Inverse kinematics method for redundant seven-degree-of-freedom robot

Abstract

The invention discloses an inverse kinematics method for a redundant seven-degree-of-freedom robot. The method specifically comprises the following steps: step 1, establishing forward kinematics modeling of the seven-degree-of-freedom robot; step 2, inputting a target pose, and defining a tail end pose error of the seven-degree-of-freedom robot as a Riemannian distance on a three-dimensional special Euclidean group manifold; 3, adopting a three-stage hybrid optimization strategy; 4, carrying out constraint processing between joints; and 5, verifying convergence and robustness. The adaptive differential evolution algorithm is used as a core optimizer, parameters of the adaptive differential evolution algorithm can be dynamically adjusted along with an iteration process, and global exploration and local development capabilities are balanced; and a dynamic parameter adjustment strategy of nonlinear progressive increase of a scaling factor and linear progressive decrease of a crossover probability is designed, and a DE / current-to-pbest variation strategy is adopted, so that the algorithm pays attention to global exploration in the initial stage of iteration and is biased to fine development in the later stage, and the convergence speed and the global search capability are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and in particular to a method for inverse kinematics solution of a redundant seven-degree-of-freedom robot. Background Technology

[0002] Currently, with the development of science and technology and the transformation of production methods, industrial robots occupy a crucial position in fields such as science and technology and production. The diversification of industrial robot applications also demands that industrial robots possess higher flexibility and precision.

[0003] Compared to the six-degree-of-freedom industrial robots used in traditional manufacturing, seven-degree-of-freedom redundant robots have advantages in obstacle avoidance, torque optimization, and flexibility due to their redundancy. Therefore, they have great application prospects and research value in industries such as aviation, shipbuilding, and transportation. The superior performance of seven-degree-of-freedom redundant robots in complex working conditions such as aviation and shipbuilding fundamentally relies on their advanced control system design.

[0004] Kinematics is the core of robot motion control and has a decisive impact on the precise realization of a robot's motion functions. Inverse kinematics, inverse kinematics, involves determining the joint angles of a robotic arm given its end-effector pose. The accuracy of these joint angle calculations directly determines the accuracy of the robot's execution of specified actions. Seven-DOF redundant robots, due to their configuration not satisfying conditions such as the pipe criterion, make it difficult to individually disassemble each joint and calculate its analytical solution.

[0005] Currently, commonly used methods for solving the inverse kinematics of redundant robots include numerical methods, geometric analytical methods, and methods based on intelligent algorithms. Among numerical methods, the gradient projection method is the most representative, but it has higher computational complexity and is more sensitive to singular configurations. In singular configurations, null space projection may fail, requiring additional regularization. The arm angle method is a geometric analytical method for solving the inverse kinematics of redundant seven-DOF robots. It selects a robot configuration as a reference and then constrains this configuration using arm angles, ensuring that the number of degrees of freedom equals the number of constraints, thus obtaining the inverse kinematics. However, the arm angle method struggles with singular configurations; when the robot approaches a singular configuration, the definition of the arm angle may fail, requiring the introduction of singular configuration avoidance strategies, increasing computational difficulty. Moreover, as an analytical method, the arm angle method has significant computational complexity and workload. Although the inverse kinematics solution method for redundant robots based on intelligent algorithms has advantages in adapting to the environment and handling complex tasks, its high data dependence, insufficient generalization ability, and limited real-time performance result in insufficient computational efficiency and poor stability when using intelligent algorithms.

[0006] Therefore, there is an urgent need to provide a redundant seven-DOF robot inverse kinematics solution method to solve the problems of high computational complexity, sensitivity to singular configurations, and poor real-time performance in the existing technology. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of the prior art by providing a method for inverse kinematics of a redundant seven-degree-of-freedom robot.

[0008] The objective of this invention is achieved through the following technical solution: a method for inverse kinematics of a redundant seven-degree-of-freedom robot, the specific method of which is as follows: Step 1: Establish forward kinematics modeling for a seven-DOF robot; Step 2: Input the target pose and define the end-effector pose error of the seven-DOF robot as the Riemann distance on the three-dimensional special Euclidean group manifold. Step 3: Adopt a three-stage hybrid optimization strategy, the specific method of which is as follows: The first stage involves a global search in the solution space using a differential evolution algorithm to locate regions of high-quality solutions. The specific method is as follows: a first-stage convergence threshold is set, and the population is uniformly initialized in the joint space. The fitness of each solution in the current population is calculated, and then an adaptive differential evolution iteration is performed. The weight ratio of each objective item in the fitness calculation process is adjusted in real time according to the current state. The process ends when the first-stage convergence condition is met. Second stage: Set the second stage convergence threshold. Based on the obtained high-quality solution region, use a neighborhood search strategy based on Gaussian sampling to generate candidate solutions, calculate the fitness of candidate solutions and select the best one to update the current optimal solution; repeat the above process until the second stage convergence condition is met. The third stage: using pattern search for final deterministic local optimization; Step 4: Joint restraint treatment; Step 5: Convergence and robustness verification.

[0009] As a preferred option, in step one, the DH method is used to establish the forward kinematics model of the seven-degree-of-freedom robot.

[0010] Preferably, in step three, the joint angle of each individual joint is determined by the following formula: ; in, Represents an individual index. N is the population size; For joint indexing, ; and These represent the upper and lower limits of the angle of the individual at the j-th joint, respectively; Scaling factor during adaptive differential evolution iteration Calculate using the following formula: ; In the above formula, This represents the number of iterations. Crossover probability It decreases linearly using the following formula: ; in, This represents the maximum number of iterations.

[0011] As a preferred option, fitness The calculation formula is as follows: ; In the above formula, For the end-effector pose error objective term, The end-effector pose error is used to measure the difference between the actual pose and the expected pose of the end-effector of a seven-degree-of-freedom robot. The weighting coefficients for the end-effector pose error; To avoid singular errors in the target term, This is used to avoid singularity errors and guide algorithms to avoid singular regions in the robot's configuration space. The weighting coefficients for singularity avoidance error.

[0012] Preferably, the weighting coefficient for the end-effector pose error is... and the weighting coefficient of singularity avoidance error The calculation formula is as follows: ; In the formula, Joint angle, Represents an individual index.

[0013] As a preferred approach, in step three, when performing adaptive differential evolution iteration, a DE / current-to-pbest mutation strategy is adopted, using the top 30% of the best individuals in the current population as the guiding source to search for optimal solutions; then, crossover and selection operations are performed; in the crossover phase, a binary crossover strategy is adopted to ensure that at least one dimension of the experimental vector comes from the mutation vector to maintain the population update momentum; in the selection phase, a greedy algorithm is used to decide whether to accept newly generated experimental individuals.

[0014] As a preferred option, the specific method for step four is as follows: The seventh axis angle of a seven-DOF robot has a numerical coupling multiple relationship with the sixth axis angle. The seventh axis and the sixth axis of the seven-DOF robot must satisfy the following constraints: ; In the formula, n represents the gear transmission ratio between the sixth and seventh axes. A fixed offset representing the angular error; The joint angle of the seventh axis. The joint angle of the sixth axis; during the initialization of the population, a feasible solution that satisfies the above constraints is generated, and during the adaptive differential evolution iteration process, the solution is modified after each mutation and crossover operation to ensure that it always meets the constraints of the seventh and sixth axes before entering the selection operation. After generating candidate solutions, joint limit checks are performed on all candidate solutions; if a candidate solution exceeds the physical limits of the joint, it is projected to the nearest running boundary value to ensure that the generated candidate solution is within the allowable running angle range of the mechanical structure.

[0015] As a preferred option, in step five, to ensure the optimal solution is obtained, the accuracy of the inverse solution, joint angle limits, and joint coupling constraints are verified respectively; the verification formula for the accuracy of the inverse solution is as follows: ; in, This is the final calculated end-effector pose matrix. The target end pose matrix; The verification formula for joint angle limit is as follows: ; in, For the minimum operating boundary angle, For the maximum operating boundary angle, Joint angle; The formula for verifying joint coupling constraints is as follows: ; in, A fixed offset representing the angular error. The joint angle of the seventh axis. This is the joint angle of the sixth axis.

[0016] The optimal solution must satisfy the above verification formula simultaneously.

[0017] As a preferred approach, in step five, a restart mechanism is used to address the situation of getting stuck in a local optimum. The restart conditions are as follows: ; in, The standard deviation of population fitness is used to measure population diversity. The mean fitness of the population reflects the degree of convergence; For the number of iterations, This is an additional condition to avoid accidentally triggering a restart in the early stages of iteration when the population has not yet fully evolved; if the above restart condition is met, the current best individual is retained and the population is reinitialized.

[0018] The beneficial effects of this invention are as follows: 1. In the three-stage hybrid optimization strategy of step three of this invention, an adaptive differential evolution algorithm is used as the core optimizer. Its parameters can be dynamically adjusted with the iteration process, balancing global exploration and local development capabilities. In the subsequent local development and pattern search stages, it can converge quickly based on high-quality solution regions, significantly reducing the overall computational complexity and enabling it to meet the real-time control requirements of industrial robots. Furthermore, a dynamic parameter adjustment strategy with nonlinearly increasing scaling factors and linearly decreasing crossover probabilities is designed, and a DE / current-to-pbest mutation strategy is adopted, so that the algorithm focuses on global exploration in the early stage of iteration and leans towards fine development in the later stage, effectively improving the convergence speed and global search capability.

[0019] 2. This invention introduces the SE(3) manifold distance based on spinor theory as a measure of pose error, which can more comprehensively reflect the end pose difference than the traditional Euclidean distance. Combined with a three-stage hybrid optimization strategy and a avoidance term for singular points, it can stably find high-precision inverse solutions in complex solution spaces, effectively avoiding the problem of failure or sharp drop in accuracy of traditional methods near singular configurations.

[0020] 3. This invention constructs a fitness function that integrates pose error and singularity avoidance term, and innovatively proposes a three-stage hybrid optimization process consisting of global exploration, local development, and fine optimization. The global exploration stage adopts the differential evolution algorithm, the local development stage adopts the Gaussian sampling strategy, and the fine optimization stage adopts the pattern search method. This process systematically solves the problem of balancing global convergence and local accuracy in inverse kinematics solution.

[0021] 4. This invention fully considers the actual physical constraints of the robot. Through the projection repair strategy, it strictly ensures that the joint angles are within the mechanical limits. By embedding coupling relationship processing in the algorithm flow, it ensures that the kinematic constraints of the sixth and seventh axis transmission gear structure are always satisfied. This makes the solution not only the mathematically optimal solution, but also a physically feasible solution that can be directly executed. Furthermore, it establishes multiple verification standards including pose accuracy, joint limits, and coupling relationships, and designs a restart mechanism based on population diversity monitoring. When the algorithm may get stuck in a local optimum, it can automatically reinitialize, which significantly improves the robustness and success rate of the algorithm. Attached Figure Description

[0022] Figure 1 This is a linkage model diagram of the seven-degree-of-freedom robot of the present invention.

[0023] Figure 2This is a flowchart of the inverse kinematics algorithm of the present invention. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the scope of protection of the present invention.

[0025] Those skilled in the art should understand that, in the disclosure of this invention, the terms "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the above terms should not be construed as limiting this invention.

[0026] It is understood that the term "a" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of an element can be one, while in another embodiment, the number of the element can be multiple, and the term "a" should not be understood as a limitation on the number.

[0027] like Figures 1 to 2 As shown, a method for inverse kinematics of a redundant seven-DOF robot is characterized by the following specific method: Step 1: Establish forward kinematics modeling for a seven-DOF robot.

[0028] Step 2: Input the target pose and define the end-effector pose error of the seven-DOF robot as the Riemann distance on the three-dimensional special Euclidean group manifold. Step 3: Adopt a three-stage hybrid optimization strategy, the specific method of which is as follows: The first stage involves a global search in the solution space using a differential evolution algorithm to locate regions of high-quality solutions. The specific method is as follows: a first-stage convergence threshold is set, and the population is uniformly initialized in the joint space. The fitness of each solution in the current population is calculated, and then an adaptive differential evolution iteration is performed. The weight ratio of each objective item in the fitness calculation process is adjusted in real time according to the current state. The process ends when the first-stage convergence condition is met. Second stage: Set the second stage convergence threshold. Based on the obtained high-quality solution region, use a neighborhood search strategy based on Gaussian sampling to generate candidate solutions, calculate the fitness of candidate solutions and select the best one to update the current optimal solution; repeat the above process until the second stage convergence condition is met. The third stage: using pattern search for final deterministic local optimization; Step 4: Joint restraint treatment; Step 5: Convergence and robustness verification.

[0029] Specifically, in step one, the DH method is used to establish the forward kinematics model of the seven-DOF robot. The details are as follows: ; .

[0030] In formula (1), This represents the transformation matrix between adjacent rotational joints i and i-1, where i is the joint number.

[0031] In formula (2), θ i The joint angle is defined as... X i-1 Rotate to X i Angle (see attached) Figure 1 ), d i The link offset is defined as the distance from the beginning of the link. X i-1 Move to X i distance, a i-1 The length of the link is defined as... Z i-1 Move to Z i distance, α i-1 The twist angle is defined as the angle from which the torsion angle originates. Z i-1 Rotate to Z i The angle. In the formula, , , .

[0032] Specifically, in step two, based on the redundant seven-DOF robot, its inverse kinematics model exhibits nonlinearity and strong coupling characteristics. Therefore, screw theory is introduced to construct the optimization objective function. The end-effector pose error is defined. Let Riemann distance be the distance on a manifold of a special Euclidean group (in 3 dimensions, SE(3)), and its formula is as follows: (3); In the formula, The target end pose matrix, The end pose matrix corresponding to the current joint angle is calculated by formulas (1) and (2); The Frobenius norm is used. The SE(3) manifold distance calculation uses a decomposition form: (4); in It is the antisymmetric matrix of the rotated part. It is the translation part.

[0033] Specifically, in step three, under the redundant seven-DOF robot inverse kinematics solution method, the initial population is the starting search basis for the differential evolution algorithm. It refers to a set of "joint angle combinations" randomly generated in a uniform distribution within the seven-dimensional joint space. Each joint angle combination corresponds to a potential solution to the robot inverse kinematics problem.

[0034] The joint angle of each individual joint is determined by the following formula: (5); In the above formula (5), Represents an individual index. N is the population size; For joint indexing, ; and and represent the upper and lower bounds of the angle of the individual at the j-th joint, respectively. This initialization strategy aims to ensure that the population is evenly distributed in the solution space, laying the foundation for subsequent global search.

[0035] Scaling factor during adaptive differential evolution iteration Calculate using the following formula: (6); In the above formula (6), Number of iterations. Scaling factor. In the early stages of iteration, the value is set to a lower value, which helps with fine-grained searching; as the iteration progresses, the value gradually increases, enhancing the global exploration capability.

[0036] Crossover probability It decreases linearly using the following formula: (7); In the above formula (7), This represents the maximum number of iterations. A high initial crossover probability. The initial value helps to introduce more new genes, while a later decrease promotes the retention and convergence of superior genes.

[0037] To further improve the algorithm performance during adaptive differential evolution iteration, a DE / current-to-pbest mutation strategy is adopted, as shown in the following formula (8): (8); in, Indicates the first k In the first generation of the population, the first i The mutation vector generated by each individual A new solution is formed by combining information from the current individual with that from other individuals in the population; Indicates the first k The first generation of the population i One target individual; For the first k The adaptive scaling factor of the generation is a positive real number; and Indicates from the first k Two distinct individuals, different from the target individual, are randomly selected from the population. Individuals. This design uses individuals ranked in the top 30% of fitness in the current population as guides to search for optimal solutions while maintaining population diversity, balancing convergence speed and global applicability. It guides the search for optimal solutions by using the top 30% of fitness individuals in the current population as the source.

[0038] Then, crossover and selection operations are performed. During the crossover phase, a binary crossover strategy is employed to ensure that at least one dimension of the experimental vector originates from the mutated vector, thus maintaining the population renewal dynamics. (9); in, Indicates the first k In the generation, the j-th dimension component of the test vector generated by the i-th individual; Indicates the first k In the generation, the component of the j-th dimension of the mutation vector of the i-th individual; This represents the angle value of the j-th joint of the i-th candidate solution (individual / robotic arm configuration) in the current population (candidate solution set) during the k-th algorithm iteration. The dimension index is randomly selected.

[0039] During the selection phase, a greedy algorithm is used to decide whether to accept newly generated test individuals. The specific formula is as follows: (10) This algorithm only applies to the generated test individuals. The fitness of the individual is better than that of the original individual. Replacement is performed periodically to ensure that the quality of the population continuously improves during iteration, eventually converging to a high-quality solution.

[0040] Greedy algorithms exhibit a "survival of the fittest" selection rule: for new experimental individuals generated through mutation and crossover during the iteration process... A new individual is used to replace its parent in the next generation of the population only if the new individual's fitness is better than its corresponding parent in the original population; if the new individual's fitness is worse, it is discarded, and the original parent is retained. The greedy algorithm is essentially a locally optimal decision-making logic that "only accepts better solutions and rejects inferior solutions."

[0041] Among them, fitness The calculation formula is as follows: (11); In the above formula (11), For the end-effector pose error objective term, The end-effector pose error is used to measure the difference between the actual pose and the expected pose of the end-effector of a seven-degree-of-freedom robot. The weighting coefficients for the end-effector pose error; To avoid singular errors in the target term, This is used to avoid singularity errors and guide algorithms to avoid singular regions in the robot's configuration space. The weighting coefficients for singularity avoidance error.

[0042] Weighting coefficients for end-effector pose error and the weighting coefficient of singularity avoidance error As the differential evolution iteration proceeds, adaptive adjustment will be achieved, thereby adjusting the weight ratio of each objective item in real time during the fitness calculation. The weight coefficients are dynamically adjusted according to the optimization process to adapt to the needs of different optimization stages, as shown in the following formula: Among them, the weighting coefficient of the end-effector pose error and the weighting coefficient of singularity avoidance error The calculation formula is as follows: ; In the formula, Joint angle, Represents an individual index.

[0043] Step 3's first stage is a global exploration, employing the standard difference evolutionary algorithm to perform a broad search in the solution space. The parameters are set as follows: population size of 30 and maximum number of iterations of 40. The main objective of this stage is to locate the region of high-quality solutions within the entire joint space. The convergence threshold for this first stage is set to... To avoid premature convergence, the convergence condition for the first stage is that the fitness of all solutions in the population is less than the first stage convergence threshold. That is, the first stage ends when the fitness of all solutions in the population is less than the first stage convergence threshold.

[0044] The second stage in step three is local development. Based on the obtained high-quality solution regions, this stage shifts to local fine-tuning search to further improve the quality of the solutions. A neighborhood search strategy based on Gaussian sampling is employed, and its candidate solutions... The generated formula is: (12); Where I is the identity matrix, Represents a random vector with a multivariate Gaussian distribution; The variance is linearly decreasing. The expression is: (13); In the above formula (13), This represents the current iteration number. This represents the total number of iterations.

[0045] This strategy utilizes linearly decreasing variance. This process achieves a coarse-to-fine search granularity adjustment. Candidate solutions are generated by sampling around the current optimal solution, their fitness is evaluated, and the current optimal solution is updated accordingly. This process is repeated until the local convergence condition is met.

[0046] The third stage of step three is fine-tuning. When the optimization iterations approach the optimal solution, to ensure numerical stability and convergence accuracy, this study employs pattern search for final deterministic local optimization. The advantage of this method is that it does not require gradient information, avoiding numerical risks caused by ill-conditioned or non-smooth Jacobian matrices, and theoretically provides a clear guarantee of local convergence. The convergence criterion formula is as follows: (14); in, This refers to the Frobenius norm. Using the Frobenius norm to comprehensively evaluate pose error can improve the accuracy of the inverse kinematics solution.

[0047] In this application, the seventh axis of the seven-DOF robot is a transmission gear structure, and the angle of the seventh axis has a numerical coupling multiple relationship with the angle of the sixth axis. To leverage the greater flexibility of the seven-DOF robot in space, joint constraint processing is required. The specific method for step four is as follows: The seventh axis angle of a seven-DOF robot has a numerical coupling multiple relationship with the sixth axis angle. The seventh axis and the sixth axis of the seven-DOF robot must satisfy the following constraints: ; In the formula, n represents the gear transmission ratio between the sixth and seventh axes. A fixed offset representing the angular error; The joint angle of the seventh axis. The joint angle of the sixth axis; during the initialization of the population, a feasible solution that satisfies the above constraints is generated, and during the adaptive differential evolution iteration process, the solution is modified after each mutation and crossover operation to ensure that it always meets the constraints of the seventh and sixth axes before entering the selection operation. After generating candidate solutions, joint limit checks are performed on all candidate solutions. If a candidate solution exceeds the physical limits of an individual joint, it is projected to the nearest operational boundary value to ensure that the generated candidate solution is within the allowable operating angle range of the mechanical structure, thus guaranteeing the physical feasibility of the motion scheme. For solutions that exceed joint limits, a projection repair strategy is adopted, as follows: (15); In the above formula (15), Indicates the minimum operating boundary angle. This indicates the maximum operating boundary angle.

[0048] This strategy directly projects the out-of-bounds joint angle to its nearest limit value. This strategy strictly guarantees the feasibility of all solutions, the calculation process is simple and efficient, and it does not cause additional interference to the optimization process.

[0049] Specifically, to ensure the optimal solution is obtained, step five verifies the inverse solution accuracy, joint angle limits, and joint coupling constraints. The verification formula for the inverse solution accuracy is as follows: (16); In the above formula (16), The calculated end pose matrix, The target end pose matrix; To ensure all joint angles Since the movement is within the robot's limit range, the joint angle limit needs to be verified. The verification formula for the joint angle limit is as follows: (17); Formula (17) above. For the minimum operating boundary angle, For the maximum operating boundary angle, This refers to the joint angle.

[0050] The formula for verifying joint coupling constraints is as follows: (18); In the above formula (18), A fixed offset representing the angular error. The joint angle of the seventh axis. This is the joint angle of the sixth axis.

[0051] The optimal solution must satisfy the above verification formula simultaneously.

[0052] Furthermore, to address the possibility of the algorithm getting stuck in local optima, a restart mechanism based on population diversity detection is designed in step five. The restart mechanism addresses the issue of getting stuck in local optima, and the restart conditions are as follows: ; in, The standard deviation of population fitness is used to measure population diversity. The mean fitness of the population reflects the degree of convergence; For the number of iterations, This is an additional condition to avoid accidentally triggering a restart in the early stages of an iteration when the population has not yet fully evolved. If the above restart condition is met, the current best individual is retained, and the population is reinitialized to restore global exploration capabilities.

[0053] The present invention has the following advantages: 1. In the three-stage hybrid optimization strategy of step three of this invention, an adaptive differential evolution algorithm is used as the core optimizer. Its parameters can be dynamically adjusted with the iteration process, balancing global exploration and local development capabilities. In the subsequent local development and pattern search stages, it can converge quickly based on high-quality solution regions, significantly reducing the overall computational complexity and enabling it to meet the real-time control requirements of industrial robots. Furthermore, a dynamic parameter adjustment strategy with nonlinearly increasing scaling factors and linearly decreasing crossover probabilities is designed, and a DE / current-to-pbest mutation strategy is adopted. This allows the algorithm to focus on global exploration in the early stages of iteration and lean towards fine-grained development in the later stages, effectively improving the convergence speed and global search capability.

[0054] 2. This invention introduces the SE(3) manifold distance based on spinor theory as a measure of pose error, which can more comprehensively reflect the end pose difference than the traditional Euclidean distance. Combined with a three-stage hybrid optimization strategy and a avoidance term for singular points, it can stably find high-precision inverse solutions in complex solution spaces, effectively avoiding the problem of failure or sharp drop in accuracy of traditional methods near singular configurations.

[0055] 3. This invention constructs a fitness function that integrates pose error and singularity avoidance term, and innovatively proposes a three-stage hybrid optimization process consisting of global exploration, local development, and fine optimization. The global exploration stage adopts the differential evolution algorithm, the local development stage adopts the Gaussian sampling strategy, and the fine optimization stage adopts the pattern search method. This process systematically solves the problem of balancing global convergence and local accuracy in inverse kinematics solution.

[0056] 4. This invention fully considers the actual physical constraints of the robot. Through the projection repair strategy, it strictly ensures that the joint angles are within the mechanical limits. By embedding coupling relationship processing in the algorithm flow, it ensures that the kinematic constraints of the sixth and seventh axis transmission gear structure are always satisfied. This makes the solution not only the mathematically optimal solution, but also a physically feasible solution that can be directly executed. Furthermore, it establishes multiple verification standards including pose accuracy, joint limits, and coupling relationships, and designs a restart mechanism based on population diversity monitoring. When the algorithm may get stuck in a local optimum, it can automatically reinitialize, which significantly improves the robustness and success rate of the algorithm.

[0057] This invention is not limited to the preferred embodiments described above. Anyone can derive other products in various forms under the guidance of this invention. However, regardless of any changes in shape or structure, any technical solution that is the same as or similar to this application falls within the protection scope of this invention.

Claims

1. A method for inverse kinematics of a redundant seven-DOF robot, characterized in that, The specific method is as follows: Step 1: Establish forward kinematics modeling for a seven-DOF robot; Step 2: Input the target pose and define the end-effector pose error of the seven-DOF robot as the Riemann distance on the three-dimensional special Euclidean group manifold. Step 3: Adopt a three-stage hybrid optimization strategy, the specific method of which is as follows: The first stage involves a global search in the solution space using a differential evolution algorithm to locate regions of high-quality solutions. The specific method is as follows: a first-stage convergence threshold is set, and the population is uniformly initialized in the joint space. The fitness of each solution in the current population is calculated, and then an adaptive differential evolution iteration is performed. The weight ratio of each objective item in the fitness calculation process is adjusted in real time according to the current state. The process ends when the first-stage convergence condition is met. Second stage: Set the second stage convergence threshold. Based on the obtained high-quality solution region, use a neighborhood search strategy based on Gaussian sampling to generate candidate solutions, calculate the fitness of candidate solutions and select the best one to update the current optimal solution; repeat the above process until the second stage convergence condition is met. The third stage: using pattern search for final deterministic local optimization; Step 4: Joint restraint treatment; Step 5: Convergence and robustness verification.

2. The inverse kinematics method for a redundant seven-degree-of-freedom robot according to claim 1, characterized in that, In step one, the forward kinematics model of the seven-degree-of-freedom robot is established using the DH method.

3. The inverse kinematics solution method for a redundant seven-degree-of-freedom robot according to claim 1, characterized in that, In step three, the joint angle of each individual joint is determined by the following formula: ； in, Represents an individual index. N is the population size; For joint indexing, ; and These represent the upper and lower limits of the angle of the j-th joint individual, respectively; Scaling factor during adaptive differential evolution iteration Calculate using the following formula: ； In the above formula, This represents the number of iterations. Crossover probability It decreases linearly using the following formula: ； in, This represents the maximum number of iterations.

4. The inverse kinematics method for a redundant seven-degree-of-freedom robot according to claim 1, characterized in that, fitness The calculation formula is as follows: ； In the above formula, For the end-effector pose error objective term, The end-effector pose error of a seven-DOF robot is used to measure the difference between the actual pose and the desired pose of the end-effector of a seven-DOF robot. The weighting coefficients for the end-effector pose error; To avoid singular errors in the target term, This is used to avoid singularity errors and guide algorithms to avoid singular regions in the robot's configuration space. The weighting coefficients for singularity avoidance error.

5. The inverse kinematics method for a redundant seven-degree-of-freedom robot according to claim 4, characterized in that, Weighting coefficients of end-effector pose error and the weighting coefficient of singularity avoidance error The calculation formula is as follows: ； In the formula, Joint angle, Represents an individual index.

6. The inverse kinematics method for a redundant seven-degree-of-freedom robot according to claim 3, characterized in that, In step three, when performing adaptive differential evolution iteration, a DE / current-to-pbest mutation strategy is adopted, using the top 30% of the best individuals in the current population as the guide source to search for optimal solutions; then crossover and selection operations are performed; in the crossover phase, a binary crossover strategy is adopted to ensure that at least one dimension of the experimental vector comes from the mutation vector to maintain the population update momentum; in the selection phase, a greedy algorithm is used to decide whether to accept newly generated experimental individuals.

7. The inverse kinematics method for a redundant seven-degree-of-freedom robot according to claim 1, characterized in that, The specific method for step four is as follows: The seventh axis angle of a seven-DOF robot has a numerical coupling multiple relationship with the sixth axis angle. The seventh axis and the sixth axis of the seven-DOF robot must satisfy the following constraints: ； In the formula, n represents the gear transmission ratio between the sixth and seventh axes. A fixed offset representing the angular error; The joint angle of the seventh axis. The joint angle of the sixth axis; during the initialization of the population, a feasible solution that satisfies the above constraints is generated, and during the adaptive differential evolution iteration process, the solution is modified after each mutation and crossover operation to ensure that it always meets the constraints of the seventh and sixth axes before entering the selection operation. After generating candidate solutions, joint limit checks are performed on all candidate solutions; if a candidate solution exceeds the physical limits of the joint, it is projected to the nearest running boundary value to ensure that the generated candidate solution is within the allowable running angle range of the mechanical structure.

8. The inverse kinematics method for a redundant seven-degree-of-freedom robot according to claim 1, characterized in that, In step five, to ensure the optimal solution is obtained, the accuracy of the inverse solution, joint angle limits, and joint coupling constraints are verified respectively; the verification formula for the accuracy of the inverse solution is as follows: ； in, This is the final calculated end-effector pose matrix. The target end pose matrix; The verification formula for joint angle limit is as follows: ； in, For the minimum operating boundary angle, For the maximum operating boundary angle, Joint angle; The formula for verifying joint coupling constraints is as follows: ； in, A fixed offset representing the angular error. The joint angle of the seventh axis. This is the joint angle of the sixth axis.

9. The optimal solution must satisfy the above verification formulas simultaneously.

10. The inverse kinematics method for a redundant seven-degree-of-freedom robot according to claim 8, characterized in that, In step five, a restart mechanism is used to address the situation of getting stuck in a local optimum. The restart conditions are as follows: ； in, The standard deviation of population fitness is used to measure population diversity. The mean fitness of the population reflects the degree of convergence; For the number of iterations, This is an additional condition to avoid accidentally triggering a restart in the early stages of iteration when the population has not yet fully evolved; if the above restart condition is met, the current best individual is retained and the population is reinitialized.

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