A cooperative robot real-time trajectory acquisition and high-precision restoration method

Abstract

The application discloses a kind of cooperative robot real-time trajectory acquisition and high-precision reduction system and method, comprising: real-time acquisition robot joint data, utilize improved Ju-Gibbs quaternion to the pre-processing of acquisition data;According to the change rate and change amplitude of real-time data, the filtered data is filtered using dynamic adaptive sliding filter;According to the filtered data, the trajectory is reconstructed, the inverse operation of Ju-Gibbs quaternion is used, the initial state and intermediate state robot posture are deduced from the final quaternion state, and the motion trajectory of the robot is reconstructed;The reconstructed trajectory is compared with the actual robot motion trajectory, the error index is calculated to evaluate the accuracy and efficiency of the reconstructed trajectory, and the quaternion parameters and filtering algorithm are adjusted and optimized according to the evaluation result.The application improves the ability of high-precision trajectory capture and playback of robot in complex environment.

Description

Technical Field

[0001] This invention belongs to the field of robot trajectory acquisition and reconstruction technology, specifically relating to a method for real-time trajectory acquisition and high-precision reconstruction of collaborative robots. Background Technology

[0002] In the field of modern industrial automation, robotics has become a key factor in improving production efficiency and ensuring operational safety. The emergence of collaborative robots (Cobots) has greatly promoted the possibilities of human-robot collaboration. Collaborative robots can work alongside human workers without the need for safety barriers, thus significantly improving production flexibility and efficiency. In terms of robot control and path planning, real-time trajectory acquisition and high-precision reconstruction are core technologies to ensure the efficient and safe operation of robots in complex environments. These technologies are not only widely used in manufacturing but also demonstrate great potential in many fields such as healthcare, services, and entertainment.

[0003] Currently, significant progress has been made in robot trajectory acquisition and reconstruction technology. Typical trajectory acquisition methods include sensor-based data acquisition and vision-based trajectory tracking. The acquired trajectory data typically requires processing and filtering to reduce the impact of noise on path planning. Existing trajectory reconstruction techniques mainly rely on path planning algorithms, such as Rapidly-exploring Random Tree (RRT) and Artificial Potential Field (APF). These algorithms perform well when dealing with static obstacles, but still have some shortcomings when facing dynamic obstacles and complex operating environments.

[0004] For example, sensor-based trajectory acquisition methods such as LiDAR and depth cameras, while providing high-precision position information, face challenges in data processing and real-time performance. On the other hand, vision-based trajectory tracking technologies, such as RGB-D cameras and monocular vision, while exhibiting good environmental adaptability, still require improvement in accuracy and stability in complex scenarios. The shortcomings and deficiencies of existing technologies mainly include the following two points:

[0005] 1. Insufficient accuracy in trajectory acquisition.

[0006] Existing trajectory acquisition methods often struggle to balance accuracy and real-time performance when faced with complex industrial environments and diverse tasks. Particularly in high-noise environments, the acquired trajectory data is easily interfered with, leading to reduced path planning accuracy. These problems are mainly reflected in the following aspects:

[0007] Insufficient dynamic response: During high-speed motion and complex task execution, traditional attitude and position calculation methods struggle to respond accurately and in real-time to rapid changes in the robot's state. This insufficient response can lead to deviations between the executed trajectory and the preset trajectory, affecting the quality of task execution.

[0008] Data processing lag: When dealing with large amounts of rapidly generated data, traditional methods often cannot update the robot's status information in real time due to limited processing capabilities, resulting in data processing lag, which in turn affects the accuracy and efficiency of the overall operation.

[0009] Data noise: Existing sensor technologies are affected by environmental noise when collecting trajectory data, resulting in a significant amount of noise in the collected data. This noise can cause trajectory deviations in subsequent path planning, affecting the robot's operational accuracy.

[0010] 2. Low data processing efficiency.

[0011] Existing trajectory capture systems typically require processing large amounts of sensor input data, including position, velocity, and acceleration information. In high-speed robot operations, sensors generate hundreds or even thousands of data points per second. Due to the lack of effective data filtering and preprocessing mechanisms, the system often has to process a large amount of redundant data. This not only increases the consumption of computing resources but also prolongs data processing time, thereby reducing the overall efficiency of the system.

[0012] In dynamically changing environments, especially on industrial production lines, environmental factors (such as vibration, temperature changes, and machine-to-machine interference) can change rapidly. This requires trajectory capture systems to process and respond to these changes in real time. Existing data processing algorithms typically employ batch processing methods and lack the ability to update and adjust in real time, which is particularly inadequate for applications requiring high real-time performance.

[0013] Traditional filtering techniques, such as simple moving average filters or Kalman filters, typically have fixed parameter settings (e.g., window size or noise estimation), making them ineffective in adapting to rapid changes in data characteristics. When environmental conditions or robot operating modes change, these filters may fail to accurately reflect these changes, leading to inaccurate data processing results and increasing errors in subsequent trajectory reconstruction.

[0014] 3. The computational stability is poor.

[0015] Gimbal lock problem: When using Euler angles as a robot pose description, a gimbal lock problem occurs when the rotation angle approaches 90 degrees. This causes the pose calculation to lose one degree of freedom, resulting in instability in kinematic calculations. This is unacceptable in precision robot manipulation because it leads to incorrect trajectory execution.

[0016] The quaternion normalization problem: When using traditional quaternions for attitude calculation, due to the cumulative error of quaternions during the calculation process, normalization needs to be performed periodically to prevent the error from increasing. However, in high-speed dynamic operations, frequent normalization operations increase the computational burden and may introduce additional computational errors. Summary of the Invention

[0017] Objective: To address the above problems, this invention proposes a method for real-time trajectory acquisition and high-precision reconstruction of collaborative robots. This improves the accuracy of trajectory acquisition and the efficiency of trajectory reconstruction for collaborative robots in complex industrial environments, ensuring high-precision and high-stability operation of the robot in dynamic obstacle environments.

[0018] Technical solution: To achieve the objectives of this invention, the technical solution adopted is as follows:

[0019] A method for real-time trajectory acquisition and high-precision reconstruction of a collaborative robot includes the following steps:

[0020] Step 1: Collect real-time position and velocity data of the robot joints, including angle, velocity, and acceleration;

[0021] Step 2: Preprocess the collected raw data using improved Ju-Gibbs quaternions to obtain the preprocessed position and velocity data of the robot joints;

[0022] Step 3: Based on the rate and magnitude of change of the real-time data, apply a dynamic adaptive sliding filter to filter the preprocessed data;

[0023] Step 4: Reconstruct the trajectory based on the filtered data. Using the inverse operation of Ju-Gibbs quaternions, deduce the robot's posture in the initial and intermediate states from the final quaternion state to reconstruct the robot's motion trajectory.

[0024] Step 5: Compare the reconstructed trajectory with the actual robot motion trajectory, calculate the error index to evaluate the accuracy and efficiency of the reconstructed trajectory, and adjust and optimize the quaternion parameters and filtering algorithm based on the evaluation results.

[0025] Furthermore, the collected raw data is preprocessed using improved Ju-Gibbs quaternions, as follows:

[0026] First, obtain the connection data θ from link l-1 to link l. l and n l , where θ l It is the angular position about the axis, n l It is an axis vector; the Ju-Gibbs quaternion expression is calculated as follows:

[0027]

[0028] in, It is the Ju-Gibbs quaternion describing the l-th link relative to the global reference coordinate system o. o q l This represents the unit quaternion of the l-th link relative to the reference coordinate system o, where o is the symbol representing the reference coordinate system. n l ,τ l It is a vector. It is a scalar;

[0029] During the rotation of robot joints, Ju-Gibbs quaternions are written in general form as follows:

[0030]

[0031] in, It is a Ju-Gibbs quaternion describing the attitude from the reference coordinate system o to the (l-1)th link. It is a Ju-Gibbs quaternion describing the relative attitude transformation from the (l-1)th link to the lth link. It is the square of the modulus of a Ju-Gibbs quaternion;

[0032] By combining the rotation axis and rotation angle of each joint using Ju-Gibbs quaternions, a unified mathematical representation is formed to describe the rotation of each joint; the rotation of each joint is continuously combined through quaternion multiplication to express the posture changes of the entire robotic arm.

[0033] Furthermore, a dynamic adaptive sliding filter is applied to filter the preprocessed data, as follows:

[0034] First, the difference between each data point in the data stream and the previous data point is calculated to obtain the rate and magnitude of data change; the data stream refers to the data sequence continuously collected by the robot's sensors, and the data points include position, velocity, or acceleration information.

[0035] Then, based on the rate and magnitude of change, the size of the filtering window and the weight coefficients are dynamically adjusted, with the weight coefficients adjusted according to the time interval between the data point and the current processing point;

[0036] The weights are calculated using the exponential decay model, with the formula w. i =e -α*# , where w i α is the weight coefficient assigned to each data point by the filter, d is the time step from the current data point, and α is the decay coefficient, which controls the rate at which the weight decreases.

[0037] If both the rate and magnitude of data change exceed the set thresholds, the filter window is narrowed and the α value is increased; conversely, if neither the rate nor the magnitude of change exceeds the set thresholds, the filter window is expanded and the α value is decreased.

[0038] Furthermore, trajectory reconstruction is performed based on the filtered data, as follows:

[0039] After the robot completes a series of actions, the data collected and processed in real time by the sensor system is converted into a final quaternion state. Using the inverse operation of the Ju-Gibbs quaternion formula, the robot's posture in the initial and intermediate states is deduced from the final quaternion state, thus reproducing the robot's motion trajectory. The mathematical model describing the robot's transition from one posture to another is as follows:

[0040]

[0041]

[0042] in, Let be the Ju-Gibbs quaternion of the (l-1)th joint, representing the pose transformation from the reference coordinate system o to the corrected state d. It is the rotation axis vector of the (l-1)th joint. is the scalar part of the rotation angle of the (l-1)th joint, d is the correction or target state, and o is the reference coordinate system; It is the symmetric rotation axis matrix under the corrected state d. It is the rotation axis vector of the l-th joint. It is a symmetric matrix representation of the rotation axis of the l-th joint, n l It is the rotation axis vector of the l-th joint.

[0043] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0044] Existing technologies typically employ standard quaternions to handle static or slowly changing scenarios, describing and calculating robot joint poses. However, these methods are prone to computational delays or accuracy losses in fast-moving environments. This invention utilizes improved Ju-Gibbs quaternions, incorporating a dynamic adjustment mechanism that enables the quaternions to adaptively adjust based on real-time dynamic data, thereby improving computational stability and accuracy under rapidly changing conditions.

[0045] Traditional moving average filters perform poorly when processing high-frequency data variations because their parameters remain constant and cannot adapt to changes in environmental noise and data fluctuations. The Dynamic Adaptive Moving Filter (DASF) designed in this invention automatically adjusts filtering parameters, such as window size and weighting factors, based on the characteristics of the real-time data stream. This allows it to adapt to different data fluctuations, more effectively eliminate noise and reduce data redundancy, and improve the accuracy of data processing.

[0046] This invention not only optimizes the data processing flow but also provides a new solution for robot dynamic control. It significantly improves the robot's ability to capture and replay high-precision trajectories in complex environments, and has broad prospects for industrial applications. Attached Figure Description

[0047] Figure 1 This is a flowchart of the collaborative robot real-time trajectory acquisition and high-precision reconstruction method of the present invention.

[0048] Figure 2 This is a schematic diagram of the collaborative robot real-time trajectory acquisition and high-precision reconstruction system of the present invention.

[0049] Figure 3 This is an iiwa robot simulation run.

[0050] Figure 4 This is the actual data acquisition process of the iiwa robot in motion.

[0051] Figure 5 This is an experimental comparison before and after the introduction of filtering function at position X.

[0052] Figure 6 This is an experimental comparison before and after the introduction of filtering function at position Y.

[0053] Figure 7 This is an experimental comparison before and after the introduction of filtering function at position Z. Detailed Implementation

[0054] The technical solution of the present invention will be further described below with reference to the accompanying drawings and examples.

[0055] The present invention discloses a method for real-time trajectory acquisition and high-precision reconstruction of a collaborative robot, the process of which is as follows: Figure 1 As shown, the specific implementation steps are as follows:

[0056] Step 1: Data Acquisition. High-precision sensors are used to collect real-time position and velocity data of the robot joints, including parameters such as angle, velocity, and acceleration, providing raw input for subsequent data processing.

[0057] Step 2: Data Preprocessing. The collected raw data is preprocessed using improved Ju-Gibbs quaternions, primarily for data standardization, laying the foundation for ensuring the accuracy and efficiency of subsequent processing.

[0058] First, obtain the raw data θ l and n l , where θ l It is the angular position about the axis, n l These are axis vectors, representing connections from link l-1 to link l. The Ju-Gibbs quaternion form can be calculated as follows:

[0059]

[0060] in, It is the Ju-Gibbs quaternion describing the l-th link relative to the global reference coordinate system o. o q l This represents the unit quaternion of the l-th link relative to the reference coordinate system o, where o is the symbol representing the reference coordinate system. n l ,τ l It is a vector. It is a scalar.

[0061] During the rotation of robot joints, Ju-Gibbs quaternions are written in general form as follows:

[0062]

[0063] This yields the rotations of each joint, expressed in Ju-Gibbs quaternion form. It is a Ju-Gibbs quaternion describing the attitude from the reference coordinate system o to the (l-1)th link. It is a Ju-Gibbs quaternion describing the relative attitude transformation from the (l-1)th link to the lth link. It is the modulus square of a Ju-Gibbs quaternion.

[0064] By combining the rotation axis and rotation angle of each joint using Ju-Gibbs quaternions, a unified mathematical representation is formed to describe the rotation of each joint; the rotation of each joint is continuously combined through quaternion multiplication to express the posture changes of the entire robotic arm.

[0065] Step 3: Data Filtering. A Dynamic Adaptive Sliding Filter (DASF) is applied to further filter the preprocessed data.

[0066] First, the filter automatically adjusts its parameters based on data changes. Specifically, it calculates the difference between each data point in the data stream and the previous data point to assess the rate and magnitude of data change. The data stream refers to the sequence of data continuously collected by the robot's sensors, and the data points include position, velocity, or acceleration information.

[0067] Then, based on the real-time calculation results of the rate and magnitude of change, the DASF algorithm dynamically adjusts the size of the filtering window and the weight coefficients. If the data changes significantly, the window may shrink, and the weight distribution will be more biased towards the most recent data points to respond quickly to data changes; conversely, if the data changes gradually, the window will expand, and the weight distribution will be more even to smooth out noise and avoid over-response.

[0068] The weighting coefficients are adjusted based on the time interval between the data point and the current processing point. An exponential decay model is used to calculate the weights, with more recent data points receiving higher weights. The formula is w. i =e -α*# , where w i α is the weight coefficient assigned to each data point by the filter, d is the time step from the current data point, and α is the decay coefficient, which controls the rate at which the weight decreases.

[0069] If both the rate and magnitude of data change exceed the set thresholds, the filter window will shrink from the standard size to 50% to enhance the response to new data, and the weight of recent data points will be increased by increasing the α value, so that the weight coefficients are more concentrated on recent data.

[0070] Conversely, if the rate of change and the magnitude of change do not exceed the set threshold, the filter window is expanded to 150% to increase stability and reduce the impact of noise, and the weights are distributed more evenly across all data points by reducing the α value.

[0071] Step 4: Trajectory Reconstruction and Playback. Based on the filtered and optimized data, trajectory reconstruction is performed, converting this data back into motion commands or position states for the robot joints. In the robot control system, these reconstructed motion commands are input to the robot's control unit, and the robot's execution system simulates the physical motion, thereby reproducing the original or designed motion trajectory.

[0072] After the robot completes a series of actions, the data collected and processed in real time by the sensor system is converted into a final quaternion state. Using the inverse operation of Ju-Gibbs quaternions, the robot's pose, either the initial state or any intermediate state, is deduced from the final quaternion state. This calculation involves quaternion composition and inverse operations, and will accurately describe the robot's transition from one pose to another through the following mathematical model:

[0073]

[0074] Therefore, we can obtain

[0075]

[0076] as well as

[0077]

[0078] in, Let be the Ju-Gibbs quaternion of the (l-1)th joint, representing the pose transformation from the reference coordinate system o to the corrected state d. It is the rotation axis vector of the (l-1)th joint. is the scalar part of the rotation angle of the (l-1)th joint, d is the correction or target state, and o is the reference coordinate system; It is the symmetric rotation axis matrix under the corrected state d. It is the rotation axis vector of the l-th joint. It is a symmetric matrix representation of the rotation axis of the l-th joint, n l It is the rotation axis vector of the l-th joint.

[0079] Step 5: Performance Evaluation and Optimization. Finally, the system will evaluate the accuracy and efficiency of trajectory reconstruction based on feedback data from real-world applications. Based on the evaluation results, necessary adjustments and optimizations will be made to the quaternion parameters and filtering algorithm to ensure optimal system performance in constantly changing real-world environments.

[0080] Specifically, the system compares the reconstructed trajectory with the actual trajectory of the robot's movement, and evaluates the accuracy of the reconstructed trajectory by calculating error indices, namely mean square error and maximum deviation. The system collects feedback data on trajectory execution, including the robot's response time, execution efficiency, and abnormal situations during operation, for the operator to analyze, process, and optimize.

[0081] This invention also provides a real-time trajectory acquisition and high-precision reconstruction system for collaborative robots, aiming to provide an efficient and accurate robot motion trajectory processing scheme by integrating improved Ju-Gibbs quaternions and a dynamic adaptive sliding filter (DASF). The system includes five main modules, such as... Figure 2 As shown, it includes a sensor module, a data processing unit, a control execution unit, a user interface, and a communication module. They cooperate with each other through a clear data flow and control commands to achieve accurate capture and reproduction of robot motion.

[0082] The sensor module is responsible for acquiring motion data from the robot's joints and actuators in real time, including but not limited to parameters such as position, velocity, and acceleration. This raw data is sent to the data processing unit, which uses improved Ju-Gibbs quaternions for initial data normalization and noise filtering, improving data usability and accuracy. The data processing unit is also equipped with an innovative Dynamic Adaptive Sliding Filter (DASF), which automatically adjusts its processing parameters, such as window size and filter weights, according to changes in real-time data, thereby optimizing data processing and reducing errors and latency.

[0083] The processed data is transmitted to the control execution unit, which precisely controls the robot's movements based on the data instructions, achieving high-precision trajectory reproduction. The user interface provides operators with an intuitive platform for inputting operation commands, setting system parameters, and monitoring the robot's status and system operation in real time. Furthermore, the communication module supports data exchange with other industrial control systems, enabling external data synchronization and remote control, enhancing the system's flexibility and application scope.

[0084] The high-precision trajectory capture and playback system of this invention has innovative applications in the field of robot control, especially by combining improved Ju-Gibbs quaternions with dynamic adaptive sliding filters (DASF) to improve the accuracy and efficiency of trajectory processing.

[0085] First, the system starts from the "Start" node and enters the "Sensor Data Acquisition" phase. In this phase, the system uses sensors installed on the robot's joints and other key components to collect various motion data in real time, including but not limited to position, velocity, and acceleration. This data is fundamental to the accuracy of trajectory reconstruction and must be collected and transmitted precisely.

[0086] The raw sensor data collected is then sent to the "data preprocessing" module. In this module, the data undergoes preliminary cleaning and formatting to remove potential noise and outliers, providing clean and standardized data input for subsequent advanced processing steps.

[0087] After data preprocessing, the process enters the "Applying Improved Ju-Gibbs Quaternions" stage. This stage is the core of the system, utilizing improved Ju-Gibbs quaternion technology to accurately calculate and model the robot's 3D motion and posture. This technology outperforms traditional quaternion methods, better handling complex spatial rotations and avoiding common mathematical singularity problems.

[0088] The data then flows to the "Data Filtering and Processing (DASF)" module. This module uses DASF technology to automatically adjust filtering parameters based on real-time changes in the data. This intelligent filtering process significantly improves the usability and accuracy of the data, providing a high-quality data foundation for trajectory reconstruction.

[0089] The filtered data is fed into the "trajectory reconstruction calculation" module, where the system calculates the robot's motion trajectory based on the processed data. This calculation result is directly used in the "trajectory playback" stage to ensure that the robot can accurately reproduce the original motion trajectory.

[0090] After the trajectory playback is completed, the system not only marks the "end" of a complete data processing and trajectory reconstruction cycle, but also feeds some data back to the "Feedback and Optimization" module. This module analyzes the performance of the trajectory playback, optimizes system settings, and adjusts the data processing flow to achieve higher accuracy and efficiency.

[0091] Furthermore, the high-precision trajectory acquisition and reconstruction system of this invention has been successfully applied to the KUKA iiwa robot, demonstrating its efficiency and accuracy in actual industrial robot operation. The KUKA iiwa is an advanced industrial robot renowned for its flexibility and precision, widely used in fields such as automotive manufacturing, electronics assembly, and precision engineering. Figure 3 , Figure 4 By integrating this system into KUKA iiwa, this invention not only verified the system's functionality and performance, but also provided innovative technical support for the precise operation of robots.

[0092] During implementation, high-precision sensors installed on various joints and key components of the KUKA iiwa system first collect real-time key motion data such as the robot's position, velocity, and acceleration. This data is captured through the system's "sensor data acquisition" module, ensuring the comprehensiveness and accuracy of the data collection.

[0093] The collected data is then transmitted to the "data preprocessing" module, which performs preliminary data cleaning and formatting to provide clean and standardized data input for subsequent data processing. Next, the data is further processed in the "applying improved Ju-Gibbs quaternions" stage. The improved quaternion method in this invention can effectively handle the spatial rotation and attitude adjustment problems encountered by robots in complex industrial environments, thereby improving the accuracy and reliability of data processing.

[0094] During the data filtering stage, the system incorporates DASF (Data Analytical Spinning Function), which automatically adjusts filtering parameters based on real-time data changes. This intelligent processing not only improves data quality but also optimizes the system's responsiveness to environmental changes. Through this advanced data processing, the system can accurately calculate the robot's motion trajectory and generate detailed motion commands in the "Track Reconstruction Calculation" module.

[0095] Ultimately, these motion commands were used in the "trajectory playback" stage, and the KUKA iiwa robot was able to accurately reproduce the original motion trajectory, demonstrating a highly precise operational capability, with results such as... Figures 5 to 7 As shown in the diagram, the system also includes a "Feedback and Optimization" module, which continuously adjusts and optimizes system settings by analyzing the performance of trajectory playback, further improving the accuracy and efficiency of trajectory reconstruction.

[0096] Through its successful application on the KUKA iiwa robot, this invention not only demonstrates its technological innovation in the field of high-precision trajectory acquisition and reconstruction, but also provides valuable practical experience and technological accumulation for the future development and application of robot technology.

Claims

1. A method for real-time trajectory acquisition and high-precision reconstruction of a collaborative robot, characterized in that, Includes the following steps: Step 1: Collect real-time position and velocity data of the robot joints, including angle, velocity, and acceleration; Step 2: Preprocess the collected raw data using improved Ju-Gibbs quaternions to obtain the preprocessed position and velocity data of the robot joints; First, obtain the connection data θ from link l-1 to link l. l and n l , where θ l It is the angular position about the axis, n l It is an axis vector; the Ju-Gibbs quaternion expression is calculated as follows: in, It is the Ju-Gibbs quaternion describing the l-th link relative to the global reference coordinate system o. o q l This represents the unit quaternion of the l-th link relative to the reference coordinate system o, where o is the symbol representing the reference coordinate system. n l ,τ l It is a vector. It is a scalar; During the rotation of robot joints, Ju-Gibbs quaternions are written in general form as follows: in, It is a Ju-Gibbs quaternion describing the attitude from the reference coordinate system o to the (l-1)th link. It is a Ju-Gibbs quaternion describing the relative attitude transformation from the (l-1)th link to the lth link. It is the square of the modulus of a Ju-Gibbs quaternion; The rotation axis and rotation angle of each joint are combined using Ju-Gibbs quaternions to form a unified mathematical representation to describe the rotation of each joint; the rotation of each joint is continuously combined by quaternion multiplication to express the posture changes of the entire robotic arm. Step 3: Based on the rate and magnitude of change of the real-time data, apply a dynamic adaptive sliding filter to filter the preprocessed data; Step 4: Reconstruct the trajectory based on the filtered data. Using the inverse operation of Ju-Gibbs quaternions, deduce the robot's posture in the initial and intermediate states from the final quaternion state to reconstruct the robot's motion trajectory. Trajectory reconstruction is performed based on the filtered data, as follows: After the robot completes a series of actions, the data collected and processed in real time by the sensor system is converted into a final quaternion state. Using the inverse operation of the Ju-Gibbs quaternion formula, the robot's posture in the initial and intermediate states is deduced from the final quaternion state, thus reproducing the robot's motion trajectory. The mathematical model describing the robot's transition from one posture to another is as follows: in, Let be the Ju-Gibbs quaternion of the (l-1)th joint, representing the pose transformation from the reference coordinate system o to the corrected state d. It is the rotation axis vector of the (l-1)th joint. is the scalar part of the rotation angle of the (l-1)th joint, d is the correction or target state, and o is the reference coordinate system; It is the symmetric rotation axis matrix under the corrected state d. It is the rotation axis vector of the l-th joint. It is a symmetric matrix representation of the rotation axis of the l-th joint, n l It is the rotation axis vector of the l-th joint; Step 5: Compare the reconstructed trajectory with the actual robot motion trajectory, calculate the error index to evaluate the accuracy and efficiency of the reconstructed trajectory, and adjust and optimize the quaternion parameters and filtering algorithm based on the evaluation results.

2. The method for real-time trajectory acquisition and high-precision reconstruction of collaborative robots according to claim 1, characterized in that, The preprocessed data is filtered using a dynamic adaptive sliding filter, as follows: First, the difference between each data point in the data stream and the previous data point is calculated to obtain the rate and magnitude of data change; the data stream refers to the data sequence continuously collected by the robot's sensors, and the data points include position, velocity, or acceleration information. Then, based on the rate and magnitude of change, the size of the filtering window and the weight coefficients are dynamically adjusted, with the weight coefficients adjusted according to the time interval between the data point and the current processing point; The weights are calculated using the exponential decay model, with the formula w. i =e -α*d , where w i α is the weight coefficient assigned to each data point by the filter, d is the time step from the current data point, and α is the decay coefficient, which controls the rate at which the weight decreases. If both the rate and magnitude of data change exceed the set thresholds, the filter window is narrowed and the α value is increased; conversely, if neither the rate nor the magnitude of change exceeds the set thresholds, the filter window is expanded and the α value is decreased.

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