6-DOF Stewart Platform Research Articles

Unified dynamics analysis of parallel manipulators: A joint-based approach and generalized inertia constraint matrix for parallel manipulators (GICM-P) framework

Parallel manipulators, a distinctive subset of closed-loop multi-body systems, are in high demand due to their precision-centric applications. This research introduces a unified approach to tackle both inverse and forward dynamic analyses of parallel manipulators, rooted in joint-based principles. The methodology dissects a given parallel manipulator into symmetric open-loop subsystems and a mobile body within either a planar or spatial context, depending on the manipulator’s nature. Conventional practices, involving the introduction of joint cuts at relevant locations, are employed to partition the system into multiple open-loop subsystems. Subsequently, the joint coordinate-based approach, typically applied to open-loop systems such as industrial manipulators, is utilized to derive solutions. In particular, this approach focuses on forward dynamics by introducing the generalized inertia constraint matrix for parallel manipulators (GICM-P), a concept built upon the authors’ prior work, originally addressing the GICM for general closed-loop systems. Notably, GICM-P aligns conceptually with the operational space inertia matrix (OSIM) designed for closed-loop systems elsewhere. However, unlike OSIM, which requires mapping joint-space inertia to operational-space inertia, GICM-P leverages acceleration-level constraints between subsystems and the moving platform through straightforward matrix operations. GICM-P offers a deeper understanding of the physics of the problem compared to OSIM, primarily due to its ability to explicitly express subsystem-level interactions via various block matrices – an aspect not previously documented. The paper provides explicit numerical values for GICM-P in the context of a spatial six degrees of freedom (6-DOF) Stewart platform and a planar 3-DOF parallel manipulator along with interpretations.

Five-axis parallel mechanism system (PMS) CNC partial link control system based on modified inverse kinematic of 6-DOF UPS parallel manipulator

This paper presents a control system algorithm for a five-axis parallel mechanism system (PMS) CNC milling machine based on a 6-DOF Stewart platform parallel manipulator with a universal-prismatic-spherical (UPS) configuration. The control system reads the G-Code commands as standard CNC machine language, then extract data points and interpolates them to generate the robot trajectory patterns as motion references. Then, the control system uses the modified inverse kinematic equation to determine the length of each link to move the end effector to track the trajectory patterns from the previous G-code extraction process. The inverse kinematic equation is modified especially for the five-axis PMS CNC milling machine by including machine-offset and tools-offset parameters so it will be easier for the control system to implement the kinematic equation. As expected, the system simulation results successfully followed the G-Code program moving commands. The average error of the length control system is 0,1 mm, while the average error of the length change rate control system is 1,8 mm/s. The maximum error is 26.9 mm was caused by the system's inability to follow the motion profile in transient. It can be concluded that 6-DOF Stewart platform parallel structures,which provide better performance than serial structures, can be implemented as a new concept for the motion mechanism of five-axis CNC milling machines. The five-axis PMS CNC milling machine also promises better performance than conventional five-axis gantry structures CNC.

A Control Algorithm of Active Wave Compensation System Based on the Stewart Platform

Aim at the actual engineering requirements of wind power operation and maintenance under complex sea conditions, a control method of the active wave compensation system for maintenance ships based on the Stewart platform is presented. The kinematics of the platform is analyzed, and the coordinate transformation, pose, and inverse solutions are analyzed and calculated. The multi-body dynamics simulation model is established by using MATLAB. For the problem of the load nonlinearity and strong coupling of the nonlinear Stewart platform, an active wave compensation active disturbance rejection control (ADRC) is built to attain the high-precision control of the six-degree-of-freedom (6-DOF) Stewart platform. The numerical simulation shows that the proposed control scheme has good tracking accuracy and strong anti-interference ability.

Method of high precision pointing control for spacecraft system based on the active-passive integrated orthogonal micro-vibration isolation platform

To acquire the high precision pointing control for spacecraft system under the disturbance of micro-vibration, and resolve conflicts between the vibration suppression and pointing control, a simultaneous-distributed control method was proposed in this paper. Based on this method and the Stewart platform, an active-passive integrated orthogonal micro-vibration isolation platform with multiple dimensions was developed. Six line-actuators according to the configuration of Gough-Stewart parallel mechanism were selected to build the platform. Specially, the displacement of the line-actuator was converted from the end deflection of two groups of active and passive integrated cantilever beams, which contained viscoelastic damping plate, aluminum material and macro fiber composite (MFC). It should be noted that the dynamic model of the platform system was strongly coupled and it was decoupled by employing the orthogonal configuration. By employing the simultaneous-distributed control strategy, the integrated control algorithm of vibration isolation and pointing was deeply studied. Furthermore, the dynamic behavior and control effects for the 6 degree of freedom (6-DOF) Stewart platform with different control strategies were compared and analyzed. Results showed the method had a good vibration isolation effect and reliable pointing accuracy, which could be applied for the spacecraft requiring high precision pointing.

Adaptive time-delay estimation and control of optimized Stewart robot

Aiming at a more efficient and accurate performance of parallel manipulators in the existence of complex kinematics and dynamics, a robust generalizable methodology is proposed here for an integrated 6-DOF Stewart platform with rotary time-delayed actuators torque control. The suggested method employs a time-delay linear–quadratic integral regulator with online artificial neural network gain adjustment. The unknown time-delay is estimated through a novel robust adaptive estimator. The global asymptotic stability of the estimator is proved via a Lyapunov function. The controller is developed in MATLAB software and implemented on the robot designed in ADAMS software to ensure that the real-time tracking error of a nonlinear system with an unknown time-delay is kept to a minimum. The sensitivity of the controller to the parameter choices is studied via implementing the controller in ADAMS software and is validated by investigating the performance on a naturalistic fabricated robot. The approach is assessed using simulation and experimental tests to show the feasibility, optimum, and zero-error convergence of the technique developed.

Quantitative analysis of decoupling and spatial isotropy of a generalised rotation-symmetric 6-DOF Stewart platform

The Stewart platform is one of the most frequently studied six-degree-of-freedom (6-DOF) parallel robots. Although it has an uncomplicated architecture, it still poses some remaining research challenges, especially regarding Cartesian stiffness, decoupling, and isotropy. Although it is well established that spatial isotropy is only dependent on the direction vectors of the six links, the diagonal values in the stiffness matrix, and in particular the relationship between the first three elements and the last three elements, are affected by other factors. The methodology proposed in this paper aims at designing decoupled and spatially isotropic Stewart platforms with user-selected values of these diagonal elements. A parametric model of a generalised rotation-symmetric Stewart platform is established and the expression of the corresponding Cartesian stiffness matrix is derived. The approach in this paper is first to find the different cases when the expressions of off-diagonal elements of the Cartesian stiffness matrix are zero and then, within each case, quantitatively derive conditions for decoupling and spatial isotropy. By applying this approach, several novel decoupled and spatially isotropic architectures with three horizontal links were derived.

Kinematics and Dynamics Simulation of a Stewart Platform

Position and orientation adjustment of the secondary mirror is one of the effective ways to improve the image quality of space camera. In order to optimize the structural design of a 6-DOF Stewart platform for secondary mirror, simulation method of kinematics and dynamics of parallel manipulator based on virtual prototyping technology was studied. Firstly, the ADAMS parametric model and inverse mathematical model are built. Secondly, theory analysis of inverse kinematics of Stewart platform was performed, and the analytical results of inverse kinematics were obtained by mathematical modeling. Thirdly, simulation of inverse kinematics run in ADAMS after the virtual prototype of parallel manipulator was established. The simulation results in ADAMS and analysis results are consistent, which proved the correctness of the virtual prototype model. Lastly, the kinematics and inverse dynamics simulation were realized by driving each strut using result of inverse kinematics. The analysis method of kinematics and dynamics of parallel manipulator provided a theoretical basis for optimizing design of a Stewart platform.

Application of Stewart Platform in the Low-Frequency Vibration Characteristic Test of Space Truss Deployable Antenna on Satellite

The space truss deployable antenna has low natural frequency, multi-closed-loop, and multiredundant structure characteristics, which is a kind of flexible antenna. It is hard to obtain the vibration characteristics under low frequency by finite element analysis or conventional shaking table test. To verify the structure characteristics of the antenna in the folded state below 2 Hz, a low-frequency vibration system is established based on the 6-DOF Stewart platform. Rotation matrix analysis method was adopted to obtain the platform’s velocity and acceleration characteristics. Then, a low-frequency vibration test was carried out on the platform. The results show that the natural frequency of the antenna is 1.51 Hz and the maximum dynamic displacement is 140.6 mm, which provides a certain foundation for the further development of the space truss antenna.

A six degree-of-freedom set-up for wind tunnel testing of floating wind turbines

In this paper we present a six-degree-of-freedom (DoF) experimental set-up for wind tunnel testing of floating offshore wind turbines (FOWTs). The system is composed of a 6-DoF Stewart platform that can be used to mimic realistically the motions of a floating turbine at laboratory scale. The platform is specifically made for the Model Wind Turbine Oldenburg 0.6 (MoWiTO 0.6). First, the methodology followed to design the system as well as the scaling issues are depicted. Then, the characterisation of the platform is presented. Finally, limitations of the set-up are discussed.

Ground Robotic Platform for Simulation of On-Orbit Servicing Missions

Autonomous on-orbit servicing missions require high precision because any unwanted contact forces can cause damage to space systems. This makes the on-ground hardware-in-the-loop simulations necessary as operations must be thoroughly evaluated before such missions are carried out in space. A robotic platform is proposed, where a 3-degree-of-freedom (3-DOF) robotic arm is placed atop a 6-DOF Stewart platform. A mathematical model is developed for the resulting 9-DOF redundant manipulator, and the corresponding dynamics are modeled and verified. Simulation studies are conducted using a constrained and singularity-robust pseudo-inverse control scheme, and the system’s capability to follow a scaled-down orbital trajectory is tested. The results are presented, and the future implications of this study are discussed.

Assessment of Whole-body Vibration via Integrating a Stewart Platform and SimWise Simulation

In this study, multi-body simulations have been performed to identify the safety limits for human whole-body dynamic responses under vibration along the caudal-cranial axis while the subject is seated. Computer simulated data can be used to evaluate the level of acceleration capable of inducing dynamic forces that could cause injury to specific joints. In this study, the force at the seat pan and operator interface, the acceleration of the pelvis and head, as well as the force on the neck and lumbar will be tested. These force levels can be found in the ergonomics literature based on evaluation of workers intended to reduce their injury rate during daily operations. These safety limits can be used to ascertain the acceleration of piloting maneuvers in a physical vehicle simulator obtained by retrofitting a 6 DOF Stewart platform.

Discrete-time Adaptive Control of Pneumatic Actuators for 6-DoF Stewart Platform

This paper deals with computer-controlled pneumatic actuators for the Gough-Stewart platform with 6 degrees of freedom. An important feature considered in the paper pneumatic actuator is the use of a group of valves rather than a spool valve to control the pressure in the chambers, which leads to a significant quantization in terms of the level of the control action. In addition, there is a sampling in time in the control loop. The present work is aimed at ensuring the robustness of the pneumatic actuators for the Stewart platforms concerning their parameters and the effect of changing the load on the drive caused by the interdependence of the drives due to the movement of the platform. Two discrete-time (parametric, and signal-parametric) adaptive control algorithms, based on the concept of an implicit reference model with anti-windup correction are proposed. The simulation results are presented, demonstrating the efficiency of the signal-parametric algorithm.

Real-time trajectory tracking control of Stewart platform using fractional order fuzzy PID controller optimized by particle swarm algorithm

PurposeThe purpose of this paper is to address a fractional order fuzzy PID (FOFPID) control approach for solving the problem of enhancing high precision tracking performance and robustness against to different reference trajectories of a 6-DOF Stewart Platform (SP) in joint space.Design/methodology/approachFor the optimal design of the proposed control approach, tuning of the controller parameters including membership functions and input-output scaling factors along with the fractional order rate of error and fractional order integral of control signal is tuned with off-line by using particle swarm optimization (PSO) algorithm. For achieving this off-line optimization in the simulation environment, very accurate dynamic model of SP which has more complicated dynamical characteristics is required. Therefore, the coupling dynamic model of multi-rigid-body system is developed by Lagrange-Euler approach. For completeness, the mathematical model of the actuators is established and integrated with the dynamic model of SP mechanical system to state electromechanical coupling dynamic model. To study the validness of the proposed FOFPID controller, using this accurate dynamic model of the SP, other published control approaches such as the PID control, FOPID control and fuzzy PID control are also optimized with PSO in simulation environment. To compare trajectory tracking performance and effectiveness of the tuned controllers, the real time validation trajectory tracking experiments are conducted using the experimental setup of the SP by applying the optimum parameters of the controllers. The credibility of the results obtained with the controllers tuned in simulation environment is examined using statistical analysis.FindingsThe experimental results clearly demonstrate that the proposed optimal FOFPID controller can improve the control performance and reduce reference trajectory tracking errors of the SP. Also, the proposed PSO optimized FOFPID control strategy outperforms other control schemes in terms of the different difficulty levels of the given trajectories.Originality/valueTo the best of the authors’ knowledge, such a motion controller incorporating the fractional order approach to the fuzzy is first time applied in trajectory tracking control of SP.

Workspace Identification of Stewart Platform

The workspace identification of 6-DOF Stewart Platform has been done in this paper through inverse kinematic modeling. This Stewart Platform has six linear cylinder–piston actuators connected within fixed and the moving platform. The motions of the moving platform such as surge, sway, heave, roll, pitch and yaw have been generated from the combined motions of piston of actuators. The mathematical formulations for Inverse-Kinematic modeling of Stewart Platform have been formulated to find out the individual piston motion for the required platform motion. The platform motions and the actuator motions have been studied for the workspace identification of the Stewart Platform.

Modeling and control of magnetorheological 6-DOF stewart platform based on multibody systems transfer matrix method

A 6-DOF vibration isolation system with magneto-rheological damper (MRD) based on Stewart mechanism was designed to reduce the mechanical vibration more effectively. To make the isolation system perform well, an effective control method was also proposed. Using the linear multibody systems transfer matrix method (MSTMM), the dynamic model of the MRD 6-DOF vibration isolation system was established to obtain the dynamic characteristics. Firstly, based on the test mechanical property of magnetorheological damper, the electromagnetic coupling model of magnetorheological damper was established. Secondly, the transfer equation of 6-DOF vibration isolation system was established by linear MSTMM. And the state space equation was derived using the modal superposition method, which was based on the augmented eigenvector and body dynamics equation. Thirdly, the linear quadratic Gaussian control method of MRD 6-DOF vibration isolation system was designed. Finally, the numerical simulation was carried out. The results showed that MRD 6-DOF vibration isolation system with optimal control improved the dynamic performance of mechanical equipment effectively. Compared with passive vibration isolation system, the translation of the vibration isolation system in the X, Y, and Z directions, as well as the rotation around the X axis, Y axis and Z axis were reduced by 51.85%, 58.71%, 64.43%, 75.43%, 66.45% and 52.87%, respectively. Similarly, the percentage drops were 50.00%, 56.16%, 34.94%, 53.09%, 38.14% and 46.76% compared to the PID control based vibration isolation system, respectively. The established dynamic model and control strategy provided theoretical basis for relevant vibration isolation tests.

DESIGN AND IMPLEMENTATION OF FEEDBACK CONTROL SYSTEM FOR 6-DOF STEWART PLATFORM.

02Oct 2019 DESIGN AND IMPLEMENTATION OF FEEDBACK CONTROL SYSTEM FOR 6-DOF STEWART PLATFORM. Gopiya Naik S , Manojgowda S.P and Kishor G. Associate Professor, Students, Department of Electrical & Electronics Engineering, PES College of Engineering, Mandya, Karnataka (India).

Inverse kinematics analysis of 6 – DOF Stewart platform based on homogeneous coordinate transformation

ABSTRACTAt present, the mainstream method is directly reduced the platform of the six series branch to six drive rods for analysis and modeling refers to inverse kinematic of the parallel six-degree-of-freedom (6-DOF) Stewart platform, and ignored the influence of the joints that excluded the driving leg on the Stewart platform, resulted in the mathematical model lack of accuracy, there is error in the actual platform. In this paper, the mathematical analysis method of inverse kinematic of the parallel six-degree-of-freedom Stewart platform based on homogeneous coordinate transformation is studied. The relationship of spatial coordinate system is worked up by using the Denavit-Hartenberg (DH) method on the upper and lower platforms and each branch of parallel 6-DOF Stewart platform. Considering the influence among the series branch joints, the transfer relationship is established by using the three-dimensional vector and the homogeneous coordinate transformation matrix between the adjacent joint coordinate systems. The length of the branch drive lever is treated as a variable, the vector equation of the platform system is deduced based on the geometric relation of the parallel 6–DOF Stewart platform. The application of this method in the kinematic inverse solution of parallel 6–DOF Stewart platform is given, verified the correctness of this method. Thinks to the data validation of the actual Stewart platform, it is proved that the proposed method can be applied to the kinematic inverse of parallel 6–DOF Stewart platform that composed of series branch.

Self-tuning MIMO disturbance feedforward control for active hard-mounted vibration isolators

This paper proposes a multi-input multi-output (MIMO) disturbance feedforward controller to improve the rejection of floor vibrations in active vibration isolation systems for high-precision machinery. To minimize loss of performance due to model uncertainties, the feedforward controller is implemented as a self-tuning generalized FIR filter. This filter contains a priori knowledge of the poles, such that relatively few parameters have to be estimated which makes the algorithm computationally efficient. The zeros of the filter are estimated using the filtered-error least mean squares (FeLMS) algorithm. Residual noise shaping is used to reduce bias. Conditions on convergence speed, stability, bias, and the effects of sensor noise on the self-tuning algorithm are discussed in detail. The combined control strategy is validated on a 6-DOF Stewart platform, which serves as a multi-axis and hard-mounted vibration isolation system, and shows significant improvement in the rejection of floor vibrations.

Verification of the Kinematic Analysis of the 6-DOF Stewart Platform Manipulator

A probabilistic seismic hazard assessment in terms of Arias intensity is presented for the city of Tehran. Tehran is the capital and the most populated city of Iran. From economical, political and social points of view, Tehran is the most significant city of Iran. Many destructive earthquakes happened in Iran in the last centuries. Historical references indicate that the old city of Rey and the present Tehran have been destroyed by catastrophic earthquakes at least 6 times. Existence of active faults like North of Tehran, Mosha and North and South of Rey is the main causes of seismicity of this city. Seismicity parameters on the basis of historical and instrumental earthquakes for a time period, from 4th century BC to the present time are calculated using Tavakoli’s approach and Kijko method. The earthquake catalogue with a radius of 200 km around Tehran has been used to calculate seismicity parameters. Iso-intensity contour lines maps of Tehran on the basis of different attenuation relationships are plotted. They display the probabilistic estimate of Arias intensity with Rock and Soil beds for the return periods of 72, 224, 475, 2475 years. SEISRISKIII software has been employed for seismic hazard assessment. Effects of different parameters such as seismicity parameters, length of fault rupture relationships, and attenuation relationships are considered using logic tree.

Dynamic Modeling of a Six Degree-of-Freedom Flight Simulator Motion Base

This paper presents a closed-form solution for the direct dynamic model of a flight simulator motion base. The motion base consists of a six degree-of-freedom (6DOF) Stewart platform robotic manipulator driven by electromechanical actuators. The dynamic model is derived using the Newton–Euler method. Our derivation is closed to that of Dasgupta and Mruthyunjaya (1998, “Closed Form Dynamic Equations of the General Stewart Platform Through the Newton–Euler Approach,” Mech. Mach. Theory, 33(7), pp. 993–1012), however, we give some insights into the structure and properties of those equations, i.e., a kinematic model of the universal joint, inclusion of electromechanical actuator dynamics and the full dynamic equations in matrix form in terms of Euler angles and platform position vector. These expressions are interesting for control, simulation, and design of flight simulators motion bases. Development of a inverse dynamic control law by using coefficients matrices of dynamic equation and real aircraft trajectories are implemented and simulation results are also presented.