A framework for formal verification of robot kinematics

As robotic applications continue to expand and task complexity increases, the adoption of more advanced and sophisticated control algorithms and models becomes critical. Traditional methods, relying on manual abstraction and modeling to verify these algorithms and models, may not fully encompass all potential design paths, leading to incomplete models, design defects, and increased vulnerability to security risks. The verification of control systems using formal methods is crucial for ensuring the safety of robots. This paper introduces a formal verification framework for robot kinematics implemented in Coq. It constructs a formal proof for the theory of robot motion and control algorithms, specifically focusing on the theory of robot kinematics, which includes the homogeneous representation of robot coordinates and the transformation relations between different coordinate systems. Subsequently, we provide formal definitions and verification for several commonly used structural robots, along with their coordinate transformation algorithms. Finally, we extract the Coq code, convert the functional algorithms into OCaml code, and perform data validation using various examples. It is worth emphasizing that the framework we have built possesses a high level of reusability, providing a solid technological foundation for the development of kinematics theorem libraries.