Research On Inverse Kinematics And Motion Planning Algorithm Of 7-DOF Redundant Manipulators

Compared with 6-degree-of-freedom(DOF)manipulators,7-DOF redundant manipulators have incomparable advantages in the obstacle avoidance,singularity avoidance,joint torque optimization and enhanced operability,etc.Therefore,they are widely used for different tasks in different fields,such as the assembly,painting and welding in the manufacturing field,the neurosurgery in the medical field and the satellite maintenance and orbital trash removal in the aerospace filed,etc.In this paper,taking 7-DOF manipulators as the research object,using the geometric intuition and the geometric algebra operation of conformal geometric algebra(CGA),the inverse kinematic analysis is investigated and a new geometric modeling and analytical solution method for this problem is proposed;aimed at the motion planning problem,an improved random sampling(RRT)motion planning algorithm is presented.The main contents and contributions can be summarized as follows:(1)The CGA-based algorithm is proposed for the inverse kinematic analysis of 7-DOF manipulators combined with the joint angle parameterized and ann angle parameterized respectively.According to the shoulder,elbow or wrist parts with or without link offsets,7-DOF manipulators are classified;then,combined with the joint angle parameterized or arm angle parameterized,the inverse kinematic analysis is modeled and solved based on CGA respectively.Under the CGA frame,based on the representations of basic geometric elements such as point,line,surface,sphere and point pair and the operations of inner product,outer product,dual,projection and rotation transformation etc.,the geometric constraint equations are deduced for the inverse kinematic analysis,whose derivation is free of coordinate,and no elimination solution process is required.Finally,several different configurations of 7-DOF manipulators are taken as numerical examples,and their corresponding 3D configurations based on SolidWorks are provided to verified the correctness and effectiveness of the proposed two algorithms.(2)The improved RRT algorithm is proposed for the motion planning of 7-DOF manipulators.Firstly,a target guidance strategy to guide sampling directions is introduced;next,the regression strategy and adaptive step size strategy are introduced to improve the algorithm’s search and obstacle avoidance capabilities,and to reduce redundant probing in space;and then the Dijkstra algorithm is applied to eliminate redundant nodes in the path and shorten the path length;finally,the B-spline curve is utilized to fit the path.The simulation results based on Matlab show the search effectiveness and path quality of the improved RRT algorithm are further improved compared to the existed RRT algorithm.(3)The motion planning algorithm for 7-DOF manipulators is simulated and verified based on ROS.Aimed at the motion planning of 7DOF manipulators,the path planners based on the basic RRT algorithm,RRT-Connect algorithm,RRT*algorithm and the improved RRT algorithm are respectively designed using the motion planning module Movelt! in the ROS system,in non-obstacle and obstacle environment and the comparations for the performance analysis are carried out.The simulation results show that:compared with the existed RRT algorithm,the improved RRT algorithm has significantly improvements in the sampling points number,the planning time,the path length and the path smoothness,etc.,and hence the effectiveness of the improved RRT algorithm for 7-DOF manipulators is verified.