A strictly convergent real‐time solution for inverse kinematics of robot manipulators

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Abstract
Inverse Kinematics has been recognized as an important problem in robotics applications. A robot independent solution can only be obtained through numerical methods, but most solutions which use this approach have problems with convergence especially near singularity points. This article develops a strictly convergent algorithm and a special‐purpose Inverse Kinematics Processor (IKP) to obtain the solution in real time. While the algorithm is based on open‐loop integration of rates, the absolute position deviation is used as a criterion to control the iteration, and a feedback mechanism has been especially designed to eliminate problems with long‐term drift or with initial errors in the solution. The architecture of the IKP is based on a high‐speed floating‐point arithmetic processor and is designed to perform the common matrix‐vector operations efficiently with a minimum processor cycle time. The algorithm has been simulated on the proposed architecture, and the results show its robustness and real‐time capability. For a six degree‐of‐freedom robot manipulator (for which no closed‐form solution exist), the Inverse Kinematics solution may be obtained at an approximate 2 khz rate with an error which is within standard repeatability limits.

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