Research On Modular Algorithm Of Inverse Kinematics For Robots

Inverse kinematic algorithm of robots is the basis of algorithm design on robotic motion control and motion planning of robotic manipulators. It is concerned with control precision and real time performance of robots. Traditional solvers on inverse kinematics of robots have the disadvantages of computational complexity, inaccurate result, lack in general use. Therefore, it is significant and necessary to research and develop a more efficiency, more universal geometric algorithm for inverse kinematics of robors.In order to overcome the shortage of modeling methods for kinematics of robots by use of link's D?H matrix, a geometrical closed-form inverse kinematic method, utilizing the product of exponentials (POE) formula of direct kinematics mapping, is proposed based on screw theory. In this method, the inverse kinematics problem of a serial-type robot is decomposed into several canonical subproblems. These subproblems are also geometrically meaningful and numerically stable and can be reused. Because of the decomposition, the complexity of the inverse kinematic problem is reduced and the computing efficiency is greatly improved.In this paper, some representative canonical subproblems are put forward by analyzing the familiar structural types of robotic mechanisms. The basic subproblems are defined such that each can solve the inverse kinematics of a distinct sub-structure which can be a part of a robot's kinematic structure in a geometric way.Subsequently, three reduction techniques are presented to properly decompose a POE equation of the inverse kinematics into one or several simpler POE equations based on the properties of various simple rigid motions. The condition that a POE equation can be decomposed is discussed. Based on the difference in structure, the non-redundant robot architectures which can be solved by subproblem measure are divided into two categories: architectures with intersecting revolute joints and architectures with non-intersecting revolute joints. A systematic inverse kinematics solver process is proposed. In this process the inverse kinematics of a given robot is solved in three steps: (1) the determination of decomposability; (2) the execution of decomposition; (3) the application of subproblems.The application of subproblem measure may help us to solve the inverse kinematics of possible geometrical structures robot in a systematic and modular way. It provides the theoretical basis for the further development of robotics technology.