL − ACD)- the limbus belongs to the surface of the eyeball, so its distance from O is equal to R- the two reference points of the distance LT and the vertical axis z are coplanar.

[0002] These five quantities and these three hypotheses make it possible to determine, using known geometric tools, the position of point O in the R reference frames. ^ ^ ^^^^ and R ^ ^ ^^^^. x= −R sin θ sin α R sin θ sin α^ = ^ y = R sin θ cos α R sin θ cos αz = R cos θ R cos θ R ^ ^ ^^^^ Definition of the operating scene and change of reference frameThanks to a set of geometric transformations within the scene S it is possible to locate any point in one of the reference frames associated with each element of the scene. To simplify the expression of the calculations with the transformations in the previous table, let us introduce the following notations (with R^^^^^ ^^^^^ ^ and R^ associated with the same body / element):R ^ ^ ^^^ to R ^ ^ ^^^ : transformation ^ ^^^^ are defined to be oriented in the same way. R ^ ^ ^^^ to R ^^^^^^ ^: transformation ^^^^^^^, these two markers have the same origin, the transformation ^ ^^^^^^ is only a rotation. R ^ ^ ^^^^^ to R ^ ^ ^^^ : transformation ^ ^^^^ R ^ ^ ^^^ to R^ ^ ^^^^ : transformation ^ ^^^^^ allows you to position the end of each arm in the R scene ^ ^ ^^^^ to R ^ ^ ^^^^ : transformation ^ ^^^^^ , the R reference ^ ^ ^^^^ and the R marker ^ ^ ^^^^are oriented in the same way: the transformation ^^^^^^ is a single translation along one dimension (here the axis of the tool) is necessary to move from one reference frame to another. To move from one element to another, it is enough to refer to the geometric chain thus defined and, if necessary, define a succession of transformations. The model of the scene thus obtained makes it possible to calculate the transformation that exists between two reference frames. Knowing the transformation that exists between two reference frames of the model makes it possible to make changes of reference frame: knowing the expression of a geometric object in a given reference frame, it is possible to determine the expression of the same object in another reference frame. In the model thus constructed, three transformations are free: the transformation^ ^^^^^^ and transformations ^ ^^^^^^ , ^ ^^^^^^ . giving a certain orientation to the eye we can determine ^ ^^^^^^ then it will be a question of determining which transformations ^ ^^^^^^ , ^^^^^^^ will allow the end of the tools to be placed at given positions taking into account ^^^^^^^. Advantageously, the axis of the tool must constantly pass through the trocar, the coordinates ^ and y of the point ^ in the reference frame ^^ ^^^^^ are zero. This allows to obtain a unique solution for the transformations ^ ^^^^^^ , ^ ^^^^^^.Control method (figure 4)The control of the surgical device 10 is implemented by the control unit 7 and is based on a model of the operating scene (see below). In particular and as illustrated in figure 3 a position instruction of the end I1, I2 of each tool 41, 42 in their insertion point 52, 53 is received (steps REC1, REC2) by the control unit 7 as well as an orientation instruction of the eyeball in its orbit (step REC3). Then, the corresponding geometric model of the operating scene is configured (step DET MOD) taking into account the positions and the orientation received. This configuration of the model allows in particular the calculation (step TRANS1, TRANS2) of the transformations ^^^^^^^ ,^ ^^^^^^robots which will place the ends E1, E2 of each arm so that the positions of the tools in the eye correspond well to the position instructions of the end I1, I2 of each tool 41, 42 in their insertion point 52, 53, and so that the positions of the instantaneous centers of rotation of the tools ensure that the positions of the trocars correspond well to the position instructions of the insertion points 52, 53 generated by the desired orientation of the eyeball. From the transformations calculated for each robot, each arm is piloted (PIL1, PIL2) according to these transformations. The piloting of the arms then consists of transmitting to them the transformations thus calculated as positioning instructions (PIL1, PIL2).The control therefore makes it possible to move the tools in space to simultaneously position their ends at the desired locations and orient them so that they drive the insertion points and thus rotate the eye in its orbit. The positions and orientation are calculated and sent to the control unit 7, to control the arms 21, 22 accordingly, more than 1000 times per second for high transparency and thus follow the wishes of the user 9 who specifies the orientation (step DEFΩ) via the control station 7 and, possibly with the help of the imaging system 8 to control the operations. The steps implemented by the control unit 7 for controlling the surgical device 10 are now described in detail. In an initialization step (step INIT), the position of the center O of the eye is determined by means of the eye model described above (INIT1).Then, from this position of the center O of the eye, the transformation ^^^^^ is determined (INIT2) also from the positions of the insertion points 52, 53 which correspond to the origins of the R reference points. ^ ^ ^^^^ , R ^ ^ ^^^^ . Then, the transformation ^^^^^ is determined (INIT3) by means of a known referencing method. Each tool is positioned at the end E1, E2 of each arm and the position of the end E1, E2 of each arm in such a way that the transformation ^ ^^^^^ is either known in advance (thanks to a repeatable assembly) or determined by a referencing method (INIT4). In this respect, the end I1, I2 of the tool is known relative to that of the end E1, E2 of the arm. Advantageously, the positioning of the reference mark R ^ ^ ^^^^ relative to the R reference point ^^^^^^^ is known and constant throughout the process and is the subject of any referencing method. The tools being placed by the surgeon in their respective insertion point 52, 53, the process comprises the reception (REC1, REC2) by the control unit 7 of the positions of the tools in the reference points R ^ ^ ^^^^ , R ^ ^ ^^^^ of origin the insertion points T1, T2. The position of the tools must evolve during the surgery, in order to carry out the surgical gestures desired by the surgeon. The determination of these positions can be the result of trajectory planning, or for a telemanipulation system, the result of a measurement on a dedicated interactor. We note by ^^to designate the posi ^ ^^^^ and I ^ / ^^ tions des ^ ^^^^ ends I1 and I2 of each tool in the R frame ^ ^ ^^^^ and in the R frame ^ ^ ^^^^. Then, an orientation of the eyeball in its orbit, defined by a rotation ^^ ^Ω ^^^^^^ ^which orients the reference point R ^ ^ ^^^ associated with the eyeball 52 with respect to the reference frame R^^^^^^^ ^ associated with the orbit (step DEFΩ) is defined by the surgeon by means of the control station 7. This rotation is then communicated to the control unit 7 (step REC3). As already mentioned, steps REC1, REC2 and REC3 are implemented periodically (preferably more than 1000 times per second) for optimal transparency. In addition, the orbital body being the common link in the two geometric chains of robots, its transformation reorients the reference frame associated with the center of the eye R ^ ^ ^^^ , to obtain a fixed reference point relative to the patient's head: R ^ ^ ^^^ . It consists of only one rotation, ^ ^^^^^ ^^ Ω . The inverse of this rotation, Ω ^^^^^^, describes how the eyeball is oriented relative to the patient's head. It is precisely this orientation that we wish to adjust and correct during surgery. Ω ^^ ^^ evolved ^^^^ can be described by three Euler angles θ ^ , θ ^ andθ^ which, in ZYX convention, correspond to the rotation of the eye along the x, y and z axes of the reference frame R^ = R ^ ^ ^^^. These elementary rotations correspond to the elementary movements that the eye is capable of generating by the contraction or extension of muscles (in relation to figure 5): - θ^: rotation upwards or downwards, resulting mainly from the contraction or extension of the inferior rectus muscles 53 and superior rectus muscles 54; - θ^: rotation to the left or right, resulting mainly from the contraction or extension of the internal rectus muscles 55 and external rectus muscles 56; - θ^: torsional rotation, resulting mainly from the contraction or extension of the inferior oblique muscles 57 and superior oblique muscles 58. Since muscles have a limited capacity for contraction and extension, elementary rotations are also limited. The following conditions are therefore imposed ([Bargaryet al.]): θ^ ∈ [−48 , +42] deg ; θ^ ∈ [−50 , +50] deg ; θ^ ∈ [−30 , +30] deg.^ ^^^^ ^^ The rotation ^Ω ^ ^ , positions I ^ / ^^^^^ and I ^ / constitute entries to a ^ ^^ ^ ^ ^^^^ step of configuring the entire geometric model of the scene (DET MOD step) to allow the transformations to be obtained ^ ^^^^^^ and ^ ^^^^^ . Indeed, once the positions of each tool and the rotation are defined, we know through the chain of bodies how to go from the eye to the base and from the robot to the tool. It then remains to determine the link between the robot and the base which satisfies the positions of each tool and the rotation defined and which allows us to determine the robot control instructions: the transformations ^^^^^^^ and^ ^^^^^ presented above. We first determine the transformation ^ ^^^^^^ (step S1) which is defined by the received rotation. Then, for each robot it is a question of determining from the received orientation and the position of the end of the tool in the R frame ^^^^^ the geometric transformation ^^^^^^^so as to generate instructions for controlling the arm to place the end (E1, E2) of the arm such that the end I1, I2 of the tool is in a position such that the eyeball is oriented relative to its orbit according to the orientation received while being at the position of the tool received (step S2). More precisely, to obtain the transformation ^^^^^^ sought, we seek the expression of the position of the end I1, I2 of the tool and the insertion point T1, T2 in two different frames of reference: the frame R ^ ^ ^^^ (step S21) and the R marker ^ ^ ^^^^ (step S22). The position of the insertion point T1, T2 in the R coordinate system ^ ^ ^^^^ (noted T / ^^ ^ ^^^^) is obtained by T / ^^ ^ ^^^^= ^^^^^^^⃗ / ^ corresponding to the depth ^^ ^^^^of the desired tool in the eye, calculable directly with the position of the end of the tool in the eye (noted ^ / ^^ ^^^^). The position of the end of the tool in the R frame ^ ^ ^^^^ (noted I / ^^ ^ ^^^^) is obtained by being the origin of the reference frame ^^^^^ The position of the insertion point T in the R coordinate system ^ ^ ^^^ (noted T / ^^ ^ ^^^) is obtained by involving rotation of the eyeball in relation to the orbit and which makes it possible to define the transformation ^^^^^^^ and known transformations ^ ^^^^ and ^ ^^^^ . Also the position of the end I1, I2 of the tool in the R reference frame ^ ^ ^^^ is obtained by At this stage, the scene model is set as it must be to satisfy both the position and orientation instructions of the globe. Knowing for each robot the transformation ^^^^^^ which in other words position the end E1, E2 of the arm relative to the bases 31, 32, the control instructions for each arm are calculated (steps CALC1, CALC2). Each arm is finally controlled according to these instructions (steps PIL1, PIL2). Definition of the eye rotation instruction (step DEF^) To specify during surgery what rotation we want to give to the eyeball, several means can be implemented. A first means of specifying the rotation of the eye consists of providing, on the control station, a dedicated interactor. Two types of control can be envisaged: a position control or a speed control.Position control With this type of control, the objective is to allow the user to directly indicate in which position he wishes to place the eye. Several types of interactors can fulfill this role: Graphical controls as seen in Figure 6: on a touchscreen, the user can directly specify the amplitude of the three elementary rotations θ. ^ , θ ^ and θ ^ constituent Ω ^^^^^^^^. These values ​​can be set by adjusting the slider, or more ergonomically by sliding the finger on a representation of the eye according to the desired adjustment direction. A trackball type device visible in Figure 7: this type of device consists of a movable ball in a fixed base. The ball can be rotated on itself by the user, and the device is capable of directly measuring the elementary rotations θ^, θ^ and θ^ corresponding to its orientation relative to the base. By assimilating the trackball ball to the eyeball, we can have a direct measurement of the desired orbital rotation Ω^^^^^^^^. Speed ​​control With this type of control visible in Figure 8, the objective is to allow the user to choose a direction and a speed of rotation for the eye rather than directly its position. Joystick 71 or space mouse 72 type interactors can fulfill this role.In both cases, the device consists of a fixed support and a gripper that can be moved away from a central position in the three directions of space^, ^ and ^. The amplitude of the gripper is limited, and an elastic return tends to bring the gripper back to its central position so that it returns there as soon as it is no longer manipulated. These devices are able to measure how far the gripper is from its central position using elementary values ​​between -1 and 1 along each of the three axes: ^^^ , ^^ , ^^^ ∈ [−1,1]^. The values ​​^^^ , ^^ , ^^^ ∈ {0,0,0} are measured when the gripper is in the central position, while for each axis, the values ​​of -1 and 1 are measured when it reaches its maximum amplitude in one direction and the other. With these devices, we can periodically update the values ​​of the elementary rotations θ. ^ , θ ^ and θ ^, preferably more than 100 times per second for optimal responsiveness: with dt the update period and θ̇^^^ the maximum variation of amplitude that we allow ourselves at each updateA second way visible in figure 9 to specify the rotation of the eye is to respond directly to the initial need to rotate the eye in its orbit: to allow the user to center a point of interest on the microscope images. An image I from the imaging system 4 is provided with a mark ^ ^^^^^ whose origin is a point ^ defined such that it appears at the center of the image when no rotation has been^ ^^^^^ →^^ ^^^^^^ applied to the eye. There is a transformation ^ which allows us to know the coordinates of a point in the reference frame ^ ^ ^^^^^^ from its coordinates in the ^ frame ^^^^^. This transformation is determined from a registration method considered to be known. List of references: [Marilou thesis] Marilou Isidore. Description of ocular biometry parameters in preoperative cataract surgery in a population in the South of France: a multicenter cross-sectional study. Human Medicine and Pathology. 2021. (dumas-03436986) [Hashemi et al.] Hashemi H, Khabazkhoob M, Emamian MH, Shariati M, Yekta A, Fotouhi A. White-to-white corneal diameter distribution in an adult population. J Curr Ophthalmol. 2015 Oct 19;27(1-2):21-4. doi: 10.1016 / j.joco.2015.09.001. PMID: 27239570; PMCID: PMC4877715. [Kourous] Kourous Rezaei MD, Complications in Vitreoretinal Surgery [Bargary et al.] Bargary, G., Bosten, J., Goodbourn, P. et al. Individual differences in human eye movements: An oculomotor signature? 2017.

Claims

CLAIMS 1. Surgical device (10) comprising at least two robots (11, 12), each robot (11, 12) comprising an articulated arm (21, 22) mounted on a base (31, 32), a tool (41, 42) being fixed to the end (E1, E2) of the arm (21, 22), each tool comprising a distal end (I1, I2) adapted to be inserted into an insertion point (T1, T2) of an eye, the device comprising a control unit (7) configured to move the end (E1, E2) of the arm of each robot, the control unit (7) being configured to implement the following steps for each robot: a) Receiving (REC1, REC2) a position instruction for the end (I1, I2) of the tool expressed in a reference frame (R ^ ^ ^^^^ , R ^ ^ ^^^^) linked to the insertion point (T1, T2) the tool being inserted into the eyeball of the eye, the eyeball being by anatomical mobile in rotation relative to its orbit which is fixed relative to the base (31, 32) of the robots (11, 12), the orbit comprising a center (O) of the eye; b) Reception (REC3) of an orientation instruction of the eyeball in the orbit; c) Configuration (DET MOD) of a model of a geometric scene defined by each robot and a model of the eye, the geometric model making it possible to locate any point in a reference frame associated with an element of the scene, said configuration of the model being implemented from the position instructions received and the orientation instruction received, the model of the geometric scene consisting of two geometric chains (SG1, SG2), the two geometric chains (SG1, SG2) having a common link corresponding to the orbit of the eye;d) calculation (TRANS1, TRANS2) from the configured model, of the transformation (^^^^^^^, ^^^^^^^) of each robot defining the position and orientation of the end (E1, E2) of each arm positioning the tools so as to obtain a globe oriented according to the orientation instruction received and placing the end of the tools according to the position instructions received;e) piloting (PIL1, PIL2) each robot to position each arm according to the calculated transformation.

2. Device according to the preceding claim, wherein the control unit is configured to implement a repetition of steps a) to c) to continuously position each arm (21, 22) according to the positions and orientation received in steps a) and b).

3. Device according to one of the preceding claims, wherein the control unit (7) implements the configuration of the geometric model of the scene defined for each robot by a first transformation (^^^^^^^ , ^^^^^^) known between a reference frame linked to the point of insertion of the tool in the eye and a reference frame linked to the center of the eyeball; a second transformation (^; ^^^^^^ ) defined solely by a rotation between a reference frame linked to the center of the eyeball and a fixed reference frame linked to the center of the orbit, said rotation corresponding to the received orientation; a third transformation (^ ^^^^^ , ^ ^^^^^) known between the reference frame linked to the center of the orbit and a fixed reference frame linked to the base; a transformation of a robot (^^^^^^^, ^^^^^^^) between a reference frame linked to the end of the arm and the reference frame linked to the base, said transformation defining the position of the end of the arm in the reference frame linked to the base; a fourth transformation (^^^^^^^, ^^^^^^^) known between the reference frame linked to the end of the arm and the reference frame linked to the end of the tool. 4.Device according to claim 3, wherein the control unit (7) is configured to in step d) implement the following sub-steps for each robot: d1) determining the coordinates of a vector between the insertion point and the end of the tool in the frame linked to the end of the arm from the position of the insertion point in the frame linked to the end of the arm obtained from the received position and the fourth known transformation; d2) determining the coordinates of the vector between the insertion point and the end of the tool in the frame linked to the base from the position of the insertion point in the frame linked to the base obtained from the second and third transformations and the received position; d3) calculating the transformation of the robot from the coordinates of the vector obtained in steps d1) and d2). 5.Device according to one of the preceding claims, in which the position of the insertion point (T1, T2) in the reference frame linked to the end (I1, I2) of the tool depends on the position of the end (I1, I2) of the tool in the reference frame linked to the insertion point, the end (E1, E2) of the arm, the end (I1, I2) of the tool and the insertion point (T1, T2) being aligned.

6. Device according to one of claims 3 to 4, in which the reference frames linked to the end of the tool and to the end of the arm are oriented in the same way, the fourth transformation being a single translation along the axis of the tool.

7. Device according to one of the preceding claims, in which the control unit is configured to implement a determination of the position of the center (O) of the eye in the reference frame linked to the insertion point of the tool.8.Device according to claim 7, in which the position of the center (O) of the eye in the reference frame linked to the insertion point of the tool is determined by means of a model of the eye defined by - an axial length AL which is the distance between the top of the cornea and the fovea; - an anterior chamber depth ACD distance between the top of the cornea and the top of the lens; - a white-to-white distance WW: horizontal diameter of the cornea; - a limbus-trocar distance LT: this is the distance separating the limbus, i.e. the edge of the iris, from the insertion point of the trocar, measured radially relative to the iris; - the opening angle of the trocar α: this is the angle formed by the line OT and the longitudinal axis of the patient from the feet to the head, projected onto the plane (x^⃗ Oy^⃗ ) of the reference frame R. ^ ^ ^^^ , model in which -the radius of the eyeball R is worth R = OT = (AL − ACD) ;- the limbus belongs to the surface of the eyeball, its distance from O is equal to R;- the two reference points of the distance LT and the vertical axis z are coplanar the position of point O in the reference frames linked to the eye noted R ^ ^ ^^^^ and R ^^^^^ ^ being given by:

9. Device according to one of the preceding claims, comprising an imaging system (8) configured to acquire at least one image of the eye, a control system (6) being configured to specify a movement of the eye in combination with the acquired image of the eye and thus defining a desired position of the eyeball to define the orientation of the eyeball in its orbit.

10. Device according to claim 9, in which the control system comprises a touch control screen or a trackball so as to define the desired rotation of the eye. 11.A computer-implemented method for controlling a surgical device (10) comprising at least two robots (11, 12), each robot (11, 12) comprising an articulated arm (21, 22) mounted on a base (31, 32), a tool (41, 42) being attached to the end (E1, E2) of the arm (21, 22), each tool comprising a distal end (I1, I2) adapted to be inserted into an insertion point (T1, T2) of an eye, the device comprising a control unit (7) configured to move the end (E1, E2) of the arm of each robot, the control unit (7) being configured to implement the following steps for each robot: a) Receiving (REC1, REC2) a position instruction for the end (I1, I2) of the tool expressed in a reference frame (R. ^ ^ ^^^^ , R ^ ^ ^^^^) linked to the insertion point (T1, T2) the tool being inserted into the eyeball of the eye, the eyeball being by anatomical rotational motion relative to its orbit which is fixed relative to the base (31, 32) of the robots (11, 12), the orbit comprising a center (O) of the eye; b) Reception (REC3) of an orientation instruction for the eyeball in the orbit; c) Configuration (DET MOD) of a model of a geometric scene defined by each robot and a model of the eye, the geometric model making it possible to locate any point in a reference frame associated with an element of the scene, said configuration of the model being implemented from the position instructions received and the orientation instruction received, the model of the geometric scene consisting of two geometric chains (SG1, SG2), the two geometric chains (SG1, SG2) having a common link corresponding to the orbit of the eye;d) calculation (TRANS1, TRANS2) from the configured model, of the transformation (^^^^^^^, ^^^^^^^) of each robot defining the position and orientation of the end (E1, E2) of each arm positioning the tools so as to obtain a globe oriented according to the orientation instruction received and placing the end of the tools according to the position instructions received; e) piloting (PIL1, PIL2) of each robot to position each arm according to the calculated transformation.;

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