Research On Inverse Kinematic Algorithm Of Industrial Robot With Complex Multiple Joint

The inverse kinematics of robots has always been a research hotspot in robotics,and it is also the basis for offline programming,trajectory planning,motion control and other operations of robots.The methods of solving the inverse kinematics of robot include geometry,iteration,algebra and intelligent algorithm.It is difficult to apply the geometric method to solve the inverse kinematics of the robot with complex structure.The result of iteration method is easily affected by the singularity of jacobian matrix and the initial value.Algebraic method can obtain all the solutions of non-redundant robots,and when the design of 6R robot meets the spherical wrist structure,the analytical solution can be obtained by this method.However,algebraic method requires complex elimination transformation,and the solution process is very complicated.Compared with the iterative method and the algebraic method,the intelligent algorithm does not need to derive the complex inverse kinematics formula,only needs to establish the objective function to search the appropriate solution in the joint space.However,it is difficult to solve the problem of multiple solutions in inverse kinematics effectively.In order to solve this problem,a new method based on uniqueness domains is proposed:using the boundary confirmed by robot's Jacobian matrix determinant equal to zero,the joint space of the robot is divided into uniqueness domains with the same number of solutions as the inverse kinematics,the boundary of each uniqueness domain is used as a constraint condition,the inverse kinematics solution in the uniqueness domain is transformed into the constrained optimization of the CMA-ES algorithm,and the initial mean point of the CMA-ES algorithm in the uniqueness domain is optimized by using the characteristics of the uniform distribution of the good point set.In the simulation experiment,8 inverse solutions of the spherical 6R robot and KUKA humanoid arm were obtained successfully,and the position accuracy of the robot could reach 10-5mm.With the continuous expansion of robot applications,some new structures of robotic arms have been produced.The complex motion structure makes it difficult to determine the uniqueness domain boundary.Therefore,a new M-CMA-ES algorithm is proposed in this paper to solve the inverse solution of general 6R robots and redundant robots.Aiming at the fact that CMA-ES algorithm can only search without constraint,the generation of initial mean point and the updating of step size are improved respectively.Simulation results show that the M-CMA-ES algorithm proposed in this paper is superior to GA in terms of computational speed,solution accuracy and robustness.Compared with the original CMA-ES,M-CMA-ES converges faster,and the solution is in the range of constraints.The average solution speed of M-CMA-ES within 10ms/time and the position error of 10-5mm level provide an effective solution for the high precision and real-time inverse kinematics solution of any 6R robot and redundant robot.The algebraic method can obtain the analytical solution of the inverse kinematics of the 6R spherical wrist robot,but it is very complicated and lacks geometric intuition when extended to the case of non-spherical wrist.In this paper,an efficient method based on the decomposition and reconnection technique is proposed in this paper to solve the inverse kinematic problems of industrial manipulators with non-spherical wrist.The main idea is to simplify the elimination process by using the geometric relationship between the decomposition positions.In this method,the modified POE,which is employed to model the kinematic problem of an n-degree-of-freedom manipulator,has been rearranged into a special kind of expression with separated terms.General geometric constrains have been applied to build the connection between decomposed parts.The decomposing method and the constrains in reconnection is developed for the 6R manipulators with non-spherical wrist.The equations of the constrains is rewritten into a closed-formed nonlinear equation with single variable.Other joint angles are derived directly from the involved variable.The resulted nonlinear equation is finally solved through a searching method.With the proposed method,the algorithm runs less than 0.4ms at a time,and the error of the calculated pose is within 10-12 mm,which meets the requirements of real-time,high precision and stability.