Research On Kinematics And Simulation Of A Nine-DOF Surgical Robot

Surgical robots have developed rapidly in recent years and have received extensive research attention.The surgical robot system mainly includes four parts: master hand part,slave hand part,image system and control system.Among them,the design of the slave hand part and its control algorithm are the core technology of the surgical robot.The slave hand robot needs to pass through the fixed point of the RCM telecentric point.In response to the requirement of RCM telecentric point,this paper proposes a 9-degree-of-freedom surgical robot model,and establishes a 9-degree-of-freedom robot model based on the D-H modeling method.Innovatively,the 9-degree-of-freedom model is decomposed into two6-degree-of-freedom models with the RCM telecentric point as the node,and the two models are analyzed and solved separately,and finally merged into the solution of the9-degree-of-freedom robot.Based on the homogeneous pose matrix,the robot forward kinematics calculation formula is derived,and the forward mapping from the joint space to the operating space is realized.The analytic method is used to solve the matrix equations to obtain the inverse kinematics solutions of the two robot models.Finally,the solutions of the equations are combined to obtain 32 sets of solutions of the nine-degree-of-freedom robot,which realizes the inverse mapping of the operating space pose to the joint space.In the process of solving,through the analysis of the variable parameters of the equation,the occurrence position and geometric meaning of the internal singularity are listed,and the value range of the end pose parameter is deduced,and the reachable working space and flexible working space of the model are obtained.Based on the differential transformation method,the speed Jacobian matrix of the robot is solved,and the forward and reverse mapping from the operating space speed to the joint space is realized.Through the analysis and calculation of the Jacobian matrix,the occurrence position and geometric meaning of the boundary singularity are listed,and the singularity configuration is further improved.Finally,use MATLAB to program the inverse kinematics solution and verify its correctness.The transposition based on the Jacobian matrix solves the statics,realizes the forward and inverse mapping of the joint space static torque to the operating space,and analyzes the application of the Jacobian singularity in robot statics.The Jacobian matrix based on the vector product solves the inverse acceleration,and realizes the inverse mapping from the acceleration in the operating space to the joint space.The velocity and acceleration are transferred and deduced,the forward mapping of the velocity and acceleration of each joint is realized,and the motion parameters of the center of mass of each joint are derived.The Newton-Euler method is used to convert the relationship between force and motion in dynamics into the balance of force and moment,and the theoretical formula of the model dynamics force spin is completed.Finally,the forward and inverse mapping from the joint space force spin to the operating space force spin is realized through outward recursion and inward recursion.For joint space trajectory planning,the fifth-order polynomial interpolation method and the five-segment position S-curve method joint space trajectory planning are realized through formula derivation and programming,and two improved fifth-order polynomial interpolation methods are proposed,and the trajectory planning is demonstrated through programming Curved image.Two common linear interpolation and circular interpolation are derived,and the interpolation point solution of circular interpolation is realized by coordinate system conversion.The arc curve of the operating space is reversely mapped,which further improves the mapping relationship from the joint space to the operating space.Based on the ROS simulation platform,the circular interpolation method is used to draw a circle using Python programming,which further verifies the feasibility of the model and the correctness of the overall algorithm.This research provides an idea and solution for surgical robots,and kinematics and dynamics calculations and simulations can provide a theoretical calculation basis for the subsequent research of this robot.