Joint with three degrees of freedom for a robot, and corresponding control method

Abstract

A joint with three degrees of freedom for a robot, the joint comprising a platform (2), three motors (3a, 3b, 3c), each motor being connected to a ring gear (4, 4a, 4b, 4c) via a pinion (5a, 5b, 5c), each ring gear (4, 4a, 4b, 4c) being arranged inside a hollow disk (6a, 6b, 6c) stacked on a base, so that each disk (6, 6a, 6b, 6c) is integrated with the ring gear (4, 4a, 4b, 4c), and each disk (6, 6a, 6b, 6c) is connected to a ring gear (4, 4a, 4b, 4c) via a pinion (5a, 5b, 5c). b, 6c) itself is also integral with a disk head (7, 7a, 7b, 7c), which extends in the same direction as the base and the stack of disks (6, 6a, 6b, 6c), for each disk head (7, 7a, 7b, 7c), an arm (8, 8a, 8b, 8c) is rotationally connected to the disk head (7, 7a, 7b, 7c) on the one hand and to the platform (2) on the other hand, each motor (3a, 3b, 3c) is at least partially contained inside at least one disk (6, 6a, 6b, 6c).

Description

Technical Field

[0001] The technical field of the invention is actuators for robots, and more particularly actuators with three axes of freedom.

[0002] The technical field of the invention is also the control of actuators having three axes of freedom. Background Art

[0003] Social robots are developed to enable natural interaction with humans in public and domestic spaces, especially for recreational uses of robots.

[0004] In particular, such a robot must have the following characteristics:

[0005] - are safe in interaction, especially physical interaction during touching or manipulation by a human,

[0006] - makes it possible to perform dynamic movements in order to both react to unplanned events and create more pleasant interactions and facilitate the illusion of living,

[0007] - Allows to perform high-quality animations, which facilitates intuitive human understanding of the robot’s intentions and enables actions in the real physical world by manipulating objects.

[0008] Operational safety is derived in particular from the mass of the robot or its components in order to limit inertia in the control and to limit the risk of injury to the public.

[0009] In robotics, when it is desired to create an articulation that can move according to three axes, the most common technical solution is a string of three actuators in series. This is found to be the case on most industrial robots, but also at the shoulders and hips of humanoid robots.

[0010] The problem with these series joints is the mechanism and dynamics.

[0011] From a mechanical point of view, the rotational properties of the spherical head (which can rotate in any direction at any time) are only implemented around the initial area. The further away from this area, the less the properties of the spherical head are preserved. By moving further, a position called gimbal lock is reached, in which one of the degrees of freedom is lost.

[0012] From a dynamic point of view, the first actuator in series supports the mass of the second and third actuators in addition to the payload. For the second actuator, it must also support the mass of the third actuator. Therefore, in order to ensure that the joint can be reactive and dynamic, the size of the first actuator must be increased, which, however, burdens the entire system and also increases its inertia and cost.

[0013] An alternative to joints with serial actuators is joints with parallel actuators. These mechanisms are much more complex to implement and control, but they have the advantage that all actuators are fixed to the frame of the robot. This makes it possible to have a lighter structure on the moving parts and also benefit from increasing the power of each of these actuators in order to move the structure. Finally, this makes it possible to design very dynamic systems, able to move quickly and accurately.

[0014] From the prior art the following examples of joints with parallel actuators are known.

[0015] The document by Bulgarelli et al. (“A Low-Cost Open Source 3D Printable Dexterous Anthropomorphic Robotic Hand with a Parallel Spherical Joint Wrist for Sign Languages ​​Reproduction”, A. Bulgarelli et al., International Journal of Advanced Robotic Systems, Vol. 13, No. 3, January 1, 2016) discloses such a joint with parallel actuators, the purpose of which is to develop an artificial wrist for remote sign language communication.

[0016] The document of Bulgarelli et al. discloses the control of joints by Euler angles. This representation is commonly used for such complex systems, but is unstable. Therefore, it may lead to universal lock.

[0017] Furthermore, when moving away from the initial position of the joint, it becomes increasingly difficult to characterize the orientation that one is trying to give, since one then needs to know how to combine rotations about different axes, which in this case becomes complicated by using an Euler representation.

[0018] The paper by Sudki et al. (“Marine Propulsor based on a Three-Degree-of-Freedom Actuated Spherical Joint”, Third International Symposium on Marine Propulsors, smp’13, May 2013) discloses an actuator with three degrees of freedom for a marine propeller in order to replicate the shoulders of marine animals, especially penguins.

[0019] Prior art joints with parallel actuators have the following disadvantages: The frame size to which the motors are fixed is large. These joints are difficult to integrate into mobile robots.

[0020] The technical problem to be solved is how to benefit from the advantages of parallel actuators by reducing the size. Summary of the invention

[0021] An object of the invention is a joint with three degrees of freedom for a robot, the joint comprising a platform, three motors, each motor connected via a pinion to a ring gear, each ring gear being arranged inside a hollow disk stacked on a base so that each disk is integral with the ring gear (as one),

[0022] Each disc itself is also integral with a disc head extending in the same direction as the stack of discs and base.

[0023] For each pan head, an arm is rotatably connected to the pan head on the one hand and to the platform on the other hand.

[0024] Each motor is at least partially contained within at least one disk.

[0025] The motors may be offset relative to the rotational axis of the disks and arranged in different angular sectors, for example to contain three motors in a cavity defined by the base and the stacked disks.

[0026] At the rest position of each disk head, there may be an offset angle, which corresponds to the offset angle between the motors.

[0027] Furthermore, each motor may be provided with a device for determining the position of an output shaft of the motor relative to a reference, the device being in particular a magnetic encoder.

[0028] Another object of the invention is a method for controlling a joint with three axes of freedom making it possible to guide the platform according to a desired position of a vector associated with the platform and a desired angle of rotation about the vector associated with the platform, the method comprising the steps of:

[0029] determining the coordinates of a three-axis reference system associated with the platform of the joint for the initial position and receiving a vector perpendicular to the platform corresponding to the desired position and the desired rotation angle,

[0030] determining the coordinates of the rotation vector so that the rotation vector can pass from the initial position of the platform to the middle position of the platform in a three-axis reference system associated with the platform of the joint for the initial position, the middle position being such that passing from the middle position of the platform to the desired position includes the rotation of the platform itself according to the desired rotation angle,

[0031] Determine the initial rotation angle so that the initial rotation angle can pass from the initial position of the platform to the middle position of the platform,

[0032] determining the coordinates of the three-axis reference system associated with the platform of the joint for the desired position in the three-axis reference system associated with the platform of the joint for the initial position,

[0033] determining the rotation angle of the first arm according to the coordinates of the three-axis reference system associated with the platform of the joint for the desired position, the coordinates of the desired rotation angle, the coordinates of the initial rotation angle and the coordinates of the parameters associated with the configuration of the joint,

[0034] determining the rotation angle of the second arm according to the coordinates of the three-axis reference system associated with the platform of the joint for the desired position, the coordinates of the desired rotation angle plus the angle offset value, the coordinates of the initial rotation angle and the coordinates of the parameters associated with the configuration of the joint,

[0035] determining the rotation angle of the third arm according to the coordinates of the three-axis reference system associated with the platform of the joint for the desired position, the coordinates of the desired rotation angle minus the angular offset value, the coordinates of the initial rotation angle and the coordinates of the parameters associated with the configuration of the joint,

[0036] For each disk, the rotation angle of the disk is determined from the rotation angle of the corresponding arm and the coordinates of the three-axis reference system associated with the joint platform for the desired position in the three-axis reference system associated with the joint platform for the initial position,

[0037] Each motor is controlled at a rotation angle corresponding to the disk of the motor.

[0038] The rotation vector may be determined as the vector product between a vector perpendicular to the platform in the initial position and a vector perpendicular to the platform in the desired position.

[0039] Parameters associated with the configuration of the joint may be the diameter of the distal circle, the diameter of the proximal circle, and the center of the proximal circle. The distal circle is the circle traced by the arm around the platform. The proximal circle is the circle traced by the disc.

[0040] The rotation angle may be defined as the arc cosine of the dot product of a vector perpendicular to the platform in the initial position and a vector perpendicular to the platform in the desired position.

[0041] in order to determine the coordinates of the three-axis reference system associated with the platform of the joint for the desired position in the three-axis reference system associated with the platform of the joint for the initial position, determining a first quaternion making it possible to pass from the initial position to the intermediate position, and determining a second quaternion making it possible to pass from the intermediate position to the desired position by the rotation of the platform itself,

[0042] By applying the two quaternions successively to the initial position of the platform, the desired position of the platform in the reference frame of the platform in the initial position can be determined.

[0043] The system according to the invention has the advantage of being reversible, i.e. the joint can be used as a transducer. In other words, the action on the joint is converted into an electric current by the motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Other objects, features and advantages of the present invention will become apparent on reading the following description given only as a non-limiting example and with reference to the accompanying drawings, in which:

[0045] [ Figure 1 ] shows a three-dimensional view of a joint according to the invention,

[0046] [ Figure 2 ] shows a side view of an arm according to the present invention; and

[0047] [ Figure 3 ] shows a cross-sectional view of a disc according to the present invention. DETAILED DESCRIPTION

[0048] The joint according to the invention comprises a system of three concentric axes controlling actuators. The motors which move the concentric axes are integrated in the joint.

[0049] The joint 1 enables the platform 2 to move relative to the base along three free axes by controlling the rotation of three motors.

[0050] The joint 1 comprises a base in which three motors 3a, 3b, 3c are arranged, each connected to a ring gear 4a, 4b, 4c via a pinion 5a, 5b, 5c. Figure 1 , the motor 3c is shown inside the ring gears 4a, 4b, 4c. For the sake of clarity, the motors 3a and 3b are not shown as points of interest. However, the motor 3b is arranged inside the ring gears 4a, 4b, and the motor 3a is arranged inside the ring gear 4a. Each ring gear 4a, 4b, 4c is arranged inside the hollow disks 6a, 6b, 6c stacked on the base, so that each disk 6a, 6b, 6c is integrated with the ring gears 4a, 4b, 4c. Each disk 6a, 6b, 6c itself is also integrated with a disk head 7a, 7b, 7c, which extends in the same direction as the stacking of the base and the disks 6a, 6b, 6c. Each motor 3a, 3b, 3c is also provided with a device for determining the angular position of the output shaft of the motor relative to a reference position. Such a device for determining can be an angular position sensor or a magnetic encoder.

[0051] Figure 2 The connection of the arm to the platform and the tray is shown in the general case, which connection can be reversed for each arm 8a, 8b, 8c.

[0052] For each pan head 7, 7a, 7b, 7c, an arc-shaped arm 8, 8a, 8b, 8c is rotationally connected to the pan head 7, 7a, 7b, 7c on the one hand and to the platform 2 on the other hand. The rotation axis between the pan head 7, 7a, 7b, 7c and the arm 8, 8a, 8b, 8c, and the rotation axis between the arm 8, 8a, 8b, 8c and the platform 2 are contained in the same plane as the plane containing the corresponding arm 8, 8a, 8b, 8c. Advantageously, the arc represents a quarter of a circle.

[0053] The disks 6, 6a, 6b, 6c form a housing and are provided with bearings making it possible to facilitate the movement of the disks, reduce friction and wear and maintain the alignment of the disks 6, 6a, 6b, 6c relative to the base and between them.

[0054] In other words, the first tray 6a is connected to the first arm 8a via the tray head 7a, and the first tray 6a is driven by the first motor 3a via the first ring gear 4a and the first pinion gear 5a.

[0055] The same arrangement is provided for the second tray 6b and the third tray 6c.

[0056] More precisely, the second disk 6b is connected to the second arm 8b via the disk head 7b, and the second disk 6b is driven by the second motor 3b via the first ring gear 4b and the second pinion 5b. Similarly, the third disk 6c is connected to the third arm 8c via the disk head 7c, and the third disk 6c is driven by the third motor 3c via the first ring gear 4c and the third pinion 5c.

[0057] The first tray 6a is stacked on the second tray 6b, which itself is stacked on the third tray 6c. The third tray 6c is arranged on the base. The first arm 6a, the second arm 6b and the third arm 6c are connected to the platform.

[0058] refer to Figure 1 , it can be seen that each pinion 5a, 5b, 5c is arranged at a different height from the base, so as to mechanically drive the corresponding ring gear 4a, 4b, 4c. In addition, for example in order to contain three motors 3a, 3b, 3c in the cavity defined by the base and the stacked disks 6a, 6b, 6c, each motor 3a, 3b, 3c is offset relative to the axis of rotation of the disks 6a, 6b, 6c and is arranged in a different angular sector. This arrangement Figure 3 Thus, in the case of three motors 3a, 3b, 3c, each motor 3a, 3b, 3c is arranged in a different 120° sector.

[0059] This offset angle of 120° is also found in the rest position of each disk head 7, 7a, 7b, 7c, which is arranged at 120° to the other two.

[0060] The motors 3a, 3b, 3c are controlled to control the orientation of the platform 2, which drives the rotation of each disk 6a, 6b, 6c on a circle (called the proximal circle). The rotation of each disk 6a, 6b, 6c drives the rotation of an arm 8a, 8b, 8c, which is mechanically connected to another circle (called the distal circle).

[0061] refer to Figure 1 , it can be seen that in Figure 1, a reference frame R associated with platform 2 is shown. A direct orthonormal three-dimensional reference frame R is defined to include: an origin O (0, 0, 0), which is located at the center of gravity of platform 2; a vector Z (0, 0, 1), which is perpendicular to platform 2; a vector Y (0, 1, 0), which extends parallel to the surface of platform 2 and passes through the connection between the third arm 8c and platform 2; a vector X (1, ​​0, 0), which is orthogonal to vector Z and vector Y to form a direct orthonormal reference frame. Recall that a three-dimensional rectangular reference frame is a reference frame in which the angle between vector X and vector Y is a right angle, the angle between vector Y and vector Z is a right angle, and the angle between vector Z and vector X is a right angle.

[0062] Attention will now be drawn to the control of the system making it possible to position the platform 2 in a predetermined position.

[0063] To prevent gimbal lock, a quaternion is used. A quaternion is a normalized vector in three-dimensional space combined with a rotation around this vector by an angle θ.

[0064] The following quantities are defined:

[0065] R0 = (X0, Y0, Z0): A rectangular reference system defining the initial position of platform 2

[0066] Rreq = (Xreq, Yreq, Zreq) defines the required position of the platform 2.

[0067] V = (a, b, c): rotation vector orthogonal to the plane defined by vectors R0 and Rreq

[0068] θ: rotation angle around vector V defining the desired position of platform 2,

[0069] β: The rotation angle of the platform 2 itself between the initial position and the desired position.

[0070] An attempt is made to control the platform 2 in such a way that it passes from an initial position defined by the reference system R0 to a desired position defined by the reference system Rreq.

[0071] Then, the motion is decomposed into two rotations. The first rotation is a rotation by an angle θ about a vector V perpendicular to the plane defined by the reference frames R0 and Rreq.

[0072] The second rotation is a rotation by β about the vector normal to the platform 2. Note that the normal vector to the platform 2 may be the vector Z0, the vector Zreq, or any other intermediate vector.

[0073] The order of the rotations (chaining) is irrelevant. Thus, the second rotation can be performed before the first.

[0074] Then, the vector V is defined as the vector product of the vector Z0 and the vector Zreq, according to the following method:

[0075] [Mathematical formula 1]

[0076]

[0077] The rotation angle θ is defined based on the components of R0 and Rreq that are perpendicular to the platform 2 .

[0078] [Mathematical formula 2]

[0079] θ=acos(Z0.Zreq)

[0080] The vector V is then normalized to be able to be used with the quaternion.

[0081] The first quaternion q1 associated with the first rotation around the vector V by an angle θ is written as follows:

[0082] [Mathematical formula 3]

[0083] q1=(w1,x1,y1,z1)

[0084] in:

[0085] [Formula 4]

[0086]

[0087] [Formula 5]

[0088]

[0089] [Mathematical formula 6]

[0090]

[0091] [Formula 7]

[0092]

[0093] Then, a second quaternion q2 is defined making it possible to perform a second rotation by an angle β around a vector perpendicular to the platform 2. Using the same formalism as presented for the first quaternion q1, the following result is obtained:

[0094] [Mathematical formula 8]

[0095] q2=(w2,x2,y2,z2)

[0096] in:

[0097] [Mathematical formula 9]

[0098]

[0099] [Formula 10]

[0100]

[0101] [Mathematical formula 11]

[0102]

[0103] [Mathematical formula 12]

[0104]

[0105] The vector perpendicular to platform 2 is of the form (0, 0, Z). The x2 and y2 terms of the quaternion are then zero.

[0106] There are therefore two quaternions associated with the two rotations making it possible to pass from the reference frame R0 associated with the initial position to the reference frame Rreq associated with the desired position.

[0107] However, it is still necessary to determine the rotation angles of the three motors (denoted as θ11, θ12, θ13) in order to perform the rotation defined by these quaternions so that the arm moves the platform 2 from the initial position R0 to the desired position Rreq.

[0108] To determine these rotation angles, the following elements are defined:

[0109] Rd: The radius of the circle traced by the arm around platform 2, also called the distal circle

[0110] Rp: The radius of the circle traced by the disk, also called the proximal circle

[0111] Cp = (0, 0, Cz): coordinates of the center of the circle traced by the disk, also called the near side circle

[0112] Pc = (0, 0, 0): coordinates of the center of the far circle,

[0113] θ3i: Angle of arm i relative to platform 2

[0114] θ1i: Angle of disk i relative to its reference position

[0115] The equation of the distal circle Xi and the proximal circle Xip The equation of is expressed by the following equation.

[0116] [Mathematical formula 13]

[0117] X i =P c +Rcos(θ3i)Zreq+Rsin(θ3i)Xreq

[0118] [Mathematical formula 14]

[0119]

[0120] Thus, a first displacement is defined by applying a first quaternion q1 making it possible to pass from an initial position defined by the reference system R0 to an intermediate position defined by the reference system Rinter:

[0121] [Mathematical formula 15]

[0122]

[0123] A second displacement is defined by applying a second quaternion q2, making it possible to pass from an intermediate position defined by the reference system Rinter to the desired position defined by the reference system Rreq:

[0124] [Formula 16]

[0125]

[0126] So when we apply the quaternion at coordinate Z, we get the following result:

[0127] [Mathematical formula 17]

[0128]

[0129] [Mathematical formula 18]

[0130]

[0131] However, the rotation defined by the second quaternion q2 is performed around the direction Z. Therefore, the direction Z is invariant, and it follows from this that Zinter=Zreq.

[0132] Note: If the rotation vector is normalized, then is the conjugate of the quaternion q1 and is equal to the reciprocal of the quaternion q1. Thus we obtain and

[0133] Since there is no rotation about the axes X and Y during the application of the second quaternion q2 , the calculation of the coordinates Xreq and Yreq can be performed in a single step involving the two quaternions q1 and q2 .

[0134] [Mathematical formula 19]

[0135]

[0136] [Mathematical formula 20]

[0137]

[0138] Accompanying the change of the reference system, the coordinates X0, Y0, Z0 and the coordinates Xreq, Yreq, Zreq are defined in the reference system R0 associated with the initial position of the platform.

[0139] Therefore, in reference frame R0, we have the following expression:

[0140] X0=(X0,0,0)

[0141] Y0=(0,Y0,0)

[0142] Z0=(0,0,Z0)

[0143] Xreq=(Xx,Yx,Zx)

[0144] Yreq=(Xy,Yy,Zy)

[0145] Zreq=(Xz,Yz,Zz)

[0146] Knowing the coordinates Xreq, Yreq, Zreq, the angles θ11, θ12, θ13 of the disk can then be determined.

[0147] By solving the equation Xi = Xp derived from Eq. 1 and Eq. 2, the following system of equations is obtained:

[0148] [Mathematical formula 21]

[0149] Rcos(θ3i)×X z +Rsin(θ3i)×X x =R p cos(θ1i)

[0150] [Mathematical formula 22]

[0151] Rcos(θ3i)×Y z +Rsin(θ3i)×Y x =R p sin(θ1i)

[0152] [Mathematical formula 23]

[0153] Pc z +R cos(θ3i)×Z z +Rsin(θ3i)×Z x =C z

[0154] By solving the equation group [Math. 21], [Math. 22], and [Math. 23], the following expressions for the angles θ3i and θ1i are obtained respectively.

[0155] [Mathematical formula 24]

[0156]

[0157] [Mathematical formula 25]

[0158] θ1i=atan2(cos(θ3i)×Y z +sin(θ3i)×Y x , cos(θ3i)×X z +sin(θ3i)×X x )

[0159] The angle θ3i of each arm i of the system is first determined by applying equation [Math 24]. The angle θ1i of each disk i of the system is then determined by applying equation [Math 25].

[0160] As described above, the vector Zreq is not modified by the rotation according to the second rotation angle β. On the other hand, the vector Xreq and the vector Yreq are indeed modified by this rotation.

[0161] At rest, the disks are offset by 120° relative to each other. If the angular position of the first disk is used as a reference, the angular position of the second disk can be obtained by applying an offset of +120° to the second rotation angle β, and the angular position of the third disk can be obtained by applying an offset of -120° to the second rotation angle β.

[0162] Therefore, the values ​​Xx, Yx, and Zx of equations [Math. 24] and [Math. 25] are modified due to this offset.

[0163] The embodiments described above include: a second rotation along the axis Z of the reference frame associated with the platform. In other embodiments, the second rotation can be performed along the axis X or the axis Y, or along a vector associated with the platform. A person skilled in the art will adjust the mathematical form described above according to the axis under consideration.

[0164] Likewise, the first rotation and the second rotation may be reversed without departing from the scope of the present invention.

[0165] A method for controlling a joint with three axes of freedom, so as to be able to guide a platform 2 according to a desired position and a desired angle of rotation of the platform 2, the method comprising the following steps:

[0166] During a first step, the coordinates of the rectangular three-axis reference system associated with the articulated platform 2 are determined for an initial position and for a desired position and a desired rotation angle.

[0167] During a second step, the coordinates of the rotation vector V are determined so that it can pass from the reference system associated with the initial position of platform 2 to the reference system associated with the intermediate position of platform 2 in the three-axis reference system associated with the platform 2 of the joint for the initial position, and the intermediate position makes the passage from the intermediate position of platform 2 to the desired position include the rotation of platform 2 itself according to the desired rotation angle.

[0168] During a third step, an initial rotation angle is determined such that it can pass from an initial position of the platform 2 to an intermediate position of the platform 2 .

[0169] During a fourth step, the coordinates of the three-axis reference system associated with the articulated platform 2 for the desired position are determined in the three-axis reference system associated with the articulated platform 2 for the initial position.

[0170] During the fifth step, the rotation angle θ31 of the first arm is determined based on the coordinates of the three-axis reference system associated with the platform 2 of the joint for the initial position, the coordinates of the required rotation angle, the coordinates of the initial rotation angle and the coordinates of the parameters associated with the construction of the joint in the three-axis reference system associated with the platform 2 of the joint for the desired position.

[0171] During the sixth step, the rotation angle θ32 of the second arm is determined based on the coordinates of the three-axis reference system associated with the platform 2 of the joint for the initial position, the coordinates of the required rotation angle plus the angle offset value, the coordinates of the initial rotation angle and the coordinates of the parameters associated with the construction of the joint.

[0172] During the seventh step, the rotation angle θ33 of the third arm is determined based on the coordinates of the three-axis reference system associated with the platform 2 of the joint for the initial position, the coordinates of the three-axis reference system associated with the platform 2 of the joint for the required position, the coordinates of the required rotation angle minus the angle offset value, the coordinates of the initial rotation angle and the coordinates of the parameters associated with the construction of the joint.

[0173] During an eighth step, for each disk, the rotation angle of the disk is determined from the rotation angle of the corresponding arm and the coordinates of the three-axis reference system associated with the joint platform 2 for the desired position in the three-axis reference system associated with the joint platform 2 for the initial position.

[0174] Each motor is controlled at a rotation angle corresponding to the disk of the motor.

Claims

1. A method for controlling a joint with three degrees of freedom, the joint comprising a platform (2), three motors (3a, 3b, 3c), three ring gears (4, 4a, 4b, 4c), three pinions (5a, 5b, 5c), three hollow disks (6a, 6b, 6c) and three arms (8, 8a, 8b, 8c), each motor being connected to the ring gear (4, 4a, 4b, 4c) via the pinion (5a, 5b, 5c), each ring gear (4, 4a, 4b, 4c) being arranged on the inner side of the hollow disks (6a, 6b, 6c) stacked on the base so that each disk (6, 6a, 6b, 6c) is integrated with the ring gear (4, 4a, 4b, 4c), Each disk (6, 6a, 6b, 6c) itself is also integral with a disk head (7, 7a, 7b, 7c) extending in the same direction as the stack of the base and the disks (6, 6a, 6b, 6c), For each pan head (7, 7a, 7b, 7c), an arm (8, 8a, 8b, 8c) is rotationally connected on the one hand to the pan head (7, 7a, 7b, 7c) and on the other hand to the platform (2), Each motor (3a, 3b, 3c) is at least partially contained inside at least one disk (6, 6a, 6b, 6c), The method enables guiding the platform (2) according to a desired position of a vector associated with the platform (2) and a desired rotation angle around the vector associated with the platform (2), the method comprising the following steps: determining the coordinates of a three-axis reference system associated with the platform (2) of the joint for an initial position and receiving a vector perpendicular to the platform (2) corresponding to the desired position and the desired rotation angle, determining the coordinates of a rotation vector so that the rotation vector can pass from the initial position of the platform (2) to the middle position of the platform (2) in a three-axis reference system associated with the platform (2) of the joint for the initial position, the middle position making the passage from the middle position of the platform (2) to the desired position include the rotation of the platform (2) itself according to the desired rotation angle, determining an initial rotation angle so that the initial rotation angle can pass from an initial position of the platform (2) to an intermediate position of the platform (2), determining the coordinates of the three-axis reference system associated with the platform (2) of the joint for the desired position in the three-axis reference system associated with the platform (2) of the joint for the initial position, determining the rotation angle of the first arm according to the coordinates of the three-axis reference system associated with the platform (2) of the joint for the desired position, the coordinates of the desired rotation angle, the coordinates of the initial rotation angle and the coordinates of the parameters associated with the configuration of the joint, determining the rotation angle of the second arm according to the coordinates of the three-axis reference system associated with the platform (2) of the joint for the desired position, the coordinates of the desired rotation angle plus the angular offset value, the coordinates of the initial rotation angle and the coordinates of the parameters associated with the configuration of the joint, determining the rotation angle of the third arm according to the coordinates of the three-axis reference system associated with the platform (2) of the joint for the desired position, the coordinates of the desired rotation angle minus the angular offset value, the coordinates of the initial rotation angle and the coordinates of the parameters associated with the configuration of the joint, determining, for each disk, the rotation angle of the disk according to the rotation angle of the corresponding arm and the coordinates of the three-axis reference system associated with the platform (2) of the joint for the desired position in the three-axis reference system associated with the platform (2) of the joint for the initial position, Each motor is controlled at a rotation angle of the disk corresponding to the motor.

2. The method according to claim 1, wherein: The rotation vector is determined as the vector product between a vector perpendicular to the platform (2) in the initial position and a vector perpendicular to the platform (2) in the desired position.

3. The method according to claim 1 or 2, wherein: The parameters associated with the configuration of the joint are the diameter of the distal circle, the diameter of the proximal circle and the center of the proximal circle.

4. The method according to claim 1 or 2, wherein: The rotation angle is defined as the arc cosine of the dot product of a vector perpendicular to the platform in the initial position and a vector perpendicular to the platform in the desired position.

5. The method according to claim 1 or 2, wherein: in order to determine the coordinates of the three-axis reference system associated with the platform (2) of the joint for the desired position in the three-axis reference system associated with the platform (2) of the joint for the initial position, determining a first quaternion making it possible to pass from the initial position to the intermediate position, and determining a second quaternion making it possible to pass from the intermediate position to the desired position by means of a rotation of the platform itself, The desired position of the platform in the reference frame of the platform in the initial position is determined by applying two quaternions successively to the initial position of the platform.

6. A joint with three degrees of freedom for a robot, the joint comprising a platform (2), three motors (3a, 3b, 3c), three ring gears (4, 4a, 4b, 4c), three pinions (5a, 5b, 5c), three hollow disks (6a, 6b, 6c) and three arms (8, 8a, 8b, 8c), each motor being connected to the ring gear (4, 4a, 4b, 4c) via the pinion (5a, 5b, 5c), each ring gear (4, 4a, 4b, 4c) being arranged on the inner side of the hollow disks (6a, 6b, 6c) stacked on the base, so that each disk (6, 6a, 6b, 6c) is integrated with the ring gear (4, 4a, 4b, 4c), Each disk (6, 6a, 6b, 6c) itself is also integral with a disk head (7, 7a, 7b, 7c) extending in the same direction as the stack of the base and the disks (6, 6a, 6b, 6c), For each pan head (7, 7a, 7b, 7c), an arm (8, 8a, 8b, 8c) is rotationally connected on the one hand to the pan head (7, 7a, 7b, 7c) and on the other hand to the platform (2), Each motor (3a, 3b, 3c) is at least partially contained inside at least one disk (6, 6a, 6b, 6c), the joint being controlled by a processing device executing the method according to claim 1.

7. The joint according to claim 6, wherein: Each motor (3a, 3b, 3c) is offset relative to the rotation axis of the disks (6, 6a, 6b, 6c) and is arranged in different angular sectors to contain the three motors (3a, 3b, 3c) in a cavity defined by the base and the stacked disks (6, 6a, 6b, 6c).

8. The joint according to claim 6, wherein: The rest position of each disk head (7, 7a, 7b, 7c) has an offset angle corresponding to the offset angle between the motors.

9. The joint according to claim 6, wherein: Each motor (3a, 3b, 3c) is also provided with means for determining the angular position of the output shaft of said motor relative to a reference position.

10. The joint according to claim 9, wherein: The means for determining the angular position of the output shaft of the motor relative to a reference position is a magnetic encoder.

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