Research On Singularity Avoidance Methods Of Multi-DOF Manipulators

When the manipulator passes across the singular region,the system stability and trajectory tracking accuracy will be deteriorated,and the system will be out of control,which would lead to serious safety problems.Therefore,the singularity avoidance of the manipulator is one of the key problems that must be solved in the control system of the multi-degree of freedom(DOF)manipulator.Accordind to the research background of the multi-DOF industrial handling manipulator,multi-DOF deep-sea hydraulic manipulator and multi-DOF redundant space manipulator,this thesis proposes the singularity avoidance method based on singular factors to solve the singularity detection and singularity avoidance problems.Compared with the traditional methods,the proposed methods have the characteristics of wider applicability,lower computational complexity and higher trajectory accuracy.The research results can be widely applied to the control system of similar manipulators,which not only helps to improve the working accuracy of the manipulators around the singularities,but also guarantees the safety of the manipulators in the industrial,underwater and space application scenarios,which has important research significance and practical value.The main work and innovation of this thesis are as follows:(1)Forward and inverse kinematics of three different configurations of multidegree-of-freedom manipulators are analyzed.Aiming at the deep-sea hydraulic manipulator and the redundant space manipulator with non-spherical wrist satisfying PIEPER criterion,the analytic solution and iterative solution of the inverse kinematics were deduced respectively,and the algorithm complexity of inverse kinematics of the redundant manipulator was reduced.The trajectory planning of the multi-DOF manipulator is realized by using quartic multinomial the spline method,and the synchronization and emergency stop problems in the trajectory planning are studied deeply.It provides the necessary foundation and support for realizing the singularity avoidance of the manipulator.(2)A singularities detection method for the non-redundant manipulator based on singular factor is proposed.Firstly,according to the decoupling of position and attitude of the non-redundant industrial handling manipulator with a spherical wrist,the singularities of the spherical wrist manipulator were decomposed into wrist singularities and front singularities,and the singular factors of the manipulator were extracted to detect the singularities of the spherical wrist manipulator.Then the Grassmann geometry method was used to analyze the singular configurations of the non-spherical wrist nonredundant deep-sea hydraulic manipulator,then the matrix transformation and decomposition of the Jacobian matrix were carried out based on the singular configurations,and the singular factors of the manipulator were derived to detect the singularities of the manipulator.Finally,the damping reciprocal(DR)method based on the singular factor is used to avoid the singularity of the deep-sea hydraulic manipulator.Theoretical analysis and research results show that the computational cost of the proposed method is only 1/30～1/20 of the traditional method,and it is effective for the manipulator with relatively complex configuration,so it has a wide range of application.(3)A singularity avoidance method for non-redundant manipulator based on approximate damped reciprocal(ADR)is proposed.In this method,the reciprocal of the singular factor in the Jacobian inverse matrix is replaced by the damped reciprocal to realize the singularity avoidance of non-redundant manipulators.Firstly,a mathematical expression for the approximate damped reciprocal is presented,and the characterisics of the mathematical expression are analyzed.Then the relationship between the joint rates and accelerations of the manipulator and the approximate damped reciprocal is analyzed theoretically.Finally,the proposed singularity avoidance method is verified by simulation on a spherical wrist industrial handling manipulator.The results show that this method improves the trajectory accuracy of the end-effector near the singularity by 4～5 times at least,and can ensure the stability of the system near the singular region.(4)A singularity avoidance method for redundant manipulator based on singular factor optimization(SFO)is proposed.Firstly,the matrix transformation and dimensionality reduction of the redundant manipulator are carried out,and seven groups of singular factors of the seven-degree-of-freedom redundant manipulator are extracted.Then,according to the singular factors of each group,the singularity of the redundant manipulator is divided into two categories:avoidable singularity and non-avoidable singularity.A singularity avoidance algorithm for redundant manipulator is proposed based on the singular factor optimization.The algorithm can ensure that a set of singular factors always do not satisfy the singular condition during the manipulator’s movement,so as to realize the singularity avoidance of redundant manipulator.Simulation results show that the proposed method achieves singularity avoidance in redundant space manipulator.Complexity theory analysis and simulation results shows that this method does not need to calculate the pseudo-inverse and partial derivative of the Jacobian matrix,and the computational complexity of this method is reduced by tens of times compared with the traditional algorithm.The results show that this method can ensure that the trajectory accuracy of the manipulator near the avoidable singularity is not affected,and improve the trajectory accuracy of the manipulator near the non-avoidable singularity.