A lifting and active vibration damping control method for a robot operating in inaccessible areas

Abstract

This invention discloses a lifting and active vibration suppression control method for a robot operating in inaccessible areas, belonging to the field of industrial robot automatic control technology. The method includes establishing a stable operating base; smoothly lifting the operating module to near the target height using an S-shaped acceleration / deceleration curve; achieving millimeter-level precise positioning by combining visual servoing; collecting high-frequency vibration and pose deviation through an inertial measurement unit and a visual sensor; using a Kalman filter for multi-source data fusion to predict real-time pose disturbances; and driving the robotic arm to perform active motion compensation based on a composite control law to suppress base vibration, maintain the spatial positioning accuracy of the end effector, and complete force control operations on the target equipment. This invention achieves coordinated vibration suppression control of the lifting mechanism and the robotic arm, solving the problem of insufficient operating accuracy in high-altitude, high-vibration environments. It has advantages such as high positioning accuracy, strong anti-interference ability, and good reliability, and is suitable for automated maintenance operations in high-risk environments such as nuclear power plants and chemical plants.

Description

Technical Field

[0001] This invention relates to the field of industrial robot automatic control technology, and in particular to a lifting and active vibration damping control method for a robot operating in inaccessible areas. Background Technology

[0002] In robot systems operating in inaccessible areas (such as high altitudes, deep pits, and nuclear radiation environments), a lifting mechanism is typically used to mount a robotic arm to expand the working space. However, existing technologies have the following shortcomings: The patent with publication number CN105090339B discloses a two-degree-of-freedom vibration suppression system for a high-altitude construction robot operating platform. It uses a five-bar linkage and a vertical vibration reduction mechanism to achieve two-dimensional vibration suppression. However, its vibration suppression strategy is passive mechanical damping, which lacks active intervention capability and is difficult to adapt to complex vibration environments with multiple sources such as wind load and foundation excitation.

[0003] The patent with publication number CN222118759U proposes a robot support platform and aerial work vehicle. It absorbs vibration energy by setting a shock absorber in the support base. However, this solution only solves the vibration isolation problem of the robot on the work platform and does not consider the dynamic coupling between the lifting mechanism and the robotic arm. The reaction force generated when the robotic arm moves will still cause additional vibration to the lifting platform.

[0004] Patent CN114086754B discloses a stabilization control system and its high-altitude work platform, which uses an auxiliary stabilization device to connect the wall and the work platform to suppress vibration. However, this method relies on external wall constraints and its applicability is limited in open space environments such as nuclear power plants and chemical plants where there are no reliable walls to support them.

[0005] In summary, existing technologies have significant shortcomings in dynamic vibration suppression, collaborative control of lifting and robotic arm, and multi-source sensor fusion, resulting in severely limited positioning accuracy of the end effector in complex high-altitude environments. The purpose of this invention is to overcome these shortcomings and provide a lifting and active vibration suppression control method for robots operating in inaccessible areas. By constructing a collaborative control architecture between the lifting mechanism and the robotic arm, and combining a multi-source sensor fusion strategy of IMU high-frequency vibration detection and visual servo pose measurement, millimeter-level precision operation can be achieved.

[0006] Therefore, there is an urgent need for a lifting and active vibration damping control method for robots operating in inaccessible areas. Summary of the Invention

[0007] To address the aforementioned issues, this application proposes a lifting and active vibration damping control method for robots operating in inaccessible areas. The aim is to overcome the shortcomings of existing high-altitude robot technologies in dynamic vibration damping, precise positioning, and system coordination. Specific steps include: S1. Control the robot to move to the target area and deploy the active leveling mechanism to establish a stable working base; S2. Start the lifting mechanism of the robot and raise the working module at the top of the robot to the target height range according to the preset S-shaped acceleration and deceleration curve. S3. The real-time position of the operation module is revised based on a high-precision vision sensor to achieve the target height; S4. The lifting mechanism and robotic arm of the work robot work together to actively suppress vibration and perform precise spatial positioning. S5. The end effector of the working robot performs force control operations on the target equipment.

[0008] Preferably, the specific content of S3 includes: While the lifting mechanism is moving, the target image is acquired in real time based on the vision sensor installed on the operation module; The visual servo algorithm calculates the height deviation from the target in real time and feeds back to control the lifting mechanism to achieve millimeter-level precision stopping.

[0009] Preferably, the real-time calculation of the height deviation from the target using a visual servoing algorithm includes constructing a Gaussian scale space, the expression of which is: ; The Gaussian function is defined as follows: , For the original image, For convolution operations, A scale-space image at scale σ; through multiple scales The system performs Hough circle detection and accumulates the voting results to robustly identify the target circular outline and calculate the accurate distance.

[0010] Preferably, the specific content of S4 includes: S41. The high-frequency vibration attitude of the working module is measured in real time at a first frequency by an inertial measurement unit (IMU) installed at the top of the lifting mechanism. S42. Using the vision sensor, the target is identified in real time at a second frequency and its pose deviation from the end effector is calculated, wherein the second frequency is lower than the first frequency; S43. By fusing the high-frequency vibration attitude with the pose deviation using a Kalman filter, the real-time pose disturbance of the working module is predicted. S44. Based on the predicted disturbance, feed forward to the inverse kinematics model of the robotic arm to generate a compensating motion command, drive the robotic arm joints to perform reverse motion, thereby maintaining the spatial positioning accuracy of the end effector on the vibrating base.

[0011] Preferably, the Kalman filter fusion process in S43 is represented by a state-space equation, the specific contents of which include: State prediction: ; Observation update, Kalman gain calculation: ; Status Update: ; Wherein, the state vector It must include at least the tilt angle and angular velocity of the operating module; The observation vector is derived from the angular velocity and acceleration data of the IMU and the pose deviation calculated by the vision system. This process outputs the predicted real-time pose perturbation. .

[0012] in, For the first The prior state estimation vector for the step includes at least the tilt angle and angular velocity of the task module; This is the state transition matrix; To control the input matrix; This is the control input vector from the previous time step; The prior estimate is the error covariance matrix; The observation matrix; To observe the noise covariance matrix; The Kalman gain matrix; For the first The posterior state estimation vector of the step; For the first The step observation vector is derived from the angular velocity and acceleration data of the IMU and the pose deviation calculated by the vision system; For the predicted real-time pose perturbation, by The calculation yielded, where This is the perturbation output matrix.

[0013] Preferably, the expression for the composite control law that generates the robotic arm compensation motion command in S44 is: ; in, This is the calculated increment of the robotic arm joint angle; For the robotic arm at the joint position The pseudo-inverse of the Jacobian matrix at time; The error of image features calculated for the vision system; For the predicted real-time pose perturbation; and These are the control gain matrices for visual feedback and feedforward compensation, respectively.

[0014] Preferably, the S-shaped acceleration / deceleration curve in S2 is used to control the servo motor of the lifting mechanism, and its speed curve... The expression is continuous in the acceleration, constant speed, and deceleration phases, and the derivative is continuous, in order to minimize the impact and sway during the lifting and stopping process.

[0015] Smooth acceleration and deceleration control based on S-shaped acceleration and deceleration curves: ; in, For the lifting mechanism at all times speed; The set maximum lifting speed; To shorten the duration of the segment, The starting time of the uniform speed segment. The end time of the deceleration phase (i.e., the total duration of the entire ascent and descent process); in The interval is the acceleration segment, where the speed smoothly increases from 0 to [a certain value] according to a cosine rise curve. ;exist The interval is a constant speed segment, and the speed remains constant. ;exist The interval is the deceleration section, and the speed decreases according to the cosine curve from... The speed is smoothly reduced to 0; the entire speed curve is continuous and the derivative is continuous, in order to minimize the impact and sway during the lifting and stopping process.

[0016] On the other hand, the robot system architecture in this application adopts a modular design, comprising three core subsystems: (1) Mechanical body system: including mobile chassis, multi-stage sleeve lifting mechanism, six-degree-of-freedom robotic arm and flexible end effector. Among them, the mobile chassis is equipped with four-wheel independent drive and four-corner electric leveling outriggers. The multi-stage sleeve lifting mechanism adopts a square nested structure, with wear-resistant polymer sliders between stages, and is equipped with a mechanical ratchet self-locking device.

[0017] (2) Sensing System: A multi-source heterogeneous sensor configuration is adopted, including a binocular vision sensor, an IMU inertial measurement unit, a laser rangefinder, a torque sensor, and an encoder. The sensors synchronize data through a unified timestamp to form a complete sensing network.

[0018] (3) Control system: adopts a hierarchical distributed architecture, including a task planning layer (Windows host computer), a perception and decision layer (NVIDIA Jetson Orin) and an execution control layer (PLC + servo drive).

[0019] High-speed data exchange between layers is achieved via industrial Ethernet, and a TCP / UDP hybrid communication protocol is used to ensure the reliability and real-time performance of control commands.

[0020] In summary, the lifting and active vibration damping control method for a robot operating in inaccessible areas, as proposed in this invention, has the following advantages compared to traditional technologies: 1. This application addresses the problem of vibration accumulation caused by independent control of the lifting mechanism and the robotic arm; 2. This application breaks through the accuracy limitations of traditional visual positioning methods in dynamic high-altitude environments; 3. This application establishes an active vibration suppression mechanism based on multi-source sensor fusion to achieve millimeter-level operational accuracy; 4. This application provides a fully automated maintenance solution suitable for high-risk environments such as nuclear power plants and chemical plants.

[0021] The technical method of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0022] Figure 1 System architecture diagram; Figure 2 Flowchart of a high-precision lifting and active vibration damping control method; Figure 3 A block diagram illustrating the combined control principle of visual servoing and active vibration damping; Figure 4 This is a schematic diagram of an S-shaped acceleration / deceleration curve. Detailed Implementation

[0023] The technical method of the present invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application.

[0024] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the scope of this application and its application or use.

[0025] Techniques, systems, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, they should be considered part of the instruction manual.

[0026] In all the examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0027] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0028] A lifting and active vibration suppression control method for robots operating in inaccessible areas, which utilizes multi-source sensor fusion and advanced control algorithms, enables robots to perform fully automated and high-precision maintenance operations on target equipment in complex industrial environments such as high altitudes and high radiation.

[0029] Example 1 This embodiment proposes a lifting and active vibration damping control method for a robot operating in inaccessible areas, such as... Figure 2 As shown, the specific steps include: S1. Control the robot to move to the target area and deploy the active leveling mechanism to establish a stable working base; S2. Activate the lifting mechanism of the work robot, and raise the work module at the top of the work robot to the target height range according to the preset S-shaped acceleration and deceleration curve. The preset S-shaped acceleration and deceleration curve is as follows: Figure 4 As shown; Furthermore, the S-shaped acceleration / deceleration curve in S2 is used to control the servo motor of the lifting mechanism, and its speed curve... The expression is continuous in the acceleration, constant speed, and deceleration phases, and the derivative is continuous, in order to minimize the impact and sway during the lifting and stopping process.

[0030] Smooth acceleration and deceleration control based on S-shaped acceleration and deceleration curves: ; in, For the lifting mechanism at all times speed; The set maximum lifting speed; To shorten the duration of the segment, The starting time of the uniform speed segment. The end time of the deceleration phase (i.e., the total duration of the entire ascent and descent process); in The interval is the acceleration segment, where the speed smoothly increases from 0 to [a certain value] according to a cosine rise curve. ;exist The interval is a constant speed segment, and the speed remains constant. ;exist The interval is the deceleration section, and the speed decreases according to the cosine curve from... The speed is smoothly reduced to 0; the entire speed curve is continuous and the derivative is continuous, in order to minimize the impact and sway during the lifting and stopping process.

[0031] S3. The real-time position of the operation module is revised based on a high-precision vision sensor to achieve the target height; Furthermore, such as Figure 3 As shown, the specific content of S3 includes: While the lifting mechanism is moving, the target image is acquired in real time based on the vision sensor installed on the operation module; The visual servo algorithm calculates the height deviation from the target in real time and feeds back to control the lifting mechanism to achieve millimeter-level precision stopping.

[0032] Furthermore, the height deviation from the target is calculated in real time using a visual servoing algorithm, including the construction of a Gaussian scale space, the expression of which is: ; The Gaussian function is defined as follows: , For the original image, For convolution operations, A scale-space image at scale σ; through multiple scales The system performs Hough circle detection and accumulates the voting results to robustly identify the target circular outline and calculate the accurate distance.

[0033] S4. The lifting mechanism and robotic arm of the work robot work together to actively suppress vibration and perform precise spatial positioning: Furthermore, the specific content of S4 includes: S41. The high-frequency vibration attitude of the working module is measured in real time at a first frequency by an inertial measurement unit (IMU) installed at the top of the lifting mechanism. S42. Using the vision sensor, the target is identified in real time at a second frequency and its pose deviation from the end effector is calculated, wherein the second frequency is lower than the first frequency; S43. By fusing the high-frequency vibration attitude with the pose deviation using a Kalman filter, the real-time pose disturbance of the working module is predicted. Furthermore, the Kalman filter fusion process in S43 is represented by a state-space equation, the specific contents of which include: State prediction: ; Observation update, Kalman gain calculation: ; Status Update: ; Wherein, the state vector It must include at least the tilt angle and angular velocity of the operating module; The observation vector is derived from the angular velocity and acceleration data of the IMU and the pose deviation calculated by the vision system.

[0034] This process outputs the predicted real-time pose perturbation. .

[0035] in, For the first The prior state estimation vector for the step includes at least the tilt angle and angular velocity of the task module; This is the state transition matrix; To control the input matrix; This is the control input vector from the previous time step; The prior estimate is the error covariance matrix; The observation matrix; To observe the noise covariance matrix; The Kalman gain matrix; For the first The posterior state estimation vector of the step; For the first The step observation vector is derived from the angular velocity and acceleration data of the IMU and the pose deviation calculated by the vision system; For the predicted real-time pose perturbation, by The calculation yielded, where This is the perturbation output matrix.

[0036] S44. Based on the predicted disturbance, feed forward to the inverse kinematics model of the robotic arm to generate a compensating motion command, drive the robotic arm joints to perform reverse motion, thereby maintaining the spatial positioning accuracy of the end effector on the vibrating base.

[0037] Furthermore, the expression for the composite control law that generates the robotic arm's compensating motion commands in S44 is as follows: ; in, This is the calculated increment of the robotic arm joint angle; For the robotic arm at the joint position The pseudo-inverse of the Jacobian matrix at time; The error of image features calculated for the vision system; For the predicted real-time pose perturbation; and These are the control gain matrices for visual feedback and feedforward compensation, respectively.

[0038] S5. The end effector of the working robot performs force control operations on the target equipment.

[0039] Example 2 This embodiment provides a robot designed for operation in inaccessible areas. The system employs a modular design, such as... Figure 1 As shown, it comprises three core subsystems: (1) Mechanical body system: including mobile chassis, multi-stage sleeve lifting mechanism, six-degree-of-freedom robotic arm and flexible end effector. Among them, the mobile chassis is equipped with four-wheel independent drive and four-corner electric leveling outriggers. The multi-stage sleeve lifting mechanism adopts a square nested structure, with wear-resistant polymer sliders between stages, and is equipped with a mechanical ratchet self-locking device.

[0040] (2) Sensing System: A multi-source heterogeneous sensor configuration is adopted, including a binocular vision sensor, an IMU inertial measurement unit, a laser rangefinder, a torque sensor, and an encoder. The sensors synchronize data through a unified timestamp to form a complete sensing network.

[0041] (3) Control system: adopts a hierarchical distributed architecture, including a task planning layer (Windows host computer), a perception and decision layer (NVIDIA Jetson Orin) and an execution control layer (PLC + servo drive).

[0042] High-speed data exchange between layers is achieved via industrial Ethernet, and a TCP / UDP hybrid communication protocol is used to ensure the reliability and real-time performance of control commands.

[0043] Force control operation and safety assurance: (1) Adaptive grasping control: By monitoring the change of the drive motor current, the contact state is determined, and a smooth transition from rapid approach to compliant contact is achieved.

[0044] (2) Intelligent torque control: The output torque is dynamically adjusted according to the different needs of the disassembly / installation stage, including three stages: starting torque, unscrewing torque and locking torque.

[0045] (3) Multiple safety protections: including electromagnetic brake, mechanical self-locking device, emergency stop button and software limit switch, forming a complete hardware-software dual safety system.

[0046] System integration and performance optimization: (1) Structural optimization based on finite element analysis: Topology optimization of key components is carried out using software such as ANSYS to achieve lightweight design while ensuring stiffness.

[0047] (2) Thermal management and energy consumption optimization: Intelligent heat dissipation system and dynamic power allocation strategy are adopted to ensure the system operates stably for a long time.

[0048] (3) Modular software architecture: Each functional module is deployed using Docker containers to ensure the maintainability and scalability of the system.

[0049] Example 3 The implementation case study takes the replacement of fire alarm detectors in the demineralized water plant of a nuclear power plant as an example.

[0050] System hardware configuration and integration: The robot system used in this embodiment adopts a modular integrated design, comprising four core components: a mobile platform, a lifting mechanism, a robotic arm system, and a sensing system. The mobile platform uses an 800mm × 800mm chassis structure, equipped with a four-wheel independent servo drive system and a LiDAR-IMU integrated navigation system, ensuring precise movement and positioning in complex industrial environments. The lifting mechanism uses a five-stage square sleeve structure, achieving stepless speed regulation and lifting within a 0-15m travel range through a servo motor, planetary reducer, and synchronous belt drive system, with a positioning accuracy of ±1mm. The robotic arm system uses a six-degree-of-freedom serial structure, with a 1200mm working radius and a ±0.1mm repeatability, capable of meeting various complex operational requirements. The sensing system integrates a 2-megapixel industrial camera, a 500Hz sampling frequency IMU sensor, a laser rangefinder with a measurement range of 0.1-20m, and a torque sensor with a range of 0-10Nm, constructing a complete sensing network.

[0051] Control software architecture and algorithm implementation: The control system software adopts a layered modular architecture, integrating three core modules: task management, vision processing, and motion control. The task management module provides a graphical user interface, supporting the creation, editing, and execution monitoring of tasks, and enabling drag-and-drop programming and real-time system status display. The vision processing module implements the entire process of image acquisition, preprocessing, and target recognition, integrating an improved Hough circle detection algorithm based on Gaussian scale space, significantly improving the accuracy and robustness of target recognition through multi-scale fusion technology. The motion control module realizes the coordinated control of the lifting mechanism and the robotic arm, integrating an S-curve acceleration / deceleration planning algorithm and a Kalman filter-based vibration compensation algorithm to ensure stable system operation in dynamic environments.

[0052] Workflow and performance: The complete workflow of this embodiment includes six stages: task preparation and system self-check, autonomous movement and platform leveling, lifting and coarse positioning, active vibration suppression and fine alignment, force control operation, and task completion and system reset. In the task preparation stage, the system automatically loads the target equipment parameters and performs a comprehensive self-check to ensure that all sensors are functioning properly and that the battery is fully charged. In the autonomous movement stage, environmental obstacles are perceived in real time using lidar, enabling dynamic obstacle avoidance and precise positioning, with platform leveling accuracy reaching ±0.5°. In the lifting and coarse positioning stage, an S-shaped acceleration / deceleration curve is used to achieve smooth lifting, and visual guidance enables millimeter-level precise positioning. In the active vibration suppression and fine alignment stage, multi-source data is fused using a Kalman filter, and vibration suppression and precise alignment are achieved based on a composite control law. In the force control operation stage, intelligent torque control enables non-destructive assembly and disassembly, and finally, the system automatically generates a detailed report including operation time and quality assessment.

[0053] Safety protection and reliability assurance: This embodiment employs a multi-layered safety protection mechanism, including a dual protection system of hardware and software security. For hardware security, the lifting mechanism is equipped with dual protection of an electromagnetic brake and a mechanical pawl; the robotic arm system has joint torque limits and software limits; and the power system has overcurrent and overtemperature protection functions. For software security, the system implements real-time status monitoring and automatic shutdown in case of abnormalities. The emergency stop button has the highest priority, and the system also has data integrity verification and fault self-diagnosis capabilities.

[0054] These safety measures together ensure the reliable operation of the system under extreme conditions, providing a solid guarantee for automated operations in high-risk industrial environments.

[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical methods of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical methods of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical methods to deviate from the spirit and scope of the technical methods of the present invention.

Claims

1. A lifting and active vibration damping control method for a robot operating in inaccessible areas, characterized in that, include; S1. Control the robot to move to the target area and deploy the active leveling mechanism to establish a stable working base; S2. Start the lifting mechanism of the robot and raise the working module at the top of the robot to the target height range according to the preset S-shaped acceleration and deceleration curve. S3. The real-time position of the operation module is revised based on a high-precision vision sensor to achieve the target height; S4. The lifting mechanism and robotic arm of the work robot work together to actively suppress vibration and perform precise spatial positioning. S5. The end effector of the working robot performs force control operations on the target equipment.

2. The lifting and active vibration damping control method for a robot operating in inaccessible areas according to claim 1, characterized in that, The specific content of S3 includes: While the lifting mechanism is moving, the target image is acquired in real time based on the vision sensor installed on the operation module; The visual servo algorithm calculates the height deviation from the target in real time and feeds back to control the lifting mechanism to achieve millimeter-level precision stopping.

3. The lifting and active vibration damping control method for a robot operating in inaccessible areas according to claim 2, characterized in that, The height deviation from the target is calculated in real time using a visual servoing algorithm, including the construction of a Gaussian scale space, the expression of which is: ； The Gaussian function is defined as follows: , For the original image, For convolution operations, A scale-space image at scale σ; through multiple scales The system performs Hough circle detection and accumulates the voting results to robustly identify the target circular outline and calculate the accurate distance.

4. The lifting and active vibration damping control method for a robot operating in inaccessible areas according to claim 3, characterized in that, The specific content of S4 includes: S41. The high-frequency vibration attitude of the working module is measured in real time at a first frequency by an inertial measurement unit (IMU) installed at the top of the lifting mechanism. S42. Using the vision sensor, the target is identified in real time at a second frequency and its pose deviation from the end effector is calculated, wherein the second frequency is lower than the first frequency; S43. By fusing the high-frequency vibration attitude with the pose deviation using a Kalman filter, the real-time pose disturbance of the working module is predicted. S44. Based on the predicted disturbance, feed forward to the inverse kinematics model of the robotic arm to generate a compensating motion command, drive the robotic arm joints to perform reverse motion, thereby maintaining the spatial positioning accuracy of the end effector on the vibrating base.

5. The lifting and active vibration damping control method for a robot operating in inaccessible areas according to claim 4, characterized in that, The Kalman filter fusion process in S43 is represented by a state-space equation, the specific contents of which include: State prediction: ; Observation update, Kalman gain calculation: ; Status Update: ; This process outputs the predicted real-time pose perturbation. ; in, For the first The prior state estimation vector for the step includes at least the tilt angle and angular velocity of the task module; This is the state transition matrix; To control the input matrix; This is the control input vector from the previous time step; The prior estimate is the error covariance matrix; The observation matrix; To observe the noise covariance matrix; The Kalman gain matrix; For the first The posterior state estimation vector of the step; For the first The step observation vector is derived from the angular velocity and acceleration data of the IMU and the pose deviation calculated by the vision system; For the predicted real-time pose perturbation, by The calculation yielded, where This is the perturbation output matrix.

6. The lifting and active vibration damping control method for a robot operating in inaccessible areas according to claim 5, characterized in that, The expression for the composite control law that generates the robotic arm's compensating motion commands in S44 is: ； in, This is the calculated increment of the robotic arm joint angle; For the robotic arm at the joint position The pseudo-inverse of the Jacobian matrix at time; The error of image features calculated for the vision system; For the predicted real-time pose perturbation; and These are the control gain matrices for visual feedback and feedforward compensation, respectively.

7. The lifting and active vibration damping control method for a robot operating in inaccessible areas according to claim 6, characterized in that, The S-shaped acceleration / deceleration curve in S2 is used to control the servo motor of the lifting mechanism, and its speed curve... The expression is continuous in the acceleration, constant speed, and deceleration phases, and the derivative is continuous, in order to minimize the impact and sway during the lifting and stopping process.

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