Formal Kinematics Analysis of The Two-Link Planar Manipulator

Abstract

Kinematic analysis is used for trajectory planning of robotic manipulators and is an integral step of their design. The main idea be- hind kinematic analysis is to study the motion of the robot based on the geometrical relationship of the robotic links and their joints. Given the continuous nature of kinematic analysis, traditional computer-based verification methods, such as simulation, numerical methods or model checking, fail to provide reliable results. This fact makes robotic de- signs error prone, which may lead to disastrous consequences given the safety-critical nature of robotic applications. Leveraging upon the high expressiveness of higher-order logic, we propose to use higher-order-logic theorem proving for conducting formal kinematic analysis. As a first step towards this direction, we utilize the geometry theory of HOL-Light to develop formal reasoning support for the kinematic analysis of a two-link planar manipulator, which forms the basis for many mechanical struc- tures in robotics. To illustrate the usefulness of our foundational for- malization, we present the formal kinematic analysis of a biped walking robot.

 

Two Link Kinematic Model

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Publications

1) B. Farooq, O. Hasan and S. Iqbal, ” Kinematic Analysis of the Two-Link Planar Manipulator” 15th International Conference on Formal Engineering Methods (ICFEM-2013),Springer LNCS 8144, Queenstown, New Zealand, pp. 348–363.