Adaptive optimization-based NURBS curve robot trajectory offset point focusing fitting method

Abstract

The invention discloses an NURBS curve robot trajectory offset point focusing fitting method based on adaptive optimization, which remarkably improves trajectory precision and calculation efficiency through adaptive optimization focused on an error offset point. The method comprises the steps of initial path planning, NURBS curve fitting, error evaluation and offset point extraction, adaptive optimization and real-time feedback adjustment. In error evaluation, double indexes of a root-mean-square error and a maximum absolute error are adopted, an offset point is accurately identified, a control point, a weight and a node vector are focused and optimized by using a genetic algorithm, and local optimum is effectively avoided. A regularization item is introduced into a fitness function, curve complexity and precision are balanced, and smoothness and feasibility of a track are achieved. And finally, real-time adjustment of the trajectory is realized through a multi-feedback mechanism, and the robustness of the robot in a dynamic environment is improved. Compared with the prior art, the precision, the real-time performance and the environmental adaptability of track generation are realized, and particularly, an efficient and accurate track fitting effect is achieved in a complex dynamic environment.

Description

Technical Field

[0001] The present invention relates to the technical 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 Art

[0002] With the rapid development of robotics technology, robots have been widely used in industries such as industry, service industry, and medical care. In these complex environments, robots must generate accurate trajectories that meet kinematic constraints to ensure efficient completion of tasks. Usually, robot trajectory planning requires smoothness and real-time performance, but existing trajectory generation technologies have many shortcomings in practical applications and are 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 and it is difficult to adapt to the 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 make the trajectory smoother and more flexible through the combination of control points, weights and node vectors. However, even with the use of NURBS curves, existing technologies still face a series of difficult-to-solve problems in practical applications: 1. High computational complexity: Existing trajectory optimization algorithms, especially those involving nonlinear constraints and multi-objective optimization, have large computational complexity and are difficult to achieve real-time trajectory optimization in complex environments. This problem is particularly evident in dynamic environments, where robots are often unable to quickly generate or adjust trajectories, affecting task execution efficiency.

[0004] 2. Lack of robustness: The existing technology is prone to failure in the face of environmental changes or path uncertainty. In particular, when the robot encounters obstacles or interference, the existing optimization algorithm is difficult to adjust the trajectory in time, resulting in task interruption. This lack of robustness is particularly prominent in industrial production lines and service robot applications.

[0005] 3. Local optimality problem: Many trajectory optimization algorithms are prone to fall into local optimal solutions, especially in high-dimensional spaces or under complex constraints. Although some optimization methods (such as simulated annealing or standard genetic algorithms) can avoid local optimality to a certain extent, in practical applications, due to the constraints of complex environments, these methods still have great difficulties in obtaining global optimal solutions.

[0006] To solve the above problems, existing technologies usually combine multiple methods. For example, to reduce computational complexity, some solutions use preset trajectories or simplified algorithm models; to improve robustness, some technologies add sensor feedback to correct the trajectory; to reduce local optimal phenomena, some methods expand the search space by adding random perturbations. However, these remedial measures often have limited effects and cannot systematically meet the needs of trajectory generation in complex dynamic environments. For example, although simplifying the algorithm can reduce the amount of calculation, it will sacrifice accuracy; although sensor feedback can enhance robustness, real-time performance and accuracy cannot be guaranteed; although random perturbations can reduce local optimality, they increase uncertainty, resulting in a decrease in the stability of trajectory generation.

[0007] Therefore, how to achieve high precision, strong robustness and real-time adjustment of the trajectory while ensuring computational efficiency has become a technical problem to be solved by the present invention. Summary of the invention

[0008] The technical problem solved by the present invention is to provide a NURBS curve robot trajectory offset point focusing fitting method based on adaptive optimization in response to the defects existing in the above-mentioned prior art, so as to solve the problem of insufficient adaptability of the existing trajectory generation technology proposed in the above-mentioned background technology in complex dynamic environments.

[0009] In order to solve the above technical problems, the technical solution adopted by the present invention is as follows: A NURBS curve robot trajectory offset point focusing fitting method based on adaptive optimization includes the following steps: S1: Initial path planning, generating an initial path through a path planning algorithm, and providing basic points for NURBS curve fitting based on the path; S2: NURBS curve fitting, based on the initial path, control points are selected and corresponding weights and node vectors are set to generate a preliminary NURBS curve so that the curve has basic smoothness; S3: Error evaluation and objective function construction, build an error evaluation model, including: Calculate the root mean square error RMSE between the generated NURBS curve and the initial path. The formula is: in, is the coordinate point on the initial path, The corresponding predicted points on the NURBS curve generated by the fitting; The maximum absolute error MAE is calculated to evaluate the maximum value of the path deviation. The formula is: The root mean square error (RMSE) is used to determine whether the overlap of the path segments meets the requirements. If the overlap does not meet the preset requirements, the maximum offset point is extracted as the object of adaptive optimization. S4: Adaptive optimization of the offset point, using a genetic algorithm to dynamically adjust the maximum offset point parameters extracted in S3, including the following sub-steps: The first sub-step: Initialize the population, randomly generate the initial population based on the control points, weights, and node vectors in the interval before and after the maximum offset; The second sub-step: fitness evaluation, establish a fitness function including a regularization term to balance the fitting error and curve complexity. The fitness function formula is: Among them, 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 a complexity measure, such as but not limited to the number of control points and the second-order derivative of the curve, and λ is the regularization weight parameter; The third sub-step: selection, crossover and mutation, through genetic operations to select individuals with smaller fitness values, and perform crossover and mutation operations to generate a new generation of population; The fourth sub-step: iterative optimization, continuously adjusting the control points, weights and node vectors of the NURBS curve according to the fitness evaluation results until the preset termination conditions are met; S5: Convergence judgment and trajectory output, set the error threshold or the maximum number of iterations. When the optimization process reaches the preset conditions, judge the algorithm convergence and output the final optimized NURBS curve trajectory; S6: Trajectory execution and real-time adjustment, which controls the robot motion based on the optimized NURBS curve trajectory. At the same time, the trajectory is dynamically adjusted according to environmental changes through a real-time feedback mechanism to improve the robustness of the trajectory.

[0010] As a further solution of the present invention, 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.

[0011] As a further solution of the present invention, the dual indicators of root mean square error and maximum absolute error are used for error evaluation in 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.

[0012] As a further solution of the present invention, the fitness function used in S4 controls the complexity of the curve through a regularization term, and the regularization term is used to suppress the excessive growth of the number of control points to avoid excessive smoothness of the trajectory.

[0013] As a further solution of the present invention, in the iterative optimization process in S4, the control points, weights, and node vectors are dynamically adjusted according to the feedback results of the fitness evaluation, and the NURBS curve trajectory finally generated gradually approaches the global optimal solution.

[0014] As a further solution of the present invention, the trajectory execution in S6 includes using a feedback control module to perform real-time deviation adjustment so that the optimized NURBS curve trajectory can adapt to dynamic environmental changes.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. Improved accuracy and computational efficiency: By introducing the offset point focus optimization strategy, the present invention 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 complexity and are difficult to apply in real time. However, the present invention significantly reduces the computational overhead by only optimizing the points with large offsets, improves the optimization efficiency, and ensures the global accuracy of the trajectory, making the present invention suitable for dynamic environments with high real-time requirements.

[0016] 2. High balance between smoothness and adaptability: The present invention adopts a dynamic adjustment mechanism in the setting of control points, weights and node vectors of NURBS curves, allowing the curve to flexibly adapt to different environmental complexities and path requirements. Through adaptive adjustment of control point weights, the trajectory generated by this method has high smoothness, reduces jitter and energy consumption in robot motion, and at the same time complies with the robot's kinematic and dynamic constraints, ensuring the practical feasibility of the trajectory.

[0017] 3. Effectively avoid local optimal traps: The fitness function of the present invention introduces a regularization term, which controls the complexity of the curve and suppresses the excessive growth of the number of control points, thereby reducing the local optimal problem 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.

[0018] 4. Real-time dynamic adjustment capability with high robustness: The present invention adopts multiple feedback mechanisms in the trajectory execution stage, so that the robot can adjust the trajectory in real time according to environmental changes. Especially in complex and dynamic application scenarios, the feedback control structure can achieve fine-tuning of the trajectory and effectively deal with uncertain factors in the environment. Compared with the single planning in the prior art, the present invention provides a more flexible and intelligent real-time optimization solution, which enables the robot to have higher environmental adaptability and task robustness.

[0019] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0021] Figure 1 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0022] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0023] See also Figure 1 In an embodiment of the present invention, a NURBS curve robot trajectory offset point focusing fitting method based on adaptive optimization includes the following steps: S1: Initial path planning, generating an initial path through classic path planning algorithms (such as A*, RRT), and providing basic points for NURBS curve fitting based on the path; S2: NURBS curve fitting, based on the initial path, control points are selected and corresponding weights and node vectors are set to generate a preliminary NURBS curve so that the curve has basic smoothness; S3: Error evaluation and objective function construction, build an error evaluation model, including: Calculate the root mean square error RMSE between the generated NURBS curve and the initial path. The formula is: in, is the coordinate point on the initial path, The corresponding predicted points on the NURBS curve generated by the fitting; The maximum absolute error MAE is calculated to evaluate the maximum value of the path deviation. The formula is: The root mean square error (RMSE) is used to determine whether the overlap of the path segments meets the requirements. If the overlap does not meet the preset requirements, the maximum offset point is extracted as the object of adaptive optimization. S4: Adaptive optimization of the offset point, using a genetic algorithm to dynamically adjust the maximum offset point parameters extracted in S3, including the following sub-steps: The first sub-step: Initialize the population, randomly generate the initial population based on the control points, weights, and node vectors in the interval before and after the maximum offset; The second sub-step: fitness evaluation, establish a fitness function including a regularization term to balance the fitting error and curve complexity. The fitness function formula is: Among them, 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 a complexity measure, such as but not limited to the number of control points and the second-order derivative of the curve, and λ is the regularization weight parameter; The third sub-step: selection, crossover and mutation, through genetic operations to select individuals with smaller fitness values, and perform crossover and mutation operations to generate a new generation of population; The fourth sub-step: iterative optimization, continuously adjusting the control points, weights and node vectors of the NURBS curve according to the fitness evaluation results until the preset termination conditions are met; S5: Convergence judgment and trajectory output, set the error threshold or the maximum number of iterations. When the optimization process reaches the preset conditions, judge the algorithm convergence and output the final optimized NURBS curve trajectory; S6: Trajectory execution and real-time adjustment, which controls the robot motion based on the optimized NURBS curve trajectory. At the same time, the trajectory is dynamically adjusted according to environmental changes through a real-time feedback mechanism to improve the robustness of the trajectory.

[0024] As a further solution of the present invention, 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.

[0025] As a further solution of the present invention, the dual indicators of root mean square error and maximum absolute error are used for error evaluation in 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.

[0026] As a further solution of the present invention, the fitness function used in S4 controls the complexity of the curve through a regularization term, and the regularization term is used to suppress the excessive growth of the number of control points to avoid excessive smoothness of the trajectory.

[0027] As a further solution of the present invention, in the iterative optimization process in S4, the control points, weights, and node vectors are dynamically adjusted according to the feedback results of the fitness evaluation, and the NURBS curve trajectory finally generated gradually approaches the global optimal solution.

[0028] As a further solution of the present invention, the trajectory execution in S6 includes using a feedback control module to perform real-time deviation adjustment so that the optimized NURBS curve trajectory can adapt to dynamic environmental changes.

[0029] Example 1 In the field of industrial production automation, robots are widely used in precision operations such as welding, spraying, and grinding. These operations usually require robots to execute precise trajectories in complex dynamic environments to ensure high quality and consistency of processing. However, existing trajectory generation technologies often fail to achieve real-time adjustments when faced with ever-changing path requirements during the production process, and are prone to trajectory deviations due to environmental interference, affecting the stability and accuracy of task execution.

[0030] This embodiment proposes a NURBS curve robot trajectory offset point focusing fitting method based on adaptive optimization to improve the trajectory accuracy, real-time response capability and robustness of the robot in the above application scenarios. The specific application scenarios are as follows: In assembly line operations, when the robot performs welding tasks, the size and position of the workpiece will shift with slight changes in the production batch, and there may be interference from other mechanical equipment on the assembly line, which requires the robot to be able to adjust the welding path in real time to maintain the accuracy of the welding position.

[0031] 1. Initial path planning and NURBS curve fitting: After the system is started, the initial path is first generated through the classic path planning algorithm (such as A* algorithm or RRT algorithm). This path is used as the basic point for NURBS curve fitting. According to the initial path, control points, weights and node vectors are set to generate a preliminary NURBS curve to make the path have basic smoothness. This preliminary path can meet basic welding requirements, but it still cannot adapt to unpredictable changes such as equipment movement and workpiece offset on the assembly line.

[0032] 2. Error evaluation and offset point identification: During the path execution process, the system will collect the actual data of the robot's welding position in real time through sensors, and compare 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 overlap between the preliminary NURBS curve and the actual path meets the requirements. When it is found that the offset 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, optimize the area in a targeted manner, avoid invalid adjustments to the entire path, and thus save computing resources.

[0033] 3. Adaptive optimization: Based on the offset point, the system starts the 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 for each path and evaluates it through a fitness function containing a regularization term. The fitness function not only considers the fitting error, but also introduces a regularization term to control the complexity of the curve and avoid excessive smoothness of the trajectory due to 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 best fitness, updates the NURBS curve parameters, and generates an optimized trajectory.

[0034] 4. Real-time feedback and dynamic adjustment: During the welding task, the system continuously monitors the execution of the trajectory through sensors. When the workpiece position is offset or equipment interference occurs on the assembly line, the system can dynamically adjust the control points and weights through the real-time feedback mechanism and make fine adjustments to ensure 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.

[0035] The technical solution of this embodiment achieves significant progress in robot trajectory generation technology through offset point focus 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. Secondly, the introduction of the regularization term in the fitness function achieves a balance between trajectory smoothness and accuracy by controlling the trajectory complexity, avoiding the local optimal trap of the traditional algorithm, and making the path always close to the global optimum. In addition, the real-time feedback mechanism ensures the robot's high adaptability to environmental changes, and can maintain path accuracy and task stability even in the case of equipment interference and workpiece offset. Compared with traditional single planning or simplified algorithm models, this 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.

[0036] Embodiment 2: In the application scenario of medical rehabilitation robots, robots assist patients in rehabilitation training, and their movement trajectories need to be precisely controlled to ensure the training effect while avoiding secondary injuries to patients. However, the patient's limb movements during rehabilitation training are uncertain, and rehabilitation robots must adapt to the patient's posture changes in real time and control the smoothness and accuracy of the trajectory to achieve efficient and smooth movement.

[0037] 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: Initial path planning and NURBS curve fitting: After receiving the initial action instruction, the rehabilitation robot generates the basic trajectory of the patient's rehabilitation training through the path planning algorithm. This trajectory is used as the initial path for NURBS curve fitting. The system selects control points and sets weights and node vectors according to the patient's limb position to generate a preliminary NURBS curve to ensure the basic smoothness and accuracy of the trajectory. The preliminary fitted NURBS curve can meet basic rehabilitation needs, but in actual training, the patient may produce unexpected deviations due to fatigue or active adjustment of the posture, making it difficult to maintain the accuracy and flexibility of the trajectory execution. Error evaluation and offset point extraction: During the training process, the system collects feedback data of the patient's limb position in real time through sensors, calculates the overlap between the NURBS curve and the patient's actual movement, and constructs an error evaluation model. The system uses the root mean square error (RMSE) and maximum absolute error (MAE) indicators to accurately identify the position points with large deviations by comparing the deviation between the actual path and the preliminary NURBS curve, so as to determine the key positions that may affect the effect of rehabilitation training. This approach allows the system to focus on areas with greater excursions and optimize the trajectory in that area, ensuring precision and smoothness in rehabilitation movements.

[0038] Adaptive optimization: After the offset point is determined, the system uses genetic algorithms to adaptively optimize the control points, weights, and node vectors of the point. First, the system generates an initial population and randomly generates several control point combinations based on the front and back trajectory information of the offset point. The fitness function is used for evaluation, and a regularization term is introduced in the fitness function to ensure the balance between the fitting accuracy and complexity of the trajectory. Trajectories with higher fitness gradually replace individuals with larger errors. After multiple rounds of iterations, the optimal control point combination is output. The optimized NURBS curve is closer to the patient's actual movement trajectory, ensuring the flexibility and accuracy of the rehabilitation movement trajectory. Real-time feedback and trajectory adjustment: During the training process, the patient's movement 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 point position to ensure the real-time and flexibility of the robot trajectory. Through this multiple feedback mechanism, the robot can respond to the patient's movement changes in a timely manner, continuously maintain the smoothness and accuracy of the trajectory, and avoid unnecessary oppression and injury to the patient.

[0039] Through the application of this embodiment, the rehabilitation robot realizes high-compliance and high-precision trajectory generation under the condition of patient movement uncertainty. First, the offset point focus optimization ensures that the system can quickly identify and optimize the area with the largest error, reduces the computational complexity of global adjustment, and enables the system to have real-time response capabilities in dynamic training. Secondly, the application of the regularization term in the fitness function effectively controls the trajectory complexity and achieves a high degree of trajectory accuracy while ensuring the smoothness of the trajectory. Thirdly, the real-time feedback mechanism enables the robot to respond immediately when the patient's posture changes, thereby improving the safety and adaptability of rehabilitation training. Compared with the traditional fixed-trajectory rehabilitation training method, the system of this embodiment significantly enhances the safety of the rehabilitation process and the comfort of the patient while improving the training effect, and is suitable for medical rehabilitation robot scenarios that require high compliance and high responsiveness.

[0040] In the present invention, unless otherwise clearly stipulated and limited, the terms "installation", "setting", "connection", "fixation", "screw-on" and the like should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral one; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be the internal connection of two elements or the interaction relationship between two elements. Unless otherwise clearly defined, ordinary technicians in this field can understand the specific meanings of the above terms in the present invention according to the specific circumstances.

[0041] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, the embodiments should be considered exemplary and non-restrictive in all respects, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims be included in the present invention.

Claims

1. A NURBS curve robot trajectory offset point focusing fitting method based on adaptive optimization, characterized in that: The following steps are involved: S1: Initial path planning, generating an initial path through a path planning algorithm, and providing basic points for NURBS curve fitting based on the path; S2: NURBS curve fitting, based on the initial path, control points are selected and corresponding weights and node vectors are set to generate a preliminary NURBS curve so that the curve has basic smoothness; S3: Error evaluation and objective function construction, build an error evaluation model, including: Calculate the root mean square error RMSE between the generated NURBS curve and the initial path. The formula is: in, is the coordinate point on the initial path, The corresponding predicted points on the NURBS curve generated by the fitting; The maximum absolute error MAE is calculated to evaluate the maximum value of the path deviation. The formula is: The root mean square error (RMSE) is used to determine whether the overlap of the path segments meets the requirements. If the overlap does not meet the preset requirements, the maximum offset point is extracted as the object of adaptive optimization. S4: Adaptive optimization of the offset point, using a genetic algorithm to dynamically adjust the maximum offset point parameters extracted in S3, including the following sub-steps: The first sub-step: Initialize the population, randomly generate the initial population based on the control points, weights, and node vectors in the interval before and after the maximum offset; The second sub-step: fitness evaluation, establish a fitness function including a regularization term to balance the fitting error and curve complexity. The fitness function formula is: Among them, 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 a complexity measure, such as but not limited to the number of control points and the second-order derivative of the curve, and λ is the regularization weight parameter; The third sub-step: selection, crossover and mutation, through genetic operations to select individuals with smaller fitness values, and perform crossover and mutation operations to generate a new generation of population; The fourth sub-step: iterative optimization, continuously adjusting the control points, weights and node vectors of the NURBS curve according to the fitness evaluation results until the preset termination conditions are met; S5: Convergence judgment and trajectory output, set the error threshold or the maximum number of iterations. When the optimization process reaches the preset conditions, judge the algorithm convergence and output the final optimized NURBS curve trajectory; S6: Trajectory execution and real-time adjustment, which controls the robot motion based on the optimized NURBS curve trajectory. At the same time, the trajectory is dynamically adjusted according to environmental changes through a real-time feedback mechanism to improve the robustness of the trajectory.

2. The method for focusing the trajectory offset point of a NURBS curve robot based on adaptive optimization 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 to ensure the smoothness of the curve.

3. The method for focusing fitting a NURBS curve robot trajectory offset point based on adaptive optimization according to claim 1, characterized in that: In S3, dual indicators of root mean square error and maximum absolute error are used to perform error evaluation. 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.

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

5. The method for fitting the trajectory offset point of a NURBS curve robot based on adaptive optimization according to claim 1, characterized in that: During the iterative optimization process in S4, the control points, weights, and node vectors are dynamically adjusted according to the feedback results of the fitness evaluation, and the NURBS curve trajectory finally generated gradually approaches the global optimal solution.

6. The method for fitting the trajectory offset point of a NURBS curve robot based on adaptive optimization according to claim 1, characterized in that: The trajectory execution in S6 includes using a feedback control module to perform real-time deviation adjustment so that the optimized NURBS curve trajectory can adapt to dynamic environmental changes.

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