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Inverse kinematics for modular reconfigurable robots

Inverse kinematics solutions of a reconfigurable robot system built upon a collection of standardized components are difficult to obtain because of its varying configuration. This paper addresses the formulation of a generic numerical inverse kinematics model and automatic generation of the model for arbitrary robot geometry including serial type and branching type geometry. 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 formulas. The Newton-Raphson iteration method is employed for the solution. The automated model generation is accomplished through the introduction of assembly incidence matrix 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.