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Application

6-DOF Position-Controlled HexapodPlatform in MKS Mechanics

Introduction

Parallel kinematics are a very active field of research and engineering. One of itsmost famous application examples is the so called hexapod, also known as theStuart platform. Such platforms allow the independent, fast, and accuratepositioning of the device mounted on the platform in all 6 mechanical degrees offreedom (DOF), i.e., in x, y, z and in rotations around the three coordinate axes.Typical applications are driving and flight simulators, highly precise positioningdevices for astronomical telescopes, or parallel-structured machine tools.Simulating the behavior of a hexapod requires multibody kinematics for themovement of the system, as well as the capability to implement thecorresponding control structures. For higher degrees of detail the behavior of theactuators should be modeled and simulated in the corresponding physicaldomain (e.g. hydraulics or translatory and rotary mechanics).In this application brief we show, that this modeling and simulation problem isstraightforwardly and easily solved in SimulationX. The modeling task took lessthan one day to complete, from which a great deal was spent in reviewingfundamentals of MBS mechanics and in system tuning.

System Structure and ModelA typical hexapod setup is shown inFigure 1 . 6 length-controlled actuators (dependingon the application these could be hydrauliccylinders or feed arbors) are driven according tolength presets calculated from the position presetsfor the platform. In the modeling example a force-actuated device (such as a hydraulic cylinder) is as-sumed, which requires a feedback control loop inorder to position the platform. Figure 1: HexapodMechanical Model

The mechanical part of the simulation model is assembled from the SimulationXMBS Mechanics library, using cylinder bodies (which are shaped as hydrauliccylinders), spheres, and a complexly shaped 3D model of a Cessna airplane, im-ported via the CAD import facility of SimulationX. For the airplane model thecenter of mass and the inertia tensor are calculated automatically.

Presets and Coordinate Transformations

In order to control the motion of the platform, position signals are prescribed for eachDOF. These of course have to be translated into length signals for the six actuators.The transformations are well describable in an algorithm using vector and matrixoperations. Since SimulationX provides the Modelica language and the possibilityto use vector signals without any modification to the signal processing blocks, these

tasks are solved very easily, leading to a comprehensive model design, as shown inFigure 1.

3D modelingincluding CADimport

User-definedfunctionality

exploiting theintegratedmodelinglanguage

Modelica

Support of vectorand matrix opera-tions in pro-gramming andsignal processing

Parallel signalprocessingstructures usingvector signals

Live 3D animationduring simulation

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ITI Headquarters Schweriner Strae 1 01067 Dresden Germany T +49 (0) 351 26050 0 F +49 (0) 351 260 50 155 sales@simulationx.comSimulationX For your local representative please visit www.simulationx.com/global

ITI and SimulationX are registered trademarks of ITI GmbH Dresden. ITI GmbH, Dresden, Germany, 2013. All rights reserved.

Figure 2: Hexapod Simulation Model. The text boxes show the coupling of the control structure to the physical

The 6 DOF Position ControllerFor controlling the lengths of the actuators by means of forces a PID controller is an appropriatechoice. As the other signal blocks the controller is capable to handle vector signals each of the inputvector components is then processed by a separate PID controller, having its own initial condition andindependent behavior, but using the same set of controller parameters. So, building just onecontroller model from the signal blocks achieves the independent control of all actuators.Exploiting the object-oriented modeling approach in SimulationXthe vector of the current lengths ofthe actuators is assembled in a signal block by referencing the corresponding result variables of theactuators. In exactly the same way the individual force signals are collected by the 1D force sourcesvia a reference to the appropriate component of the controllers output vector.

Simulation

During simulation the behavior of the model can be observed live in terms of result quantities aswell as in terms of the 3D visualization and animation. This gives the possibility to quickly interactwith the simulation for parameter changes and system tuning.The 3D display can be freely rotated, zoomed and switched between different modes such asperspective and isometric or solid and wire frame. Thus the positioning and movement of the 3Dobjects can be exactly observed and even can be modified by dragging the particular objects.

All potential and flow quantities in the mechanical parts of the model (i.e., displacements, velocities,accelerations, forces, and torques in all DOF) are available as result quantities, thus providing meansto analyze, e.g., peak loads or limit performances of the hexapod under different control strategies.

y = {Actuator1.l,...

Actuator6.l

F = PID.y[6]

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ITI Headquarters Schweriner Strae 1 01067 Dresden Germany T +49 (0) 351 26050 0 F +49 (0) 351 260 50 155 sales@simulationx.comSimulationX For your local representative please visit www.simulationx.com/global

ITI and SimulationX are registered trademarks of ITI GmbH Dresden. ITI GmbH, Dresden, Germany, 2013. All rights reserved.

Figure 3: Snapshots of the 3D view at starting time and during simulation of the hexapod example model shown in Figure 2.

Summary

With its holistic multi-domain approach to modeling and simulation SimulationXprovides means for

the quick and straightforward assembly of models of complex dynamical systems and thus saves timeand costs when reaching a solution.Combining programming capabilities and advanced signal processing features, such as matrix andvector operations (which are not only available using the programming interface but are an integralpart of the signal processing library too), the models remain clearly structured and comprehensible.Modifications can be applied on the fly.The orientation on physical objects in the modeling in SimulationX makes it easy to modify thesimulation model by replacing parts or extending the functionality of existing components. The com-ponent boundaries in the real system coincide with the element or submodel boundaries in thesimulation model and thus alterations often turn out to be simply Cut&Paste operations.