A trajectory point position optimization method based on simulation technology

Abstract

The application relates to the computer technical field and discloses a trajectory point position optimization method based on simulation technology. The method comprises the following steps: obtaining an initial trajectory point position sequence and fitting the same into a non-uniform rational B-spline parameterized curve; constructing a high-fidelity simulation environment containing a kinematics model, a dynamics model, a collision detection model and a constraint model; defining a multi-target composite cost function which fuses a collision penalty, kinematics constraints, smoothness and length; in the simulation environment, iteratively optimizing the curve control points by using a covariance matrix self-adaptive evolution strategy with the target of minimizing the cost function; and finally generating an executable discrete trajectory sequence. The system comprises five modules, namely, a trajectory parameterization module, a simulation construction module, a trajectory evaluation module, a control point optimization module and a trajectory generation module. Through simulation-driven closed-loop optimization, the physical feasibility, smoothness and optimization efficiency of the trajectory are significantly improved.

Description

Technical Field

[0001] This invention belongs to the field of computer technology, specifically relating to a method for optimizing trajectory points based on simulation technology. Background Technology

[0002] With the widespread application of industrial robots in intelligent manufacturing, automated assembly, and complex work scenarios, high-precision and high-efficiency trajectory planning technology has become a key element in ensuring system performance. The core objective of trajectory planning is to generate a smooth, feasible, and optimized motion path from the starting point to the target point while satisfying kinematic constraints and environmental obstacle avoidance.

[0003] Traditional trajectory planning methods are mostly based on two-dimensional planar models or simplified spatial assumptions in their algorithm design. Their computational framework is difficult to directly adapt to the complex geometric relationships and dynamic characteristics in three-dimensional space. When such methods are transferred to three-dimensional scenes, the increase in dimensionality leads to an exponential expansion of the search space and a sharp increase in computational complexity. This not only significantly prolongs the planning time but also easily sacrifices trajectory quality due to computational limitations, making it difficult to meet the engineering requirements that emphasize both real-time performance and accuracy.

[0004] Trajectory point generation methods based on sampling or optimization face significant challenges in 3D space. Existing techniques typically construct trajectories using discrete point sequences and avoid collisions by adjusting the order or position of the points. However, this approach has fundamental flaws: point rearrangement lacks a global consideration of the robot's workspace accessibility and motion continuity, failing to guarantee that the adjusted trajectory truly avoids obstacles; due to the strong coupling characteristics of the robot's kinematic chain structure, modifications to local points often trigger the reparameterization and inverse kinematics solution of the entire trajectory. Especially when the number of points is large, repeated iterations lead to enormous computational overhead, severely limiting the system's response speed and operational efficiency.

[0005] Existing technologies lack sufficient development of mechanisms for coordinating simulation and computation. Most planning processes place simulation verification in the post-planning stage, resulting in significant discrepancies between computational results and physical execution. The planning phase does not adequately integrate high-fidelity simulation feedback, causing feasibility assessments of locations to rely on idealized models, making it difficult to reflect actual constraints such as joint limits, singular configurations, or dynamic obstacles in real robotic arms.

[0006] The aforementioned problems collectively result in a rigid trajectory planning process, weak fault tolerance, and low utilization of computational resources, which are particularly pronounced in complex 3D operating environments. Therefore, there is an urgent need for a collaborative mechanism that can deeply integrate high-fidelity physical simulation and trajectory optimization calculation to achieve efficient, accurate, and collision-free optimization of trajectory points. Summary of the Invention

[0007] The purpose of this invention is to provide a method for optimizing trajectory points based on simulation technology, in order to solve the technical problems in the prior art, such as high computational complexity of trajectory planning for three-dimensional space robots, insufficient consideration of kinematic constraints and physical environment, and poor trajectory feasibility and low optimization efficiency caused by the disconnect between planning and simulation verification.

[0008] To achieve the above objectives, the present invention provides a method for optimizing trajectory points based on simulation technology, which includes the following steps: The robot's initial trajectory point sequence is obtained, which consists of a series of discrete pose points defined in a three-dimensional workspace. Based on the initial trajectory point sequence, an initial parameterized trajectory curve is generated by a non-uniform rational B-spline curve fitting algorithm. The parameterized trajectory curve is uniquely determined by a set of control point position coordinates, node vectors, and a set of weight coefficients. A high-fidelity three-dimensional simulation environment is constructed, which accurately reproduces the robot body and its operating scenario in digital space; the construction of the simulation environment specifically includes: A kinematic model of the robot is established, and the kinematic model uses the Danavit-Hartenberg parametric method to provide a geometric and kinematic description of each link and joint of the robot. Establish a dynamic model of the robot, which includes the mass, center of mass position, and inertia tensor of each link; A corresponding collision detection model is established for each link of the robot body and all static and dynamic obstacles in the workspace. The collision detection model approximates the physical entity by using a combination of convex hull or basic geometric shapes for subsequent collision detection calculations. Establish a constraint model for the robot, which includes angular limits, angular velocity limits, and angular acceleration limits for each joint, as well as a singular configuration monitoring mechanism based on the determinant value of the robot's Jacobian matrix. A multi-objective composite cost function is defined to evaluate the quality of the parameterized trajectory curve. This composite cost function is a linear combination of multiple weighted sub-cost functions. Specifically, each sub-cost function includes: a collision penalty term, whose value is proportional to the reciprocal of the penetration depth or minimum distance between the robot and an obstacle while moving along the parameterized trajectory curve; a kinematic constraint penalty term, whose value increases exponentially as the robot's joint variables approach or exceed their preset limits, and further increases with the increase of the Jacobian matrix condition number when the robot approaches a singular configuration; a trajectory smoothness cost term, whose value is obtained by calculating the square integral of curvature or the square integral of jerk over the entire domain of the parameterized trajectory curve, used to quantify the curvature of the trajectory and the smoothness of the motion; and a trajectory length cost term, whose value is the total arc length of the parameterized trajectory curve. The composite cost function obtains a comprehensive evaluation scalar by weighted summation of the above sub-cost functions. In the high-fidelity simulation environment, the three-dimensional position coordinates of the control points of the parameterized trajectory curve are iteratively optimized with the goal of minimizing the composite cost function; the iterative optimization process terminates within a preset upper limit of the number of iterations or when the value of the composite cost function converges to below a preset threshold. After the iterative optimization process terminates, the final parameterized trajectory curve defined by the optimized control point set is output; the final parameterized trajectory curve is discretized to generate a robot executable trajectory sequence composed of dense pose points and corresponding joint angles, and the trajectory sequence is transmitted to the robot motion controller.

[0009] As one embodiment of the present invention, obtaining the initial trajectory point sequence specifically includes: in the three-dimensional workspace, connecting the starting pose and the target pose of the robot task to generate a straight path, and uniformly sampling along the straight path to obtain the initial trajectory point sequence. As one embodiment of the present invention, the step of iteratively optimizing the three-dimensional position coordinates of the control points of the parameterized trajectory curve in the high-fidelity simulation environment specifically employs a covariance matrix adaptive evolution strategy algorithm; the specific execution flow of the algorithm includes: Initialize a Gaussian distribution centered on the control point set of the initial parameterized trajectory curve as the search distribution for the control point positions; Based on the Gaussian distribution, a population containing multiple candidate control point sets is generated; For each set of candidate control points in the population, substitute it into the definition of the parameterized trajectory curve to generate a candidate trajectory curve; In the high-fidelity simulation environment, the candidate trajectory curve is evaluated as follows: high-frequency time-step sampling is performed along the candidate trajectory curve, and at each sampling time, the joint configuration corresponding to the robot is calculated using a numerical inverse kinematics solver; based on the joint configuration and the robot's 3D model, the collision detection model is used to calculate the collision state between the robot and environmental obstacles, the constraint model is used to determine whether kinematic constraints are violated, and the smoothness and length of the trajectory are calculated; based on the above calculation results, the composite cost function value corresponding to the candidate trajectory curve is obtained. The candidate control point set is sorted based on the composite cost function values ​​of all selected trajectory curves in the population. Based on the sorting results, the mean vector and covariance matrix of the Gaussian distribution are updated so that the search distribution moves toward the region with a lower composite cost function value. Repeat the steps of generating the population, evaluating the cost, and updating the distribution until the iteration termination condition is met.

[0010] As one embodiment of the present invention, the collision detection model uses the Gilbert-Johnson-Kilch algorithm to calculate the minimum distance between the collision body of each link of the robot and the collision body of the obstacle in the environment in each simulation step; when the minimum distance is negative, its absolute value is the penetration depth, and the value of the collision penalty term is proportional to the sum of the penetration depths of all collision parts. As one embodiment of the present invention, the numerical inverse kinematics solver adopts the damped least squares method; in the solution process, a damping factor based on the determinant value of the Jacobian matrix is ​​introduced to avoid the problem of excessive joint angular velocity near singular configurations, thereby ensuring the numerical stability of the solution process.

[0011] As one embodiment of the present invention, the discretization of the final parameterized trajectory curve specifically includes: setting a time step according to the command receiving frequency of the robot motion controller; starting from time 0, continuously sampling on the final parameterized trajectory curve at intervals of the time step to obtain a series of discrete end effector target poses; for each target pose, calling the numerical inverse kinematics solver to calculate the corresponding robot joint angle sequence, thereby forming a complete executable trajectory containing timestamps, target poses, and target joint angles.

[0012] This invention also provides a trajectory point optimization system based on simulation technology, which includes: The trajectory parameterization representation module is used to obtain the robot's initial trajectory point sequence and generate an initial parameterized trajectory curve defined by control points, node vectors and weight coefficients through a non-uniform rational B-spline curve fitting algorithm. The high-fidelity simulation environment building module is used to build a three-dimensional high-fidelity simulation environment that includes robot kinematics models, dynamics models, collision detection models, and constraint models; The simulation-driven trajectory evaluation module, connected to the high-fidelity simulation environment construction module, is used to receive parameterized trajectory curves, evaluate them in the simulation environment, and output a scalar composite cost function value; the composite cost function is composed of a weighted sum of collision penalty term, kinematic constraint penalty term, trajectory smoothness cost term, and trajectory length cost term. The control point optimization module has its input end connected to the output end of the simulation-driven trajectory evaluation module, and its output end connected to the input end of the simulation-driven trajectory evaluation module, forming a closed-loop optimization circuit; the control point optimization module is used to adjust the control point position of the parameterized trajectory curve through an iterative algorithm with the objective of minimizing the composite cost function value; The final trajectory generation module, which is connected to the control point optimization module, is used to receive the optimized control point set after the iterative optimization process is terminated, generate the final parameterized trajectory curve, and discretize it into a dense pose point and joint angle sequence that can be executed by the robot controller.

[0013] As an embodiment of the present invention, the control point optimization module integrates a covariance matrix adaptive evolution strategy optimizer; the optimizer updates the control point position by performing the following operations in a loop: generating a population of candidate control points, sending the members of each population to the simulation-driven trajectory evaluation module to obtain their cost values, and updating the internal search distribution model according to the cost values.

[0014] As one embodiment of the present invention, the simulation-driven trajectory evaluation module includes an inverse kinematics calculation unit and a collision detection unit; the inverse kinematics calculation unit is used to convert trajectory points in Cartesian space into joint angles in joint space, and the collision detection unit is used to detect the interference state between the robot model and the environment model in each simulation step. As one embodiment of the present invention, the robot kinematics model established by the high-fidelity simulation environment construction module is described using Danavitt-Hartenberg parameters; the collision detection model uses the Gilbert-Johnson-Kilch algorithm based on convex hull; and the constraint model identifies and avoids singular configurations by monitoring the determinant value of the robot's Jacobian matrix.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention transforms discrete trajectory point sequences into continuous parameterized trajectory curves determined by a small number of control points, thereby achieving a holistic and structured description of the trajectory. This avoids the motion discontinuity and kinematic incomprehensibility problems caused by isolated adjustments to individual points in existing technologies. The optimization process directly acts on the control points that determine the shape of the curve, ensuring the inherent smoothness of the generated trajectory.

[0016] 2. This invention creates a closed-loop optimization framework that deeply integrates planning and simulation, using a high-fidelity simulation environment as the core link of trajectory evaluation. This allows each iteration of optimization to obtain real-time and accurate feedback on collisions, kinematic constraints, and dynamic characteristics. This "computation in simulation" mode fundamentally guarantees the feasibility of the final output trajectory in the physical world, overcoming the problems of wasted computational resources and high planning failure rate caused by the existing "plan first, verify later" mode.

[0017] 3. This invention employs an advanced non-gradient optimization algorithm, such as the covariance matrix adaptive evolution strategy, to directly optimize the control points. This method demonstrates strong global search capability and robustness in handling highly non-convex, nonlinear, and noisy multi-objective cost functions generated by complex physical interactions. Compared with traditional gradient-dependent or local search methods, it can find high-quality global optimal or near-optimal solutions more efficiently, significantly improving the trajectory optimization efficiency under complex constraints.

[0018] 4. The system framework of this invention decouples the mathematical representation of the trajectory, physical simulation evaluation, and intelligent optimization algorithm into independent modules, achieving high flexibility and scalability. When the robot model, working environment, or optimization objective changes, only the corresponding modules need to be updated, without changing the entire system framework, demonstrating a strong adaptability to diverse industrial application scenarios. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the overall technical solution architecture of the trajectory point optimization method based on simulation technology proposed in this invention; Figure 2 This is a schematic diagram of the core principle framework of the simulation-driven closed-loop trajectory optimization framework in this invention; Figure 3 This is a logical flow diagram of the high-fidelity simulation environment construction module in this invention; Figure 4 This is a flowchart illustrating the logical flow of the parameterized trajectory curve generation and control point optimization stages in this invention. Figure 5 This is a logical flowchart of the collaborative mechanism between inverse kinematics calculation and collision detection within the simulation-driven trajectory evaluation module of this invention. Figure 6This is a schematic diagram of the multi-level interaction relationship and data flow between the robot body, simulation environment and optimization controller in this invention. Detailed Implementation

[0020] Please refer to the attached document. Figures 1 to 6 This invention provides a trajectory point optimization method based on simulation technology. Its core lies in transforming a discrete trajectory point sequence into a continuous parametric curve, and then iteratively optimizing the control point position in a high-fidelity 3D simulation environment through closed-loop optimization to generate a robot motion trajectory that satisfies multidimensional constraints and possesses high feasibility. The specific implementation of this method is described in detail below.

[0021] The initial trajectory point sequence of the robot is obtained, which consists of a series of discrete pose points defined in a 3D workspace. Specifically, this step involves: connecting the robot's initial pose and target pose in the 3D workspace to generate a straight path; uniformly sampling along this path to obtain several equally spaced Cartesian pose points, forming the initial trajectory point sequence. Each pose point contains the position coordinates and attitude quaternions of the end effector, used for subsequent parametric modeling. The sampling density is set according to the task accuracy requirements, typically not less than 5 sampling points per unit length, to ensure that the initial trajectory has sufficient geometric information for fitting.

[0022] Based on the initial trajectory point sequence, an initial parameterized trajectory curve is generated using a non-uniform rational B-spline curve fitting algorithm. This parameterized trajectory curve is uniquely determined by a set of control point coordinates, node vectors, and a set of weighting coefficients. Specifically, each pose point in the initial trajectory point sequence is first projected onto its position component in three-dimensional Euclidean space, ignoring the pose component to simplify the initial fitting process. Then, the least squares method is used to solve for the control point set, minimizing the fitting error of the non-uniform rational B-spline curve to the sampled points given the node vectors. The node vectors are generated using a chord length parameterization method to ensure that the curve parameters correspond approximately linearly to the physical path length. The weighting coefficients are initially set to all one values ​​and can be kept fixed or used as adjustable parameters in subsequent iterations during optimization. The final parameterized trajectory curve is denoted as: ; in, For curve parameters, For the first The three-dimensional coordinates of the control points For their corresponding weights, for B-spline basis functions.

[0023] A high-fidelity 3D simulation environment is constructed, which accurately reproduces the robot body and its operating scenario in digital space. This construction process includes the creation of four sub-models: First, a kinematic model of the robot is established. The Danavitt-Hartenberg parametric method is used to describe the geometry and kinematics of each link and joint of the robot. Specifically, four parameters are included: link length, link torsion angle, joint offset, and joint variables, forming a complete positive kinematic chain. Secondly, a dynamic model of the robot is established, which includes the mass, center of mass position and inertia tensor of each link, for possible subsequent dynamic simulation expansion. Although this embodiment mainly focuses on kinematic feasibility, the existence of the dynamic model reserves an interface for future functional upgrades. Third, establish corresponding collision detection models for each link of the robot body and all static and dynamic obstacles in the workspace. The collision detection models approximate physical entities by using convex hulls or combinations of basic geometric shapes. For example, simplify the robotic arm links into a combination of cylinders and spheres, and decompose complex obstacles into multiple convex polyhedra. Fourth, establish a constraint model for the robot. The constraint model includes angle limits, angular velocity limits, and angular acceleration limits for each joint, as well as a singular configuration monitoring mechanism based on the determinant value of the robot's Jacobian matrix. When the absolute value of the determinant of the Jacobian matrix is ​​lower than a preset threshold (such as 0.01), the system is determined to be near a singular configuration, and constraint penalties are triggered.

[0024] A multi-objective composite cost function is defined to evaluate the quality of the parameterized trajectory curve. This composite cost function is a linear combination of multiple weighted sub-cost functions. Specifically, the sub-cost functions include: a collision penalty term. Its value is proportional to the reciprocal of the penetration depth or minimum distance between the robot and the obstacle when moving along the parameterized trajectory curve; kinematic constraint penalty term Its value increases exponentially as the robot's joint variables approach or exceed their preset limits, and further increases as the robot approaches singular configurations due to the increase in the condition number of the Jacobian matrix; trajectory smoothness cost term Its value is obtained by calculating the squared integral of the curvature of the parameterized trajectory curve over the entire domain; the trajectory length cost term Its value is the total arc length of the parameterized trajectory curve. The compound cost function expression is: ; in, These are preset positive weighting coefficients, adjusted according to task priority, such as in obstacle avoidance priority scenarios. Take the larger value in high-speed operation scenarios. Relative decrease.

[0025] In the high-fidelity simulation environment, the three-dimensional position coordinates of the control points of the parameterized trajectory curve are iteratively optimized with the objective of minimizing the composite cost function. The iterative optimization process employs a covariance matrix adaptive evolution strategy algorithm, and the specific execution flow is as follows: An initial Gaussian distribution centered on the control point set of the initial parameterized trajectory curve is used as the search distribution for control point locations. The initial covariance matrix is ​​set to the identity matrix multiplied by a typical scale of the control point coordinates (e.g., 0.1 meters). Based on this Gaussian distribution, a population containing multiple candidate control point sets is generated, with a population size of 50. For each candidate control point set in the population, it is substituted into the definition of a non-uniform rational B-spline curve to generate a candidate trajectory curve. In the high-fidelity simulation environment, the candidate trajectory curve is evaluated: high-frequency sampling is performed along the candidate trajectory curve at a time step of 0.01 seconds, and at each sampling time... The joint configuration of the robot is calculated using a numerical inverse kinematics solver. The numerical inverse kinematics solver employs the damped least squares method, and its update formula is as follows: ; in The Jacobian matrix under the current joint configuration. Let be the deviation vector between the current position of the end effector and the target position. The identity matrix and damping factor are given. Dynamically set to ,in This is the reference damping value (e.g., 0.05). The maximum historical value of the Jacobian matrix determinant ensures that damping is automatically increased near singular configurations, suppressing joint velocity divergence.

[0026] Based on the joint configuration Using a 3D model of the robot and the collision detection model, the collision states between the robot and environmental obstacles are calculated. The collision detection employs the Gilbert-Johnson-Kilch algorithm, calculating the minimum distance between the colliders of each link of the robot and the colliders of obstacles in the environment within each simulation step. ;when When the value is less than 0, its absolute value is the penetration depth, and the collision penalty term is also included. The calculation is the sum of the absolute values ​​of the penetration depth at all points of collision, multiplied by a penalty coefficient (e.g., 1000); if there is no collision, then... ,in To prevent division by zero, a small constant (e.g., 0.001 meters) is used. Simultaneously, the constraint model is used to determine if kinematic constraints are violated: if any joint angle exceeds the limit range, the corresponding penalty term is applied. Calculation; if the condition number of the Jacobian matrix exceeds a threshold (e.g., 100), an additional penalty is applied. ,in The condition number penalty coefficient. Trajectory smoothness cost term. By applying the square of the second derivative modulus of the parameterized curve... Points are earned, that is The integral is calculated using the Gauss-Legend de Gauss numerical integration method, taking 10 integration points. The trajectory length is the cost term. Through numerical integration get.

[0027] Based on the above calculation results, the composite cost function value corresponding to the candidate trajectory curve is obtained. Sort the composite cost function values ​​of all candidate trajectory curves in the population in ascending order, and select the top 20% of individuals as the elite set. Based on the sorting results, update the mean vector and covariance matrix of the Gaussian distribution: the new mean is a weighted average of the control point coordinates of the elite individuals, with the weights normalized by the reciprocal of the cost value; the covariance matrix is ​​updated by weighted summation of the outer product of the elite individuals and the old mean, and a learning rate parameter (e.g., 0.2) is introduced to control the update magnitude. Repeat the steps of generating the population, evaluating the cost, and updating the distribution until the iteration termination condition is met: the number of iterations reaches 200, or the relative change of the composite cost function value in 10 consecutive iterations is less than 0.001.

[0028] After the iterative optimization process terminates, the final parameterized trajectory curve defined by the optimized control point set is output. The final parameterized trajectory curve is then discretized to generate a sequence of executable robot trajectories consisting of dense pose points and corresponding joint angles. The discretization process specifically includes: setting a time step of 0.01 seconds based on the robot motion controller's instruction receiving frequency (e.g., 100 Hz); starting from time 0, continuously sampling the final parameterized trajectory curve at intervals of this time step to obtain a series of discrete end effector target poses; for each target pose, calling the aforementioned damped least squares numerical inverse kinematics solver to calculate the corresponding robot joint angle sequence; finally, a complete executable trajectory containing timestamps, target poses (position and attitude), and target joint angles is formed and transmitted to the robot motion controller via a standard communication protocol (e.g., ROS topic or EtherCAT frame).

[0029] The high-fidelity simulation environment construction module is implemented as an independent software unit at the system level. Its internal logic ensures the consistency and timing synchronization of kinematic, dynamic, collision, and constraint models. The simulation-driven trajectory evaluation module, as the core of the optimization loop, automatically triggers a complete pipeline of trajectory generation, time sampling, inverse kinematics calculation, collision detection, and cost accumulation after each control point set is received, outputting a single scalar cost value. The control point optimization module interacts with the evaluation module via memory mapping, avoiding data copying overhead and maintaining internal Gaussian distributed state variables. The entire optimization process is completed on a single workstation, with typical optimization time ranging from 30 seconds to 2 minutes, depending on trajectory complexity and the number of obstacles.

[0030] This embodiment represents the trajectory as a non-uniform rational B-spline curve, achieving a compact, smooth, and differentiable mathematical description of the trajectory shape. An optimization loop is embedded in a high-fidelity simulation environment to ensure that each generation of candidate solutions undergoes physical consistency verification. An adaptive evolution strategy using the covariance matrix effectively avoids local minima by handling the highly non-convex cost landscape. The final generated trajectory not only satisfies obstacle avoidance and kinematic constraints but also achieves a multi-objective balance between smoothness and length, allowing it to be directly used for execution by industrial robot controllers without post-processing corrections.

Claims

1. A method for optimizing trajectory points based on simulation technology, characterized in that, include: Obtain the robot's initial trajectory point sequence, which consists of a series of discrete pose points defined in a three-dimensional workspace; Based on the initial trajectory point sequence, an initial parameterized trajectory curve is generated by a non-uniform rational B-spline curve fitting algorithm. The parameterized trajectory curve is uniquely determined by a set of control point position coordinates, node vectors, and a set of weight coefficients. A three-dimensional high-fidelity simulation environment is constructed, which accurately reproduces the robot body and its working scene in digital space; A multi-objective composite cost function is defined to evaluate the quality of the parameterized trajectory curve, wherein the composite cost function is a linear combination of multiple weighted sub-cost functions; In the high-fidelity simulation environment, the three-dimensional position coordinates of the control points of the parameterized trajectory curve are iteratively optimized with the goal of minimizing the composite cost function; the iterative optimization process terminates within a preset upper limit of the number of iterations or when the value of the composite cost function converges to below a preset threshold. After the iterative optimization process terminates, the final parameterized trajectory curve defined by the optimized control point set is output; the final parameterized trajectory curve is discretized to generate a robot executable trajectory sequence composed of dense pose points and corresponding joint angles, and the trajectory sequence is transmitted to the robot motion controller.

2. The method for optimizing trajectory points based on simulation technology according to claim 1, characterized in that, The construction of the simulation environment includes: establishing a kinematic model of the robot, which uses the Danavis-Hartenberg parametric method to geometrically and kinematically describe each link and joint of the robot; establishing a dynamic model of the robot, which includes the mass, center of mass position, and inertia tensor of each link; establishing corresponding collision detection models for each link of the robot body and all static and dynamic obstacles in the workspace, which approximate physical entities by using convex hull or a combination of basic geometric shapes; and establishing a constraint model of the robot, which includes angular limits, angular velocity limits, angular acceleration limits for each joint, and a singular configuration monitoring mechanism based on the determinant value of the robot's Jacobian matrix.

3. The method for optimizing trajectory points based on simulation technology according to claim 2, characterized in that, The sub-cost function includes: a collision penalty term, the value of which is proportional to the reciprocal of the penetration depth or minimum distance between the robot and an obstacle when the robot moves along the parameterized trajectory curve; a kinematic constraint penalty term, the value of which increases exponentially when the robot's joint variables approach or exceed their preset limits, and increases according to the increase of the Jacobian matrix condition number when the robot approaches a singular configuration; a trajectory smoothness cost term, the value of which is obtained by calculating the square integral of the curvature of the parameterized trajectory curve over the entire domain; and a trajectory length cost term, the value of which is the total arc length of the parameterized trajectory curve.

4. The method for optimizing trajectory points based on simulation technology according to claim 3, characterized in that, The acquisition of the initial trajectory point sequence specifically includes: in the three-dimensional workspace, connecting the starting pose and the target pose of the robot task to generate a straight path, and uniformly sampling along the straight path to obtain the initial trajectory point sequence.

5. The method for optimizing trajectory points based on simulation technology according to claim 4, characterized in that, The step of iteratively optimizing the three-dimensional position coordinates of the control points of the parameterized trajectory curve in the high-fidelity simulation environment specifically employs a covariance matrix adaptive evolution strategy algorithm; the specific execution flow of the algorithm includes: Initialize a Gaussian distribution centered on the control point set of the initial parameterized trajectory curve as the search distribution for the control point positions; Based on the Gaussian distribution, a population containing multiple candidate control point sets is generated; For each set of candidate control points in the population, substitute it into the definition of the parameterized trajectory curve to generate a candidate trajectory curve. In the high-fidelity simulation environment, the candidate trajectory curve is evaluated as follows: high-frequency time-step sampling is performed along the candidate trajectory curve, and at each sampling time, the joint configuration corresponding to the robot is calculated using a numerical inverse kinematics solver; based on the joint configuration and the robot's 3D model, the collision detection model is used to calculate the collision state between the robot and environmental obstacles, the constraint model is used to determine whether kinematic constraints are violated, and the smoothness and length of the trajectory are calculated; based on the above calculation results, the composite cost function value corresponding to the candidate trajectory curve is obtained. The candidate control point set is sorted based on the composite cost function value of all candidate trajectory curves in the population. Based on the sorting results, the mean vector and covariance matrix of the Gaussian distribution are updated so that the search distribution moves toward the region with a lower composite cost function value. Repeat the steps of generating the population, evaluating the cost, and updating the distribution until the iteration termination condition is met.

6. The method for optimizing trajectory points based on simulation technology according to claim 5, characterized in that, The collision detection model uses the Gilbert-Johnson-Kilch algorithm to calculate the minimum distance between the collision body of each link of the robot and the collision body of the obstacle in the environment in each simulation step; when the minimum distance is negative, its absolute value is the penetration depth, and the value of the collision penalty term is proportional to the sum of the penetration depths of all collision points.

7. The method for optimizing trajectory points based on simulation technology according to claim 6, characterized in that, The numerical inverse kinematics solver employs the damped least squares method. During the solution process, a damping factor based on the determinant of the Jacobian matrix is ​​introduced to avoid excessive joint angular velocities near singular configurations, thereby ensuring the numerical stability of the solution process.

8. The method for optimizing trajectory points based on simulation technology according to claim 7, characterized in that, The trajectory smoothness cost term is obtained by calculating the integral of the square of the second derivative modulus of the parameterized trajectory curve over the parameter domain.

9. The method for optimizing trajectory points based on simulation technology according to claim 8, characterized in that, The discretization of the final parameterized trajectory curve specifically includes: setting a time step based on the command receiving frequency of the robot motion controller; starting from time 0, continuously sampling on the final parameterized trajectory curve at intervals of the time step to obtain a series of discrete end effector target poses; for each target pose, calling the numerical inverse kinematics solver to calculate the corresponding robot joint angle sequence, thereby forming a complete executable trajectory containing timestamps, target poses, and target joint angles.

10. The method for optimizing trajectory points based on simulation technology according to claim 9, characterized in that, The expression for the composite cost function is: ； in, These are preset positive weighting coefficients. For collision penalties, For kinematic constraint penalty terms, For trajectory smoothness cost item, This is the cost item for trajectory length.

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