Adaptive optimization based nurbs curve robot trajectory offset point focused fitting method

Abstract

The application discloses a kind of NURBS curve robot trajectory deviation point focusing fitting method based on adaptive optimization, and the trajectory precision and calculation efficiency are significantly improved by focusing on the adaptive optimization of error deviation point.The method includes initial path planning, NURBS curve fitting, error evaluation and deviation point extraction, adaptive optimization and real-time feedback adjustment.In error evaluation, the dual indicators of root mean square error and maximum absolute error are used to accurately identify the deviation point, and the genetic algorithm is used to focus on the optimization of control points, weights and node vectors to effectively avoid local optimum.The fitness function introduces a regularization term to balance the complexity and accuracy of the curve, achieving smoothness and feasibility of the trajectory.The final trajectory is adjusted in real time through a multi-feedback mechanism to improve the robustness of the robot in dynamic environments.Compared with the prior art, the application achieves precision, real-time and environmental adaptability in trajectory generation, especially in complex dynamic environments, achieving efficient and accurate trajectory fitting.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of robot trajectory optimization and curve fitting, and in particular to a NURBS curve robot trajectory offset point focusing fitting method based on adaptive optimization. BACKGROUND

[0002] With the rapid development of robot technology, robots have been widely used in industry, service industry and medical treatment, etc. In these complex environments, robots must generate accurate and kinematically constrained trajectories to ensure efficient task completion. Generally, robot trajectory planning requires smoothness and real-time performance, but existing trajectory generation techniques have many shortcomings in practical applications, making it difficult to meet the increasingly complex application requirements.

[0003] Traditional trajectory generation methods mostly use preset paths or single curve fitting, such as polynomial curves or spline curves. These methods generate trajectories by calculating control points, but their flexibility is limited, making it difficult to adapt to uncertainty and complexity in dynamic environments. To this end, the industry has gradually introduced more flexible NURBS (Non-Uniform Rational B-Spline) curve fitting methods, which combine control points, weights and node vectors to make the trajectory have certain smoothness and flexibility. However, even with NURBS curves, existing technologies still face a series of problems in practical applications:

[0004] 1. High computational complexity: Existing trajectory optimization algorithms, especially those involving nonlinear constraints and multi-objective optimization, have large computational loads, making it difficult to achieve real-time trajectory optimization in complex environments. This problem is particularly evident in dynamic environments, where robots often cannot quickly generate or adjust trajectories, affecting task execution efficiency.

[0005] 2. Lack of robustness: Existing technologies are prone to failure when faced with environmental changes or path uncertainty, especially when robots encounter obstacles or interference. Existing optimization algorithms are difficult to adjust trajectories in a timely manner, leading to task interruption. This lack of robustness is particularly prominent in industrial production lines and service robot applications.

[0006] 3. Local optimal problem: Many trajectory optimization algorithms are prone to local optimal solutions, especially in high-dimensional space or complex constraint conditions. Although some optimization methods (such as simulated annealing or standard genetic algorithm) can avoid local optimality to some extent, in practical applications, due to the constraints of complex environments, these methods still have great difficulty in achieving global optimal solutions.

[0007] To solve the above problems, the prior art usually combines multiple methods. For example, to reduce the computational complexity, some schemes use preset trajectories or simplified algorithm models; to improve robustness, some technologies add sensor feedback to correct the trajectory; to reduce local optimal phenomenon, some methods add random disturbance to expand the search space. However, these remedies often have limited effect and cannot systematically meet the trajectory generation requirements in complex dynamic environments. For example, simplified algorithms can reduce computational load, but at the expense of accuracy; sensor feedback can enhance robustness, but real-time performance and accuracy cannot be guaranteed; random disturbance can reduce local optimum, but increases uncertainty, resulting in decreased stability of trajectory generation.

[0008] Therefore, how to realize high-precision, strong robustness and real-time adjustment of the trajectory under the premise of ensuring computational efficiency has become a technical problem to be solved by the present application. SUMMARY

[0009] The technical problem solved by the present application is to provide a NURBS curve robot trajectory offset point focusing fitting method based on adaptive optimization to solve the problem of insufficient adaptability of the existing trajectory generation technology in complex dynamic environments.

[0010] To solve the above technical problems, the technical solutions adopted by the present application are as follows:

[0011] A NURBS curve robot trajectory offset point focusing fitting method based on adaptive optimization, comprising the following steps:

[0012] S1: initial path planning, generating an initial path through a path planning algorithm, and providing basis points for NURBS curve fitting based on the path;

[0013] S2: NURBS curve fitting, selecting control points based on the initial path and setting corresponding weights and node vectors to generate a preliminary NURBS curve, so that the curve has basic smoothness;

[0014] S3: error evaluation and target function construction, constructing an error evaluation model, specifically including:

[0015] Calculating the root mean square error RMSE of the generated NURBS curve and the initial path, the formula is:

[0016]

[0017] wherein, is the coordinate point on the initial path, is the corresponding prediction point on the fitted NURBS curve;

[0018] A maximum absolute error MAE is calculated to evaluate the maximum value of the path deviation, and the formula is:

[0019]

[0020] A root mean square error RMSE is used to determine whether the coincidence degree of the path segment meets the requirements, and if the coincidence degree does not meet the preset requirements, the maximum deviation point is extracted as the object of adaptive optimization.

[0021] S4: Adaptive optimization of the deviation point, the genetic algorithm is used to dynamically adjust the maximum deviation point parameters extracted in S3, including the following sub-steps:

[0022] First sub-step: initialization of the population, the initial population is randomly generated based on the control points, weights, and node vectors of the intervals before and after the maximum deviation;

[0023] Second sub-step: fitness evaluation, a fitness function including a regularization term is established to balance the fitting error and the complexity of the curve, and the formula of the fitness function is:

[0024]

[0025] Wherein, F(I) is the fitness, the smaller the value, the better the fitting effect; RMSE(I) is the fitting error of the current individual; C(I) is the complexity measure, including but not limited to the number of control points, the second derivative of the curve, and λ is the regularization weight parameter;

[0026] Third sub-step: selection, crossover and mutation, the individuals with smaller fitness values are selected through genetic operations, and crossover and mutation operations are performed to generate a new generation of population;

[0027] Fourth sub-step: iterative optimization, the control points, weights and node vectors of the NURBS curve are continuously adjusted according to the fitness evaluation results until the preset termination condition is met;

[0028] S5: Convergence judgment and trajectory output, set an error threshold or a maximum number of iterations, when the optimization process meets the preset condition, judge the algorithm to converge and output the final optimized NURBS curve trajectory;

[0029] S6: Trajectory execution and real-time adjustment, based on the optimized NURBS curve trajectory, the robot motion is controlled, and through the real-time feedback mechanism, the trajectory is dynamically adjusted according to the environmental changes to improve the robustness of the trajectory.

[0030] As a further scheme of the present application, the initial weights of the NURBS curve control points set in S2 are uniformly distributed, and the node vectors are initially uniformly distributed to ensure the smoothness of the curve.

[0031] As a further scheme of the present application, the double indicators of root mean square error and maximum absolute error are used in the error evaluation of S3, the root mean square error is used to evaluate the overall accuracy of the fitting path, and the maximum absolute error is used to identify and mark the point with the largest deviation.

[0032] As a further scheme of the present application, the fitness function used in S4 controls the complexity of the curve through a regularization term, which is used to suppress the excessive growth of the number of control points to avoid excessive smoothing of the trajectory.

[0033] As a further scheme of the present application, in the iterative optimization process in S4, the dynamic adjustment of control points, weights, and node vectors is based on the feedback results of fitness evaluation, and the finally generated NURBS curve trajectory gradually approaches the global optimal solution.

[0034] As a further scheme of the present application, the trajectory execution in S6 includes real-time deviation adjustment using a feedback control module, so that the optimized NURBS curve trajectory can adapt to dynamic environmental changes.

[0035] Compared with the prior art, the present application has the following advantages:

[0036] 1. Precision improvement and calculation efficiency: By introducing the deviation point focusing optimization strategy, the present application not only focuses on the overall accuracy of the trajectory, but also focuses on the local optimization of key error points. Traditional global optimization algorithms usually have large computational load and are difficult to apply in real time. By focusing on the optimization of points with large deviations, the present application significantly reduces the computational overhead, improves the optimization efficiency, and guarantees the global accuracy of the trajectory, making the present application suitable for dynamic environments with high real-time requirements.

[0037] 2. High balance between smoothness and adaptability: The present application adopts a dynamic adjustment mechanism in the setting of control points, weights and node vectors of NURBS curve, allowing the curve to adapt flexibly to different environmental complexity and path requirements. Through adaptive adjustment of the control point weight, the trajectory generated by this method not only has high smoothness, reducing the jitter and energy consumption in robot motion, but also meets the kinematics and dynamics constraints of the robot, ensuring the practical feasibility of the trajectory.

[0038] 3. Effectively avoid local optimal trap: The fitness function of the present application introduces a regularization term to control the complexity of the curve, which suppresses the excessive growth of the number of control points, thereby reducing the problem of local optimum caused by excessive smoothing. In the iterative optimization process, the dynamic adjustment of control points and weights makes the trajectory gradually approach the global optimal solution.

[0039] 4. Real-time dynamic adjustment capability with high robustness: The application adopts a multiple feedback mechanism in the trajectory execution phase, enabling the robot to adjust the trajectory in real time according to environmental changes. Especially in complex and dynamic application scenarios, this feedback control structure can fine-tune the trajectory and effectively cope with uncertain factors in the environment. Compared with the single planning in the prior art, the application provides a more flexible and intelligent real-time optimization scheme, enabling the robot to have higher environmental adaptability and task robustness.

[0040] Additional aspects and advantages of the application will be described in the following description, will become apparent from the following description, or will be learned by practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0042] Figure 1 The flowchart of the present application. DETAILED DESCRIPTION

[0043] The technical solutions in the embodiments of the present application will be described in detail below. Obviously, the described embodiments are only some of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0044] Please refer to Figure 1 In the embodiments of the present application, a NURBS curve robot trajectory offset point focusing fitting method based on adaptive optimization includes the following steps:

[0045] S1: initial path planning, generating an initial path through a classic path planning algorithm (such as A*, RRT), and providing basis points for NURBS curve fitting based on the path;

[0046] S2: NURBS curve fitting, selecting control points based on the initial path and setting corresponding weights and node vectors, generating a preliminary NURBS curve to make the curve have basic smoothness;

[0047] S3: error evaluation and target function construction, constructing an error evaluation model, specifically including:

[0048] The root mean square error RMSE of the calculation-generated NURBS curve and the initial path is calculated, and the formula is:

[0049]

[0050] wherein, is a coordinate point on the initial path, is a corresponding prediction point on the fitting-generated NURBS curve;

[0051] The maximum absolute error MAE is calculated, which is used to evaluate the maximum value of the path offset, and the formula is:

[0052]

[0053] The root mean square error RMSE is used to determine whether the coincidence degree of the path segment meets the requirements, and if the coincidence degree does not meet the preset requirements, the maximum offset point is extracted as the object of adaptive optimization;

[0054] S4: Adaptive optimization of the offset point, the genetic algorithm is used to dynamically adjust the maximum offset point parameters extracted in S3, including the following sub-steps:

[0055] First sub-step: initialization of the population, the initial population is randomly generated based on the control points, weights and node vectors of the intervals before and after the maximum offset;

[0056] Second sub-step: fitness evaluation, a fitness function including a regularization term is established to balance the fitting error and the complexity of the curve, and the formula of the fitness function is:

[0057]

[0058] wherein, F(I) is the fitness, the smaller the value, the better the fitting effect; RMSE(I) is the fitting error of the current individual; C(I) is the complexity measure, including but not limited to the number of control points, the second derivative of the curve, and λ is the regularization weight parameter;

[0059] Third sub-step: selection, crossover and mutation, the individuals with smaller fitness values are selected through genetic operation, and crossover and mutation operations are performed to generate a new generation of population;

[0060] Fourth sub-step: iterative optimization, the control points, weights and node vectors of the NURBS curve are continuously adjusted according to the fitness evaluation results until the preset termination condition is met;

[0061] S5: Convergence judgment and trajectory output, set an error threshold or a maximum number of iterations, when the optimization process meets the preset condition, judge the algorithm to be converged and output the final optimized NURBS curve trajectory;

[0062] S6: Trajectory execution and real-time adjustment, based on the optimized NURBS curve trajectory to control the robot motion, while through the real-time feedback mechanism to dynamically adjust the trajectory according to the environmental changes, to improve the robustness of the trajectory.

[0063] As a further scheme of the present application, the initial weights of the NURBS curve control points set in S2 are uniformly distributed, and the node vectors are initially uniformly distributed to ensure the smoothness of the curve.

[0064] As a further scheme of the present application, the dual indicators of root mean square error and maximum absolute error are used in S3 for error evaluation, the root mean square error is used to evaluate the overall accuracy of the fitted path, and the maximum absolute error is used to identify and mark the points with the largest deviation.

[0065] As a further scheme of the present application, the fitness function used in S4 controls the complexity of the curve through a regularization term, which is used to suppress the excessive growth of the number of control points to avoid excessive smoothing of the trajectory.

[0066] As a further scheme of the present application, in the iterative optimization process in S4, the dynamic adjustment of control points, weights, and node vectors is based on the feedback results of fitness evaluation, and the finally generated NURBS curve trajectory gradually approaches the global optimal solution.

[0067] As a further scheme of the present application, the trajectory execution in S6 includes real-time deviation adjustment using a feedback control module, so that the optimized NURBS curve trajectory can adapt to dynamic environmental changes.

[0068] Embodiment 1

[0069] In the field of industrial production automation, robots are widely used in welding, spraying, grinding and other fine operations. These operations usually require the robot to execute precise trajectories in complex dynamic environments to ensure high quality and consistency of processing. However, existing trajectory generation techniques often fail to achieve real-time adjustment when faced with changing path requirements in the production process, and are prone to trajectory deviation due to environmental interference, affecting the stability and accuracy of task execution.

[0070] This embodiment proposes a NURBS curve robot trajectory deviation point focusing fitting method based on adaptive optimization to improve the trajectory accuracy, real-time response capability and robustness of robots in the above application scenarios. The specific application scenarios are as follows: in the pipeline operation, when the robot performs a welding task, due to the slight changes in the size and position of the workpiece with each production batch, as well as the interference of other mechanical equipment on the pipeline, the robot is required to adjust the welding path in real time to maintain the accuracy of the welding position.

[0071] 1. Initial path planning and NURBS curve fitting: After the system starts, an initial path is generated through classic path planning algorithms (such as A* algorithm or RRT algorithm). This path serves as the basis for NURBS curve fitting. Based on the initial path, control points, weights, and node vectors are set to generate a preliminary NURBS curve, making the path have basic smoothness. This preliminary path can meet the basic welding requirements, but it still cannot adapt to unpredictable changes such as equipment movement on the assembly line and workpiece deviation.

[0072] 2. Error evaluation and offset point identification: During path execution, the system collects real-time data of the robot's welding position through sensors and compares it with the fitted path to build an error evaluation model. The system calculates the root mean square error (RMSE) and the maximum absolute error (MAE) to determine whether the coincidence of the preliminary NURBS curve and the actual path meets the requirements. When the deviation exceeds the preset threshold, the system automatically extracts the maximum offset point as the target point for adaptive optimization. In this way, the system can accurately identify the area with the most significant deviation in the path and optimize that area specifically, avoiding unnecessary adjustments to the entire path and saving computational resources.

[0073] 3. Adaptive optimization: Based on the offset point, the system initiates a genetic algorithm for adaptive optimization. First, the system initializes the population and randomly generates a set of control points, weights, and node vector combinations to form multiple optimization candidate paths. In the fitness evaluation stage, the system calculates the fitness of each path and evaluates it through a fitness function that includes a regularization term. The fitness function not only considers fitting errors but also introduces a regularization term to control the complexity of the curve, avoiding excessive smoothing of the trajectory caused by too many control points, thereby achieving the best balance between smoothness and trajectory accuracy. After multiple rounds of crossover and mutation operations, the system outputs the path with the optimal fitness and updates the NURBS curve parameters to generate the optimized trajectory.

[0074] 4. Real-time feedback and dynamic adjustment: During the execution of the welding task, the system continuously monitors the execution of the trajectory through sensors. When the workpiece position deviates or equipment interference occurs on the assembly line, the system can dynamically adjust the control points and weights through a real-time feedback mechanism for fine-tuning, ensuring that the robot always runs along the optimal path. This feedback mechanism enables the robot to adapt flexibly in complex dynamic environments, significantly improving the robustness of the task.

[0075] The technical solution of the embodiment realizes significant progress in robot trajectory generation technology through offset point focusing optimization, dynamic control point adjustment, and real-time feedback mechanism. First, in a dynamic environment, the robot can accurately identify and optimize key offset points according to the actual path offset, reducing the computational cost of global path adjustment. Second, the introduction of the regularization term in the fitness function balances the smoothness and accuracy of the trajectory by controlling the trajectory complexity, avoiding the local optimal trap of traditional algorithms, and making the path always approach the global optimal. In addition, the real-time feedback mechanism ensures the high adaptability of the robot to environmental changes, even in the case of equipment interference and workpiece offset, the path accuracy and task stability can be maintained. Compared with traditional single planning or simplified algorithm model, the embodiment can meet the real-time, flexibility and robustness requirements in high-precision welding tasks, and provides an effective solution for robot trajectory optimization in complex dynamic environments.

[0076] Embodiment 2:

[0077] In the application scenario of medical rehabilitation robots, the robot assists the patient in rehabilitation training, which requires precise control of the action trajectory to ensure the training effect while avoiding secondary harm to the patient. However, the patient's limb movement in rehabilitation training is uncertain, and the rehabilitation robot must adapt to the patient's posture changes in real time and control the smoothness and accuracy of the trajectory to achieve efficient and compliant motion.

[0078] The NURBS curve robot trajectory offset point focusing fitting method based on adaptive optimization proposed in this embodiment is suitable for such medical rehabilitation scenarios. For example:

[0079] Initial path planning and NURBS curve fitting: After receiving the initial motion instructions, the rehabilitation robot generates a basic trajectory for the patient's rehabilitation training through a path planning algorithm. This trajectory serves as the initial path for NURBS curve fitting. The system selects control points, sets weights and node vectors based on the patient's limb position to generate a preliminary NURBS curve, ensuring the basic smoothness and accuracy of the trajectory. The preliminary NURBS curve can meet the basic rehabilitation needs, but during actual training, the patient may deviate unexpectedly due to fatigue or active adjustment of the action posture, making it difficult to maintain the accuracy and flexibility of the trajectory. Error evaluation and offset point extraction: During training, the system collects real-time feedback data on the patient's limb position through sensors and calculates the degree of coincidence between the NURBS curve and the patient's actual action to build an error evaluation model. The system uses the root mean square error (RMSE) and the maximum absolute error (MAE) as indicators to accurately identify the position points with large deviations by comparing the actual path with the preliminary NURBS curve, thereby determining the key positions that may affect the rehabilitation training effect. This method enables the system to focus on areas with large deviations, optimize the trajectory in that area, and ensure the accuracy and flexibility of the rehabilitation movement.

[0080] Adaptive optimization: After determining the offset points, the system uses a genetic algorithm to adaptively optimize the control points, weights and node vectors at these points. First, the system generates an initial population and randomly generates several control point combinations based on the trajectory information before and after the offset points. Through an evaluation of the fitness function, a regularization term is introduced to ensure a balance between the fitting accuracy and complexity of the trajectory. Trajectories with higher fitness gradually replace individuals with larger errors, and after multiple iterations, the optimal control point combination is output. The optimized NURBS curve further approximates the actual action trajectory of the patient, ensuring the flexibility and accuracy of the rehabilitation movement. Real-time feedback and trajectory adjustment: During training, the patient's action posture may change at any time. The system obtains real-time feedback data through sensors and dynamically adjusts the control point weights and node vectors of the NURBS curve based on the offset points to ensure the real-time and flexibility of the robot trajectory. Through this multi-feedback mechanism, the robot can respond to changes in the patient's actions in a timely manner, continuously maintain the smoothness and accuracy of the trajectory, and avoid unnecessary pressure and harm to the patient.

[0081] Through the application of the embodiment, the rehabilitation robot realizes high compliance and high-precision trajectory generation under the condition of patient motion uncertainty. First, the offset point focusing optimization ensures that the system can quickly identify and optimize the area with the largest error, reducing the computational complexity of global adjustment, so that the system has real-time response capability in dynamic training. Second, the application of the regularization term in the fitness function effectively controls the trajectory complexity, achieving high trajectory accuracy while ensuring trajectory smoothness. Third, the real-time feedback mechanism enables the robot to respond immediately when the patient's posture changes, improving the safety and adaptability of rehabilitation training. Compared with the traditional fixed trajectory rehabilitation training method, the system of the embodiment improves the training effect while significantly enhancing the safety of the rehabilitation process and the comfort of the patient, and is suitable for medical rehabilitation robot scenarios that require high compliance and high responsiveness.

[0082] In the present application, unless otherwise explicitly specified and limited, the terms "mounting", "setting", "connecting", "fixing", "screw connecting" and the like should be understood in a broad sense, for example, can be fixed connection, can also be detachable connection, or integral; can be mechanical connection, can also be electrical connection; can be directly connected, can also be indirectly connected through an intermediate medium, can be the internal communication of two elements or the interaction relationship between two elements, unless otherwise explicitly limited, those skilled in the art can understand the specific meaning of the above-mentioned terms in the present application according to the specific circumstances.

[0083] It is obvious for those skilled in the art that the present application is not limited to the details of the above exemplary embodiments, and the present application can be implemented in other specific forms without departing from the spirit or essential characteristics of the present application. Therefore, the embodiments should be regarded as exemplary and non-limiting, the scope of the present application is defined by the appended claims rather than the above description, and all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present application.

Claims

1. A method of adaptive optimization based NURBS curve robot trajectory offset point focused fitting, characterized in that, Comprise the following steps: S1: initial path planning, generating an initial path by a path planning algorithm, and providing basis points for NURBS curve fitting based on the path; S2: NURBS curve fitting, selecting control points based on the initial path and setting corresponding weights and node vectors to generate a preliminary NURBS curve so that the curve has basic smoothness; S3: error evaluation and target function construction, constructing an error evaluation model, specifically including: Calculate the root mean square error RMSE of the generated NURBS curve and the initial path, the formula is: ； wherein, is a coordinate point on the initial path, is a corresponding predicted point on the NURBS curve generated by the fitting; Calculate the maximum absolute error MAE, which is used to evaluate the maximum value of path deviation, the formula is: ； Use the root mean square error RMSE to judge whether the coincidence degree of the path segment meets the requirements, if the coincidence degree does not meet the preset requirements, extract the maximum deviation point as the object of adaptive optimization; S4: adaptive optimization of the deviation point, dynamically adjusting the parameters of the maximum deviation point extracted in S3 using a genetic algorithm, including the following sub-steps: First sub-step: initialize the population, randomly generate an initial population based on the control points, weights, and node vectors of the interval before and after the maximum deviation; Second sub-step: fitness evaluation, establish a fitness function containing a regularization term to balance the fitting error and the complexity of the curve, the fitness function formula is: ； Where F(I) is the fitness, the smaller the value, the better the fitting effect; RMSE(I) is the fitting error of the current individual; C(I) is the complexity measure, including but not limited to the number of control points, the second derivative of the curve, and λ is the regularization weight parameter; Third sub-step: selection, crossover and mutation, select individuals with smaller fitness values through genetic operations, and perform crossover and mutation operations to generate a new generation of population; Fourth sub-step: iterative optimization, continuously adjust the control points, weights and node vectors of the NURBS curve according to the fitness evaluation results until the preset termination condition is met; S5: convergence judgment and trajectory output, set an error threshold or a maximum number of iterations, when the optimization process reaches the preset condition, judge whether the algorithm converges and output the final optimized NURBS curve trajectory; S6: trajectory execution and real-time adjustment, control the robot motion based on the optimized NURBS curve trajectory, and dynamically adjust the trajectory according to environmental changes through a real-time feedback mechanism.

2. The adaptive optimization based NURBS curve robot trajectory offset point focused fitting method according to claim 1, characterized in that, The initial weights of the NURBS curve control points set in S2 are uniformly distributed, and the node vectors are initially uniformly distributed.

3. The adaptive optimization based NURBS curve robot trajectory offset point focused fitting method according to claim 1, characterized in that, In S3, the double indicators of root mean square error and maximum absolute error are used for error evaluation, the root mean square error is used to evaluate the overall accuracy of the fitted path, and the maximum absolute error is used to identify and mark the point with the maximum deviation.

4. The adaptive optimization based NURBS curve robot trajectory offset point focused fitting method according to claim 1, characterized in that, The fitness function used in S4 controls the complexity of the curve through a regularization term, which is used to suppress the excessive growth of the number of control points.

5. The adaptive optimization based NURBS curve robot trajectory offset point focused fitting method according to claim 1, characterized in that, In the iterative optimization process in S4, the dynamic adjustment of the control points, weights and node vectors is based on the feedback results of the fitness evaluation, and the finally generated NURBS curve trajectory gradually approaches the global optimal solution.

6. The adaptive optimization based NURBS curve robot trajectory offset point focused fitting method according to claim 1, wherein, The trajectory execution in S6 includes real-time deviation adjustment using a feedback control module.

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