Abstract
Kinematic analysis is a significant method when planning the trajectory of robotic manipulators. The main idea behind kinematic analysis is to study the motion of the robot based on the geometrical relationship of the robotic links and their joints, such as the Denavit-Hartenberg parameters. Given the continuous nature of kinematic analysis and the shortcoming of the traditional verification methods, we propose to use high-order-logic theorem proving for conducting formal kinematic analysis. Based on the screw theory in HOL4, which is newly developed by our research institute, we utilize the geometrical theory of HOL4 to develop formal reasoning support for the kinematic analysis of a robotic manipulator. To illustrate the usefulness of our fundamental formalization, we present the formal kinematic analysis of a general 6R manipulator.
Highlights
Kinematic analysis [1] is the study of motion of a machine or mechanism without considering the forces that cause the motion
Given the continuous nature of kinematic analysis and the shortcoming of the traditional verification methods, we propose to use high-order-logic theorem proving for conducting formal kinematic analysis
This paper proposes a high-order-logic theorem proving method for kinematic analysis, which is an essential design step for all robotic manipulators
Summary
Kinematic analysis [1] is the study of motion of a machine or mechanism without considering the forces that cause the motion. Theorem proving, based on higher-order-logic, can provide the ability to formally reason on the correctness of kinematic analysis and guarantee the high reliable kinematic performances of robots. Farooq et al applied high-order-logic theorem proving in kinematic analysis of a biped robot and verified the continuous mechanical system in HOL-light without using any abstractions and maintaining a higher accuracy [5]. Enlightened by these works, we plan to apply high-orderlogic theorem proving for kinematic analysis based on screw theory [11], which is a more general way to analyze the three dimensional robotic kinematics and easier to implement compared with Farooq et al.’s method.
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