Cable-driven soft actuator with magnetorheological stiffness and control method for end position

Abstract

The application provides a rope-driven magnetic-rigidity-variation soft actuator and a control method for an end desired position, and the actuator comprises a flexible shell which can be bent and deformed, three rope holes being arranged on the flexible shell in a uniform distribution; a rope for driving the flexible shell to be bent and deformed; a magnetorheological elastomer which extends along the axial direction of the flexible shell and is embedded in the flexible shell; a pair of electromagnets, one of which is fixed to one end of the magnetorheological elastomer and the other of which is fixed to the other end of the magnetorheological elastomer; the magnetic field directions generated by the two electromagnets are different; and an adjustable stabilized DC power supply which is arranged outside the flexible shell and supplies power to the electromagnets so that the electromagnets generate magnetic fields to change the rigidity of the magnetorheological elastomer unit, and the electromagnets are electrically connected to the stabilized DC power supply. The application can predict the desired position of the end of the actuator by changing the length of the rope and can quickly change the rigidity.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of variable stiffness soft robot, and particularly relates to a rope-driven magnetostrictive variable stiffness soft actuator and a control method for an end desired position. BACKGROUND

[0002] Soft robots are widely used in the fields of industry, agriculture, medicine, rescue and public service due to their high flexibility, good environmental adaptability and safe interaction, etc. They are mainly composed of soft functional materials, and have more degrees of freedom compared with traditional rigid robots.

[0003] However, since the main material of the soft robot is a flexible high polymer, the stiffness is too low, so the output force of the soft robot is limited, and it is difficult to complete the operation and predict the desired position under high load. These characteristics greatly restrict the application ability of the soft robot. Therefore, it is extremely important to improve the motion ability of the soft robot, that is, the ability to actively adjust the stiffness and reach the desired position. Therefore, the present application focuses on the variable stiffness technology of the soft robot, and proposes a multi-joint rope-driven soft actuator based on the principle of magnetostrictive variable stiffness, and focuses on the design of the actuator, stiffness modeling and desired position. SUMMARY

[0004] The application aims to provide a rope-driven magnetostrictive variable stiffness soft actuator and a control method for an end desired position, which can predict the desired position of the end of the actuator by changing the length of the rope, and can quickly change the stiffness. In order to achieve the above-mentioned purpose, the scheme is as follows:

[0005] A rope-driven magnetostrictive variable stiffness soft actuator comprises:

[0006] A flexible shell which can be bent and deformed, the cross section of which is circular, and three rope holes which are uniformly distributed are formed on the flexible shell;

[0007] Ropes which are used to drive the flexible shell to bend and deform, and are arranged correspondingly to the rope holes, one rope is passed through each rope hole, one end of each rope is fixed to the flexible shell, and the other end of each rope is passed through the inside of the flexible shell and fixed to the output end of the rope driving module;

[0008] A magneto-rheological elastomer which extends along the axial direction of the flexible shell and is embedded in the flexible shell;

[0009] A pair of electromagnets, one of which is fixed to one end of the magneto-rheological elastomer, and the other of which is fixed to the other end of the magneto-rheological elastomer; the magnetic fields generated by the two electromagnets are in the same direction;

[0010] The adjustable voltage-stabilized direct current power supply supplies power to the electromagnet outside the flexible shell, so that the electromagnet generates a magnetic field to change the stiffness of the magneto-rheological elastic unit, which is electrically connected with the electromagnet.

[0011] Preferably, the magneto-rheological elastomer comprises a plurality of magneto-rheological elastic units, and one electromagnet is shared between adjacent magneto-rheological elastic units.

[0012] Preferably, the magneto-rheological elastic unit comprises a high polymer matrix uniformly distributed with ferromagnetic particles.

[0013] Preferably, the rope driving module is a ball screw module, and each output end of the ball screw module is connected with a rope.

[0014] Preferably, the flexible shell is made of silica gel.

[0015] A control method for the desired position of the end of a soft actuator, comprising the following steps:

[0016] Step 1, based on the forward kinematics model FKM, introduce the actuation space Q, the configuration space K and the task space X, the bottom reference frame of the flexible shell The end reference frame of the flexible shell

[0017] Wherein, Q=(l1, l2, l3); X=(X, Y, Z);

[0018] (X, Y, Z)-Cartesian coordinates of the center point of the end cross section circle of the flexible shell;

[0019] l1~l3-the length of the rope between the flexible shell and the rope driving module;

[0020] θ-bending angle, measured in the bending plane, which is always perpendicular to the X0Y0 plane and rotates around the Z0 axis;

[0021] -rotation angle of the actuator around the Z0 axis;

[0022] κ-curvature of the bending plane;

[0023] Step 2, deform the configuration space K, and the task space X into:

[0024]

[0025] Step 3, based on the actuation space Q, deform the configuration space K into:

[0026]

[0027] The specific steps include:

[0028] Step 3A, O k-1 and point B i The corresponding distance between them is:

[0029]

[0030] where r is the distance between the rope hole and the center axis of the actuator;

[0031] Step 3B, the length of the actuator forms three concentric circular arcs with different radii of curvature at O k-1 C k The radius of the three concentric circular arcs; using the geometric relationship of the circular arc: arc length = radius of curvature x subtended angle, the relationship between the driver length and the curve parameters is expressed as:

[0032]

[0033] Step 3C, solve the expression of the configuration space K about l 1,k ,l 2,k ,l 3,k Add equations (2), (3) and (4) to get:

[0034]

[0035] Subtract equation (3) from equation (4) and rearrange the terms to get:

[0036]

[0037] Rearrange equation (2) to get:

[0038]

[0039] Apply equations (6) and (7) to the triangle identity Remove from the relationship to get:

[0040]

[0041] Substitute θ in equation (5) into equation (8) to get:

[0042]

[0043] Then substitute the result given by equation (9) into equation (5) to get:

[0044]

[0045] Divide equation (6) by (7) and substitute (9) (10) to get:

[0046]

[0047] The formula from the kth module of the actuator is extended to the entire actuator:

[0048]

[0049] Step 4, the model in step 3 is brought into the model in step 2 to obtain a soft actuator end desired position model; wherein the soft actuator end desired position model is:

[0050]

[0051] L sum = l1+l2+l3;

[0052]

[0053] Step 5, change the length of the rope, thereby changing the desired position of the soft actuator end.

[0054] Compared with the prior art, the advantages of the present application are:

[0055] 1. The driving mode of the soft robot is rope driving, the length of the rope is changed by controlling the motor movement, and the desired position of the actuator end can be predicted by the model.

[0056] 2. The stiffness of the soft robot is too low, and its carrying capacity is weak. If this characteristic is to be changed, the stiffness of the soft robot itself should be changed. The present application changes the stiffness of the soft robot by controlling the magnetic field, and the stiffness changing speed is fast. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 is a structural diagram of a rope-driven magnetostrictive stiffness soft actuator;

[0058] Figure 2 is a schematic diagram of the installation of a magneto-rheological elastomer;

[0059] Figure 3 is a schematic diagram of the end coordinate system of the actuator and the bending curve;

[0060] Figure 4 is a schematic diagram of the bending state of the actuator;

[0061] Figure 5 is a structural diagram of the forward kinematics model FKM;

[0062] Figure 6 is a schematic diagram of the bending model of the magneto-rheological elastomer and the projection in the bending plane;

[0063] Figure 7 is a schematic diagram of the magneto-rheological elastomer simplified as a cantilever beam;

[0064] Figure 8 Schematic diagram of magnetic rheological effect shear mode;

[0065] Figure 9 Schematic diagram of magnetic rheological effect;

[0066] Figure 10 End working range diagram of actuator.

[0067] Wherein, 1-rope drive module, 2-assistant support module, 3-rigidity adjustment module, 4-fixed pulley, 5-planetary carrier, 6-flexible shell, 7-ball screw module, 8-controller, 9-upper computer, 10-adjustable DC regulated power supply. DETAILED DESCRIPTION

[0068] The rope-driven magnetically stiffened soft actuator and the control method of the end desired position will be described in more detail below with reference to the accompanying drawings, in which the preferred embodiments of the present application are shown, it should be understood that those skilled in the art can modify the present application described herein while still achieving the advantageous effects of the present application. Therefore, the following description should be understood as a broad knowledge for those skilled in the art, and not as a limitation of the present application.

[0069] As Figures 1-2 A rope-driven magnetically stiffened soft actuator, comprising:

[0070] The flexible shell 6 is made of silica gel and can be bent and deformed, and has a circular cross section, and three rope holes are arranged on the end cross section in a uniform distribution;

[0071] Ropes for driving the flexible shell 6 to bend and deform, which are arranged corresponding to the rope holes, and one rope is arranged in each rope hole, one end of each rope is fixed to the end of the flexible shell 6, and the other end passes through the inside of the flexible shell 6 and is fixed to the output end of the rope drive module 1.

[0072] At most two rope drive modules 1 are started to make the flexible shell 6 bend and deform.

[0073] That is, by controlling the stepper motor of the rope drive module 1 to pull (or release) different ropes through the upper computer, the deformation control of the soft robotic arm with multiple degrees of freedom can be realized.

[0074] The spatial motion can be applied by controlling one or two motors to move simultaneously to exert sufficient force on the ropes to generate tension to control the deflection of the actuator.

[0075] The magnetorheological elastomer extends along the axial direction of the flexible shell 6 and is embedded in the flexible shell 6.

[0076] The rectangular spline is a simple and reliable mechanical connection, which is composed of a convex rectangular spline and a corresponding groove. It has the advantages of simple structure and firm connection. It can withstand large axial and radial forces while maintaining good positioning accuracy. In addition, the rectangular spline connection also has the characteristics of easy disassembly and assembly. As shown in the following figure, the magneto-rheological elastomer and the flexible silicone shell are assembled together in the form of a rectangular spline. The magneto-rheological elastomer is the inner spline, and the flexible silicone shell is the outer spline. They can be nested and fixed together.

[0077] In the soft actuator, the electromagnet is also placed inside the flexible silicone shell, at both ends of the magneto-rheological elastomer, as shown in Figure 2 As known from the magneto-rheological elastomer stiffness change principle in the previous section: in the case of no magnetic field without electromagnet working, the base is like normal silicone rubber, with excellent tensile properties, which can be driven by air pressure to produce movement and deformation; under the action of magnetic field, the magnetic shear modulus of the base increases, and the stiffness improves.

[0078] A pair of electromagnets, one of which is fixed to one end of the magneto-rheological elastomer, and the other is fixed to the other end of the magneto-rheological elastomer; the magnetic fields generated by the two electromagnets are in the same direction;

[0079] The structural parameters of the disc-type electromagnet selected in the design are shown in Table 1.

[0080] Table 1 Electromagnet structure parameters

[0081]

[0082] The adjustable DC regulated power supply 10 supplies power to the electromagnet outside the flexible shell 6, so that the electromagnet generates a magnetic field to change the stiffness of the magneto-rheological elastomer unit, which is electrically connected with the electromagnet. The adjustable DC regulated power supply can adjust the output voltage, and can realize multi-stage and rapid stiffness adjustment. Specifically, the positive poles of the two electromagnets are connected to the positive pole of the power supply, and the negative poles are connected to the negative pole of the power supply.

[0083] The planet carrier 5 is used to connect the flexible shell 6 and the base of the rope driving module 1, and the fixed pulley 4 is rotatably installed thereon. The fixed pulley 4 is correspondingly arranged with the rope, and the rope is led out from the flexible shell 6, passes through the fixed pulley 4 and is fixed to the output end of the rope driving module 1.

[0084] The magneto-rheological elastomer includes a plurality of magneto-rheological elastomer units, and adjacent magneto-rheological elastomer units share an electromagnet.

[0085] Specifically, the magneto-rheological elastic unit includes a high polymer matrix, in which ferromagnetic particles are uniformly distributed. It has strong magneto-rheological effect: in the absence of a magnetic field, the ferromagnetic particles are randomly arranged in the matrix; in the presence of a magnetic field, the ferromagnetic particles in the high polymer matrix will change from random arrangement to chain or columnar structure, at which time the elastic modulus of the magneto-rheological elastomer will also change, thereby changing its stiffness as shown. Figure 9

[0086] Because the hydroxyl iron powder has good magnetic properties and biocompatibility, the hydroxyl iron powder is selected as the magnetic particle. The high polymer is selected as silica gel, which has strong plasticity and can be solidified within a few hours.

[0087] The rope driving module 1 is a ball screw module 7, and the output end of each ball screw module is connected with a rope.

[0088] The auxiliary support module 2 includes a planet carrier and a fixed pulley 4.

[0089] The stiffness adjusting module 3 includes a flexible shell, a magneto-rheological elastomer and an electromagnet.

[0090] The upper computer 9 and the controller 8 are used to run programs and control the motion of the rope-driven magneto-rheological soft actuator.

[0091] A soft actuator system includes a rope-driven magneto-rheological soft actuator, and further includes a control method for the desired position of the end of the soft actuator, which includes the following steps:

[0092] Step 1, as Figures 3-5 described, based on the forward kinematics model FKM, the actuation space Q, the configuration space K and the task space X, the bottom reference system of the actuator the end reference system of the actuator

[0093] Q=(l1, l2, l3); X=(X, Y, Z);

[0094] (X, Y, Z)-Cartesian coordinates of the end of the actuator;

[0095] l1-l3-the length of the rope between the flexible shell and the rope driving module;

[0096] θ-bending angle, measured in the bending plane, which is always perpendicular to the X0Y0 plane and rotates around the Z0 axis;

[0097] orientation angle;

[0098] κ-curvature of the bending plane. ​

[0099] Spatial motion can be imposed by controlling one or two motors to move simultaneously with enough force on the cable to generate tension to control the deflection of the actuator.

[0100] The design adopts the forward kinematics model (FKM) of the rope-driven actuator. Three spaces are used to describe the state of the rope-driven actuator.

[0101] Step 2, on the basis of the constant curvature kinematics assumption, and assuming that the magneto-rheological elastomer can avoid torsional motion around the Z0 axis.

[0102] The configuration space K is deformed into the task space X:

[0103]

[0104] Step 3, in order to express the arc parameter θ as a function of the cable length Q, the structure of the rope-driven actuator is assimilated into a series connection of multiple identical modules, as described in Figure 6 .

[0105] The structure of the rope-driven actuator is divided into n identical modules, i.e. L = n.l i,k .

[0106] Based on the actuation space Q, the configuration space K is deformed into:

[0107]

[0108] In order to express the arc parameter θ as a function of the cable length Q, the structure of the rope-driven actuator is assimilated into a series connection of multiple identical modules, as described in Figure 6 .

[0109] As shown in Figure 6 , the actuator is divided into n identical modules; i.e. L = n.l i,k

[0110] A i , B i are one end of a rope in k modules, i = 1, 2, 3;

[0111] k is the number of modules, k = 1, 2, 3, …;

[0112] θ k is the bending angle of the kth module;

[0113] O k is the center point at the end of the kth module;

[0114] l 1,k , l 2,k , l 3,kFor the kth module, the projection of the three ropes on the bending plane;

[0115] C k For the kth module, the bending angle vertex;

[0116] For the rotation angle of the actuator around the Z0 axis;

[0117] X k-1 Parallel to the X0 axis.

[0118] Step 3 specifically includes the following steps:

[0119] Step 3A, O k-1 And the corresponding distance between points B i Is:

[0120]

[0121] Where r is the distance between the rope hole and the center axis of the actuator.

[0122] Step 3B, the length of the actuator forms three concentric circular arcs with different radii of curvature at O k-1 C k The radius of the arc. Using the geometric relationship of the circular arc: arc length = curvature radius × subtended angle, the relationship between the actuator length and the curve parameters is expressed as:

[0123]

[0124] Step 3C, solve the expression of the configuration space K about l 1,k ,l 2,k ,l 3,k .

[0125] Adding equations (2), (3) and (4) gives:

[0126]

[0127] Subtract equation (3) from equation (4) and rearrange the terms to get:

[0128]

[0129] Rearrange equation (2) to get:

[0130]

[0131] Apply equations (6) and (7) to the triangle identity Remove From the relationship to get:

[0132]

[0133] Substitute θ in equation (5) into equation (8), we get:

[0134]

[0135] Substitute the result given by equation (9) into equation (5), we get:

[0136]

[0137] Divide equation (6) by (7), and substitute (9) (10) into it, we get:

[0138]

[0139] The equation from the kth module of the actuator can be extended to the whole actuator:

[0140]

[0141] Step 4, bring the model in step 3 into the model in step 2 to obtain the soft actuator end desired position model; wherein the soft actuator end desired position model is:

[0142]

[0143] L sum = l1 + l2 + l3;

[0144]

[0145] Wherein, r-the distance between the rope and the center axis of the magnetorheological elastomer;

[0146] Step 5, change the length of the rope, so as to change the desired position of the soft actuator end.

[0147] Actuator working range test:

[0148] Rope-driven actuator working principle: by controlling the motor movement to exert enough force on the rope to generate tension to control the deflection of the actuator. The forward kinematics model is simulated using Matlab software, and the physical experiment is carried out, and the coordinates of the actuator end are obtained, as shown in Figure 10 The curve shows that the working space of the actuator end in X axis is 0-60mm, and the working space in Z axis is 180-212mm. As the working space of the actuator in the shaft increases, the simulation of the actuator in the Z axis working space is larger than the actual experiment by 3mm. The error may be caused by the following reasons: the rope-driven actuator ignores the gravity effect when measuring in the simulation operation; there is friction between the rope and the flexible shell.

[0149] Stiffness modeling:

[0150] After the actuator is deformed, it needs to generate a certain stiffness to bear, the greater the stiffness, the stronger the bearing capacity. By introducing the transformation of force and motion, the magneto-rheological elastomer is simplified as a cantilever beam, and the variable stiffness model of the actuator is established, as shown in Figure 7 .

[0151] The coils at both ends of the magneto-rheological elastomer are equivalent to two parallel plates. When one of the parallel plates is subjected to an upward shear force f, the chain-like structure formed by the magneto-rheological elastomer is affected by the shear force, and because it itself has shear resistance, it can hinder the upward movement of the parallel plate, that is, its stiffness increases, as shown in Figure 8 .

[0152] In the shear mode, the force F P between the two parallel plates can be represented as:

[0153] F P = τ·A

[0154] τ is the shear yield stress of the magneto-rheological fluid; A is the overlapping area of the magneto-rheological elastomer at both ends.

[0155] Let the length of the actuator be L, then the end deflection equation is:

[0156]

[0157] E is the elastic coefficient of silica gel, and I is the sectional moment of inertia.

[0158] When the external force and the displacement of the actuator are small enough, they can be considered as a linear relationship, and the stiffness K can be obtained:

[0159]

[0160] When the joint variable stiffness works in the magnetic induction stable region using a DC power supply to power the coil, according to the Biot-Savart law, the principle of superposition of magnetic fields and the symmetry of circular current, the magnetic induction intensity B generated by the energized coil can be obtained:

[0161]

[0162] where d is the distance between the two coils; μ0 is the vacuum permeability; r is the radius of the energized coil; V is the voltage of the external power supply, and R is the resistance of the energized coil.

[0163] The relationship between the magnetic induction intensity generated by the energized coil and the shear yield stress generated by the magneto-rheological elastomer can be fitted by the least squares method for the nonlinear function in the figure, and the theoretical calculation formula can be obtained:

[0164] τ(B) = -37.32B 4 -10.09B3 + 110.8 B 2 + 17.86 B - 0.096

[0165] In combination with the above formula, the stiffness of the soft actuator is determined by the strength of the applied magnetic field, which can be reflected by the magnetic induction intensity analysis of the electromagnetic field. It can be known that the strength of the electromagnetic field magnetic induction intensity can be determined by the voltage of the electromagnet, and the higher the voltage of the electromagnet, the greater the stiffness of the rope-driven magneto-rheological stiffness soft actuator.

[0166] The above are only preferred embodiments of the present application, and do not have any limiting effect on the present application. Any person skilled in the art can make any form of equivalent replacement or modification of the technical solutions and technical contents disclosed in the present application without departing from the scope of the technical solutions of the present application, which still belongs to the protection scope of the present application.

Claims

1. A method for controlling a desired position at the end of a soft actuator, based on a rope-driven magnetostrictive stiffness soft actuator, the rope-driven magnetostrictive stiffness soft actuator comprising: The flexible shell can be bent and deformed, and its cross-section is circular. Ropes are used to drive the flexible shell to bend and deform; A magnetorheological elastomer extends along the axial direction of a flexible shell and is embedded within the flexible shell; The control method is characterized by the following steps: Step 1: Based on the forward kinematics model FKM, introduce the actuation space Q, configuration space K, task space X, and bottom reference frame of the flexible shell. End reference frame of flexible shell where Q = (l1, l2, l3); X = (X, Y, Z); (X,Y,Z) - Cartesian coordinates of the midpoint of the end section circle of the flexible shell; l1~l3 - The length of the rope between the flexible shell and the rope drive module; θ - The bending angle is measured in the bending plane, which is always perpendicular to the X0Y0 plane and rotates around the Z0 axis. - The rotation angle of the actuator around the Z0 axis; κ - Curvature of the curved plane; Step 2: Transform the task space X into: Step 3: The actuator is divided into n identical and series-connected modules. Based on the actuation space Q, the configuration space K is transformed as follows: In the formula, r is the distance between the rope hole and the central axis of the actuator; The specific steps include: Step 3A, O k-1 and point B i The corresponding distances between them are: In the formula, O k-1 B is the center point of the end of the (k-1)th module; i Let i be one end of a rope in k modules, where i = 1, 2, 3; Step 3B, actuator length at O k-1 C k The radius of three concentric circular arcs with different radii of curvature is formed at point C; where C k For k module bending angle vertices; Using the geometric relationship of an arc: arc length = radius of curvature × opposing angle, the relationship between the actuator length and the curve parameters can be expressed as: In the formula, l 1,k ,l 2,k ,l 3,k For k modules, the projections of the three ropes onto the bending plane; θ k Let the bending angles of the k modules be denoted by . Step 3C: Solve for the configuration space K with respect to l 1,k ,l 2,k ,l 3,k The expression: Adding equations (2), (3), and (4) together, we get: Subtracting equation (3) from equation (4) and rearranging the terms, we get: Rearranging equation (2) yields: Apply equations (6) and (7) to trigonometric identities Remove from relational expression get: Substituting θ from equation (5) into equation (8), we get: Then, substituting the result given by formula (9) into formula (5), we get: Dividing formula (6) by (7), and substituting (9) and (10) into the equation, we get: Extending the formula obtained from the k-th module of the actuator to the entire actuator yields: Step 4: Substitute the model from Step 3 into the model from Step 2 to obtain the desired position model of the soft actuator end effector; wherein, the desired position model of the soft actuator end effector is: L sum ＝l1+l2+l3； Step 5: Change the length of the rope to change the desired position of the soft actuator end.

2. The method for controlling the desired position of the end effector of a soft actuator according to claim 1, characterized in that, The flexible outer shell has three evenly distributed rope holes; The ropes are arranged corresponding to the rope holes, and a rope passes through each rope hole. One end of each rope is fixed to the flexible shell, and the other end passes through the inside of the flexible shell and is fixed to the output end of the rope drive module. The rope-driven magnetostrictive stiffness soft actuator also includes: A pair of electromagnets, wherein one electromagnet is fixed to one end of a magnetorheological elastomer, and the other electromagnet is fixed to the other end of the magnetorheological elastomer; The magnetic fields generated by the two electromagnets are in the same direction. An adjustable regulated DC power supply supplies power to an electromagnet outside a flexible housing, causing the electromagnet to generate a magnetic field that changes the stiffness of the magnetorheological elastic unit. The power supply is electrically connected to the electromagnet.

3. The method for controlling the desired position of the end effector of a soft actuator according to claim 2, characterized in that, The magnetorheological elastomer comprises several magnetorheological elastic units, and adjacent magnetorheological elastic units share a common electromagnet.

4. The method for controlling the desired position of the end effector of a soft actuator according to claim 3, characterized in that, The magnetorheological elastic unit comprises a polymer matrix in which ferromagnetic particles are uniformly distributed.

5. The method for controlling the desired position of the end effector of a soft actuator according to claim 2, characterized in that, The rope drive module is a ball screw module, and the output end of each ball screw module is connected to a rope.

6. The method for controlling the desired position of the end effector of a soft actuator according to claim 2, characterized in that, The flexible shell is made of silicone.

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