A force-feedback-based robotic teleoperation guidance method

Abstract

The application discloses a kind of robot teleoperation guiding methods based on force feedback, including two parts of buffer-based force feedback obstacle avoidance position guidance and spherical guiding force field force feedback auxiliary grabbing, wherein buffer-based force feedback obstacle avoidance position guidance is based on the establishment of obstacle avoidance buffer based on obstacle bounding box, then whether the collision of mechanical arm and obstacle buffer zone occurs is judged, if collision occurs, force feedback is calculated according to the position of mechanical arm in buffer zone;With better obstacle avoidance effect.Spherical guiding force field force feedback auxiliary grabbing is to construct spherical guiding force field and spring-mass model, then the feedback force of spherical guiding force field is calculated based on spring-mass model, to assist operator to control the position of mechanical arm end within the outer layer between spherical guiding force field, reduce the attention of operator to the position of mechanical arm, so as to adjust the attitude of mechanical arm can efficiently complete clamping operation, realize the effect of reducing burden, reducing misoperation, improving teleoperation grabbing work efficiency.

Description

Technical Field

[0001] This invention relates to robot motion control methods, specifically to a robot teleoperation guidance method based on force feedback. Background Technology

[0002] Grasping is one of the main tasks of robots, and teleoperating robots for grasping enables them to possess human-like flexibility. However, insufficient presence during teleoperation can lead to low grasping efficiency and even errors. Therefore, guidance during teleoperation is essential. CN117984322A discloses a force-guided teleoperation system and control method based on a dual-arm cooperative potential field. This method uses two robotic arms and a force feedback hand controller to construct a reaction force and a target point attraction through a virtual potential field. However, after reaching the target point, it can only guide a single position and posture. The operator cannot adjust the position and posture of the robotic arms according to the actual working area, affecting grasping efficiency and user experience. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a force feedback-based robot teleoperation guidance method with high grasping efficiency and a good user experience.

[0004] Technical solution: The present invention provides a force feedback-based method for remotely controlling and guiding a robot, comprising:

[0005] The remotely operated robotic arm moves toward the target point. When the distance between the end point of the robotic arm and the target point is less than or equal to a set value, a spherical guiding force field including an inner layer, a middle layer and an outer layer is established with the target point as the center. The length s of the gripper installed at the end of the robotic arm is determined as the outer radius.

[0006] A spring-particle model is established in a spherical guiding force field to separate the middle layer from the inner and outer layers;

[0007] Based on the spherical guiding force field and the spring-mass model, the teleoperated robotic arm approaches the inner or outer layer. When it comes into contact with the spring-mass model, it deforms and generates force feedback, thus restricting the end point of the robotic arm to be between the inner and outer layers.

[0008] Once the target object is grasped, the guidance can be turned off to leave the spherical guiding force field. If the target object is not grasped but it is still desired to leave the spherical guiding force field, the teleoperated robotic arm will gradually enter the spherical guiding force field after moving away from the target object. The deformation of the spring-mass model will gradually increase, and the feedback force will gradually increase. When the feedback force increases to its maximum value, if the teleoperated robotic arm continues to move outward, the spring-mass model will break, the robotic arm will leave the spherical guiding force field, and the grasping guidance will stop.

[0009] Furthermore, the spherical guiding force field is calculated using a spring-mass model, and the force feedback calculation formula is as follows:

[0010] By analyzing the dynamic equations of the spring-particle model, the moving particle satisfies:

[0011]

[0012] In this system equation, M is the mass of the particle, X is the spatial coordinate of the particle, t is the time constant, D is the damping coefficient, K is the spring constant, and f is the feedback force.

[0013] The solution to the system equations is transformed into solving discrete particle differential equations to obtain an approximate solution; if the equations have a unique solution, then... If it is a unit of time, then within any time range Within this framework, using the time difference method and the incremental method, the equation can be transformed into the following for each discrete particle:

[0014]

[0015] Where, m i Let X be the mass of the i-th particle. i Let i be the coordinates of the i-th particle.

[0016] Substituting into the differential equation, we get:

[0017]

[0018] when When it approaches infinity, use replace use replace have:

[0019]

[0020] Solving the equation yields the displacement of the particle and the magnitude of the feedback force.

[0021] Furthermore, the set value is 1.5s.

[0022] Furthermore, ss′=s / 10, where s′ is the inner radius.

[0023] Furthermore, existing robotic arm teleoperation guidance methods, such as CN114643576A, do not consider obstacle avoidance and cannot accurately guide the operator away from obstacles to avoid collisions. Another example is CN105150210B, which, although it considers obstacle avoidance, only considers the end point of the robotic arm and does not consider obstacle avoidance for the joints of the robotic arm. During teleoperation, the joints of the robotic arm may collide with obstacles.

[0024] Therefore, the teleoperated robotic arm moves toward the target grasping point, including:

[0025] Get the target point X target and obstacle position X obstacle Based on the forward kinematics expression of the robotic arm and the joint angles of the robotic arm, the position X of the end effector of the robotic arm is calculated. EE ;

[0026] The bounding box of the obstacle is calculated, and an obstacle avoidance buffer is established by proportionally scaling up the bounding box. The range of the obstacle avoidance buffer is based on the geometric center C of the bounding box and the detection space range R. B Sure;

[0027] During the movement of the robotic arm, joint sensors are used to collect the angles of each joint. The position of the end effector is obtained through forward spectroscopy. Real-time collision detection is performed based on the coordinates of the end effector and the position of the buffer zone to determine whether the robotic arm has collided with the obstacle buffer zone. If a collision occurs, force feedback is calculated based on the position of the robotic arm in the buffer zone.

[0028] L represents the shortest distance between the end point of the robotic arm and the obstacle after a collision is detected. r arm Let r be the distance from the obstacle to the bounding box in the L direction, and r be the length of the buffer zone in the L direction.

[0029] When the robotic arm is outside the buffer zone, i.e., L > r arm When +r, the feedback force is zero; when the robotic arm is within the buffer zone, i.e., r arm <L<r arm When the radius is +r, the feedback force f increases with the distance penetrated into the buffer zone; when the robotic arm collides with the obstacle enclosure, i.e., 0 < L < r arm When +r is applied, the feedback force f is at its maximum, and the robotic arm stops moving.

[0030] Force feedback is performed based on the calculated force feedback values.

[0031] This invention uses a buffer-based force feedback obstacle avoidance method to assist the operator in moving to the target location, which can greatly improve the safety of teleoperation. Compared with other teleoperation obstacle avoidance methods, it has better accuracy and better environmental adaptability, and can achieve smooth obstacle avoidance during teleoperation without any jumps that affect the safety of teleoperation.

[0032] Furthermore, the detection spatial range R B The expression is as follows:

[0033]

[0034] Where C is the geometric center of the OBB bounding box; These are mutually perpendicular spatial vectors, serving as the direction vectors of the local coordinate system of the enclosed geometric object; r1, r2, and r3 are the side lengths of the bounding box.

[0035] Furthermore, the obstacle avoidance buffer zone has a range of 1.2R. B ~1.5R B .

[0036] Furthermore, the calculation model for the feedback force f is as follows:

[0037]

[0038] Where K is the proportionality coefficient.

[0039] Furthermore, the formula for calculating the proportionality coefficient K is as follows:

[0040]

[0041] Among them, f max This represents the maximum feedback force.

[0042] Furthermore, if the robotic arm collides with more than one obstacle during movement, the feedback force f is the sum of the feedback forces from each obstacle:

[0043]

[0044] Where n represents the number of obstacles, f i This represents the feedback force of the i-th obstacle;

[0045] The direction of the feedback force is defined as the direction of the shortest distance between the obstacle and the end effector of the robotic arm; the shortest distance between the obstacle center O and the robotic arm AB is L, that is, the point C from the obstacle enclosure center O to the central axis of the robotic arm end effector enclosure lies on line segment AB, and the direction of the feedback force f is...

[0046] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: After the teleoperated robotic arm moves to the target location, the invention uses a spherical guide area combined with a spring-mass model for force-guided grasping, assisting the operator in position control. This ensures the robotic arm is at a suitable grasping distance, reducing the operator's focus on the robotic arm's position during grasping and allowing them to concentrate more on posture control. Adjusting the robotic arm's posture is sufficient to efficiently complete the grasping task. This invention reduces the operator's workload, minimizes errors, and greatly improves the efficiency of teleoperated grasping operations. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of a remote operation control system;

[0048] Figure 2 This is a diagram of a robotic arm remotely operated grasping model;

[0049] Figure 3 This is a flowchart of force feedback obstacle avoidance position guidance;

[0050] Figure 4 This is a schematic diagram of the construction of bounding boxes and buffers;

[0051] Figure 5 This is a schematic diagram of virtual obstacle avoidance feedback force;

[0052] Figure 6 This is a schematic diagram of the construction of a spherical guiding force field;

[0053] Figure 7 This is a schematic diagram of the spring-mass algorithm;

[0054] Figure 8 This is a schematic diagram of the force feedback of the spherical guiding force field;

[0055] Figure 9 This is a diagram showing the relationship between the feedback force of the spherical guiding force field and the position of the robotic arm;

[0056] Figure 10 This is a flowchart of the force-guided crawling process. Detailed Implementation

[0057] The invention will now be further described with reference to the accompanying drawings.

[0058] This invention provides a robot teleoperation guidance method based on force feedback. Figure 1 The remote operation control system shown mainly includes a host computer 2 (control computer), a force feedback master hand 3 (six-dimensional tactile input and output device), and a robot 5 (six-joint collaborative robotic arm). The robotic arm is equipped with a gripper 4 at its end. Figure 1 In the diagram, 1 represents the operator, and 6 represents the object to be grasped and any obstacles.

[0059] The force feedback master hand is used to control the movement of the robotic arm. It communicates with the host computer to control the robotic arm's movement and grasping, and also provides force feedback to the operator to guide their actions. The host computer receives signals from the force feedback master hand, calculates and controls the robotic arm's movement, and also runs the virtual environment.

[0060] The force feedback remote control operation procedure is as follows:

[0061] Based on the collected 3D model information (which can be acquired in real-time by a vision sensor or predefined), a model of the surrounding environment is built in the host computer, and a virtual robotic arm model is added. A DH coordinate system is established based on the physical data of the robotic arm and the force feedback master hand. The forward and inverse kinematic expressions for the force feedback master hand and the robotic arm are calculated according to the DH table. The joint angles of the robotic arm are collected, and the angles of the virtual robotic arm model are adjusted in virtual space according to these joint angles to synchronize the virtual robotic arm model with the real robotic arm. The joint angles of the force feedback master hand are collected, and the forward kinematics solution is used to obtain the end-effector pose of the force feedback master hand. This pose is then magnified to the target pose of the robotic arm's end-effector, and commands are sent to the robotic arm to control its movement.

[0062] Figure 2 To obtain the position and orientation of the object to be grasped by the teleoperated robotic arm, the model diagram is generated and converted into coordinates in virtual space. This allows the determination of the target point X to be grasped by the teleoperated robotic arm. target And simultaneously obtain the obstacle position X obstacle Since the forward kinematics expression for the robotic arm and the joint angles are known, the position X of the robotic arm's end effector can be calculated. EE .

[0063] The robot teleoperation guidance method includes two parts: buffer-based force feedback obstacle avoidance position guidance and spherical guiding force field force feedback assisted grasping.

[0064] (I) Force feedback obstacle avoidance position guidance based on buffer zone

[0065] Figure 3 The flowchart illustrates the force feedback obstacle avoidance positioning guidance process. For the virtual robotic arm model, a bounding box is constructed to simplify the model's complexity and improve collision detection efficiency. During teleoperation, the robotic arm must not collide with obstacles. To generate obstacle avoidance force feedback for guidance, a buffer zone is set around the obstacle. This buffer zone is constructed by proportionally scaling up the bounding box of the obstacle.

[0066] During the movement of the robotic arm, the angles of each joint of the robotic arm are collected using the joint sensors of the robotic arm. The position of the end point of the robotic arm is obtained through forward homing. Real-time collision detection is performed based on the coordinates of the end point of the robotic arm and the position of the buffer zone to determine whether the robotic arm has collided with the obstacle buffer zone.

[0067] When the robotic arm's end effector or joint collides with an obstacle buffer zone, virtual force feedback is generated to help the operator avoid the obstacle. When a robotic arm joint collides with the buffer zone, the joint moves to avoid hitting the obstacle. If the robotic arm's end effector or joint collides with the obstacle bounding box, it means the robotic arm is about to collide with a real obstacle, requiring an emergency stop to ensure safety. Throughout this process, because the collision detection target is always the obstacle bounding box, it does not come into contact with the real obstacle, thus achieving better obstacle avoidance. Specifically:

[0068] Figure 4 (a) is a schematic diagram of obstacle avoidance during the remote operation of the robotic arm. Figure 4 (b) is a schematic diagram of the bounding box and buffer zone construction for obstacles. An OBB bounding box is the smallest hexahedron that encloses a geometric model object and whose faces are parallel to the enclosed geometric model object. The geometric center C of the bounding box and the detection space range R are determined. B Detection space range R B The expression is as follows:

[0069]

[0070] In the formula, C is the geometric center of the OBB bounding box; These are mutually perpendicular spatial vectors, serving as the direction vectors of the local coordinate system of the enclosed geometric object; r1, r2, and r3 are the side lengths of the bounding box.

[0071] The OBB bounding box has arbitrary orientation, closely fits the model, and has good collision detection accuracy. The buffer is a proportionally enlarged version of the bounding box, with its geometric center coinciding with the spatial vector. Its side length is a multiple of the bounding box's side length, typically set to 1.2 to 1.5 times, meaning the geometric center C is the same, and the detection range is 1.2R. B ~1.5R B For example, using 1.2 times:

[0072]

[0073] Figure 5 This is a schematic diagram of virtual obstacle avoidance feedback force. When a collision is detected in the obstacle buffer zone, a virtual collision force calculation model is used to calculate the magnitude and direction of the feedback force based on the distance of the collision overlap.

[0074] Since the force feedback device has an upper limit on the feedback force, let's assume the upper limit force is f. max When the robotic arm is outside the buffer zone, i.e., L > r arm When +r, the feedback force is zero; when the robotic arm is within the buffer zone, i.e., r arm <L<r arm When the radius is +r, the feedback force f increases with the distance penetrated into the buffer zone; when the robotic arm collides with the obstacle enclosure, i.e., 0 < L < r arm When +r is applied, it indicates that the robotic arm's current position is extremely dangerous, the feedback force f is at its maximum, and the robotic arm stops moving. The calculation model for the feedback force f is as follows:

[0075]

[0076] The formula for calculating the proportionality coefficient K is as follows:

[0077]

[0078] Where L is the shortest distance between the end point of the robotic arm and the obstacle after a collision is detected, and the calculation formula is: r arm Let r be the distance from the obstacle to the bounding box in the L direction, and let r be the length of the buffer in the L direction.

[0079] No feedback force is generated when the robotic arm's end effector contacts the obstacle buffer zone; when the robotic arm contacts the buffer zone but not the bounding box, the feedback force is between 0 and f. max Between; when the robotic arm contacts the enclosure, the feedback force is at its maximum and the system stops immediately to ensure safety.

[0080] The calculated force feedback value is fed back through the main force feedback arm. During the movement, if the robotic arm collides with more than one obstacle, the feedback force f is the sum of the feedback forces from each obstacle.

[0081]

[0082] Where n represents the number of obstacles, f i This represents the feedback force of the i-th obstacle.

[0083] The direction of the feedback force is defined as the direction of the shortest distance between the obstacle and the end effector of the robotic arm. The shortest distance between the obstacle center O and the robotic arm AB is L, meaning the point C from the obstacle enclosure center O to the central axis of the robotic arm end effector's enclosure lies on line segment AB. The direction of the feedback force f is...

[0084] (II) Spherical guiding force field force feedback-assisted grasping

[0085] Figure 6 A schematic diagram of the spherical guiding force field is provided, where the target point for grasping is known to be X. targe A spherical guiding force field is established in virtual space to assist the operator in grasping. The operator remotely manipulates the robotic arm to reach the vicinity of the grasping target point through path guidance. When the distance between the end point of the robotic arm and the grasping target point is less than or equal to 1.5s, the grasping target point X is determined. target A spherical guiding force field is established at the center of the sphere to guide the operator in the grasping operation.

[0086] The spherical guiding force field consists of three layers: an inner layer, a middle layer, and an outer layer. The inner and outer layers are repulsion layers, which guide the operator's teleoperated robotic arm end point to the middle layer by generating a repulsive force. Since the teleoperation target point is the robotic arm end point X... EE A gripper is installed after the end effector. The distance from the end effector of the robotic arm to the gripper's holding point is s (i.e., the gripper length is s). To facilitate gripping, the outer radius of the spherical guiding force field is set to s, and the center of the sphere is the target point X to be gripped. targetThe inner radius is s′, where s′ < s. The difference between the inner and outer radii is determined by s, typically set to ss′ ​​= s / 10. During teleoperation, the end effector of the robotic arm is confined to the middle layer, allowing the gripper at the end of the arm to extend into the force field and grasp the object. Therefore, the operator only needs to adjust the robotic arm's posture during grasping operations, without needing to focus on adjusting its position.

[0087] Figure 7 This is a schematic diagram of the spring-mass algorithm. In order to enable the operator to enter and exit the guiding area while receiving force feedback, a spring-mass model is established in the spherical guiding force field, separating the middle layer from the inner and outer layers (i.e., the spring-mass model is the isolation layer of the guiding force field). The guiding force field uses the spring-mass model to perform force feedback calculation.

[0088] In the spring-mass model, the nodes in the mesh represent the mass points in the model. When force feedback is generated, the mesh points deform to produce feedback. The spring connecting two nodes represents the interaction force generated between the nodes. To better generate the resistance effect of force feedback, damping is added to the model to ensure stability.

[0089] For example, during teleoperation, the force feedback master hand contacts the outer surface, and the operator moves the force feedback master hand away from the object to be grasped. The outer spherical mass undergoes deformation due to the force, simultaneously generating a feedback force that is sent back to the operator. The force feedback calculation formula is as follows:

[0090] By analyzing the dynamic equations of the point mass spring model, the moving point mass satisfies:

[0091]

[0092] In this system equation, M is the mass of the particle, X is the spatial coordinate of the particle, t is the time constant, D is the damping coefficient, K is the spring constant, and f is the feedback force. The solution to the system equation is transformed into solving a discrete particle differential equation to obtain an approximate solution. If the equation has a unique solution, let... If it is a unit of time, then within any time range Within this framework, using the time difference method and the incremental method, the equation can be transformed into the following for each discrete particle:

[0093]

[0094] Where, m i Let X be the mass of the i-th particle. i Let i be the coordinates of the i-th particle.

[0095] Substituting into the differential equation, we get:

[0096]

[0097] when When it approaches infinity, use replace use replace have:

[0098]

[0099] Solving the equation yields the displacement of the particle and the magnitude of the feedback force.

[0100] Figure 8 This is a schematic diagram of the force feedback of a spherical guiding force field, as shown below. Figure 8 As shown in (a), the end effector of the robotic arm is abstracted as a surrogate point for calculating the feedback force. Once the end effector is within the spherical guiding force field, the operator can adjust the gripper's posture at any time to grasp the object, ensuring the gripper remains within a suitable grasping distance. Figure 8 As shown in (b), when the end effector of the robotic arm approaches the inner and outer guiding force fields, the spring-mass model contacts the robotic arm's surrogate point. A force feedback algorithm calculates the mass displacement deformation and provides real-time force feedback to the operator. As the surrogate point gradually enters the inner and outer guiding force fields, the model deformation gradually increases, and the feedback force gradually increases. Figure 8 As shown in (c), when the agent point enters the outer layer, the feedback force increases to its maximum value f. max At this point, the spring-mass model reaches its maximum limit. If the operator continues to control the robotic arm to move outward, the spring-mass model will break, and the virtual force will then increase from the maximum force f. max The force drops to 0 and is no longer affected by the spherical guiding force field. The relationship between the feedback force of the spherical guiding force field and the position of the robotic arm is shown in the diagram below. Figure 9 As shown.

[0101] Based on the spherical guiding force field and the spring-mass model for force feedback to the operator, the end effector of the teleoperated robotic arm is restricted to between s and s′ (i.e., between the inner and outer layers), thus placing the robotic arm in the most suitable grasping range. When the operator moves the robotic arm close to the inner or outer layer, it contacts the spring-mass model, causing it to deform and generating force feedback, thus restricting the robotic arm's position. When the end effector is within the guiding force field, the end gripper will be at a relatively good grasping distance. At this point, the operator can reduce their focus on the robotic arm's position during grasping, allowing them to concentrate on controlling the posture and reducing workload.

[0102] Figure 10The diagram shows the overall flowchart of the grasping process. When using a force feedback master arm to remotely operate the robot for grasping, sensors first detect the entire grasping scene, identifying the workspace, robotic arm, and the object to be grasped. Based on the results, the operator is guided to avoid obstacles and reach the target grasping point. Then, a spherical guiding force field is generated to maintain a suitable distance between the robotic arm's end effector and the object to be grasped, assisting the operator in the grasp. During grasping, the guiding force field helps the operator remain within the spherical force field. If the robotic arm's end effector is too far from the object, the spring-mass model breaks, and the spherical guiding force field ceases to function. At this point, if the grasping is successful, no further remote guidance is provided. If the grasping is unsuccessful, the operator needs to be guided again until the grasping is successful.

Claims

1. A force-feedback-based robot teleoperation guidance method, characterized by, Comprise: The teleoperation mechanical arm moves to a grabbing target point, and when the distance between the end point of the mechanical arm and the grabbing target point is less than or equal to a set value, a spherical guiding force field including an inner layer, an intermediate layer and an outer layer is established with the grabbing target point as the spherical center, and the length of the gripper installed at the end of the mechanical arm is s The outer layer radius is determined. A spring-mass model is established in the spherical guiding force field to separate the middle layer from the inner and outer layers; Based on the spherical guiding force field and the spring-mass model, the teleoperation robot arm approaches the inner layer or the outer layer, and when it contacts the spring-mass model, the spring-mass model is deformed and generates force feedback, limiting the end point of the robot arm between the inner and outer layers; When the target object is grasped, the guiding is closed and the spherical guiding force field is left; if the target object is not grasped but still wants to leave the spherical guiding force field, after the teleoperation robot arm moves away from the target object, gradually enter the spherical guiding force field, the spring-mass model deformation gradually increases, the feedback force gradually increases, when the feedback force increases to the maximum value, if the teleoperation robot arm continues to move outward, the spring-mass model is broken, the robot arm leaves the spherical guiding force field, and the grasping guiding is stopped; The teleoperation robot arm moves to the grasping target point, comprising: Acquiring a grabbing target point and obstacle positions , according to the forward kinematics expression of the robot arm and joint angles of the robot arm, the end point position of the robot arm is calculated ; The bounding box of the obstacle is calculated, and an obstacle avoidance buffer zone is established by equi-proportionally enlarging the bounding box, and the range of the obstacle avoidance buffer zone is determined according to the geometric center of the bounding box C with the detection space range determined; During the movement of the robot arm, the angles of each joint of the robot arm are collected by the joint sensor of the robot arm, the position of the end point of the robot arm is obtained by forward solution, and real-time collision detection is performed according to the coordinates of the end point of the robot arm and the position of the buffer zone to determine whether the robot arm collides with the obstacle buffer zone; If collision occurs, the force feedback is calculated according to the position of the robot arm in the buffer zone: L to detect the shortest distance between the end point of the robot arm after collision and the obstacle, to L the distance of the obstacle to the bounding box in the direction, r to L the length of the buffer zone in the direction;​ When the robot arm is outside the buffer zone, i.e. , the feedback force is zero; when the robot arm is inside the buffer zone, i.e. , the feedback force f increases with the distance of the robot arm from the buffer zone; when the robot arm collides with the obstacle bounding box, i.e. , the feedback force f is maximum, and the robot arm stops moving at the same time; The calculated force feedback value is used for force feedback.

2. The force-feedback-based robotic teleoperation guidance method of claim 1, wherein, The spherical guiding force field uses a spring-mass model for force feedback calculation, and the force feedback calculation formula is as follows: By analyzing the dynamic equation of the spring-mass model, the moving mass point satisfies: ； In the system equation, M is the mass of the particle, X is the spatial coordinate of the particle, t is the time constant, D is the damping coefficient, K is the spring constant, and f is the feedback force. The solution of the system equation is converted into solving the differential equation of discrete particles to obtain an approximate solution; if the equation has a unique solution, set as a unit of time, then in any time range , through the time difference method and the incremental method, for each discrete particle, the equation can be converted into: ； wherein, m i is the mass of the i-th particle, x i is the coordinate position of the i-th particle; Substituting the differential equation can obtain: ； When tends to infinity, use instead of , use instead of , there is: ； Solving the equation can obtain the mass point displacement and the size of the mass point feedback force.

3. The force-feedback-based robotic teleoperation guidance method of claim 1, wherein, The set value is 1.5 s .

4. The force-feedback-based robotic teleoperation guidance method of claim 1, wherein, , is the inner layer radius.

5. The force-feedback-based robotic teleoperation guidance method of claim 1, wherein, Detection spatial range The expression is as follows: ； wherein C is the OBB bounding box geometric center; are mutually perpendicular spatial vectors, as local coordinate system direction vectors of the geometric object being enclosed; is the bounding box edge length.

6. The force-feedback-based robotic teleoperation guidance method of claim 1, wherein, The range of the obstacle avoidance buffer is 1.2 ~1.5 .

7. The force-feedback-based robotic teleoperation guidance method of claim 1, wherein, The calculation model of the feedback force f is as follows: ； wherein K is a proportionality factor.

8. The force-feedback-based robotic teleoperation guidance method of claim 7, wherein, The calculation formula of the proportional coefficient K is as follows: ； wherein, is the maximum value of the feedback force.

9. The force-feedback-based robotic teleoperation guidance method of claim 1, wherein, If the robot arm collides with more than one obstacle during movement, the feedback force f is the sum of the feedback forces of each obstacle: ； wherein, n represents the number of obstacles, represents the feedback force of the i-th obstacle; For the direction of the feedback force, it is defined as the direction of the shortest distance between the obstacle and the end of the robot arm; the shortest distance between the center O of the obstacle and the robot arm AB is L , that is, the point C of the center axis of the obstacle bounding box to the end of the robot arm bounding box is on the line segment AB, and the direction of the feedback force f is .

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