Algorithmic Modified Denavit–Hartenberg Modeling for Robotic Manipulators Using Line Geometry

This paper proposes a kinematic modeling method for robotic manipulators by extracting the modified Denavit–Hartenberg (MDH) parameters using line geometry. For single-branched manipulators, various joint axes can be represented as lines using Plücker coordinates. The forward kinematics is derived by performing the product of matrices which are the exponential maps lifted from two kinds of exponential coordinates using the MDH parameters. For extracting MDH parameters, line geometry systematically analyzes the following: (1) the closest point between a point and line, (2) the closest distance and twist angle between two lines, (3) the common perpendicular line and its intersection points, and (4) classifies line relationships into collinear, distant parallel, intersected, and skewed cases. For each case, five parameters including twist angle, closest distance, common perpendicular direction vector, and both feet on a common perpendicular line are sequentially computed as results of the line geometry block. Finally, the aforementioned line geometry blocks are utilized to extract the four MDH parameters according to their definitions. The effectiveness of the proposed algorithm is verified by four examples including a typical Selective Compliance Assembly Robot Arm (SCARA) robot and three different commercial manipulators.