A New Geometric Subproblem to Extend Solvability of Inverse Kinematics Based on Screw Theory for 6R Robot Manipulators
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
A New Geometric Subproblem to Extend Solvability of Inverse Kinematics Based on Screw Theory for 6R Robot Manipulators Josuet Leoro*, Tesheng Hsiao, and Carlos Betancourt Abstract: Geometric inverse kinematics procedures that divide the whole problem into several subproblems with known solutions, and make use of screw motion operators have been developed in the past for 6R robot manipulators. These geometric procedures are widely used because the solutions of the subproblems are geometrically meaningful and numerically stable. Nonetheless, the existing subproblems limit the types of 6R robot structural configurations for which the inverse kinematics can be solved. This work presents the solution of a novel geometric subproblem that solves the joint angles of a general anthropomorphic arm. Using this new subproblem, an inverse kinematics procedure is derived which is applicable to a wider range of 6R robot manipulators. The inverse kinematics of a closed curve were carried out, in both simulations and experiments, to validate computational cost and realizability of the proposed approach. Multiple 6R robot manipulators with different structural configurations were used to validate the generality of the method. The results are compared with those of other methods in the screw theory framework. The obtained results show that our approach is the most general and the most efficient. Keywords: Geometric subproblems, inverse kinematics, quaternions, screw theory.
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INTRODUCTION
The inverse kinematics problem of a robot manipulator constitutes one of the most fundamental issues in robotic systems and motion control [1]. This problem has been widely studied; multiple methods have been derived based on analytical, geometrical and numerical approaches. The development of new algorithms has focused on generalization, efficiency and robustness. Efficiency is one of the key considerations when solving the inverse kinematics because its computational cost impacts the real-time performance and accuracy of the motion control of industrial robot manipulators [2, 3]. Furthermore, efficient inverse kinematics methods are of great importance for other applications that require solving the inverse kinematics repeatedly. Examples of such applications are online path planning [4, 5] and compliance control [6, 7]. The most widely used parameterization of a manipulator kinematics is the Denavit-Hartenberg (D-H) representation. In this method, the coordinate system of each joint is described with respect to the previous one. Hence, the rigid body transformations obtained with these parameters represent the relative motion of each link with respect to
the previous link. An alternative approach to parameterize rigid body transformations is the use of twists coordinates to represent screw motions. A screw motion is defined as a linear motion along an axis with a rotation by an angle about the same axis in relation to the inertial frame [8]. A twist is the infinitesimal version of
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