Flexible cylindrical capacitive sensor based proprioceptive method for a telescopic continuum manipulator

Abstract

The application relates to a flexible continuum manipulator body sensing method based on a flexible cylindrical capacitive sensor, which solves the technical problems that in the process of collecting the image of a manipulator by a camera and identifying the shape and posture of a flexible continuum manipulator through image processing in the prior art, the camera setting is limited by space, the hardware cost is high, and the image processing calculation process is complex, the stretchable cylindrical capacitive sensor is used, the strain of the measuring sensor is measured, a segmented constant curvature model is established, the shape of a single unit is calculated, the spatial variable of the flexible continuum manipulator is obtained, and the shape of the flexible continuum manipulator is characterized. The application can be widely applied to the technical field of soft manipulators.

Description

Technical Field

[0001] This invention relates to the field of soft robotic arm technology, and more specifically, to a body perception method for a telescopic continuous robotic arm based on a flexible cylindrical capacitive sensor. Background Technology

[0002] Flexible continuum robotic arms, characterized by their deformability and high flexibility, are increasingly widely used in industries such as industry, minimally invasive surgery, and aerospace. The body of a flexible continuum robotic arm is typically made of flexible materials such as silicone or rubber, or simply uses springs. When using a flexible continuum robotic arm, an end effector is mounted at its front end. The position and orientation of the end effector in space are adjusted by controlling the bending and deformation of the flexible continuum robotic arm. To more accurately achieve the desired position and orientation of the end effector, a closed-loop control method is used to achieve precise control of the flexible continuum robotic arm. Feedback signals are crucial for this closed-loop control method, currently primarily provided by a vision system. The vision system's camera captures images of the flexible continuum robotic arm, which are then processed by the controller to identify the shape and orientation of the flexible continuum robotic arm.

[0003] However, the placement of cameras in vision systems is limited by space, especially in unstructured, enclosed environments such as aircraft engine maintenance, minimally invasive surgery, and disaster relief, where cameras cannot be set up and image acquisition is impossible. Furthermore, the computational process for image processing is too complex, and the hardware cost of cameras remains relatively high. Summary of the Invention

[0004] This invention aims to address the technical problems of existing technologies that involve camera placement being limited by space, high hardware costs, and complex image processing calculations when acquiring images of a robotic arm and then processing them to identify the shape and posture of a flexible continuous robotic arm. The invention provides a space-unrestricted, low-cost method for sensing the body of a telescopic continuous robotic arm based on a flexible cylindrical capacitive sensor.

[0005] This invention provides a method for sensing the body of a telescopic continuous robotic arm based on a flexible cylindrical capacitive sensor, comprising the following steps:

[0006] The parameterized equation for determining the left-handed, upright state of the helical body is:

[0007]

[0008] In the parameterized equation, r se θ represents the distance between the cylindrical capacitive sensor and the spiral body. h D represents the helix polar angle. h N represents the pitch. h Indicates the number of turns;

[0009] The length of the cylindrical capacitive sensor itself can be calculated using the following formula (1).

[0010]

[0011] In formula (1), This represents the initial length of the cylindrical capacitive sensor in a straight line. The initial capacitance value of the cylindrical capacitive sensor is represented by , and k represents the linear relationship coefficient between the capacitance value and the length of the cylindrical capacitive sensor.

[0012] Next, the length Li is calculated using the following formula (2). j :

[0013]

[0014] In formula (2), r se α represents the distance between the cylindrical capacitive sensor and the spiral body. i This represents the angle of torsion of each unit of the spiral body about its own centerline. α i In the calculation formula, k2 represents the linear relationship coefficient between the torsion angle and the length;

[0015] The radii of curvature ρ of the lower, middle, and upper units of the flexible continuum robotic arm are calculated using the following formula. i :

[0016]

[0017] The rotation angles of the lower, middle, and upper units of the flexible continuum robot arm around the z-axis are calculated using the following formula.

[0018]

[0019] The following formula is used to calculate the lower, middle, and upper unit rotation of the flexible continuous body robotic arm. y Rotation angle θ of the axis i :

[0020] (0<θ i ≤π)

[0021] Next, after translation and rotation along the y and z axes, we can obtain:

[0022]

[0023] Trans(ρ i (cosθim -1), 0, ρ i sinθ im -z s )r s

[0024] in,

[0025] The flexible continuum robotic arm is divided into three units: lower, middle, and upper. The coordinate transformation matrix of adjacent units...

[0026]

[0027] coordinate transformation matrix In this context, p = [ρ i (1-cosθ i )0ρ i sinθ i ];

[0028] The parametric equations of the middle and upper elements of the flexible continuum robot in the global coordinate system are:

[0029]

[0030]

[0031] Next, we will model the entire flexible continuum robotic arm.

[0032] Preferably, the process of modeling the entire flexible continuum robotic arm is as follows: The rotation angle θ i The robot arm is divided into several equal parts, and then the DH homogeneous transformation matrix method is used to model the entire flexible continuum robot arm.

[0033] The present invention also provides a telescopic flexible continuous robotic arm, comprising a helical body, three drive lines and three cylindrical capacitive sensors, wherein the three drive lines pass through the periphery of the helical body and are evenly distributed in the radial circumferential direction.

[0034] The cylindrical capacitive sensor is made by rolling a planar dielectric elastomer sensor. The planar dielectric elastomer sensor includes a dielectric layer, two electrode layers and two protective layers. After the planar dielectric elastomer sensor is rolled into a cylindrical shape, both ends are fixed with copper sleeves.

[0035] Three cylindrical capacitive sensors are connected to the outer periphery of the spiral body. The three cylindrical capacitive sensors are evenly distributed in the radial circumferential direction. The upper and lower ends of each cylindrical capacitive sensor are fixed to the spiral body. When the spiral body bends, contracts or extends, the middle part of each cylindrical capacitive sensor can slide along the outer periphery of the spiral body.

[0036] Preferably, the upper and lower ends of the cylindrical capacitive sensor are fixed to the spiral body by fixing blocks. The edge of the spiral body is provided with an embedding groove, and the embedding groove is provided with a semi-circular groove. The inner side of the fixing block is provided with a semi-circular groove. The copper sleeve at the upper end of the cylindrical capacitive sensor is located in the semi-circular groove of one embedding groove on the edge of the spiral body. The copper sleeve at the lower end of the cylindrical capacitive sensor is located in the semi-circular groove of one embedding groove on the edge of the spiral body. A fixing block is placed in the embedding groove where the upper end of the cylindrical capacitive sensor is located and fixed. Then, a fixing block is placed in the embedding groove where the lower end of the cylindrical capacitive sensor is located and fixed. The middle part of the cylindrical capacitive sensor is located in two embedding grooves on the edge of the spiral body. The two embedding grooves are respectively fixedly connected with the corresponding fixing blocks. The two embedding grooves and the corresponding fixing blocks form two circular holes. The middle part of the cylindrical capacitive sensor passes through the two circular holes and can slide.

[0037] Preferably, the spiral body is provided with three units: upper, middle and lower, and each of the three units is connected to three cylindrical capacitive sensors.

[0038] The present invention also provides a coordinate transformation method, comprising the following steps:

[0039] The parameterized equation for determining the left-handed, upright state of the helical body is:

[0040]

[0041] In the parameterized equation, r se θ represents the distance between the cylindrical capacitive sensor and the spiral body. h D represents the helix polar angle. h N represents the pitch. h Indicates the number of turns;

[0042] The length of the cylindrical capacitive sensor itself can be calculated using the following formula (1).

[0043]

[0044] In formula (1), This represents the initial length of the cylindrical capacitive sensor in a straight line. The initial capacitance value of the cylindrical capacitive sensor is represented by , and k represents the linear relationship coefficient between the capacitance value and the length of the cylindrical capacitive sensor.

[0045] Next, the length L is calculated using the following formula (2). ij :

[0046]

[0047] In formula (2), rse α represents the distance between the cylindrical capacitive sensor and the spiral body. i This represents the angle of torsion of each unit of the spiral body about its own centerline. α i In the calculation formula, k2 represents the linear relationship coefficient between the torsion angle and the length;

[0048] The radii of curvature ρ of the lower, middle, and upper units of the flexible continuum robotic arm are calculated using the following formula. i :

[0049]

[0050] The rotation angles of the lower, middle, and upper units of the flexible continuum robot arm around the z-axis are calculated using the following formula.

[0051]

[0052] The rotation angle θ of the lower, middle, and upper units of the flexible continuum robot arm around the y-axis can be calculated using the following formula. i :

[0053] (0<θ i ≤π)

[0054] Next, after translation and rotation along the y and z axes, we can obtain:

[0055]

[0056] Trans(ρ i (cosθ im -1), 0, ρ i sinθ im -z s )r s

[0057] in,

[0058] The flexible continuum robotic arm is divided into three units: lower, middle, and upper. The coordinate transformation matrix of adjacent units...

[0059]

[0060] coordinate transformation matrix In this context, p = [ρ i (1-cosθ i )0ρ i sinθ i ].

[0061] The present invention also provides a storage medium on which a computer program is stored, which, when executed by a processor, implements the various steps of the above method.

[0062] The present invention also provides an apparatus comprising a processor and a storage medium, wherein the memory is used to store a program; and the processor is used to execute the program, thereby implementing the various steps of the above-described method.

[0063] The beneficial effects of this invention are: the cylindrical capacitive sensor is not limited by the space of the application scenario, is integrated into the body of the robotic arm, does not need to be sensed by external sensors such as cameras, and will not damage the natural flexibility of the body.

[0064] The modeling method exhibits excellent positional accuracy and enables real-time shape reconstruction, providing strong support for the intelligent control of scalable continuum robotic arms. The scalable continuum robotic arm is divided into three units, and a constant curvature model is used to characterize the shape of each subdivision, achieving accurate arm shape detection and high-precision endpoint positioning.

[0065] Further features and aspects of the present invention will be clearly described in the following detailed description with reference to the accompanying drawings. Attached Figure Description

[0066] Figure 1 This is a structural diagram and a manufacturing process diagram of a cylindrical capacitive sensor;

[0067] Figure 2 This is a schematic diagram of a cylindrical capacitive sensor mounted on a spiral body.

[0068] Figure 3 yes Figure 2 In the middle, a cross-sectional view of a cylindrical capacitive sensor positioned on a spiral body;

[0069] Figure 4 yes Figure 2 A partial structural diagram, with the parameters used in the calculation process marked in the diagram;

[0070] Figure 5 This is a distribution diagram of three cylindrical capacitive sensors as a group;

[0071] Figure 6 This is a diagram showing the polar angles of the spiral body;

[0072] Figure 7 It is the modeling result, reflecting the shape of the robotic arm.

[0073] Explanation of symbols in the diagram:

[0074] 1. Spiral body, 2. Cylindrical capacitive sensor, 3. Drive line, 4. Fixing block, 5. Protective layer, 6. Electrode layer, 7. Dielectric layer; 8. Copper sleeve. Detailed Implementation

[0075] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0076] like Figure 1 As shown, the cylindrical capacitive sensor 2 is manufactured from a planar dielectric elastomer sensor through a rolling process. This planar dielectric elastomer sensor mainly consists of a dielectric layer 7, an electrode layer 6, and a protective layer 5. The connection method is as follows: the dielectric layer 7 serves as the intermediate layer, the two electrode layers 6 are connected to the front and back sides of the dielectric layer 7 respectively, and the two protective layers 5 are connected to the two electrode layers 6 respectively. This planar dielectric elastomer sensor is a conventional product in the prior art; refer to the description of flexible capacitive sensors in the invention patent application with publication number CN112230769A. The planar dielectric elastomer sensor is rolled into a cylindrical shape to form the cylindrical capacitive sensor. Specifically, the planar dielectric elastomer sensor is placed on one palm, and the other hand gently lifts the long edge of the sensor to roll it into a cylindrical shape. The two ends of the sensor are secured with copper sleeves (ensuring that the two ends of the sensor will not come loose), ultimately forming the cylindrical capacitive sensor 2. It should be noted that other fasteners can also be used to fix the two ends of the sensor. The cylindrical capacitive sensor 2 is stretchable and deformable. The cylindrical capacitive sensor 2 is installed by fixing its two ends with copper sleeves or other fasteners to the robotic arm.

[0077] like Figure 2 As shown, the flexible continuum robotic arm includes a helical body 1 and three drive lines 3. The helical body 1 is manufactured using 3D printing technology and is made of nylon. The three drive lines 3 pass through the periphery of the helical body 1 and are evenly distributed in the radial circumferential direction (with an angle of 120° between them). The helical body 1 has a helical structure with a wide range of extension, contraction, and bending deformation capabilities. Under the action of external force, pulling the three drive lines 3 can achieve omnidirectional bending of the helical body 1. Simultaneously pulling the three drive lines 3 can cause the helical body 1 to contract, shortening its length. When the helical body 1 is in a contracted state, releasing the three drive lines 3 can cause the helical body 1 to extend, lengthening its length.

[0078] refer to Figure 2 , 34. The edge of the spiral body 1 is provided with an embedding groove for matching with the fixing block 4. The embedding groove is provided with a semi-circular groove. The inner side of the fixing block 4 is provided with a semi-circular groove. The copper sleeve 8 at the upper end of the cylindrical capacitive sensor 2 is located in the semi-circular groove of the embedding groove on the edge of the spiral body 1. The copper sleeve at the lower end of the cylindrical capacitive sensor 2 is located in the semi-circular groove of the embedding groove on the edge of the spiral body 1. A fixing block 4 is placed in the embedding groove where the upper end of the cylindrical capacitive sensor 2 is located and fixed with screws (that is, the upper end of the cylindrical capacitive sensor 2 is pressed and fixed by the semi-circular groove on the inner side of the fixing block and the semi-circular groove of the embedding groove). Then, a fixing block 4 is placed in the embedding groove where the lower end of the cylindrical capacitive sensor 2 is located and fixed with screws (that is, the lower end of the cylindrical capacitive sensor 2 is pressed and fixed by the semi-circular groove on the inner side of the fixing block and the semi-circular groove of the embedding groove). The middle part of the cylindrical capacitive sensor 2 is located in two embedded grooves on the edge of the spiral body 1. These two embedded grooves are respectively fixedly connected with corresponding fixing blocks. The semi-circular groove of the embedded groove and the semi-circular groove on the inner side of the fixing block form a circular hole. There are two circular holes in total. The middle part of the cylindrical capacitive sensor 2 passes through the two circular holes. The middle part of the cylindrical capacitive sensor 2 is not squeezed and can slide in the two circular holes.

[0079] Each cylindrical capacitive sensor 2 is installed in the same way. For example... Figure 1 As shown, the three cylindrical capacitive sensors 2 at the lower part of the spiral body 1 form a group, with each sensor close to one of the three drive lines 3. The angle between the three cylindrical capacitive sensors 2 in the radial circumferential direction is 120°. The three cylindrical capacitive sensors 2 arranged in the middle of the spiral body 1 form a second group, with each sensor close to one of the three drive lines 3 and with an angle of 120°. The three cylindrical capacitive sensors 2 arranged at the upper part of the spiral body 1 form a third group, with each sensor close to one of the three drive lines 3 and with an angle of 120°. Each group of three cylindrical capacitive sensors 2 constitutes one unit corresponding to the entire flexible continuous robotic arm, and the three groups correspond to three units of the entire flexible continuous robotic arm.

[0080] For each cylindrical capacitive sensor 2, two wires are used to electrically connect the two electrode layers 6 of the cylindrical capacitive sensor 2 to the capacitance detection device. The capacitance value C of the cylindrical capacitive sensor 2 is then measured by the capacitance detection device. ijo For the three cylindrical capacitive sensors 2 at the bottom of the spiral body 1, their capacitance values ​​are C 11 C 12 C 13 The capacitance values ​​of the three cylindrical capacitive sensors in the middle of the spiral body 1 are C respectively. 21 C22 C 23 The capacitance values ​​of the three cylindrical capacitive sensors on the upper part of the spiral body 1 are C 31 C 32 C 33 .

[0081] As the three drive lines 3 drive the spiral body 1 to bend, contract, or extend, each cylindrical capacitive sensor also bends and deforms accordingly.

[0082] The parameterized equation for the left-handed, upright state of the spiral body 1 is:

[0083]

[0084] In the above parameterized equation, r se This indicates the distance between the cylindrical capacitive sensor and the spiral body 1, referenced. Figure 4 and 5 ;θ h D represents the helix polar angle. h N represents the pitch. h Indicates the number of turns.

[0085] The length of the cylindrical capacitive sensor itself can be calculated using the following formula (1).

[0086]

[0087] In formula (1), Indicates cylindrical capacitive sensor in Figure 4 and 5 The initial length in the straight line shown. denoted by , where represents the initial capacitance value of the cylindrical capacitive sensor, and k represents the linear relationship coefficient between the capacitance value and the length of the cylindrical capacitive sensor.

[0088] Next, the length L is calculated using the following formula (2). ij :

[0089]

[0090] In formula (2), r se This indicates the distance between the cylindrical capacitive sensor and the spiral body 1, referenced. Figure 4 and 5 ;α i This represents the torsion angle of each unit of the spiral body 1 about its own centerline, referenced. Figure 4 The annotation in the text, α i In the calculation formula, k2 represents the linear relationship coefficient between the torsion angle and the length (which can be calibrated through a compression torsion test).

[0091] j = 1, 2, 3, for the three cylindrical capacitive sensors in the lower unit of the spiral body 1, the length L ij It is L 11 L 12 L 13 For the three cylindrical capacitive sensors in the middle unit of the spiral body 1, the length L ij It is L 21 L 22 L 23 For the three cylindrical capacitive sensors in the upper unit of the spiral body 1, the length L ij It is L 31 L 32 L 33 .

[0092] The radii of curvature ρ of the lower, middle, and upper units of the flexible continuum robotic arm are calculated using the following formula. i :

[0093]

[0094] The rotation angles of the lower, middle, and upper units of the flexible continuum robot arm around the z-axis are calculated using the following formula.

[0095]

[0096] The rotation angle θ of the lower, middle, and upper units of the flexible continuum robot arm around the y-axis can be calculated using the following formula. i :

[0097] (0<θ i ≤π)

[0098] Next, after translation and rotation along the y and z axes, we can obtain:

[0099]

[0100] Trans(ρ i (cosθ im -1), 0, ρ i sinθ im -z s )r s

[0101] In the above formula, The parameterized equations of the spiral deformation of a single element are obtained.

[0102] The flexible continuum robotic arm is divided into three units: lower, middle, and upper. The coordinate transformation matrix of adjacent units...

[0103]

[0104] coordinate transformation matrix In this context, p = [ρ i (1-cosθ i )0ρ i sinθ i ].

[0105] Therefore, the parameterized equations of the middle and upper elements in the global coordinate system are:

[0106]

[0107]

[0108] Next, the rotation angle θ can be adjusted. i The robot is divided into several equal parts, and then the DH homogeneous transformation matrix method is used to model the entire flexible continuum robot arm to characterize the shape of the entire flexible continuum robot arm.

[0109] The present invention also provides a storage medium storing a program suitable for processor execution, the program being used to implement the various processing steps of the aforementioned modeling method for a flexible continuum manipulator. The present invention also provides a processor capable of calling the program in the storage medium.

[0110] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention can have various modifications and variations.

Claims

1. A method for sensing the body of a telescopic continuous robotic arm based on a flexible cylindrical capacitive sensor, characterized in that, Includes the following steps: The parameterized equation for determining the left-handed, upright state of the helical body is: In the parameterized equation, r se θ represents the distance between the cylindrical capacitive sensor and the spiral body. h D represents the helix polar angle. h N represents the pitch. h Indicates the number of turns; The length of the cylindrical capacitive sensor itself can be calculated using the following formula (1). In formula (1), This represents the initial length of the cylindrical capacitive sensor in a straight line. The initial capacitance value of the cylindrical capacitive sensor is represented by , and k represents the linear relationship coefficient between the capacitance value and the length of the cylindrical capacitive sensor. Next, the length L is calculated using the following formula (2). ij : In formula (2), r se α represents the distance between the cylindrical capacitive sensor and the spiral body. i This represents the angle of torsion of each unit of the spiral body about its own centerline. α i In the calculation formula, k2 represents the linear relationship coefficient between the torsion angle and the length; The radii of curvature ρ of the lower, middle, and upper units of the flexible continuum robotic arm are calculated using the following formula. i : The rotation angles of the lower, middle, and upper units of the flexible continuum robot arm around the z-axis are calculated using the following formula. The rotation angle θ of the lower, middle, and upper units of the flexible continuum robot arm around the y-axis can be calculated using the following formula. i : Next, after translation and rotation along the y and z axes, we can obtain: in, The flexible continuum robotic arm is divided into three units: lower, middle, and upper. The coordinate transformation matrix of adjacent units... coordinate transformation matrix In this context, p = [ρ i (1-cosθ i ) 0 ρ i sinθ i ]; The parametric equations of the middle and upper elements of the flexible continuum robot in the global coordinate system are: Next, we will model the entire flexible continuum robotic arm.

2. The telescopic continuous body sensing method for a robotic arm based on a flexible cylindrical capacitive sensor according to claim 1, characterized in that, The process of modeling the entire flexible continuum robotic arm is as follows: The rotation angle θ is... i The robot arm is divided into several equal parts, and then the DH homogeneous transformation matrix method is used to model the entire flexible continuum robot arm.

3. A telescopic flexible continuous robotic arm, characterized in that, It includes a spiral body, three drive lines and three cylindrical capacitive sensors. The three drive lines pass through the periphery of the spiral body and are evenly distributed in the radial circumferential direction. The cylindrical capacitive sensor is formed by rolling a planar dielectric elastomer sensor. The planar dielectric elastomer sensor includes a dielectric layer, two electrode layers, and two protective layers. After the planar dielectric elastomer sensor is rolled into a cylindrical shape, both ends are fixed with copper sleeves. The three cylindrical capacitive sensors are connected to the outer periphery of the spiral body, and are evenly distributed in the radial circumferential direction. The upper and lower ends of each cylindrical capacitive sensor are fixed to the spiral body. When the spiral body bends, contracts or extends, the middle part of each cylindrical capacitive sensor can slide along the outer periphery of the spiral body.

4. The telescopic flexible continuous robotic arm according to claim 3, characterized in that, The upper and lower ends of the cylindrical capacitive sensor are fixed to the spiral body by fixing blocks. The edge of the spiral body is provided with an embedding groove, and the embedding groove is provided with a semi-circular groove. The inner side of the fixing block is provided with a semi-circular groove. The copper sleeve at the upper end of the cylindrical capacitive sensor is located in the semi-circular groove of one embedding groove on the edge of the spiral body. The copper sleeve at the lower end of the cylindrical capacitive sensor is located in the semi-circular groove of one embedding groove on the edge of the spiral body. A fixing block is placed in the embedding groove where the upper end of the cylindrical capacitive sensor is located and fixed. Then, a fixing block is placed in the embedding groove where the lower end of the cylindrical capacitive sensor is located and fixed. The middle part of the cylindrical capacitive sensor is located in two embedding grooves on the edge of the spiral body. The two embedding grooves are respectively fixedly connected with the corresponding fixing blocks. The two embedding grooves and the corresponding fixing blocks form two circular holes. The middle part of the cylindrical capacitive sensor passes through the two circular holes and can slide.

5. The telescopic flexible continuous robotic arm according to claim 3, characterized in that, The spiral body is provided with three units: upper, middle and lower. Each of the three units is connected to a cylindrical capacitive sensor.

6. A coordinate transformation method, characterized in that, Includes the following steps: The parameterized equation for determining the left-handed, upright state of the helical body is: In the parameterized equation, r se θ represents the distance between the cylindrical capacitive sensor and the spiral body. h D represents the helix polar angle. h N represents the pitch. h Indicates the number of turns; The length of the cylindrical capacitive sensor itself can be calculated using the following formula (1). In formula (1), This represents the initial length of the cylindrical capacitive sensor in a straight line. The initial capacitance value of the cylindrical capacitive sensor is represented by , and k represents the linear relationship coefficient between the capacitance value and the length of the cylindrical capacitive sensor. Next, the length L is calculated using the following formula (2). ij : In formula (2), r se α represents the distance between the cylindrical capacitive sensor and the spiral body. i This represents the angle of torsion of each unit of the spiral body about its own centerline. α i In the calculation formula, k2 represents the linear relationship coefficient between the torsion angle and the length; The radii of curvature ρ of the lower, middle, and upper units of the flexible continuum robotic arm are calculated using the following formula. i : The rotation angles of the lower, middle, and upper units of the flexible continuum robot arm around the z-axis are calculated using the following formula. The rotation angle θ of the lower, middle, and upper units of the flexible continuum robot arm around the y-axis can be calculated using the following formula. i : Next, after translation and rotation along the y and z axes, we can obtain: in, The flexible continuum robotic arm is divided into three units: lower, middle, and upper. The coordinate transformation matrix of adjacent units... coordinate transformation matrix In this context, p = [ρ i (1-cosθ i ) 0 ρ i sinθ i ].

7. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in claim 1, 2 or 6.

8. An apparatus, characterized in that, It includes a processor and a storage medium, the memory being used to store a program; the processor being used to execute the program, thereby implementing the steps of the method of claim 1, 2 or 6.

Images