Formal Verification of Robot Rotary Kinematics

With the widespread application of robots in aerospace, medicine, automation, and other fields, their motion safety is essential for well-being humans accomplishment vital socially beneficial programs. Conventional robot hardware software designs mainly rely on experiential knowledge manual testing to ensure safety, but this fails cover all possible paths adds risks. Alternatively, formal, mathematically rigorous verifications can provide predictable reliable guarantees safety. To demonstrate feasibility approach, we formalize mathematical coordinate transformation a robot’s rigid-body kinematics using Coq Proof Assistant verify correctness its theoretical design. First, based record-type matrix formalization, define spatial geometry by constructing formal expressions matrix’ Frobenius norm, trace, inner product. Second, divide rotary into revolution rotation construct definitions. Next, formally rotational matrices angle conventions (e.g., roll–pitch–yaw Euler), complete verification Rodriguez formula theory specific rotating problems. The work paper has variety applications provides generalizable analysis framework control system verification. Moreover, it paves way automatic programming capabilities.