Formal Kinematic Analysis of a General 6R Manipulator Using the Screw Theory

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

Formal Analysis of the Kinematic Jacobian in Screw Theory

As robotic systems flourish, reliability has become a topic of paramount importance in the human–robot relationship. The Jacobian matrix in screw theory underpins the design and optimization of robotic manipulators. Kernel properties of robotic manipulators, including dexterity and singularity, are characterized with the Jacobian matrix. The accurate specification and the rigorous analysis of the Jacobian matrix are indispensable in guaranteeing correct evaluation of the kinematics performance of manipulators. In this paper, a formal method for analyzing the Jacobian matrix in screw theory is presented using the higher-order logic theorem prover HOL4. Formalizations of twists and the forward kinematics are performed using the product of exponentials formula and the theory of functional matrices. To the best of our knowledge, this work is the first to formally analyze the kinematic Jacobian using theorem proving. The formal modeling and analysis of the Stanford manipulator demonstrate the effectiveness and applicability of the proposed approach to the formal verification of the kinematic properties of robotic manipulators

Formalization and Analysis of Jacobian Matrix in Screw Theory and its Application in Kinematic Singularity

Accurate specification and rigorous analysis of Jacobian matrix are indispensable to guarantee correct evaluation on the manipulator kinematics performance. In this paper, a formal analysis method of the Jacobian matrix in the screw theory is presented by using the higher-order logic theorem prover HOL4. Formalizations of twists and the forward kinematics are characterized with the product of exponential formula and the theory of functional matrices. To the best of our knowledge, this work is the first to formally reason about the spatial Jacobian using theorem proving. The formal modeling and analysis of a 3-DOF planar manipulator substantiate the effectiveness and applicability of the proposed approach to formally verify the kinematics properties of manipulator

Changes in Soil Nutrients of Farmland with Different Cultivation Years of Panax ginseng

Through analyzing the soil organic matters (N, P, K) of farmland cultivated with different years of Panax ginseng, this paper studied the changes in soil nutrients of farmland with different vertical depths and cultivation years of P. ginseng. Results indicated that the vertical structure was obvious in soil nutrients of farmland with different cultivation years of P. ginseng; in most cases, the soil nutrient content gradually declined with the fibrous roots of P. ginseng spreading downward; the soil electrical conductivity (EC), total nitrogen (TN), total phosphorus (TP), total potassium (TK), available nitrogen, available phosphorus were manifested as surface layer > root layer > bottom layer, while the available potassium was manifested as surface soil and bottom layer > root layer; the soil pH changed in the range of 5.69-6.22, suitable for growth of P. ginseng. It is expected to provide theoretical basis for improvement of soil nutrients of farmland with cultivation of P. ginseng