Real-Time Forward Kinematics of the General 6-6 Stewart Platform Using One Extra Sensor

2000 ◽  
Author(s):  
Tae-Young Lee ◽  
Jae-Kyung Shim
Keyword(s):  
Real Time ◽  
Stewart Platform ◽  
Forward Kinematics ◽  
Double Precision ◽  
Leg Length ◽  
Precision Data ◽  
Constrained System ◽  
C Language ◽  
Estimates Of Solutions ◽  
Actual Configuration

Abstract The forward kinematics of the Stewart platform is to find the postures of the moving platform for a given set of leg lengths. In case of the general Stewart platform, the number of solutions of the problem is up to forty in the complex domain. Theoretically, it is not possible to uniquely determine the actual configuration with six leg length measurements only. An approach to get a single actual configuration is to make over-constrained system by adding extra sensors. This paper presents an algebraic elimination-based method for the real-time forward kinematics of the general Stewart platform with one extra sensor. The proposed algorithm does not require initial estimates of solutions unlike the numerical iterative methods, and can be implemented in C language using conventional double precision data with 15 significant digits. A numerical example is given to confirm the effectiveness and correctness of the developed algorithm for real-time computation.

scholarly journals Testing of a MEMS Dynamic Inclinometer Using the Stewart Platform

Sensors ◽  
2019 ◽  
Vol 19 (19) ◽  
pp. 4233 ◽  
Author(s):  
Zhihua Liu ◽  
Chenguang Cai ◽  
Ming Yang ◽  
Ying Zhang
Keyword(s):  
Mechanical System ◽  
Real Time ◽  
Degrees Of Freedom ◽  
Cross Coupling ◽  
Micro Electro Mechanical System ◽  
Stewart Platform ◽  
Forward Kinematics ◽  
Six Degrees Of Freedom ◽  
Position And Orientation ◽  
The Cross

The micro-electro-mechanical system (MEMS) dynamic inclinometer integrates a tri-axis gyroscope and a tri-axis accelerometer for real-time tilt measurement. The Stewart platform has the ability to generate six degrees of freedom of spatial orbits. The method of applying spatial orbits to the testing of MEMS inclinometers is investigated. Inverse and forward kinematics are analyzed for controlling and measuring the position and orientation of the Stewart platform. The Stewart platform is controlled to generate a conical motion, based on which the sensitivities of the gyroscope, accelerometer, and tilt sensing are determined. Spatial positional orbits are also generated in order to obtain the tilt angles caused by the cross-coupling influence. The experiment is conducted to show that the tested amplitude frequency deviations of the gyroscope and tilt sensing sensitivities between the Stewart platform and the traditional rotator are less than 0.2 dB and 0.1 dB, respectively.

New Resolution Scheme of the Forward Kinematics of Parallel Manipulators Using Extra Sensors

1996 ◽  
Vol 118 (2) ◽  
pp. 214-219 ◽  
Author(s):  
Kilryong Han ◽  
Wankyun Chung ◽  
Y. Youm
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Parallel Manipulators ◽  
Stewart Platform ◽  
Forward Kinematics ◽  
Numerical Examples ◽  
Resolution Scheme ◽  
Real Time Applications ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

This paper presents a new closed-form resolution scheme of the forward kinematics of parallel manipulators based on two concepts, local structurization and mechanism partition. This scheme is applied to 6-DOF Stewart platform manipulators and the effectiveness of this scheme is verified through numerical examples. It is shown that one extra sensor is sufficient for both 3-3 SPM and 6-3 SPM to exactly resolve the forward kinematic problem (FKP) in closed form and two sensors for 6-6 SPM. In previous research, at least three extra sensors were needed for closed-form resolution of the FKP for 6-6 SPM. Consequently, the new resolution scheme is efficient to implement and easy for real-time applications for the control of parallel manipulators.

Determination of the Actual Configuration of the General Stewart Platform Using Only One Additional Sensor

1999 ◽  
Vol 121 (1) ◽  
pp. 21-25 ◽  
Author(s):  
V. Parenti-Castelli ◽  
R. Di Gregorio
Keyword(s):  
Stewart Platform ◽  
Rigid Bodies ◽  
Displacement Sensor ◽  
Leg Length ◽  
Displacement Sensors ◽  
On Line ◽  
Actual Configuration ◽  
General Geometry

This paper presents a procedure for the determination of the actual configuration of the general geometry Stewart platform (GSP), a fully-parallel manipulator that features two rigid bodies connected to each other via spherical pairs by six controlled-length legs. The six leg length measurements, provided by the displacement sensors incorporated in the leg hardware equipment, do not make it possible to uniquely find the GSP configuration because several configurations are possible for a given set of leg lengths. Several extra sensors in addition to those incorporated in the leg equipment have been proposed in the literature in order to obtain a one-to-one correspondence between the measurements and the actual GSP configuration. The proposed procedure makes use of only one additional displacement sensor and relies upon the analytical results available in the literature for a particular type of Stewart platform. The procedure, which uniquely defines the actual configuration of the GSP, is not intended for on-line implementation. Three different algorithms are proposed for computation and their efficiency compared. A case study is reported that confirms the effectiveness of the procedure.

scholarly journals A Set of Integral Grid-Coding Algebraic Operations Based on GeoSOT-3D

2021 ◽  
Vol 10 (7) ◽  
pp. 489
Author(s):  
Kaihua Hou ◽  
Chengqi Cheng ◽  
Bo Chen ◽  
Chi Zhang ◽  
Liesong He ◽  
...  
Keyword(s):  
Real Time ◽  
Spatial Information ◽  
Data Retrieval ◽  
Geospatial Data ◽  
Algebraic Operation ◽  
Real Time Processing ◽  
C Language ◽  
Time Processing ◽  
Binary Operations ◽  
Set Operations

As the amount of collected spatial information (2D/3D) increases, the real-time processing of these massive data is among the urgent issues that need to be dealt with. Discretizing the physical earth into a digital gridded earth and assigning an integral computable code to each grid has become an effective way to accelerate real-time processing. Researchers have proposed optimization algorithms for spatial calculations in specific scenarios. However, a complete set of algorithms for real-time processing using grid coding is still lacking. To address this issue, a carefully designed, integral grid-coding algebraic operation framework for GeoSOT-3D (a multilayer latitude and longitude grid model) is proposed. By converting traditional floating-point calculations based on latitude and longitude into binary operations, the complexity of the algorithm is greatly reduced. We then present the detailed algorithms that were designed, including basic operations, vector operations, code conversion operations, spatial operations, metric operations, topological relation operations, and set operations. To verify the feasibility and efficiency of the above algorithms, we developed an experimental platform using C++ language (including major algorithms, and more algorithms may be expanded in the future). Then, we generated random data and conducted experiments. The experimental results show that the computing framework is feasible and can significantly improve the efficiency of spatial processing. The algebraic operation framework is expected to support large geospatial data retrieval and analysis, and experience a revival, on top of parallel and distributed computing, in an era of large geospatial data.

Evaluation and Representation of the Theoretical Orientation Workspace of the Gough–Stewart Platform

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Qimi Jiang ◽  
Clément M. Gosselin
Keyword(s):  
Theoretical Orientation ◽  
Robotic Manipulators ◽  
Stewart Platform ◽  
Closed Region ◽  
Leg Length ◽  
Fixed Frame ◽  
Cartesian Space ◽  
Orientation Workspace

The evaluation and representation of the orientation workspace of robotic manipulators is a challenging task. This work focuses on the determination of the theoretical orientation workspace of the Gough–Stewart platform with given leg length ranges [ρimin,ρimax]. By use of the roll-pitch-yaw angles (ϕ,θ,ψ), the theoretical orientation workspace at a prescribed position P0 can be defined by up to 12 workspace surfaces. The defined orientation workspace is a closed region in the 3D orientation Cartesian space Oϕθψ. As all rotations R(x,ϕ), R(y,θ), and R(z,ψ) take place with respect to the fixed frame, any point of the defined orientation workspace provides a clear measure for the platform to, respectively, rotate in order around the (x,y,z) axes of the fixed frame. An algorithm is presented to compute the size (volume) of the theoretical orientation workspace and intersectional curves of the workspace surfaces. The defined theoretical orientation workspace can be applied to determine a singularity-free orientation workspace.

Research on the Forward Kinematics of Stewart Platform Using Memetic Algorithms

2012 ◽  
Vol 268-270 ◽  
pp. 1416-1421
Author(s):  
Yu Hui Zhang ◽  
Li Wen Guan ◽  
Li Ping Wang ◽  
Yong Zhi Hua
Keyword(s):  
Nonlinear Equations ◽  
Rapid Development ◽  
Memetic Algorithms ◽  
Stewart Platform ◽  
Global Optimum ◽  
General Purpose ◽  
Forward Kinematics ◽  
Systems Of Nonlinear Equations ◽  
Artificial Intelligence Technology ◽  
Difficult Issue

The forward kinematics analysis of parallel manipulator is a difficult issue, which has been studied by many researchers recently. In this paper, in order to solve the difficult issue, a new computing method with higher calculation accuracy, good operation steadiness and faster speed is mentioned. Firstly, the mathematical model of direct kinematics of the Stewart platform is founded, which is nonlinear equations. Secondly, with the rapid development of artificial intelligence technology, Memetic algorithms (MA) are applied to solve the systems of nonlinear equations more and more, replacing the traditional algorithms. MA is a kind of meta-heuristic algorithm combined genetic algorithms (GA) with local search at the end of iteration. Finally, the validity of this algorithm has been testified by simulating iteration operation. The numerical simulation shows that MA can surely and rapidly get global optimum solution and greatly improve convergence rate. Thereby, MA can be widely used as a general-purpose algorithm for solving the forward kinematics of parallel mechanism.

Generating real-time trajectories for a planar biped robot crossing a wide ditch with landing uncertainties

Robotica ◽  
2018 ◽  
Vol 37 (1) ◽  
pp. 109-140 ◽  
Author(s):  
V. Janardhan ◽  
R. Prasanth Kumar
Keyword(s):  
Real Time ◽  
Degrees Of Freedom ◽  
Dynamic Balance ◽  
Surface Friction ◽  
Biped Robot ◽  
Net Energy ◽  
Leg Length ◽  
Uncertain Environments ◽  
Novel Concept ◽  
Time Planning

SUMMARYDitch crossing is one of the essential capabilities required for a biped robot in disaster management and search and rescue operations. Present work focuses on crossing a wide ditch with landing uncertainties by an under-actuated planar biped robot with five degrees of freedom. We consider a ditch as wide for a robot when the ankle to ankle stretch required to cross it is at least equal to the leg length of the robot. Since locomotion in uncertain environments requires real-time planning, in this paper, we present a new approach for generating real-time joint trajectories using control constraints not explicitly dependent on time, considering impact, dynamic balance, and friction. As part of the approach, we introduce a novel concept called the point of feasibility for bringing the biped robot to complete rest at the end of ditch crossing. We present a study on the influence of initial posture on landing impact and net energy consumption. Through simulations, we found the best initial postures to efficiently cross a wide ditch of width 1.05 m, with less impact and without singularities. Finally, we demonstrate the advantage of the proposed approach to cross a wide ditch when the surface friction is not same on both sides of the ditch.

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