Constant force following method of orthopedic robot constant force device based on Kalman filtering
Through Kalman filtering technology and load dynamic calibration method, a constant force follow-up model is established, the speed and acceleration of the cylinder are obtained in real time, and the required air pressure and intake direction of the cylinder are calculated, which solves the problem of insufficient external load perception in orthopedic surgery by pneumatic constant force devices, and achieves high-precision and robust constant force control.
Patent Information
- Application Number
- CN202510228735.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-28
- Publication Date
- 2025-07-04
AI Technical Summary
The existing pneumatic constant force devices lack external load sensing capabilities in orthopedic surgery, and cannot perceive changes in load mass, speed and acceleration in real time, resulting in significant impact on the dynamic changes of load, insufficient adaptability, delayed dynamic response, difficult to be compatible with different tools or load inclination angles, and high cost.
Kalman filtering technology and load dynamic calibration method are used to establish a constant force following model, use Kalman filter to process displacement data to obtain speed and acceleration in real time, determine the external load mass, and calculate the air pressure value and intake direction required by the cylinder based on the target output force value to realize the operation control of the cylinder.
It improves the accuracy and robustness of the pneumatic constant force device during the operation, realizes low-cost, high-adaptive constant force control without force sensors, and improves the real-time and accuracy of output force tracking.
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Figure CN120241252A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of orthopedic robots, and particularly relates to a constant force following method, device, equipment and computer-readable storage medium for an orthopedic robot constant force device based on Kalman filtering. Background Art
[0002] In orthopedic robot surgery operations, constant force control is one of the core technologies for achieving high-quality surface treatment. During the surgery process, the contact force between the tool and the object being contacted needs to be kept constant to avoid damage to the object being contacted caused by force fluctuations.
[0003] Traditional methods mostly adopt active compliance control algorithms (such as impedance control, force / position hybrid control), and achieve force control by integrating force sensors and complex algorithms in the robot controller. However, such methods have high requirements for the performance of the robot body, and the algorithms are complex to implement and costly, which limits their wide application.
[0004] To simplify the system design, researchers have proposed a passive compliance scheme of "robot + constant force device", which realizes force-position decoupling control through an independent constant force device. Existing constant force devices can be divided into mechanical, motor-driven and pneumatic types according to the driving method. For example, the mechanical constant force device based on a spring damper has a simple structure, but the output force value cannot be dynamically adjusted; the motor-driven constant force device can actively adjust the force value, but has problems such as small torque and serious heating; the pneumatic constant force device has gradually been adopted due to advantages such as simple control and good flexibility, but still faces the following technical bottlenecks:
[0005] 1. Lack of external load perception ability: Pneumatic constant force devices usually do not have force sensors and cannot perceive the changes in the external load mass, movement speed and acceleration in real time, resulting in a significant impact on the output force accuracy by the dynamic changes of the load;
[0006] 2. Insufficient adaptability: Existing devices (such as the Austrian ACF adaptive flange) have built-in sensors, but are complex in structure, costly, and cannot be compatible with different tools or load inclinations;
[0007] 3. Dynamic response lag: When the load inclination changes or the movement is slow, traditional pneumatic control strategies are difficult to adjust the air pressure in a timely manner, resulting in an increase in the force tracking error.
[0008] To address the above problems, there is an urgent need for a low-cost, highly adaptable constant force control method without a force sensor to improve the accuracy and robustness of pneumatic constant force devices during surgery. Summary of the Invention
[0009] The embodiments of the present application provide a constant force following method, device, equipment and computer-readable storage medium for an orthopedic robot constant force device based on Kalman filtering, which can effectively solve the problems of external load perception and real-time adjustment by integrating Kalman filtering technology and load dynamic calibration method, and improve the accuracy and robustness of the pneumatic constant force device during the operation.
[0010] In a first aspect, the embodiments of the present application provide a constant force following method for an orthopedic robot constant force device based on Kalman filtering, including:
[0011] Establish a constant force following model for the orthopedic robot constant force device, where the model is based on the structure and working principle of the constant force device and includes dynamic parameters such as position, velocity, acceleration and external load mass;
[0012] Use a Kalman filter to process the displacement data collected by the displacement sensor, and obtain the velocity and acceleration during the cylinder expansion and contraction process of the constant force device in real time;
[0013] Determine the external load mass of the constant force device through an external load mass calibration method;
[0014] According to the target output force value and the current state of the constant force device, calculate the required air pressure value and intake direction of the cylinder;
[0015] Control the cylinder to act according to the air pressure value and intake direction to achieve constant force following.
[0016] Optionally, the establishment of the constant force following model includes the following steps:
[0017] Conduct a force analysis on the constant force device, and construct a balance equation including cylinder thrust, external load gravity, friction force and damping force;
[0018] Convert the balance equation into a dynamic model with displacement, velocity, acceleration and external load mass as variables.
[0019] Optionally, the application of the Kalman filter includes:
[0020] Take displacement as the observation variable and velocity and acceleration as the state variables;
[0021] Through the Kalman filtering algorithm, perform iterative prediction and correction on the displacement data, and output the optimally estimated velocity and acceleration.
[0022] Optionally, the external load mass calibration method is specifically:
[0023] Adjust the cylinder air pressure to make the external load in a static equilibrium state;
[0024] Based on the cylinder air pressure value, inclination value in the static state and the known fixed mass of the constant force device, calculate the external load mass.
[0025] Optionally, in the calculation formula of the external load mass, the cylinder friction force is ignored, and the calibration is only performed through the air pressure difference on both sides of the cylinder and the inclination angle.
[0026] Optionally, the method for determining the air intake direction and air pressure of the cylinder includes:
[0027] Calculate the air pressure that the cylinder needs to generate according to the target output force value, external load mass, current inclination angle, speed and acceleration;
[0028] Compare the air pressure with a preset air pressure threshold, and select the rod chamber or the non-rod chamber as the air intake chamber of the cylinder;
[0029] Based on the selected air intake chamber type and the target air pressure, calculate the required air pressure value.
[0030] Optionally, the air pressure threshold is the product of the atmospheric pressure and the difference in the effective area of the cylinder piston, and is used to judge the direction of the air pressure.
[0031] In a second aspect, an embodiment of the present application provides a constant force following system for an orthopedic robot constant force device based on Kalman filtering, including:
[0032] A model establishment module, configured to establish a constant force following model of the orthopedic robot constant force device. The model is based on the structure and working principle of the constant force device and includes dynamic parameters such as position, speed, acceleration, and external load mass;
[0033] A displacement data acquisition module, configured to process the displacement data collected by the displacement sensor using a Kalman filter to obtain the speed and acceleration during the telescopic process of the cylinder of the constant force device in real time;
[0034] An external load mass determination module, configured to determine the external load mass of the constant force device through an external load mass calibration method;
[0035] A calculation module, configured to calculate the required air pressure value and air intake direction of the cylinder according to the target output force value and the current state of the constant force device;
[0036] A control module, configured to control the cylinder to act according to the air pressure value and air intake direction to achieve constant force following.
[0037] In a third aspect, an embodiment of the present application provides an electronic device, which includes: a processor and a memory storing computer program instructions;
[0038] When the processor executes the computer program instructions, it implements the constant force following method for the orthopedic robot constant force device based on Kalman filtering.
[0039] Fourthly, an embodiment of the present application provides a computer-readable storage medium, on which computer program instructions are stored. When the computer program instructions are executed by a processor, a constant force following method for an orthopedic robot constant force device based on Kalman filtering is implemented.
[0040] The constant force following method, device, equipment and computer-readable storage medium for an orthopedic robot constant force device based on Kalman filtering in the embodiments of the present application can effectively solve the problems of external load perception and real-time adjustment by integrating Kalman filtering technology and load dynamic calibration methods, and improve the accuracy and robustness of the pneumatic constant force device during the operation.
[0041] The constant force following method for an orthopedic robot constant force device based on Kalman filtering includes:
[0042] Establish a constant force following model for the orthopedic robot constant force device. The model is based on the structure and working principle of the constant force device and includes dynamic parameters such as position, velocity, acceleration and external load mass.
[0043] Use a Kalman filter to process the displacement data collected by a displacement sensor, and obtain the velocity and acceleration during the cylinder expansion and contraction process of the constant force device in real time.
[0044] Determine the external load mass of the constant force device through an external load mass calibration method.
[0045] According to the target output force value and the current state of the constant force device, calculate the required air pressure value and the air intake direction of the cylinder.
[0046] Control the cylinder to act according to the air pressure value and the air intake direction to achieve constant force following. Description of the Drawings
[0047] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the following drawings are some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.
[0048] Figure 1 is a flowchart of a constant force following method for an orthopedic robot constant force device based on Kalman filtering provided by an embodiment of the present application;
[0049] Figure 2 is a schematic diagram of the force on the constant force device provided by an embodiment of the present application;
[0050] Figure 3It is a schematic structural diagram of a constant force following system of an orthopedic robot constant force device based on Kalman filtering provided by an embodiment of the present application;
[0051] Figure 4 It is a schematic structural diagram of an electronic device provided by an embodiment of the present application. Detailed implementation manners
[0052] The features and exemplary embodiments of various aspects of the present application will be described in detail below. To make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present application, rather than to limit the present application. For those skilled in the art, the present application can be implemented without some of these specific details. The following description of the embodiments is only intended to provide a better understanding of the present application by showing examples of the present application.
[0053] It should be noted that, in this document, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprises", "comprising" or any other variation thereof is intended to cover a non-exclusive inclusion, such that a process, method, article or device comprising a series of elements includes not only those elements, but also other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the phrase "comprising..." does not exclude the existence of additional identical elements in the process, method, article or device comprising the element.
[0054] To solve the problems of the prior art, embodiments of the present application provide a constant force following method, device, equipment and computer-readable storage medium for an orthopedic robot constant force device based on Kalman filtering. First, the constant force following method for an orthopedic robot constant force device based on Kalman filtering provided by embodiments of the present application will be introduced below.
[0055] Figure 1 It shows a schematic flowchart of a constant force following method for an orthopedic robot constant force device based on Kalman filtering provided by an embodiment of the present application. As Figure 1 shown, the constant force following method for an orthopedic robot constant force device based on Kalman filtering includes:
[0056] S101. Establish a constant force following model for the orthopedic robot constant force device. The model is based on the structure and working principle of the constant force device and includes dynamic parameters such as position, velocity, acceleration, and external load mass;
[0057] S102. Process the displacement data collected by the displacement sensor using a Kalman filter to obtain the velocity and acceleration in real time during the telescopic process of the cylinder of the constant force device;
[0058] S103. Determine the external load mass of the constant force device through an external load mass calibration method;
[0059] S104. Calculate the required air pressure value and the air intake direction of the cylinder according to the target output force value and the current state of the constant force device;
[0060] S105. Control the cylinder to act according to the air pressure value and the air intake direction to achieve constant force following.
[0061] Figure 2 It is a schematic diagram of the force on the constant force device provided by an embodiment of the present application.
[0062] When the constant force device works, it generally hangs a terminal tool with a certain load (referred to as the external load, which will be used as the external load hereafter), receives the target value of the output force given externally, and outputs the corresponding positive pressure (referred to as the output force, which will be used as the output force hereafter). As Figure 2 shown, its working process is as follows: The controller receives the constant force value from the outside, collects the air pressure, position, and inclination information from the displacement sensor, inclination sensor, and electro-pneumatic proportional valve, obtains the required air pressure value and the air intake direction of the cylinder through data processing and algorithm operation, and sends the air pressure value and the air intake direction to the electro-pneumatic proportional valve and the electromagnetic directional valve, so that the cylinder generates the corresponding pushing and pulling forces, and then realizes the output of the target force.
[0063] In one embodiment, the establishment of the constant force following model includes the following steps:
[0064] Conduct a force analysis on the constant force device to construct a balance equation including the cylinder thrust, the gravity of the external load, the friction force, and the damping force;
[0065] Convert the balance equation into a dynamic model with displacement, velocity, acceleration, and external load mass as variables.
[0066] In one embodiment, the application of the Kalman filter includes:
[0067] Take the displacement as the observation variable, and the velocity and acceleration as the state variables;
[0068] Iteratively predict and correct the displacement data through the Kalman filter algorithm, and output the optimally estimated velocity and acceleration.
[0069] In one embodiment, the external load mass calibration method is specifically:
[0070] Adjust the air pressure of the cylinder to make the external load in a static equilibrium state;
[0071] Calculate the external load mass based on the air pressure value, inclination value of the cylinder in the stationary state, and the known fixed mass of the constant force device.
[0072] In one embodiment, the calculation formula of the external load mass ignores the cylinder friction force and is calibrated only by the air pressure difference between the two sides of the cylinder and the inclination angle.
[0073] In one embodiment, the method for determining the air intake direction and air pressure of the cylinder includes:
[0074] Calculate the air pressure that the cylinder needs to generate according to the target output force value, external load mass, current inclination angle, speed, and acceleration.
[0075] Compare the air pressure with a preset air pressure threshold, and select the rod chamber or the non-rod chamber as the air intake chamber of the cylinder.
[0076] Based on the selected air intake chamber type and the target air pressure, calculate the required air pressure value.
[0077] In one embodiment, the air pressure threshold is the product of the atmospheric pressure and the difference in the effective area of the cylinder piston, and is used to judge the direction of the air pressure.
[0078] Figure 3 It is a schematic structural diagram of a constant force following system for an orthopedic robot constant force device based on Kalman filtering provided by an embodiment of the present application.
[0079] For the constant force following system of the orthopedic robot constant force device based on Kalman filtering, the device includes:
[0080] A model establishment module 301, configured to establish a constant force following model of the orthopedic robot constant force device. The model is based on the structure and working principle of the constant force device and includes dynamic parameters such as position, speed, acceleration, and external load mass.
[0081] A displacement data acquisition module 302, configured to process the displacement data collected by the displacement sensor using a Kalman filter to obtain the speed and acceleration during the telescopic process of the cylinder of the constant force device in real time.
[0082] An external load mass determination module 303, configured to determine the external load mass of the constant force device through an external load mass calibration method.
[0083] A calculation module 304, configured to calculate the required air pressure value and air intake direction of the cylinder according to the target output force value and the current state of the constant force device.
[0084] A control module 305, configured to control the cylinder to act according to the air pressure value and air intake direction to achieve constant force following.
[0085] Figure 4The schematic structural diagram of the electronic device provided by the embodiment of the present application is shown.
[0086] The electronic device may include a processor 401 and a memory 402 storing computer program instructions.
[0087] Specifically, the above-mentioned processor 401 may include a central processing unit (CPU), or an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application.
[0088] The memory 402 may include a mass memory for data or instructions. By way of example and not limitation, the memory 402 may include a hard disk drive (HDD), a floppy disk drive, a flash memory, an optical disc, a magneto-optical disc, a magnetic tape, or a universal serial bus (USB) drive, or a combination of two or more of these. In a suitable case, the memory 402 may include a removable or non-removable (or fixed) medium. In a suitable case, the memory 402 may be inside or outside the electronic device. In a specific embodiment, the memory 402 may be a non-volatile solid state memory.
[0089] In one embodiment, the memory 402 may be a read only memory (ROM). In one embodiment, the ROM may be a mask-programmed ROM, a programmable ROM (PROM), an erasable PROM (EPROM), an electrically erasable PROM (EEPROM), an electrically rewritable ROM (EAROM), or a flash memory, or a combination of two or more of these.
[0090] The processor 401 reads and executes the computer program instructions stored in the memory 402 to implement any one of the constant force following methods of the orthopedic robot constant force device based on Kalman filtering in the above embodiments.
[0091] In one example, the electronic device may further include a communication interface 403 and a bus 410. Among them, as Figure 4 shown, the processor 401, the memory 402, and the communication interface 403 are connected through the bus 410 and complete communication with each other.
[0092] The communication interface 403 is mainly used to implement communication between each module, device, unit, and / or device in the embodiments of the present application.
[0093] The bus 410 includes hardware, software, or both, and couples the components of the electronic device to each other. By way of example and not limitation, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), a HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an InfiniBand interconnect, a Low Pin Count (LPC) bus, a memory bus, a MicroChannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or a combination of two or more of these. Where appropriate, the bus 410 may include one or more buses. Although the embodiments of the present application describe and illustrate specific buses, the present application contemplates any suitable bus or interconnect.
[0094] In addition, in combination with the constant force following method of the orthopedic robot constant force device based on Kalman filtering in the above embodiments, the embodiments of the present application can provide a computer-readable storage medium to implement. Computer program instructions are stored on the computer-readable storage medium; when the computer program instructions are executed by a processor, any one of the constant force following methods of the orthopedic robot constant force device based on Kalman filtering in the above embodiments is implemented.
[0095] It should be clear that the present application is not limited to the specific configurations and processes described above and illustrated in the figures. For the sake of brevity, the detailed description of known methods is omitted here. In the above embodiments, several specific steps are described and illustrated as examples. However, the method process of the present application is not limited to the specific steps described and illustrated, and those skilled in the art can make various changes, modifications, and additions, or change the order between steps after understanding the spirit of the present application.
[0096] The functional modules shown in the structural block diagrams described above can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, it can be, for example, an electronic circuit, an Application Specific Integrated Circuit (ASIC), appropriate firmware, a plug-in, a functional card, and so on. When implemented in software, the elements of the present application are programs or code segments used to perform the required tasks. The program or code segment can be stored in a machine-readable medium or transmitted via a data signal carried in a carrier wave on a transmission medium or a communication link. A "machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROMs, flash memories, Erasable ROMs (EROMs), floppy disks, CD-ROMs, optical discs, hard disks, fiber optic media, Radio Frequency (RF) links, and so on. The code segment can be downloaded via a computer network such as the Internet, an intranet, and so on.
[0097] It should also be noted that in the exemplary embodiments mentioned in this application, some methods or systems are described based on a series of steps or devices. However, this application is not limited to the order of the above steps. That is to say, the steps can be executed in the order mentioned in the embodiments, or different from the order in the embodiments, or several steps can be executed simultaneously.
[0098] As described above with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems) and computer program products according to embodiments of the present application. It should be understood that each block in the flowchart and / or block diagram, and the combination of blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device to generate a machine, such that these instructions executed by the processor of the computer or other programmable data processing device enable the implementation of the functions / actions specified in one or more blocks of the flowchart and / or block diagram. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field programmable logic circuit. It should also be understood that each block in the block diagram and / or flowchart, and the combination of blocks in the block diagram and / or flowchart, can also be implemented by dedicated hardware that performs the specified functions or actions, or can be implemented by a combination of dedicated hardware and computer instructions.
[0099] As mentioned above, the above are only the specific implementation manners of the present application. Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the above-described systems, modules, and units can refer to the corresponding processes in the foregoing method embodiments, and will not be elaborated herein. It should be understood that the protection scope of the present application is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present application can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should all be covered within the protection scope of the present application.
Claims
1. A constant force following method for an orthopedic robot constant force device based on Kalman filtering, characterized in that, Including: Establish a constant force following model for the constant force device of the orthopedic robot. The model is based on the structure and working principle of the constant force device and includes dynamic parameters such as position, velocity, acceleration, and external load mass. Use a Kalman filter to process the displacement data collected by the displacement sensor, and obtain the velocity and acceleration during the cylinder expansion and contraction process of the constant force device in real time. Determine the external load mass of the constant force device through an external load mass calibration method. Calculate the required air pressure value and intake direction of the cylinder according to the target output force value and the current state of the constant force device. Control the cylinder to act according to the air pressure value and intake direction to achieve constant force following.
2. The constant force following method of the orthopedic robot constant force device based on Kalman filtering according to claim 1, characterized in that, The establishment of the constant force following model includes the following steps: Conduct a force analysis on the constant force device, and construct a balance equation including cylinder thrust, external load gravity, friction force, and damping force. Convert the balance equation into a dynamic model with displacement, velocity, acceleration, and external load mass as variables.
3. The constant force following method of the orthopedic robot constant force device based on Kalman filtering according to claim 1, characterized in that, The application of the Kalman filter includes: Use displacement as the observation variable and velocity and acceleration as the state variables. Through the Kalman filter algorithm, perform iterative prediction and correction on the displacement data, and output the optimally estimated velocity and acceleration.
4. The constant force following method of the orthopedic robot constant force device based on Kalman filtering according to claim 1, wherein The specific external load mass calibration method is: Adjust the cylinder air pressure to make the external load in a static equilibrium state. Based on the cylinder air pressure value, inclination value, and known fixed mass of the constant force device in the static state, calculate the external load mass.
5. The constant force following method of the orthopedic robot constant force device based on Kalman filtering according to claim 4, characterized in that In the calculation formula of the external load mass, the cylinder friction force is ignored, and the calibration is only carried out through the air pressure difference between the two sides of the cylinder and the inclination angle.
6. The constant force following method of the orthopedic robot constant force device based on Kalman filtering according to claim 1, characterized in that, The method for determining the intake direction and air pressure of the cylinder includes: Calculate the air pressure that the cylinder needs to generate according to the target output force value, external load mass, current inclination angle, velocity, and acceleration. Compare the air pressure with a preset air pressure threshold, and select the rodless chamber or the rod chamber as the intake chamber of the cylinder. Based on the selected intake chamber type and the target air pressure, calculate the required air pressure value.
7. The constant force following method of the orthopedic robot constant force device based on Kalman filtering according to claim 6, characterized in that, The air pressure threshold is the product of the atmospheric pressure and the difference in the effective area of the cylinder piston, and is used to judge the direction of the air pressure.
8. A constant force following system for an orthopedic robot constant force device based on Kalman filtering, characterized in that, The device includes: A model establishment module for establishing a constant force following model for the constant force device of the orthopedic robot. The model is based on the structure and working principle of the constant force device and includes dynamic parameters such as position, velocity, acceleration, and external load mass. A displacement data acquisition module for using a Kalman filter to process the displacement data collected by the displacement sensor, and obtaining the velocity and acceleration during the cylinder expansion and contraction process of the constant force device in real time. An external load mass determination module for determining the external load mass of the constant force device through an external load mass calibration method. A calculation module for calculating the required air pressure value and intake direction of the cylinder according to the target output force value and the current state of the constant force device. A control module for controlling the cylinder to act according to the air pressure value and intake direction to achieve constant force following.
9. An electronic device, characterized in that, The electronic device includes: a processor and a memory storing computer program instructions; When the processor executes the computer program instructions, it implements the constant force following method for the constant force device of the orthopedic robot based on Kalman filtering as described in any one of claims 1-7.
10. A computer-readable storage medium, characterized in that, Computer program instructions are stored on the computer-readable storage medium, and when the computer program instructions are executed by a processor, the constant force following method of the orthopedic robot constant force device based on Kalman filtering described in any one of claims 1-7 is implemented.
Citation Information
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