Formal Foundations of 3D Geometry to Model Robot Manipulators

Abstract : We are interested in the formal specification of safety properties of robot manipulators down to the mathematical physics. To this end, we have been developing a formalization of the mathematics of rigid body transformations in the COQ proof-assistant. It can be used to address the forward kinematics problem, i.e., the computation of the position and orientation of the end-effector of a robot manipulator in terms of the link and joint parameters. Our formalization starts by extending the Mathematical Components library with a new theory for angles and by developing three-dimensional geometry. We use these theories to formalize the foundations of robotics. First, we formalize a comprehensive theory of three-dimensional rotations, including exponentials of skew-symmetric matrices and quaternions. Then, we provide a formalization of the various representations of rigid body transformations: isometries, homogeneous representation, the Denavit-Hartenberg convention, and screw motions. These ingredients make it possible to formalize robot manipulators: we illustrate this aspect by an application to the SCARA robot manipulator.
Complete list of metadatas

Cited literature [24 references]  Display  Hide  Download

https://hal.inria.fr/hal-01414753
Contributor : Cyril Cohen <>
Submitted on : Monday, December 12, 2016 - 3:18:50 PM
Last modification on : Monday, March 5, 2018 - 3:42:12 PM
Long-term archiving on : Tuesday, March 28, 2017 - 12:01:27 AM

File

robot_cpp_final.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01414753, version 1

Collections

Citation

Reynald Affeldt, Cyril Cohen. Formal Foundations of 3D Geometry to Model Robot Manipulators. Conference on Certified Programs and Proofs 2017, Jan 2017, Paris, France. ⟨hal-01414753⟩

Share

Metrics

Record views

716

Files downloads

751