A method for solving inverse kinematics of redundant robot arm

Abstract

This invention discloses a method for solving the inverse kinematics of a redundant robotic arm. The objective function of the robotic arm is designed with minimum energy consumption in mind. By introducing fitness function weight coefficients, the order of magnitude of the position vector and attitude matrix in the objective function is normalized. A dynamically adjusted search parameter and a population rotation prey search mechanism are employed. The search parameter gradually decreases with increasing iterations, making the search more robust. The population rotation prey search mechanism increases the optimization range, avoids local convergence, and further improves optimization accuracy. This method has the advantages of strong universality, fast solution speed, and high solution accuracy.

Description

Technical Field

[0001] This invention relates to the field of industrial robotic arm pose optimization. Specifically, it is a method for solving the inverse kinematics of redundant robotic arms. Background Technology

[0002] Robotics is a comprehensive interdisciplinary field involving robot body structure design, robot kinematics, robot dynamics, robot control, communication technology, and artificial intelligence. Robot kinematics is a fundamental and core component, and the inverse kinematics problem of robotic arms is a core research topic within robot kinematics. It serves as the premise and foundation for studying robot trajectory planning, motion control, workspace analysis, and dynamic analysis. Because the kinematic equations of a robotic arm are a complex set of strongly coupled, nonlinear transcendental equations, decoupling the joint variables from the kinematic equations is not easy, making the solution to the inverse kinematics problem quite difficult. For structurally complex robotic arms, it may even be impossible to decouple the joint variables from the kinematic equations. In such cases, there is no closed analytical inverse kinematics solution, posing a significant challenge to solving the inverse kinematics problem. Therefore, achieving high-precision solutions to the inverse kinematics of robotic arms is a crucial problem that urgently needs to be solved in the field of industrial robotic arm manufacturing. Summary of the Invention

[0003] To address the problems existing in the prior art, the purpose of this invention is to provide a method for solving the inverse kinematics of a redundant robotic arm.

[0004] To solve the above problems, the present invention adopts the following technical solution.

[0005] A method for solving the inverse kinematics of a redundant robotic arm is provided. The method is characterized by introducing fitness function weight coefficients, designing an optimization objective function for the robotic arm, and optimizing the objective function using a CSA algorithm based on dynamically adjusted search parameters and a population rotation prey search mechanism, thereby achieving high-precision inverse kinematics solution for the robotic arm.

[0006] As a further improvement of the present invention, the optimization objective function is defined as follows:

[0007]

[0008] Where, p * Let n be the position vector of the robotic arm's end effector. * o * a * The attitude matrix that constitutes the end effector of the robotic arm;

[0009] Inverse kinematics solution method by applying the objective function f(X) *The algorithm is optimized by evaluating the solution quality of the samples and normalizing the magnitudes of the attitude matrix and position vector before computation by introducing a proportionality factor λ. Specifically, the proportionality factor has a value on the order of 10. 3 .

[0010] As a further improvement of this invention, the CSA algorithm, which employs dynamically adjusted search parameters and a population rotation prey-hunting mechanism, is used to optimize the objective function, and its expression is:

[0011]

[0012] in, Let Pi be the position of individual i in the j-th dimension at the t-th iteration, Pp be the probability of sensing prey, and p1 and p2 be positive coefficients used to control the algorithm's development capability. Let r1, r2, and r3 be the optimal position of individual i in j-dimensional space after t iterations, and r1, r2, and r3 be random numbers between (0, 1). i Let r be a uniformly generated random number at index i in (0, 1). i ≥Pp, an individual can change its position based on the prey it observes in the search space; similarly, when r i If ≤Pp, the individual will randomly explore the search space in different directions and regions, which increases the probability of it sensing nearby prey. sgn(rand-0.5) represents the individual adjusting its rotation direction, taking a value of +1 or -1. μ is a search capability parameter updated with the number of iterations. The expression for μ is:

[0013] μ=γe (-αt / T)β (3)

[0014] The inverse kinematics solution method adjusts the optimal individual position based on the dynamic adjustment of search parameters and the population rotation prey search mechanism during the process of solving the objective function of the robotic arm, so as to make the search more robust, avoid local convergence, and obtain a high-precision inverse solution for the robotic arm.

[0015] As a further improvement to this invention, the optimal individual position is adjusted by introducing a population rotation prey-search mechanism, thereby further increasing the optimization accuracy. Its defining formula is:

[0016]

[0017] m=R(θ,V z1,z2 (6)

[0018] θ=rsgn(rand-0.5)×π (7)

[0019] in: Let be the centroid position of the individual in the t-th iteration. This represents the individual's position after the position transformation. m represents θ and V. z1,z2 The rotation matrix represents the rotation of the individual's position. Let z1 and z2 be the vectors after they are orthogonal. θ represents the random rotation angle of the individual. r restricts the rotation angle to be between 0 and π.

[0020] As a further improvement of the present invention, the objective function is optimized using a designed optimization method. During the optimization process, the latest joint positions of the robotic arm are continuously updated through a population iteration mechanism within the method, in order to achieve the goal of accurately solving the inverse kinematics of the robotic arm.

[0021] Beneficial effects of the present invention

[0022] Compared with the prior art, the advantages of this invention are:

[0023] This invention employs dynamically adjusted search parameters and a population rotation prey-search mechanism. The search parameters gradually decrease with increasing iterations, making the search more robust. The population rotation prey-search mechanism expands the optimization range, avoids local convergence, and further increases optimization accuracy. This method has the advantages of strong universality, fast solution speed, and high solution accuracy. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of an industrial redundant robotic arm structure.

[0025] Figure 2 for Figure 1 The diagram shows a linkage coordinate system for the robotic arm structure.

[0026] Figure 3 This is a flowchart of the overall process.

[0027] Figure 4 This is a comparison chart of the effects of the invented method and the conventional method. Detailed Implementation

[0028] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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 without creative effort are within the scope of protection of the present invention.

[0029] like Figure 1 and Figure 2 As shown, a structural model of an industrial robotic arm in an embodiment of the present invention includes an overall structural schematic diagram and a schematic diagram of the link coordinate system. The overall flowchart of the method is shown below. Figure 3 As shown.

[0030] In the above scheme, the redundant robotic arm inverse kinematics solution method designs the robotic arm's objective function from the perspective of minimizing energy consumption, and decomposes the objective function into position and attitude functions to avoid differences in convergence accuracy. Its definition is as follows:

[0031]

[0032] Where, p * Let n be the position vector of the robotic arm's end effector. * o * a * The attitude matrix that constitutes the end effector of the robotic arm.

[0033] In the above scheme, the inverse kinematics solution method is obtained by solving the objective function f(X). * The algorithm is optimized by evaluating the solution quality of the samples and normalizing the magnitudes of the attitude matrix and position vector before computation by introducing a proportionality factor λ. Specifically, the proportionality factor has a value on the order of 10. 3 .

[0034] In the above scheme, the inverse kinematics solution method optimizes the objective function using the CSA algorithm with dynamically adjusted search parameters and a population rotation prey search mechanism. Its expression is:

[0035]

[0036] in, Let Pi be the position of individual i in the j-th dimension at the t-th iteration, and let Pp be the probability of sensing prey. p1 and p2 are positive coefficients used to control the algorithm's exploitation capability. t i,j Let r1, r2, and r3 be the optimal position of individual i in j-dimensional space after t iterations, where r1, r2, and r3 are random numbers between (0, 1). i Let r be a uniformly generated random number at index i in the interval (0, 1). i ≥Pp, an individual can change its position based on the prey it observes in the search space; similarly, when r i If ≤Pp, the individual will randomly explore the search space in different directions and regions, which increases the probability of it sensing nearby prey. sgn(rand-0.5) represents the individual adjusting its rotation direction, taking a value of +1 or -1. μ is a search capability parameter updated with the number of iterations. The expression for μ is:

[0037] μ=γe (-αt / T)β (3)

[0038] In the above scheme, the inverse kinematics solution method adjusts the optimal individual position based on the dynamic adjustment of search parameters and the population rotation prey search mechanism during the process of solving the objective function of the robotic arm, so as to make the search more robust, avoid local convergence, and obtain a high-precision inverse solution for the robotic arm.

[0039] In this example, we first perform a forward kinematics model of the robotic arm based on the DH parameters of each joint. Following the principle of minimizing energy consumption during the robotic arm's movement, we introduce fitness weight coefficients and normalize the order of magnitude of the position vector and attitude matrix to design the robotic arm optimization objective function. The overall structure of the robotic arm and its link coordinate system are as follows: Figure 1-2 As shown, the objective function for optimization is defined as shown in equation (1).

[0040] In this example, the CSA algorithm, based on dynamically adjusted search parameters and a population rotation prey-hunting mechanism, is used to optimize the objective function. The optimization process is initiated by an initial population, where the joint variables of the robotic arm represent the position vector of each individual in the population, and each individual's position vector represents a candidate solution.

[0041] Its positional expression is:

[0042]

[0043] Among them: lb i and ub i These are the upper and lower limits of the region, respectively.

[0044] The position of individuals is changed during the search process according to the dynamically adjusted search parameter update strategy, as shown in equation (2). The optimal individual position is adjusted by introducing a population rotation prey-hunting mechanism, further increasing the optimization accuracy. Its definition is:

[0045]

[0046] m=R(θ,V z1,z2 (6)

[0047] θ=rsgn(rand-0.5)×π (7)

[0048] in: Let be the centroid position of the individual in the t-th iteration. This represents the individual's position after the position transformation. m represents θ and V. z1,z2 The rotation matrix represents the rotation of the individual's position. Let z1 and z2 be the vectors after they are orthogonal. θ represents the random rotation angle of the individual. r restricts the rotation angle to be between 0 and π.

[0049] The performance of the proposed optimization method is verified through simulation experiments, primarily using Matlab 2020a. The performance is validated by statistically analyzing the best, worst, mean, and standard deviation (Std.) of the simulation results, as well as the average solution time (AT) and optimization success rates (SR1, SR2). To visually demonstrate the effect, the proposed optimization method is compared with four traditional optimization methods; the convergence curves of its single-point test fitness optimization are shown below. Figure 4 As shown in the figure. CSA represents the method proposed in this invention, while the other four are traditional optimization methods.

[0050] Simulation results show that the algorithm proposed in this invention achieves better stability and convergence accuracy. Furthermore, the population optimization approach demonstrates greater universality in solving inverse kinematics problems for robotic arms.

[0051] The above description is merely a preferred embodiment of the present invention; however, the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and its improved concepts, should be covered within the scope of protection of the present invention.

Claims

1. A method for solving inverse kinematics of redundant robot arms, characterized in that, This involves designing an optimization objective function for the robotic arm by introducing fitness function weight coefficients, and then using the CSA algorithm based on dynamically adjusted search parameters and a population rotation prey search mechanism to optimize the objective function, thereby achieving high-precision inverse kinematics solution for the robotic arm. The optimization objective function is defined as follows: wherein p * is a position vector of the end of the robot arm, n * , o * , a * constitute a pose matrix of the end of the robot arm; Inverse kinematics solution method by applying the objective function Optimization was performed, the solution quality of the samples was evaluated, and a proportionality factor λ was introduced to normalize the order of magnitude of the attitude matrix and position vector before calculation. The value of the proportionality factor was on the order of 10. 3 ; The CSA algorithm, employing dynamically adjusted search parameters and a population rotation prey-hunting mechanism, optimizes the objective function, which is expressed as follows: in, Let i be the position of individual i in the j-th dimension space during the t-th iteration. To sense the probability of prey, , It is a positive coefficient used to control the algorithm development capability. Let i be the optimal position of individual i in j-dimensional space after t iterations. , and They are random numbers between (0, 1). Let i be a uniformly generated random number at index i in (0, 1). Individuals can change their position based on the prey they observe in the search space; similarly, when Individuals will randomly explore the search space in different directions and areas, which increases their probability of sensing nearby prey. This represents the individual adjusting its own rotation direction, and its value is +1 or -1. These are search capability parameters that are updated with each iteration. The expression is: The inverse kinematics solution method adjusts the optimal individual position based on the dynamic adjustment of search parameters and the population rotation prey search mechanism during the process of solving the objective function of the robotic arm, so as to make the search more robust, avoid local convergence, and obtain a high-precision inverse solution for the robotic arm.

2. The method for solving the inverse kinematics of a redundant robotic arm according to claim 1, characterized in that: By introducing a population rotation prey-hunting mechanism to adjust the optimal individual position, the search accuracy is further increased. Its definition is: in: Let be the centroid position of the individual in the t-th iteration. Let m be the individual's position after the position transformation. and The rotation matrix represents the rotation of the individual positions, and represents the vectors after z1 and z2 become orthogonal. This represents the random rotation angle of an individual, where r restricts the rotation angle to between 0 and... between.

3. The method for solving the inverse kinematics of a redundant robotic arm according to claim 2, characterized in that: The objective function is optimized using the designed optimization method. During the optimization process, the latest joint positions of the robotic arm are continuously updated through the population iteration mechanism in the method, so as to achieve the goal of accurately solving the inverse kinematics of the robotic arm.

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