Inverse Kinematics Analysis of General 6R Serial Robot Mechanism Based on Groebner Base

Hang, Lubin; Wang, Yan; Yang, Ting-Li

doi:10.1007/s11465-005-0022-7

Cited by 14 publications

(12 citation statements)

References 14 publications

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“…For the case of the PUMA robot, this step's output is the trigonometric equation system presented in Equation (20). In…”

Section: Third Step: Obtention Of the Polynomial Equation Systemmentioning

confidence: 99%

“…Nowadays, several projects are being developed in the field of Robotics that use Groebner Basis theory [18] to implement systematic methods that solve the Kinematic Problem, in a way that is independent of the geometry of the robot's structure. Among these projects, the works of Kendricks [19] and Wang et al [20] stand out, which solve the Inverse Kinematic Problem of robotic manipulators using Groebner Bases. Abbasnejad et al [21] use this theory for the kinematic analysis of cable-driven robots.…”

Section: Introductionmentioning

confidence: 99%

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Synthesis of the Inverse Kinematic Model of Non-Redundant Open-Chain Robotic Systems Using Groebner Basis Theory

et al. 2020

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One of the most important elements of a robot’s control system is its Inverse Kinematic Model (IKM), which calculates the position and velocity references required by the robot’s actuators to follow a trajectory. The methods that are commonly used to synthesize the IKM of open-chain robotic systems strongly depend on the geometry of the analyzed robot. Those methods are not systematic procedures that could be applied equally in all possible cases. This project presents the development of a systematic procedure to synthesize the IKM of non-redundant open-chain robotic systems using Groebner Basis theory, which does not depend on the geometry of the robot’s structure. The inputs to the developed procedure are the robot’s Denavit–Hartenberg parameters, while the output is the IKM, ready to be used in the robot’s control system or in a simulation of its behavior. The Groebner Basis calculation is done in a two-step process, first computing a basis with Faugère’s F4 algorithm and a grevlex monomial order, and later changing the basis with the FGLM algorithm to the desired lexicographic order. This procedure’s performance was proved calculating the IKM of a PUMA manipulator and a walking hexapod robot. The errors in the computed references of both IKMs were absolutely negligible in their corresponding workspaces, and their computation times were comparable to those required by the kinematic models calculated by traditional methods. The developed procedure can be applied to all Cartesian robotic systems, SCARA robots, all the non-redundant robotic manipulators that satisfy the in-line wrist condition, and any non-redundant open-chain robot whose IKM should only solve the positioning problem, such as multi-legged walking robots.

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“…For the case of the PUMA robot, this step's output is the trigonometric equation system presented in Equation (20). In…”

Section: Third Step: Obtention Of the Polynomial Equation Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Synthesis of the Inverse Kinematic Model of Non-Redundant Open-Chain Robotic Systems Using Groebner Basis Theory

et al. 2020

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“…This nonlinear algebraic equations system and its solvability investigation in general case exceeds framework of presented paper [11], [12], [13].…”

Section: Robot Kinematic Behaviour Descriptionmentioning

confidence: 99%

Measuring robot kinematics description and its workspace

Úředníček¹,

Drga²

2016

MATEC Web Conf.

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Abstract. Text deals with 6 degree of freedom measuring robot kinematics description enabling manipulation with measuring effector in 3D space. Mentioned description flowing from Denavit-Hartenberg notation for serial ordering of ideally stiff bodies connected by kinematic pairs, makes possible to create complete set of transformation matrices for coordinates transformation from distal to the adjoining proximal Cartesian coordinate system, which enables to calculate the coordinates of arbitrary structure point by means of joints' coordinates. Thenceforth it makes possible to determine standby and available robot workplace and mainly to perform the analysis of one fundamental control system problem of such robots-i. e. solving inverse kinematic problem.

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“…According to the decoupled judgment criteria of the PM proposed by author of paper [9], the 1T2R PM shown Fig. 3 is selected as the prototype to construct the multi-dimension vibrator because of its simplicity, and the structure synthesis and kinematics analysis are given in detail thereinafter, it consists of two basic kinematic chains (BKC).…”

Section: The Construction Of Decoupled Pmmentioning

confidence: 99%

Research on Single Drive and Multi-dimension Output Vibrator for Fuse Sand Filling Based on Decoupled 1T2R Parallel Mechanism

et al. 2016

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Abstract. In this paper a three-dimension vibrator for fuses' sand filling, including one-dimension vertically translation and two-dimension oscillating rotation (1T2R) is presented, which is used to improve the low efficiency in the process of traditional fuses' sand filling. The paper starts with a type synthesis of a new kind of 1T2R parallel mechanism (PM) which is constructed based on the POC set. After two of the driving joints in the PM are substituted by the spring-damp system, the design propose of single-input and multi-outputs can be realized. Then the kinematics analysis and simulation optimization of this mechanism was also carried out.

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Inverse Kinematics Analysis of General 6R Serial Robot Mechanism Based on Groebner Base

Cited by 14 publications

References 14 publications

Synthesis of the Inverse Kinematic Model of Non-Redundant Open-Chain Robotic Systems Using Groebner Basis Theory

Synthesis of the Inverse Kinematic Model of Non-Redundant Open-Chain Robotic Systems Using Groebner Basis Theory

Measuring robot kinematics description and its workspace

Research on Single Drive and Multi-dimension Output Vibrator for Fuse Sand Filling Based on Decoupled 1T2R Parallel Mechanism

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