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Int. J. Engg. Res. & Sci. & Tech. 2014 Ashraf Mishkat and Neelam Verma, 2014

ISSN 2319-5991 www.ijerst.com

Vol. 3, No. 2, May, 2014

© 2014 IJERST. All Rights Reserved

Research Paper

ROBUST CONTROL OF ROBOTIC MANIPULATOR

Ashraf Mishkat1* and Neelam Verma

*Corresponding Author: Ashraf Mishkat, � [email protected]

Robots are reprogrammable multifunctional manipulators designed to move material parts forthe performance of variety of task. Robots are classified as manual handling device, fixedsequence robot and many more. In 1954 George Devol developed the first programmablerobot. In this paper we have tried to understand the kinematics and dynamics of the robot by theuse of Pro E wildfire and Matlab by interfacing them and by the use of the conventional controllersand in order to remove the gravity factor gravity compensation is being used for the propermovement of the robotic arm.

Keywords: Pro E wildfire, Conventional controllers, Matlab

INTRODUCTION

Robots are reprogrammable multifunctionalmanipulators designed to move material parts forthe performance of variety of task. Robots areclassified as manual handling device, fixedsequence robot and many more. In 1954 GeorgeDevol developed the first programmable robot.The position control of robot manipulators is thesimplest aim in robot control, at the same times,it is one of the most relevant issues in practicalmanipulators. Many approaches have beenintroduced to treat this control problem. It is wellknown that a rigid robot arm can be globallyasymptotically stabilized around a given jointconfiguration via a PD controller on the jointerrors, provided that gravity is cancelled byfeedback. Under a mild condition on theproportional gain, this scheme can be simplifiedby performing only constant gravity compensation

1 Department of Mechanical Engineering, Manav Bharti University, Solan, India.

at the desired configuration. Indeed, modeluncertainties are frequently encountered inrobotics due to, e.g. unknown or changingpayload, friction, backlash, flexible joints or robotparts for which only simplified dynamical modelsare available. These model uncertainties maycause significant deviations between simulatedand experimental results. Generally, neglectingthe effects of model uncertainties significantlydecreases performance in terms of trackingaccuracy and attainable velocity. Furthermore, forall control systems there exists a well-known tradebetween robustness and performance. Obviously,the smaller the uncertainty on a dynamical model,the higher the performance attainable and anincrease in robustness margin will lead at onepoint to a decrease in performance. In thiscontext, robust control theories provide a valuableframework for determining the robustnessproperties of the proposed control strategies and


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give information on the trade- betweenperformance and robustness. They increaseproductivity, safety, efficiency, quality, andconsistency of products. They can work inhazardous environments without the need for lifesupport, comfort and concern about safety. Theyneed no environmental comfort such as lighting,air conditioning, ventilation and noise protection.Mainly, robust strategies explicitly taking intoaccount robustness against modeling un-certainties and making the robot track a time-varying reference trajectory will be reviewed. Thereview takes great care into describing themodels used and the underlying assumptions.Most of the robust controllers are nonadaptive,i.e. they possess a time invariant control law.However, for the sake of completeness, adaptivecontrol schemes are also briefly reviewed.

ROBOT KINEMATICSAND DYNAMICS

Direct kinematicsPositional analysis of the robotic manipulator.Positional analysis of the manipulator is done bydetermining the angles of the manipulator.

Inverse KinematicsDetermining the angles of the manipulatorthrough the positions. Orientation of the roboticmanipulator is also known.

Robot DynamicsTo perform assign task or to obtain the desiredposition by accelerating the manipulator from rest.To traverse the robot through a proper trajectorywith specified velocity and specific path. Torquesare calculated from the equation of motion of therobotic manipulator.

Manipulator Dynamics

The dynamics of a robot manipulatorM(x)x+V(x, x)+F(x)+G(x) = τx is the joint variable

M is the inertia matrixV is the coriolis/Centripetal vectorG is the gravity vectorN(x, x) = V(x, x)+F(x)+G(x)

Robust Control

The manipulator dynamics can be formulated as

x = Ax + B(u + h ( x ) u) + B f(x) ...(1)

h(x) = M(x1)-1 M

0 (x

1) – I ...(2)

f(x) = M(x1)-1 (N

0 (x

1 x

2) – N(x

1, x

2)) ...(3)

...(4)

Dynamic analysis

Calculate the Lagrange multiplier

L = K - P

where K is the Kinetic Energy

P is the Potential Energy

Calculation of the torque and generalised forcesis also done by taking the derivative

SOFTWARES REQUIRED

The use of software like Pro E has made theunderstanding of the robots more easier and theinterfacing of the robotic manipulator to the othersoftware that is Matlab. Pro E is is a computergraphics system for modeling various mechanicaldesigns and for performing related design andmanufacturing operations. A feature-based,parametric solid modeling system with manyextended design and manufacturing applications.The system uses a 3D solid modeling system asthe core, and applies the feature-based,parametric modeling method. The main softwarewhich is used is Sim Mechanics with the help ofthat building of robotic arm and the motion of thatis possible. SimMechanics software is a blockdiagram modeling environment for theengineering design and simulation of rigidmultibody machines and their motions, using the


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standard Newtonian dynamics of forces andtorques. SimMechanicssoftware is basedontheSimscape™ software, the platform product for theSimulink Physical Modeling family. the Figure canbe shown in this manner.

Figure 3.1: Robotic Manipulator ArmWithout any Controllers Using Simscape

Figure 3.2: Internal Subsystems

Figure 3.3: Robotic Manipulator byInterfacing Matlab and Pro E

Model build in Pro E are as follows:

Figure 3.4: Link of RoboticManipulator build in Pro E

Figure 3.5: Link of RoboticManipulator Pro E

Figure 3.6: Link of RoboticManipulator Pro E


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Figure 3.7: Gravity Compensator

The use of Gravity Compensator is required toremove the effects caused in the movement ofthe robotic arm due to gravity. More force isneeded by the arm to follow a path and inorderto remove the gravity factor we are using the grav-ity compensator to move the robotic arm freelyso that less torque is used.

CONTROLLERS

We have made use of the conventional controllerslike P, PI and PID in order to control the motionof the robotic manipulator.

Case 1: P Controller

Figure 4.1: P Controller


Figure 4.2: PI Controller

Case 3: PID Controller

Figure 4.3: PID Controller

RESULTS

We have made use of the conventional controllerslike P, PI and PID in order to control the motionof the robotic manipulator.


Figure 5.1: P Controller


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Case 2: PI Controller

Figure 5.2: PI Controller

Case 3: PID Controller

Figure 5.3: PID Controller

CONCLUSION

In the scheme proposed in this paper, Matlaband pro e are set together for getting the outputfrom the robotic manipulator with the help of theconventional controllers like P, PI and PID. Wealso made use of the gravity compensator toremove the effect of the gravitational force beingexerted on the links and joints This paperdescribes the process of modeling a simple robotmanipulator using PD control with online gravitycompensation method. The use of SimMechanicsas a tool to model the mechanics of the robotallows the possibility to verify model, as in realapplication, is unknown for the designer so thatthe ability of the control method to match the realmodel can be easily proven. That would allowthe testing of techniques like the dynamic model-

based control but also learning techniques thatextract the model of the plant under consideration.

REFERENCES

1. Bouwmans H C, Nijmeijer H and ZutvenPWM van (2012), “Gravity compensation fora bipedal humanoid robot”, Internal Report,D&C, No. 2012.017). Eindhoven: Universityof Technology, pp. 43.

2. Chung-Shi Tseng (2008), “Robust TrackingControl Design for Uncertain Robotic Sys-tems with Persistent Bounded Disturbances”,Asian Journal of Control, Vol. 10, No. 4, pp.420-429.

3. Faical Mnif, “A Robust Optimal Control forConstrained Robot”, International Journal ofComputational Cognition, Vol. 3, No. 1, pp.35-43.

4. Farzin Piltan N Sulaiman (2011), “ArtificialRobust Control of Robot Arm”.

5. Feng Lin and Robert D Brandt (1998), “AnOptimal Control Approach to Robust Controlof Robot Manipulators”, IEEE Transactionson Robotics and Automation, Vol. 14, No. 1,pp. 69-77.

6. Le Tien Dung (2010), “Robot ManipulatorModeling in Matlab Simmechanics with PDControl and Online Gravity Compensatin”,IEEE Strategic Technology (IFOST), pp. 446-449.

7. P Tomei (1991), “Adaptive PD Controller forRobot Manipulators”, IEEE Trans. RoboticAutomat, pp. 565-570.

8. Velarde-Sanchez J A (2010), “5-DOFManipulator Simulation Based on MATLABSimulink Methodology”, IEEE, pp. 295-300.

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