The inverse kinematics solutions of a reconfigurable robot system built upon a collection of standardized components is difficult to obtain because of its varying configurations. This article addresses the formulation of a generic numerical inverse kinematics model and automatic generation of the model for arbitrary robot geometry including serial and tree-typed geometries. Both revolute and prismatic types of joints are considered. The inverse kinematics is obtained through the differential kinematics equations based on the product-of-exponential (POE) formulas. The Newton-Raphson iteration method is employed for solution. The automated model generation is accomplished by using the kinematic graph representation of a modular robot assembly configuration and the related accessibility matrix and path matrix. Examples of the inverse kinematics solutions for different types of modular robots are given to demonstrate the applicability and effectiveness of the proposed algorithm.
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