  Cooperative robots can significantly assist people in their productive
activities, improving the quality of their works. Collision detection is vital
to ensure the safe and stable operation of cooperative robots in productive
activities. As an advanced geometric language, conformal geometric algebra can
simplify the construction of the robot collision model and the calculation of
collision distance. Compared with the formal method based on conformal
geometric algebra, the traditional method may have some defects which are
difficult to find in the modelling and calculation. We use the formal method
based on conformal geometric algebra to study the collision detection problem
of cooperative robots. This paper builds formal models of geometric primitives
and the robot body based on the conformal geometric algebra library in HOL
Light. We analyse the shortest distance between geometric primitives and prove
their collision determination conditions. Based on the above contents, we
construct a formal verification framework for the robot collision detection
method. By the end of this paper, we apply the proposed framework to collision
detection between two single-arm industrial cooperative robots. The flexibility
and reliability of the proposed framework are verified by constructing a
general collision model and a special collision model for two single-arm
industrial cooperative robots.
