Numeric-Symbolic Approach for Dynamic Modelling of Robotic Manipulators

1992 ◽  
Author(s):  
Shou-wen Fan ◽  
Liju Xu ◽  
Yong Chen
Keyword(s):  
Reaction Force ◽  
Dynamic Modelling ◽  
Robotic Manipulators ◽  
Symbolic Form ◽  
Symbolic Method ◽  
Model Matrix ◽  
Robotic Dynamics ◽  
Symbolic Approach ◽  
Driving Torque ◽  
Generate Model

Abstract A simple numeric-symbolic method for dynamic modelling of robotic manipulators is proposed in this paper. Problem of deriving model matrix elements is transformed into problem of solving for driving force and driving torque under specified condition by recursive dynamic equations. Expressions of reaction force in arbitrary joint in numeric-symbolic form are also derived. Corresponding software which can recognize and manipulate symbols is developed and can be used to generate model and real-time code of robotic dynamics.

scholarly journals A Symbolic Approach to Explaining Bayesian Network Classifiers

2018 ◽  
Author(s):  
Andy Shih ◽  
Arthur Choi ◽  
Adnan Darwiche
Keyword(s):  
Bayesian Network ◽  
Case Studies ◽  
Decision Diagrams ◽  
Minimal Set ◽  
Symbolic Form ◽  
Bayesian Network Classifiers ◽  
Current State ◽  
Current Classification ◽  
Decision Functions ◽  
Symbolic Approach

We propose an approach for explaining Bayesian network classifiers, which is based on compiling such classifiers into decision functions that have a tractable and symbolic form. We introduce two types of explanations for why a classifier may have classified an instance positively or negatively and suggest algorithms for computing these explanations. The first type of explanation identifies a minimal set of the currently active features that is responsible for the current classification, while the second type of explanation identifies a minimal set of features whose current state (active or not) is sufficient for the classification. We consider in particular the compilation of Naive and Latent-Tree Bayesian network classifiers into Ordered Decision Diagrams (ODDs), providing a context for evaluating our proposal using case studies and experiments based on classifiers from the literature.

Symbolically Automated Direct Kinematic Equations Solver for Robotic Manipulators

Robotica ◽  
1989 ◽  
Vol 7 (3) ◽  
pp. 243-254 ◽  
Author(s):  
C.Y. Ho ◽  
Jen Sriwattanathamma
Keyword(s):  
Jacobian Matrix ◽  
Robotic Manipulators ◽  
Industrial Robots ◽  
Heuristic Rules ◽  
Symbolic Form ◽  
Rule Based ◽  
Transformation Matrices ◽  
Trigonometric Identity ◽  
System A ◽  
Forward Kinematic

SUMMARYSolving the direct kinematic problem in a symbolic form requires a laborious process of successive multiplications of the link homogeneous transformation matrices and involves a series of algebraic and trigonometric simplifications. The manual production of such solutions is tedious and error-prone. Due to the efficiency of the Prolog language in symbolic processing, a rule–based Prolog program is developed to automate the creation of the following processes: Link transformation matrices; forward kinematic solutions; and the Jacobian matrix. This paper presents the backward recursive formulation techniques, the trigonometric identity rules, and some heuristic rules for implementing the System. A verification of the System has been demonstrated in case of several industrial robots.

Automated Symbolic Derivation of Dynamic Equations of Motion for Robotic Manipulators

1986 ◽  
Vol 108 (3) ◽  
pp. 172-179 ◽  
Author(s):  
M. C. Leu ◽  
N. Hemati
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Robotic Manipulators ◽  
Dynamic Equations ◽  
Computer Memory ◽  
Symbolic Language ◽  
Symbolic Form ◽  
General Computer Program ◽  
Lagrange Formalism ◽  
General Computer

A general computer program for deriving the dynamic equations of motion for robotic manipulators using the symbolic language MACSYMA has been developed. The program, developed based on the Lagrange formalism, is applicable to manipulators of any number of degrees of freedom. Examples are given to illustrate how to use this program for dynamic equation generation. Advantages of expanding the dynamic equations into symbolic form are presented. Techniques for improving efficiency of equation generation, overcoming computer memory limitation, and approximating manipulator dynamics are discussed.

scholarly journals Symbolic Approach for Side-Channel Resistance Analysis of Masked Assembly Codes

10.29007/hhnf ◽  
2018 ◽  
Author(s):  
Inès Ben El Ouahma ◽  
Quentin Meunier ◽  
Karine Heydemann ◽  
Emmanuelle Encrenaz
Keyword(s):  
Source Code ◽  
Side Channel ◽  
Inference Rules ◽  
Side Channel Attacks ◽  
Secret Data ◽  
Source Codes ◽  
Resistance Analysis ◽  
Channel Resistance ◽  
Symbolic Method ◽  
Symbolic Approach

Masking is a popular countermeasure against side-channel attacks, that randomizes secret data with random and uniform variables called masks. At software level, masking is usually added in the source code and its effectiveness needs to be verified. In this paper, we propose a symbolic method to verify side-channel robustness of masked programs. The analysis is performed at the assembly level since compilation and optimizations may alter the added protections. Our proposed method aims to verify that intermediate computations are statistically independent from secret variables using defined distribution inference rules. We verify the first round of a masked AES in 22s and show that some secure algorithms or source codes are not leakage-free in their assembly implementations.

Dynamic modelling and parameter identification of a 3-DOF flight simulator platform

2019 ◽  
Vol 233 (4) ◽  
pp. 968-978
Author(s):  
Zhenyu Hong ◽  
Xuan Gao ◽  
Jiaren Liu ◽  
Dongsheng Zhang ◽  
Zhixu Zhang
Keyword(s):  
Driving Forces ◽  
Dynamic Modelling ◽  
Least Square Method ◽  
Friction Torque ◽  
Flight Simulation ◽  
Least Square ◽  
Flight Simulator ◽  
Dynamic Parameters ◽  
Three Degree Of Freedom ◽  
Driving Torque

A three-degree-of-freedom flight simulator platform with a translational and two rotational movement capabilities is studied. Based on the Lagrange method the dynamic model is established and then simplified by eliminating the sub-diagonal elements of the matrixes. A washout algorithm is employed to qualify the platform for flight simulation in limited space. In order to improve the modeling and experimental accuracies further when some dynamic parameters of an actual platform are unknown, the stepwise identification method is proposed to solve this problem. By dividing the driving torque into the load torque, reducer driving torque, screw driving toque and integrated friction torque, and main dynamic parameters are identified by applying proper trajectories and estimated by the weighed least square method. The procedures of identification are verified through comparing the driving forces from the identified model and those of servo motor encoders.

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