A multi-loop control method for continuum manipulator based on fuzzy ADRC

Abstract

The application provides a continuum manipulator multi-loop control method based on fuzzy ADRC, relates to the technical field of manipulator control, and comprises the following steps: initializing a manipulator pose state and all parameters of a controller; inputting a desired end pose into a single-chip microcomputer to inversely solve a pose matrix of each joint of the manipulator; converting the pose matrix of each joint into a motor rotation signal and inputting the motor rotation signal into a pose loop ADRC to obtain a control signal; inputting the control signal into a speed loop ADRC to obtain a motor control signal; and inputting the motor control signal into a driver to drive the manipulator to move through a motor and a driving line. The application writes experience parameters into a fuzzy control algorithm, significantly improves the anti-interference ability and adaptability of the continuum manipulator in a complex and changeable environment under the requirement of meeting the control precision of the control system, and realizes a continuum manipulator control system with high stability and strong robustness.

Description

Technical Field

[0001] This invention relates to the field of robotic arm control technology, and more specifically, to a multi-loop control method for a continuum robotic arm based on fuzzy ADRC. Background Technology

[0002] Continuous robotic arms possess advantages such as light weight, simple structure, strong adaptability to unstructured environments, efficient movement in complex natural environments by altering their body shape, and high safety in human-robot interaction. Therefore, they are suitable for applications in environments where rigid robots struggle. With technological advancements and societal development, the performance requirements for continuous robotic arms are becoming increasingly stringent. They must not only possess excellent stability and precision and dynamic performance but also strong anti-interference capabilities, making it difficult to meet these requirements using classical control methods.

[0003] Currently, most applications of continuous body robotic arm control still use classic PID controllers, which are not very effective at isolating disturbances generated in complex environments. A small number of applications use ADRC or sliding diaphragm control methods, but in environments with complex and variable disturbances, the pre-tuned parameters may cause overshoot in the system output response or unsatisfactory noise compensation capabilities, which is not conducive to improving the system's adaptability and control performance. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-loop control method for a continuous robotic arm based on fuzzy ADRC, which can solve the problems of insufficient control performance of traditional controllers and difficulty in parameter tuning of active disturbance rejection control methods.

[0005] The technical solution of this invention is as follows:

[0006] In a first aspect, this application provides a multi-loop control method for a continuous body robotic arm based on fuzzy ADRC, which includes the following steps:

[0007] S1. Initialize the robot arm's pose state and all controller parameters;

[0008] S2. Input the desired end-effector pose into the microcontroller to inversely solve the pose matrix of each joint in the robotic arm;

[0009] S3. Convert the pose matrix of each joint into a motor rotation signal and input it into the pose loop ADRC to obtain a control signal;

[0010] S4. Input the control signal into the speed loop ADRC to obtain the motor control signal;

[0011] S5. Input the motor control signal into the driver to drive the robotic arm to move through the motor and drive line.

[0012] Further, step S2 includes: inputting the desired end-effector pose into the microcontroller, and using a numerical method to inversely solve the pose matrix of each joint from the desired end-effector point relative to the polar coordinate system through the transformation matrix of adjacent joints; wherein, the transformation matrix of adjacent joints is expressed as:

[0013]

[0014] in, θ represents the transformation matrix between adjacent joints. i Representing the polar coordinate system with Z i-1 Looking at the X-axis i-1 Axis and X i The included angle of the axes, where i represents the i-th joint, a i Representing the polar coordinate system with Z i-1 Looking at the X-axis i-1 Axis and X i The distance between axes, α i Represents the polar coordinate system with X i-1 Looking at Z along the axis i-1 Axis and Z i The included angle of the axis.

[0015] Furthermore, the pose matrix mentioned above includes rotation angles and joint coordinate position vectors.

[0016] Furthermore, the step of converting the pose matrix of each joint into a motor rotation signal includes:

[0017] The pose matrix of each joint is converted into a line length change value using the formula relating joint angles to the length of the actuation line.

[0018] The change in line length is converted into information about the number of motor rotations to obtain the motor rotation signal.

[0019] Furthermore, step S5 above also includes:

[0020] The end effector gyroscope of the robotic arm collects the end effector pose during the movement of the robotic arm and determines whether the end effector pose of the robotic arm meets the requirements for movement and rotation. If it does not meet the requirements, steps S3-S5 are repeated. If it does meet the requirements, the motor movement is stopped.

[0021] The gyroscope is essentially an end-effector with a pose value. Based on the established world coordinate system or machine coordinate system, it calculates the extent of the end-effector's movement and rotation, thereby determining whether the motion meets the requirements.

[0022] Secondly, this application provides an electronic device, characterized in that it includes:

[0023] Memory, used to store one or more programs;

[0024] processor;

[0025] When one or more of the above programs are executed by the above processor, a multi-loop control method for a continuous body robotic arm based on fuzzy ADRC is implemented as described in any of the first aspects above.

[0026] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a multi-loop control method for a continuous body robotic arm based on fuzzy ADRC as described in any of the first aspects above.

[0027] Compared with the prior art, the present invention has at least the following advantages or beneficial effects:

[0028] (1) This invention applies the ADRC control method to motor control, thereby enabling the continuous robotic arm to maintain good dynamic quality while having good anti-interference ability, and also has a good balance between speed and robustness in motion control.

[0029] (2) The present invention uses fuzzy control to tune the ADRC parameters. By utilizing the experience of ADRC debugging, the parameter range is written into the value range of fuzzy variables. The control coefficients of the nonlinear state error feedback control law in ADRC can be dynamically tuned through the membership function, so that it can have better control efficiency in the motion of the continuous robot arm and has a faster response speed than ordinary ADRC.

[0030] (3) The present invention uses ADRC control method to apply to the motion control of the entire continuous robot arm, including the overall motion change of the robot arm, joint change angle, speed and acceleration, and end position pose control. Through the anti-disturbance capability of ADRC, the continuous robot arm motion is smoother and the pose control is more accurate.

[0031] (4) The continuous robotic arm provided by the present invention is divided into a pose loop and a speed loop for multi-loop control. The pose signal of the end of the continuous robotic arm is fed back by the gyroscope to form an outer pose closed loop, thereby realizing precise dynamic control of the end pose of the continuous robotic arm. The pose signal generated by the gyroscope at the end of the robotic arm is used to continuously correct the dynamic pose accuracy error caused by the tension of the drive line. The motor output signal fed back by the encoder forms an inner speed closed loop, thereby realizing motion control of the continuous robotic arm. Thus, the multi-loop control enables the continuous robotic arm to have a more precise control effect and better anti-interference ability. Attached Figure Description

[0032] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 This is a flowchart illustrating the steps of a multi-loop control method for a continuum robotic arm based on fuzzy ADRC according to the present invention.

[0034] Figure 2 The flowchart shows a multi-loop control method for a continuum robotic arm based on fuzzy ADRC according to the present invention.

[0035] Figure 3 This is a diagram showing the relationship between the joint angles and rope length changes of a constant curvature continuum robotic arm according to the present invention.

[0036] Figure 4 This is a diagram showing the relationship between joint angles and rope length changes in a highly curvature continuum robotic arm according to the present invention.

[0037] Figure 5 This is a schematic structural block diagram of an electronic device according to an embodiment of the present invention.

[0038] Icons: 101, memory; 102, processor; 103, communication interface. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0040] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0041] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0042] It should be noted that, in this document, the term "comprising" or any other variation thereof is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0043] In the description of this application, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set" and "connection" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0044] The following detailed description of some embodiments of this application is provided in conjunction with the accompanying drawings. Unless otherwise specified, the various embodiments and features described below can be combined with each other.

[0045] Example 1

[0046] Please see Figure 1 , Figure 1 The diagram shows the steps of a multi-loop control method for a continuum robotic arm based on fuzzy ADRC, as provided in Embodiment 1 of this application.

[0047] In a first aspect, this application provides a multi-loop control method for a continuous body robotic arm based on fuzzy ADRC, which includes the following steps:

[0048] S1. Initialize the robot arm's pose state and all controller parameters;

[0049] S2. Input the desired end-effector pose into the microcontroller to inversely solve the pose matrix of each joint in the robotic arm;

[0050] S3. Convert the pose matrix of each joint into a motor rotation signal and input it into the pose loop ADRC to obtain a control signal;

[0051] S4. Input the control signal into the speed loop ADRC to obtain the motor control signal;

[0052] S5. Input the motor control signal into the driver to drive the robotic arm to move through the motor and drive line.

[0053] In order to achieve good anti-interference effect without excessively affecting the inner loop control effect, the gain setting of the outer loop is generally relatively small. Therefore, the initialization parameters of the pose loop's ADRC are slightly smaller than those of the velocity loop. The control quantity generated by the fuzzy ADRC of the pose loop is output to the fuzzy ADRC of the next-level velocity loop, which represents the amount of rotation required by the drive motors corresponding to the joints of the continuous body manipulator. Based on the data returned by the end-effector gyroscope of the continuous body manipulator, the closed-loop feedback control derives the output quantity, which is then used as the input quantity for the fuzzy ADRC of the next-level velocity loop. This avoids mismatch between the drive stroke and the desired pose due to issues with drive cable tension. The drivers of each motor are connected and communicate via a CAN bus. After receiving the output signal from the fuzzy ADRC of the velocity loop... The driver sends corresponding drive signals to the motor; the motor rotates, pulling its corresponding drive line to move through the reducer, lead screw, and slide rail, achieving the extension and retraction effect. The motor rotation stroke is monitored by the motor encoder, and the motor rotation amount corresponding to the drive line of each joint of the continuous robot arm is collected and fed back to the fuzzy ADRC in the speed loop to ensure the rotation accuracy of the joint motors of the continuous robot arm. Through the extension and retraction of each drive line, the corresponding joint rotates by the corresponding angle. The position of the end of the continuous robot arm after rotation is collected by the gyroscope at the end of the continuous robot arm and fed back to the fuzzy ADRC in the position loop, thereby realizing that the end point of the continuous robot arm reaches the desired position and pose requirements.

[0054] In a preferred embodiment, step S2 includes: inputting the desired end-effector pose into the microcontroller, and using a numerical method to inversely solve the pose matrix of each joint from the desired end-effector point relative to the polar coordinate system through the transformation matrix of adjacent joints; wherein, the transformation matrix of adjacent joints is expressed as:

[0055]

[0056] in, θ represents the transformation matrix between adjacent joints. i Representing the polar coordinate system with Z i-1 Looking at the X-axis i-1 Axis and X i The included angle of the axes, where i represents the i-th joint, a i Representing the polar coordinate system with Z i-1 Looking at the X-axis i-1 Axis and X i The distance between axes, α i Represents the polar coordinate system with X i-1 Looking at Z along the axis i-1 Axis and Z i The included angle of the axis.

[0057] In a preferred embodiment, the pose matrix includes rotation angles and joint coordinate position vectors.

[0058] In a preferred embodiment, the step of converting the pose matrix of each joint into a motor rotation signal includes:

[0059] The pose matrix of each joint is converted into a line length change value using the formula relating joint angles to the length of the actuation line.

[0060] The change in line length is converted into information about the number of motor rotations to obtain the motor rotation signal.

[0061] In a preferred embodiment, step S5 further includes:

[0062] The end effector gyroscope of the robotic arm collects the end effector pose during the movement of the robotic arm and determines whether the end effector pose of the robotic arm meets the requirements for movement and rotation. If it does not meet the requirements, steps S3-S5 are repeated. If it does meet the requirements, the motor movement is stopped.

[0063] Working principle:

[0064] Please see Figure 2 , Figure 2The diagram shows a flowchart of a multi-loop control method for a continuous robotic arm based on fuzzy ADRC according to the present invention. First, the robotic arm's pose state and all controller parameters are initialized. Then, the desired end-effector pose is input into the microcontroller to inversely solve the pose matrix of each joint in the robotic arm using methods such as transformation matrix, rotation matrix, or analytical methods. The pose matrix includes rotation angles and joint coordinate position vectors. The pose matrix of each joint is converted into a line length change value using the formula relating joint angles to drive line length. This line length change value can be converted into information such as the number of motor rotations, i.e., the motor rotation signal. The motor rotation signal is then input into the pose loop ADRC to obtain the control signal. Closed-loop feedback is performed using the end-effector pose change output from the end-effector gyroscope. The fuzzy control method is used to dynamically adjust the NLSEF parameters of the control law, enabling the ADRC to have a faster response speed. The resulting disturbance-resistant motor control signal is output to the driver. Through the servo motor driver, the actual motor rotation control signal is output. The main purpose is to eliminate control accuracy problems caused by drive line slack and tension issues. Then, the motor rotates... The traction drive cable extends and retracts, then drives the robotic arm to move. During this process, an encoder collects the extension and retraction length and speed of the drive cable to solve for the corresponding joint rotation angle signal, which is then fed back to the motor output signal to form an inner speed closed loop, realizing motion control of the continuous robotic arm. This multi-loop control enables the continuous robotic arm to have more precise control and better anti-disturbance capability. A gyroscope collects the end-effector pose signal to form an outer pose closed loop, realizing precise dynamic control of the end-effector pose of the continuous robotic arm. The pose signal generated by the gyroscope at the end of the robotic arm is used to continuously correct the dynamic pose accuracy error caused by the tension of the drive cable. Finally, it is determined whether the end-effector pose meets the requirements. If it does, the motor movement stops; otherwise, the previous steps are repeated. Here, the gyroscope is equivalent to having an end-effector pose value. Based on the established world coordinate system or machine coordinate system, the amount of movement and rotation of the end-effector is calculated to determine whether the motion meets the requirements.

[0065] Example 2

[0066] The formulas for the change in joint pose state and drive line length of a constant curvature continuum robotic arm are as follows:

[0067]

[0068] like Figure 3 This is a diagram showing the relationship between joint angles and rope length changes in a constant curvature continuum robotic arm. 0 P x , 0 P y , 0 P zLet x, y, and z be the components of the position vector formed by the joint coordinate system corresponding to the joint ends, and S be the length of the central axis of the constant curvature continuum robot arm. Let θ be the angle between the position vector of the end point mapped onto the XOY plane of the coordinate system and the X-axis, θ be the curvature of the constant curvature continuum robot arm, r be the distance from the drive line thread hole to the origin of the coordinate system, and Δl1, Δl2, Δl3, and Δl4 be the length changes of the four drive lines arranged counterclockwise.

[0069] The formulas for the change in joint pose state and actuation line length of a highly curvature continuum robotic arm are as follows:

[0070]

[0071] like Figure 4 As shown, Figure 4 This is a diagram showing the relationship between joint angles and rope length changes in a constant curvature continuum robotic arm according to the present invention. In this diagram, X0O0Y0Z0 forms coordinate system {0}, X1O1Y1Z1 forms coordinate system {1}, and X2O2Y2Z2 forms coordinate system {2}. Coordinate systems {1} and {2} are transformed using a matrix... 1 T2 shows that A1, B1, A2, B2, A3, and B3 are all drive line holes. β is the angle between drive line hole A1 or B1 in the {1} or {2} coordinate system and the X-axis of its own coordinate system. α is the rotation angle around the X-axis from the {0} coordinate system to the {1} coordinate system. ψ is the rotation angle around the Y-axis from the {2} coordinate system to the {0} coordinate system. d / 2 is the distance from the origin of the {0} coordinate system to the origin of the {1} or {2} coordinate system. Δl1 is the length of the change in drive line 1.

[0072] Wherein, the transformation matrix 1 The formula for T2 is as follows:

[0073]

[0074] Increase β in the above formula respectively and The changes in the lengths of the other two driving lines, Δl2 and Δl3, can then be calculated.

[0075] Example 3

[0076] Please see Figure 5 , Figure 5 This is a schematic structural block diagram of an electronic device provided in Embodiment 3 of this application.

[0077] An electronic device includes a memory 101, a processor 102, and a communication interface 103. The memory 101, processor 102, and communication interface 103 are electrically connected directly or indirectly to enable data transmission or interaction. For example, these components can be electrically connected to each other via one or more communication buses or signal lines. The memory 101 can be used to store software programs and modules. The processor 102 executes the software programs and modules stored in the memory 101 to perform various functional applications and data processing. The communication interface 103 can be used for signaling or data communication with other node devices.

[0078] The memory 101 may be, but is not limited to, random access memory (RAM), read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), etc.

[0079] The processor 102 can be an integrated circuit chip with signal processing capabilities. The processor 102 can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0080] It is understood that the structure shown in the figure is for illustrative purposes only. A multi-loop control method for a continuous body robotic arm based on fuzzy ADRC may include more or fewer components than those shown in the figure, or have a different configuration. The components shown in the figure can be implemented in hardware, software, or a combination thereof.

[0081] In the embodiments provided in this application, it should be understood that the disclosed methods can also be implemented in other ways. The embodiments described above are merely illustrative. For example, the flowcharts or block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in the flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and combinations of blocks in the block diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0082] In addition, the functional modules in the various embodiments of this application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0083] If the aforementioned functions are implemented as software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0084] In summary, the multi-loop control method for a continuous robotic arm based on fuzzy ADRC provided in this application initializes the robotic arm's pose state and all controller parameters. The desired end-effector pose is input into the microcontroller to inversely solve for the pose matrix of each joint in the robotic arm. The pose matrix of each joint is then converted into a motor rotation signal and input into the pose loop ADRC to obtain a control signal. This control signal is then input into the speed loop ADRC to obtain a motor control signal. Finally, the motor control signal is input into the driver to drive the robotic arm through the motor and drive lines. This invention uses a gyroscope to feed back the end-effector pose signal of the continuous robotic arm to form an outer pose closed loop, achieving precise dynamic control of the end-effector pose. The pose signal generated by the gyroscope at the end of the robotic arm continuously corrects dynamic pose accuracy errors caused by tension issues in the drive lines. The motor output signal fed back by the encoder forms an inner speed closed loop, achieving motion control of the continuous robotic arm. Thus, multi-loop control enables the continuous robotic arm to have more precise control and better anti-interference capabilities.

[0085] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0086] It will be apparent to those skilled in the art that this application is not limited to the details of the exemplary embodiments described above, and that this application can be implemented in other specific forms without departing from the spirit or essential characteristics of this application. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of this application is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within this application. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A multi-loop control method for a continuous body robotic arm based on fuzzy ADRC, characterized in that, Includes the following steps: S1. Initialize the robot arm's pose state and all controller parameters; S2. Input the desired end-effector pose into the microcontroller to inversely solve for the pose matrix of each joint in the robotic arm. Specifically, this includes: inputting the desired end-effector pose into the microcontroller, and using a numerical method to inversely solve for the pose matrix of each joint by using the transformation matrix of adjacent joints; wherein, the transformation matrix of adjacent joints is expressed as: ， in, This represents the transformation matrix between adjacent joints. Representing the polar coordinate system with Z i-1 Looking at the X-axis i-1 Axis and X i The included angle of the axis, i Indicates the first i One joint, a i Representing the polar coordinate system with Z i-1 Looking at the X-axis i-1 Axis and X i The distance between axes, α i Represents the polar coordinate system with X i-1 Looking at Z along the axis i-1 Axis and Z i The included angle of the axis; S3. Convert the pose matrix of each joint into a motor rotation signal and input it into the pose loop ADRC to obtain a control signal; S4. Input the control signal into the speed loop ADRC to obtain the motor control signal; S5. Input the motor control signal into the driver to drive the robotic arm to move through the motor and drive line.

2. The multi-loop control method for a continuous body robotic arm based on fuzzy ADRC as described in claim 1, characterized in that, The pose matrix includes rotation angles and joint coordinate position vectors.

3. The multi-loop control method for a continuous body robotic arm based on fuzzy ADRC as described in claim 1, characterized in that, The step of converting the pose matrix of each joint into a motor rotation signal includes: The pose matrix of each joint is converted into a line length change value using the formula relating joint angles to the length of the actuation line. The change in line length is converted into information about the number of motor rotations to obtain the motor rotation signal.

4. The multi-loop control method for a continuous body robotic arm based on fuzzy ADRC as described in claim 1, characterized in that, Step S5 also includes: The end effector gyroscope of the robotic arm collects the end effector pose during the movement of the robotic arm and determines whether the end effector pose of the robotic arm meets the requirements for movement and rotation. If it does not meet the requirements, steps S3-S5 are repeated. If it does meet the requirements, the motor movement is stopped.

5. An electronic device, characterized in that, include: Memory, used to store one or more programs; processor; When the processor executes the one or more programs, it implements a multi-loop control method for a continuous body robotic arm based on fuzzy ADRC as described in any one of claims 1-4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements a multi-loop control method for a continuum robotic arm based on fuzzy ADRC as described in any one of claims 1-4.

Images