A variable stiffness exoskeleton rehabilitation robot system
By monitoring the rotation angle and stiffness of the healthy elbow joint in real time, and using a variable stiffness drive system and a control system to coordinate the control of the exoskeleton joint, the problem that the exoskeleton system in the prior art cannot sense the stiffness of the healthy elbow joint is solved, and lightweight design and efficient rehabilitation training effect are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HANGZHOU INNOVATION RES INST OF BEIJING UNIV OF AERONAUTICS & ASTRONAUTICS
- Filing Date
- 2023-11-02
- Publication Date
- 2026-04-17
AI Technical Summary
Existing exoskeleton rehabilitation robot systems that can be used for elbow joint mirror therapy in hemiplegic patients cannot sense changes in the stiffness of the healthy elbow joint in real time, resulting in poor rehabilitation training effects. In addition, their large size and weight affect portability and wearing experience.
The rotation angle and stiffness of the healthy elbow joint are monitored in real time using electromyography (EMG) sensors and inertial measurement sensors. The position and stiffness of the exoskeleton joint are controlled in coordination by a variable stiffness drive system and a control system, and lightweight design is achieved by using ropes to transmit force.
It enables assisted movement of the affected elbow joint, improves the scientific nature and portability of rehabilitation training, reduces the weight and manufacturing cost of the exoskeleton, and enhances the wearing experience.
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Figure CN117338567B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a robotic system, and more specifically to a variable stiffness exoskeleton rehabilitation robot system. Background Technology
[0002] Mirror therapy is a type of representational training primarily used for upper limb motor function rehabilitation after stroke. It utilizes somatic sensory input in addition to visual stimulation to assist in motor function recovery, and has shown good clinical efficacy in hemiplegic patients. In mirror therapy, patients perform bilateral symmetrical motor training independently or with assistance. Mirror visual feedback can facilitate some neural motor pathways on the affected side, promoting the recovery of limb motor function.
[0003] Exoskeleton rehabilitation robots are a product of the combination of robotics technology and rehabilitation medicine. They can replace rehabilitation therapists to assist patients in exercise training, reducing labor costs. At the same time, exoskeleton rehabilitation robots can provide feedback on patients' exercise training information for rehabilitation monitoring and evaluation, improving the scientific nature and standardization of training.
[0004] In robot-assisted bilateral symmetrical movement training, exoskeleton robots help the affected upper limb mimic the movement of the healthy side, with both limbs simultaneously completing the target task. To achieve natural coordination of bilateral limb movements, the robot system needs to be able to sense the rotation angle and stiffness of the healthy side joint in real time, and use this as guidance to complete the coordinated control of the exoskeleton's position and stiffness. Existing exoskeleton rehabilitation robot systems that can be used for elbow joint mirror therapy in hemiplegic patients generally cannot sense changes in the stiffness of the healthy side joint and achieve variable stiffness control, resulting in the need for further improvement in rehabilitation training effects. Existing variable stiffness robot systems are large in size and weight, leading to problems such as poor portability and wearing experience, as disclosed in the invention patent with patent number 202111436452.0, entitled "A Variable Stiffness Drive System for Robotic Joints". Summary of the Invention
[0005] To address the shortcomings of existing technologies, the present invention aims to provide a variable stiffness exoskeleton rehabilitation robot system for elbow joint mirror therapy in hemiplegic patients. This system can sense the rotation angle and stiffness of the healthy elbow joint in real time, and reproduce the movement of the healthy elbow joint through coordinated control of motion and stiffness, thereby assisting the affected elbow joint and completing symmetrical motion training of both elbow joints in mirror therapy.
[0006] To achieve the above objectives, the present invention provides the following technical solution: a variable stiffness exoskeleton rehabilitation robot system, characterized in that it comprises:
[0007] The electromyography (EMG) sensor is attached to the biceps and triceps muscles on the patient's unaffected side to collect EMG signals from the unaffected upper limb.
[0008] Two inertial measurement sensors are strapped to the upper arm and forearm of the unaffected upper limb, respectively, to measure the rotation angle of the elbow joint.
[0009] An exoskeleton joint, which is worn on the affected upper limb by a strap, is used to drive the movement of the affected elbow joint through the rotation of the exoskeleton joint.
[0010] The control system is connected to an electromyography sensor and two inertial measurement sensors to output control signals based on the estimated stiffness of the upper limb elbow joint and the rotation angle of the elbow joint.
[0011] The variable stiffness drive system is connected to the control system and also to the exoskeleton joint via ropes and Bowden tubes to receive control signals output by the control system and generate driving force through the control signals. The driving force is remotely transmitted to the exoskeleton joint via ropes and Bowden tubes.
[0012] As a further improvement of the present invention, the variable stiffness drive system includes:
[0013] Two motors are connected to the control system and rotate after receiving control signals.
[0014] Two variable stiffness mechanisms are provided. Each variable stiffness mechanism consists of a spring, a variable stiffness rope, an input flange, an output flange, a worm gear, a worm, a winding reel and a winding reel pulley, and several pulleys. The input flange is connected to the motor shaft. The rope is wound around the winding reel, which is connected to the output flange. The worm gear and several pulleys are rotatably mounted on the input and output flanges. One end of the spring is fixed to the output flange, and the other end is connected to the variable stiffness rope. The winding reel pulley is coaxially fixed to the worm gear. The end of the variable stiffness rope facing away from the spring passes around each pulley and is fixed to the winding reel pulley. The worm is rotatably mounted on the output flange near the worm gear and meshes with the worm gear.
[0015] As a further improvement of the present invention, the control signal includes the rotation angle of the motor, which is calculated by the following formula:
[0016]
[0017]
[0018] In the formula, θ motor,1 and θ motor,2 Let θ be the rotation angle of the motor in the two variable stiffness mechanisms. exo r represents the rotation angle of the exoskeleton joint. exo For the transmission ratio, ζ1 and ζ2 are equation coefficients, and K... exoThis refers to the joint stiffness of the exoskeleton. As a further improvement of the present invention, the formula for calculating the motor rotation angle is derived through the following steps: Step one, by changing the rope preload in the variable stiffness mechanism, the variable stiffness mechanism can exhibit a quadratic torque-deflection relationship:
[0019]
[0020] Where, τ vsm It is the output torque of the variable stiffness mechanism, θ vsm It is the variable stiffness joint deflection, and ζ1 and ζ2 are equation coefficients;
[0021] Step two, calculate the relationship between the torque applied by each unit in the variable stiffness drive system and the joint torque of the exoskeleton:
[0022] τ exo =r exo (τ vsm,1 (θ vsm,1 )-τ vsm,2 (θ vsm,2 (2)
[0023] Where, τ exo For the joint torque of the exoskeleton, r exo The transmission ratio;
[0024] Step 3: Calculate the relationship between the deflection of the variable stiffness mechanism in the two units and the rotation angle of the motor and the joint angle of the exoskeleton:
[0025] θ vsm,1 =r exo θ exo +θ motor,1
[0026] θ vsm,2 =-r exo θ exo -θ motor,2 (3)
[0027] Where, θ exo θ represents the rotation angle of the exoskeleton joint. motor,1 and θ motor,2 The rotation angle of the motor in the two units;
[0028] When the exoskeleton is not subjected to external forces, θ vsm,1 and θ vsm,2 The value is 0, meaning the exoskeleton joint angle is only related to the motor's rotation angle, and its expression is:
[0029]
[0030] Step four: Substitute formulas (1) and (3) into formula (2) and differentiate formula (2) to obtain the expression for the joint stiffness of the exoskeleton:
[0031]
[0032] Step 5, according to formulas (4) and (5), the motor rotation angle can be written as an expression for the rotation angle and stiffness of the exoskeleton joint:
[0033]
[0034]
[0035] The formula for calculating the motor rotation angle is obtained.
[0036] As a further improvement of the present invention, the estimation result of the upper limb elbow joint stiffness is calculated by the following formula:
[0037] K hum =D1K STMI +D0
[0038] In the formula, K hum For elbow joint stiffness, K STMI Let D1 be the elbow joint torque, and D0 be the function coefficients.
[0039] As a further improvement of the present invention, the elbow joint stiffness calculation formula is obtained through the following steps:
[0040] Step 1: Filter the raw electromyography (EMG) signals acquired by the sensor using a low-pass filter with a cutoff frequency of 950Hz, a high-pass filter with a cutoff frequency of 750Hz, and a full-wave rectifier. Then, perform linear normalization on the filtered EMG signals.
[0041]
[0042] Where V(t) is the filtered electromyographic signal, and max(|V(t)|) represents the maximum absolute electromyographic signal value.
[0043] Obtain muscle activity:
[0044]
[0045] Where A represents the nonlinear factor;
[0046] Step 2, obtain muscle strength based on muscle activity:
[0047] F m =f CE (l)a m (t)F m.max +fPE (l)F m.max (9)
[0048] In equation (9),
[0049]
[0050] f PE (l)=e 10l-15 (11)
[0051] F represents the force-length relationship between active contractile elements and passive elastic elements in a muscle. m.max The maximum muscle strength is represented by l; in equations (9)-(11), l represents the standardized muscle length, which is a function of the elbow joint rotation angle:
[0052]
[0053] Where C0, C1, and C2 represent the function coefficients, θ hum Indicates the elbow joint angle, l m,0 This indicates the length of the muscle at maximum muscle strength.
[0054] Step 3: Based on muscle strength, the torque contributed by a single muscle to the elbow joint can be obtained:
[0055] τ i =F m,i r i (13)
[0056] Where, r i Indicates the length of the lever arm;
[0057] Step 4, obtain the torque contribution of all relevant muscles to the elbow joint:
[0058]
[0059] Where ag represents the agonist muscle and an represents the antagonist muscle;
[0060] Step 5, obtain the mapping factor between elbow joint torque and stiffness as follows:
[0061]
[0062] Step 6, the final elbow joint stiffness is expressed as:
[0063] Khum=D1KSTMI+D0 (16)
[0064] The formula for calculating elbow joint stiffness is obtained.
[0065] The beneficial effects of this invention are:
[0066] 1. The exoskeleton rehabilitation robot in this invention is driven by a variable stiffness drive system. By controlling the rotational position of the two drive motors in the system, the position and stiffness of the exoskeleton joints can be controlled simultaneously.
[0067] 2. The exoskeleton rehabilitation robot in this invention uses ropes to transmit force, which makes the variable stiffness drive system flexible in its arrangement and can be installed far away from the exoskeleton body, thus achieving a lightweight and compact design of the exoskeleton.
[0068] 3. In this invention, no sensors are installed on the exoskeleton body, which reduces the weight and manufacturing cost of the exoskeleton.
[0069] 4. The exoskeleton rehabilitation robot of the present invention has a self-feedback function for joint rotation angle and torque. Without installing any sensors on the exoskeleton body, according to formulas (2) and (3), the joint rotation angle and torque of the exoskeleton are obtained by measuring the deflection of the variable stiffness mechanism and the motor rotation angle in the variable stiffness drive system.
[0070] 5. The exoskeleton rehabilitation robot system of the present invention can measure the rotation angle and stiffness of the patient's healthy elbow joint in real time, and the exoskeleton rehabilitation robot can simulate the rotation angle and stiffness of the healthy elbow joint in real time, providing assistance to the patient's affected elbow joint and realizing robot-assisted mirror therapy. Attached Figure Description
[0071] Figure 1 This is an overall schematic diagram of the variable stiffness exoskeleton rehabilitation robot system of the present invention;
[0072] Figure 2 This is a schematic diagram of the structure of a variable stiffness drive system;
[0073] Figure 3 This is a control block diagram. Detailed Implementation
[0074] The present invention will be further described in detail below with reference to the embodiments shown in the accompanying drawings. The system of this embodiment is mainly applied to the elbow joint mirror therapy for hemiplegic patients. Therefore, the technical term "affected side" in the following description refers to the non-healthy side of the patient's arm, and "healthy side" refers to the healthy side of the patient's arm.
[0075] Reference Figures 1 to 3 As shown, a variable stiffness exoskeleton rehabilitation robot system according to this embodiment mainly includes a mechanical execution part and a control calculation part, wherein the mechanical execution part includes:
[0076] The electromyography (EMG) sensor is attached to the biceps and triceps muscles on the patient's unaffected side to collect EMG signals from the unaffected upper limb. The EMG sensor used is a Trigno™ wireless acquisition device.
[0077] Two inertial measurement sensors are strapped to the upper arm and forearm of the unaffected upper limb, respectively, to measure the rotation angle of the elbow joint. The inertial measurement sensors are XSENS-Dot acquisition devices.
[0078] An exoskeleton joint, which is worn on the affected upper limb by a strap, is used to drive the movement of the affected elbow joint through the rotation of the exoskeleton joint.
[0079] The control system is connected to an electromyography sensor and two inertial measurement sensors to output control signals based on the estimated stiffness of the upper limb elbow joint and the rotation angle of the elbow joint.
[0080] A variable stiffness drive system is connected to a control system and also to the exoskeleton joint via ropes and Bowden tubes. This system receives control signals from the control system and generates driving force based on these signals. The driving force is then remotely transmitted to the exoskeleton joint via the ropes and Bowden tubes. By employing the aforementioned mechanical actuators, the exoskeleton joint can be worn on the affected upper limb via straps, increasing the system's portability and wearing experience. Specifically, the variable stiffness drive system in this embodiment is similar to existing technologies, with the following general structure:
[0081] Two motors are connected to the control system and rotate after receiving control signals.
[0082] Two variable stiffness mechanisms are provided. Each variable stiffness mechanism consists of a spring, a variable stiffness rope, an input flange, an output flange, a worm gear, a worm, a winding reel and a winding reel pulley, and several pulleys. The input flange is connected to the motor shaft. The rope is wound around the winding reel, which is connected to the output flange. The worm gear and several pulleys are rotatably mounted on the input and output flanges. One end of the spring is fixed to the output flange, and the other end is connected to the variable stiffness rope. The winding reel pulley is coaxially fixed to the worm gear. The end of the variable stiffness rope facing away from the spring passes around each pulley and is fixed to the winding reel pulley. The worm is rotatably mounted on the output flange near the worm gear and meshes with the worm gear. Therefore, the mechanical operating principle and process of the variable stiffness drive system will not be described in detail in this embodiment.
[0083] The control calculation section is as follows:
[0084] Current variable stiffness drive systems consist of a pair of structurally identical and independent system units. Each unit mainly comprises a variable stiffness mechanism, a motor, an absolute encoder, a reel, and a transmission wire rope. The variable stiffness mechanism is an elastic mechanism, primarily composed of a spring, rope, pulley, input and output flanges, and a rope pretensioning device consisting of a worm gear and a reel. By changing the rope pretension in the variable stiffness mechanism, the mechanism can exhibit a quadratic torque-deflection relationship:
[0085]
[0086] Where, τ vsm It is the output torque of the variable stiffness mechanism, θ vsm It is the variable stiffness joint deflection, and ζ1 and ζ2 are equation coefficients.
[0087] The variable stiffness drive system works similarly to the human musculoskeletal system, achieving simultaneous control of the rotation angle and stiffness of the exoskeleton joints through the antagonistic action of two units.
[0088] The relationship between the torque applied by each unit in the variable stiffness drive system and the joint torque of the exoskeleton is as follows:
[0089] τ exo =r exo (τ vsm,1 (θ vsm,1 )-τ vsm,2 (θ vsm,2 (2)
[0090] Where, τ exo For the joint torque of the exoskeleton, r exo This is the transmission ratio.
[0091] The relationship between the deflection of the variable stiffness mechanism in the two units and the rotation angle of the motor and the joint angle of the exoskeleton is as follows:
[0092] θ vsm,1 =r exo θ exo +θ motor,1
[0093] θ vsm,2 =-r exo θ exo -θ motor,2 (3)
[0094] Where, θ exo θ represents the rotation angle of the exoskeleton joint. motor,1 and θ motor,2 The angle of rotation of the motor in the two units.
[0095] When the exoskeleton is not subjected to external forces, θ vsm,1 and θ vsm,2 The value is 0, meaning the exoskeleton joint angle is only related to the motor's rotation angle, and its expression is:
[0096]
[0097] Substituting equations (1) and (3) into equation (2), and differentiating equation (2), we obtain the expression for the joint stiffness of the exoskeleton:
[0098]
[0099] According to formulas (4) and (5), the rotation angle of the motor can be expressed as the relationship between the rotation angle and stiffness of the exoskeleton joint:
[0100]
[0101]
[0102] According to formula (6), the angle and stiffness of the exoskeleton joints can be controlled by adjusting the rotation angles of the two motors. The specific control block diagram of the robot system is shown below. Figure 3 As shown.
[0103] The exoskeleton is controlled by a two-level control system. The lower-level control uses a pair of cascade controllers to perform closed-loop position control of the motors. The cascade controllers consist of a proportional (P) algorithm and a proportional-integral (PI) algorithm to achieve high-precision and fast-response position control of the motors. The system runs at a frequency of 250Hz on an industrial computer. The upper-level control is used to determine the joint angles of the two motors. After processing the signals collected by the inertial navigation sensor and the electromyography sensor, the angle and stiffness information of the patient's healthy elbow joint are obtained, and the joint angles of the two motors in the robot system are calculated according to formula (6).
[0104] The method for estimating the stiffness of the healthy elbow joint using electromyography (EMG) sensors is as follows:
[0105] The raw electromyography (EMG) signals acquired by the sensor were filtered using a low-pass filter with a cutoff frequency of 950 Hz, a high-pass filter with a cutoff frequency of 750 Hz, and a full-wave rectifier. The filtered EMG signals were then linearly normalized.
[0106]
[0107] Where V(t) is the filtered electromyographic signal, and max(|V(t)|) represents the maximum absolute electromyographic signal value.
[0108] Obtain muscle activity:
[0109]
[0110] Where A represents the nonlinear factor.
[0111] Muscle strength is determined by muscle activity level.
[0112] F m =f CE (l)a m (t)F m.max +f PE (l)F m.max (9)
[0113] In equation (9),
[0114]
[0115] f PE (l)=e 10l-15 (11)
[0116] F represents the force-length relationship between active contractile elements and passive elastic elements in a muscle. m.max This represents the maximum muscle strength. In equations (9)-(11), l represents the standardized muscle length, which is a function of the elbow joint rotation angle:
[0117]
[0118] Where C0, C1, and C2 represent the function coefficients, θ hum Indicates the elbow joint angle, l m,0 This indicates the length of the muscle at maximum muscle strength.
[0119] The torque contributed by a single muscle to the elbow joint can be obtained based on muscle strength:
[0120] τ i =F m,i r i (13)
[0121] Where, r i This indicates the length of the lever arm.
[0122] The torque contributions of all relevant muscles to the elbow joint are as follows:
[0123]
[0124] In this context, ag represents the agonist muscle and an represents the antagonist muscle.
[0125] The mapping factor between elbow joint torque and stiffness is:
[0126]
[0127] Elbow joint stiffness is expressed as:
[0128] K hum =D1K STMI +D0 (16)
[0129] In summary, the variable stiffness exoskeleton rehabilitation robot system of this embodiment uses ropes to transmit force, which makes the variable stiffness drive system flexible in its arrangement and can be installed away from the exoskeleton body, achieving a lightweight and compact design of the exoskeleton. It can also measure the rotation angle and stiffness of the patient's healthy elbow joint in real time, and the exoskeleton rehabilitation robot can simulate the rotation angle and stiffness of the healthy elbow joint in real time, providing assistance to the patient's affected elbow joint and realizing robot-assisted mirror therapy.
[0130] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.
Claims
1. A variable stiffness exoskeleton rehabilitation robot system, characterized in that: include: The electromyography (EMG) sensor is attached to the biceps and triceps muscles on the patient's unaffected side to collect EMG signals from the unaffected upper limb. Two inertial measurement sensors are strapped to the upper arm and forearm of the unaffected upper limb, respectively, to measure the rotation angle of the elbow joint. An exoskeleton joint, which is worn on the affected upper limb by a strap, is used to drive the movement of the affected elbow joint through the rotation of the exoskeleton joint. The control system is connected to an electromyography sensor and two inertial measurement sensors to output control signals based on the estimated stiffness of the upper limb elbow joint and the rotation angle of the elbow joint. A variable stiffness drive system is connected to the control system and also to the exoskeleton joint via ropes and Bowden tubes to receive control signals output by the control system and generate driving force through the control signals. The driving force is remotely transmitted to the exoskeleton joint via ropes and Bowden tubes. The variable stiffness drive system includes: Two motors are connected to the control system and rotate after receiving control signals. Two variable stiffness mechanisms are provided, each consisting of a spring, a variable stiffness rope, an input flange, an output flange, a worm gear, a worm, a winding reel and a winding reel pulley, and several pulleys. The input flange is connected to the motor shaft. The rope is wound around the winding reel, which is connected to the output flange. The worm gear and several pulleys are rotatably mounted on the input and output flanges. One end of the spring is fixed to the output flange, and the other end is connected to the variable stiffness rope. The winding reel pulley is coaxially fixed to the worm gear. The end of the variable stiffness rope facing away from the spring passes around each pulley and is fixed to the winding reel pulley. The worm is rotatably mounted on the output flange near the worm gear and meshes with the worm gear. The control signal includes the motor's rotation angle, which is calculated using the following formula: In the formula, and Let be the rotation angle of the motor in the two variable stiffness mechanisms. This refers to the rotation angle of the exoskeleton joint. The transmission ratio is... and These are the equation coefficients. This refers to the joint stiffness of the exoskeleton.
2. The variable stiffness exoskeleton rehabilitation robot system according to claim 1, characterized in that: The formula for calculating the motor rotation angle is derived through the following steps: Step 1: By changing the preload of the variable stiffness rope, the variable stiffness mechanism can exhibit a quadratic torque-deflection relationship: (1) in, It is the output torque of the variable stiffness mechanism. It is the deflection of a variable stiffness joint. and These are the equation coefficients; Step two, calculate the relationship between the torque applied by each unit in the variable stiffness drive system and the joint torque of the exoskeleton: (2) in, For exoskeleton joint torque, The transmission ratio; Step 3: Calculate the relationship between the deflection of the variable stiffness mechanism in the two units and the rotation angle of the motor and the joint angle of the exoskeleton: (3) in, This refers to the rotation angle of the exoskeleton joint. and The rotation angle of the motor in the two units; When the exoskeleton is not subjected to external forces and The value is 0, meaning the exoskeleton joint angle is only related to the motor's rotation angle, and its expression is: (4) Step four: Substitute formulas (1) and (3) into formula (2) and differentiate formula (2) to obtain the expression for the joint stiffness of the exoskeleton: (5) Step 5, according to formulas (4) and (5), the motor rotation angle can be written as an expression for the rotation angle and stiffness of the exoskeleton joint: (6) The formula for calculating the motor rotation angle is obtained.
3. The variable stiffness exoskeleton rehabilitation robot system according to claim 2, characterized in that: The estimated result of the upper limb elbow joint stiffness is calculated using the following formula: In the formula, For elbow joint stiffness For elbow joint torque, and These are the function coefficients.
4. The variable stiffness exoskeleton rehabilitation robot system according to claim 3, characterized in that: The formula for calculating elbow joint stiffness is derived through the following steps: Step 1: Filter the raw electromyography (EMG) signals acquired by the sensor using a low-pass filter with a cutoff frequency of 950Hz, a high-pass filter with a cutoff frequency of 750Hz, and a full-wave rectifier. Then, perform linear normalization on the filtered EMG signals. (7) in, This is the filtered electromyography signal. Indicates the maximum absolute electromyographic signal value; Obtain muscle activity: (8) Where A represents the nonlinear factor; Step 2, obtain muscle strength based on muscle activity: (9) In equation (9), (10) (11) and These represent the force-length relationships between active contractile elements and passive elastic elements in a muscle, respectively. Indicates the maximum muscle strength; In equations (9)-(11), l represents the standardized muscle length, which is a function of the elbow joint rotation angle: (12) in, , and Represents the coefficients of the function. Indicates the elbow joint angle. This indicates the length of the muscle at maximum muscle strength. Step 3: Based on muscle strength, the torque contributed by a single muscle to the elbow joint can be obtained: (13) in, Indicates the length of the lever arm; Step 4, obtain the torque contribution of all relevant muscles to the elbow joint: (14) Where ag represents the agonist muscle and an represents the antagonist muscle; Step 5: Obtain the mapping factor between elbow joint torque and stiffness. for: (15) Step 6, the final elbow joint stiffness is expressed as: (16) The formula for calculating elbow joint stiffness is obtained.
Citation Information
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