Formalization of the inverse kinematics of three-fingered dexterous hand

As an effective extension of human limbs, dexterous robotic hands based on cyber-physical systems (CPS) are used to perform diverse tasks in industrial production, medical operation, outer-space exploration, etc. The reliable functioning of dexterous robotic hands depends on the proper modeling and solving of inverse kinematics problems in the design phase. The traditional D-H parameter method for modeling and solving inverse kinematics problems suffers from the singularity problem, which is avoided by methods based on the screw theory. However, the manual or computer-simulation-based development of these methods could suffer from human errors and software defects. In this paper, we address this problem by using formal techniques and tools to develop a screw-theory-based method. Firstly, we formalize theories related to the Paden-Kahan sub-problem in an interactive theorem prover. Secondly, we construct a formal model for solving the inverse kinematics problem for robotic systems. Lastly, taking the three-fingered dexterous hand as a case study, we formally verified its inverse kinematics solutions. The results presented in this article help guarantee a level of safety for robotic systems that is beyond achievable by manual and computer-simulation-based development methods.