Proceedings of the Fifth National Conference on Optimization Techniques in Engineering Sciences and Technologies – OPTEST 2010
OPTIMAL TRAJECTORY DESIGN OF RRP SERIAL MANIPULATOR K.Kiran Kumar1 Dr.P.R.Thyla2
1
1
PG scholar, 2 assistant professor
Department of Mechanical Engineering, PSG College of Technology, Coimbatore641004.
2
Department of Mechanical Engineering, PSG College of Technology, Coimbatore641004. E-mail:
[email protected]
Abstract: Robotic manipulators are needed in such fields as assembly operations, material handling, packaging, machine tending, conveyor tracking and many other operations which require fast and precise automation applications which is possible because of joint servo motor controlled system to perform high accuracy tasks. Achieving such high accuracy is difficult because of the manipulator’s size and the substantial task forces involved. Therefore, there is a need for model-based error identification which can be further used for error compensation. Their contribution to the platform positional accuracy is estimated through development of a dynamic model of serial manipulator with flexible and rigid links. The position analyses during static and dynamic using conditions rigid and elastic models are carried out using ADAMS/view and ADAMS/flex respectively. The error is predicted by comparing the results of rigid and elastic models and validated experimentally. The error is predicted by comparing the time varying position of the end effector obtained by using the rigid model and the model with flexible links. Taguchi’s design of experiments has been used to optimize the number of experiments. Anova analysis is performed along with regression and least square error method is employed to find the compliance error. The outcome of the work includes the selection of optimum parameters for minimum error in the trajectory. Keyword: Flexible Serial Robot, Kinematics, Dynamic Modeling, Flexible Link, Compliance. 1.0 INTRODUCTION Serial manipulators are, in fact, realized by the successive connection of rigid bodies, linked by appropriate joints; obviously, every member has to support the weight of all the subsequent segments in addition to its own and the transported payload which means they must be very rigid (heavy) to avoid undesired elastic deflection. Maximum workspace when compared with parallel manipulators. Can reach above or below of objects i.e, to reach any corner points. As a matter of fact, the positioning accuracy of the end-effector is highly affected by the chain flexibility, since robot internal sensors do not measure it. Serial architectures, moreover, are affected both by load and error additively, [5]. Organized by Department of Mechanical Engineering, Bannari Amman Institute of Technology, Sathyamangalam, TamilNadu.
Proceedings of the Fifth National Conference on Optimization Techniques in Engineering Sciences and Technologies – OPTEST 2010
Robots are primarily concerned with generating specific motion of the robot joints, simultaneously allowing tooling or sensors to perform certain functions. Newer technologies are concerned with robot interactions with parts such that interaction forces and torques can be controlled. This technology will permit more robot applications in assembly, which promises to be a growing application arena for robotics. Robotic manipulators are needed in such fields as assembly operations, material handling, Packaging, machine tending, conveyor tracking and many other operations which require fast and precise automation applications to perform high accuracy tasks, [3]. Achieving such high accuracy is difficult because of the manipulator‟s size and it is need to exert substantial task forces. Most of the mechanical devices for robotic applications are based on serial chains; three degrees of freedom wrists are better realized by spherical mechanisms, as this permits to decouple the position (provided by the arm) and orientation (related to the wrist) problems still keeping the actuation within the arm, [6]. Thereafter, several kinematic and mechanical solutions have been devised to implement light; stiff and dexterous robotic wrists. Most of the existing robotic manipulators are designed and built in a manner to maximize stiffness in an attempt to minimize the vibration of the end-effector to achieve good positional accuracy. This high stiffness is achieved by using heavy material and a bulky design. Hence, the existing heavy rigid manipulators are shown to be inefficient in terms of power consumption or speed with respect to the operating payload. Also, the operation of high precision robots is severely limited by their dynamic deflection, which persists for a period of time after a move is completed. The settling time required for this residual vibration delays subsequent operations, thus conflicting with the demand of increased productivity. These conflicting requirements between high speed and high accuracy have rendered the robotic assembly task a challenging research problem. Also, many industrial manipulators face the problem of arm vibrations during high speed motion. In order to improve industrial productivity, it is required to reduce the weight of the arms and/or to increase their speed of operation. For these purposes it is very desirable to build flexible robotic manipulators. 2. EXPERIMENTAL PROCEDURES Experiments have been carried on the Adept SCARA robot. The specifications of the robot are given in Table.1. For conducting experiments arbitrarily twelve points were selected , and robot is moved to that particular points and robot is moved through jog pendant and end effector co-ordinate values , the joint values leading to that position are noted down and compared with desired (or) ideal trajectory.
Organized by Department of Mechanical Engineering, Bannari Amman Institute of Technology, Sathyamangalam, TamilNadu.
Proceedings of the Fifth National Conference on Optimization Techniques in Engineering Sciences and Technologies – OPTEST 2010
Organized by Department of Mechanical Engineering, Bannari Amman Institute of Technology, Sathyamangalam, TamilNadu.
Proceedings of the Fifth National Conference on Optimization Techniques in Engineering Sciences and Technologies – OPTEST 2010
In order to accomplish the objectives, Taguchi’s Design of experiments has been used to conduct a set of sixteen experiments. The parameters considered and levels are given in Table 2.
3. EXPERIMENTAL RESULTS AND DISCUSSION 3.1. Experimental Results Experiments were conducted and the observations are presented in Table 3. It was observed that the error is maximum for experiment number ( 4.71 rad/s, 8.7975 rad/s, 275 mm/s) , and is minimum for experiment 2 ( 3.14 rad/s,5.8650 rad/s, 275 mm/s.
Organized by Department of Mechanical Engineering, Bannari Amman Institute of Technology, Sathyamangalam, TamilNadu.
Proceedings of the Fifth National Conference on Optimization Techniques in Engineering Sciences and Technologies – OPTEST 2010
So the experimentation yields output of finding significant factors which yields optimal desired trajectory with less error. Its found out that error is a function of joint speeds, if we can find a generalized equation for finding compliance error in terms of position we can use it in trajectory planning, path control of robots and for the purpose of calibration of robots. Percentage error in position=function(J1,J2,J3) X2(%)=92.9553*J199.3630*J21.41578*J34.57749*J1*J11.37867*J2*J2+0.00142619*J3 *J3+10.4974*J1*J2-0.183119*J1*J3+0.107961*J2*J3+458.989. Y2(%)=-159.669*J1+86.2225*J2+0.544897*J3+30.9095*J1*J1+8.79343*J2*J29.97205E-043.71168E-04*J3*J3-33.0280*J1*J2+0.215965*J1*J3-0.115795*J2*J377.9848. Z2(%)=12.3005*J1+9.95358*J2+0.184083*J3+1.57386E+2.25460*J1*J1+6.12810E+0.6 46240*J2*J2-2.17152E-04*J3*J3-2.84320*J1*J2+0.0210629*J1*J3-0.0112766*J2*J346.0533. These equations are obtained by regression analysis by assuming quadratic model for controlling non-linearity in the response.
Organized by Department of Mechanical Engineering, Bannari Amman Institute of Technology, Sathyamangalam, TamilNadu.
Proceedings of the Fifth National Conference on Optimization Techniques in Engineering Sciences and Technologies – OPTEST 2010
Since smaller the error better is the condition to be satisfied, it is inferred from the ANOVA Table 7, that experiment 2 i.e., Joint 1 speed 3.14 (rad/s), Joint 2 speed 5.865 (rad/s) and Joint 3 speed 275(mm/s)shows the minimum compliance error value. Therefore, the above three values are taken as the optimum condition for compliance error. It is therefore inferred that the joint 2 speed has a major influence on the compliance error. Joint 3 speed has a significant influence and Joint 1 speed has the least effect on compliance error.Experiment-3 leads to trajectory with more errors i.e, at Joint 1 speed 4.75 (rad/s), Joint 2 speed 5.865 (rad/s) and Joint 3 speed 275(mm/s).Therefore the configuration if running at conditions of experiment-3 leads to more compliance error.
Organized by Department of Mechanical Engineering, Bannari Amman Institute of Technology, Sathyamangalam, TamilNadu.
Proceedings of the Fifth National Conference on Optimization Techniques in Engineering Sciences and Technologies – OPTEST 2010
Workspace Analysis As the orientation of the platform varies from its original vertical direction, the size of the accessible workspace changes and the shape of the accessible workspace becomes as sphere more detail on workspace analysis for serial kinematics manipulator can be found in [5]
Fig.3. Comparision of workspace for rigid and compliant models S.No. experiments R-Square value R-Square value R-Square value (x%) (y%) (z%) 1. Exp-1 54.10 55.74 94.29 2. Exp-2 88.43 95.04 93.94 3. Exp-3 59.59 57.49 51.52 4. Exp-4 64.06 47.01 85.09 5. Exp-5 43.43 61.44 85.45 6. Exp-6 41.71 67.76 85.45 7. Exp-7 44.99 57.67 85.45 8. Exp-8 32.45 63.89 85.45 9. Exp-9 48.34 90.73 85.45 10. Exp-10 48.26 84.01 85.45 11. Exp-11 48.69 63.35 85.45 12. Exp-12 51.29 55.46 85.45 13. Exp-13 42.88 59.60 93.94 14. Exp-14 40.79 55.76 93.94 15. Exp-15 54.99 85.37 85.45 16. Exp-16 59.53 53.15 85.45 Since smaller the error better is the condition to be satisfied, experiment 2 i.e., robot when operating at Joint 1 speed of 3.14 (rad/s), Joint 2 speed of 5.865 (rad/s) and Joint 3 speed of 275(mm/s) in linear displacement shows the minimum compliance error value. Therefore, the above three values are taken as the optimum condition for compliance error.
Organized by Department of Mechanical Engineering, Bannari Amman Institute of Technology, Sathyamangalam, TamilNadu.
Proceedings of the Fifth National Conference on Optimization Techniques in Engineering Sciences and Technologies – OPTEST 2010
4. CONCLUSIONS Formulation of an attempt to DOE methodology in the field of robotics is made . An generalized model in form of error is made for RRP serial manipulators is made. Important significant factor which leads to best possible optimal trajectory is developed. With the developed system it is possible to maintain continuous track of the error. With the obtained data, from the experimental results we can conclude that error is less in experiment number 2 because it matches with the ideal trajectory.The current practices of finding optimized results can be improved by using this method. The existing methods of other can be replaced with the anova analysis. 5.0 REFERENCES [1] T.C.Manjunath, et.al,”Development of a Jacobean model for a 4-Axes indigenously developed SCARA system”, International Journal of computer and information science and engineering, vol.1, pp.152-158,(2007). [2] J. John Craig, Introduction to robotics mechanism and control, Pearson Education Publication, Delhi, 2005. [3] S.Dubowsky, et.al,”Planning time-optimal robotic manipulator motions and work places for point-to-point tasks”, IEEE Transcations on Robotics and Automation, vol.5, pp.349-356(1989). [4] T.C. Manjunath, “Trajectory planning design equations and control of a 4 – axes stationary robotic arm”, International Journal of computational and mathematical sciences, vol.2,pp.38-44,(2007). [5] S.P.Chan, ”Velocity estimation for robotic manipulators using neural network”, Journal of intelligent and robotic systems, vol.5, no.6,pp.157165,(1989). [6] B.W.Mooring et.al, “The effect of kinematic model complexity on manipulator accuracy”, Journal of robotics & automation, vol.12, no.8,pp.593598,(1989). [7]R.K.Mittal, et.al, Robotics and control, Pearson publicarion, USA 2003. [8] L.W.Tsai, Robot analysis, Awiley-interscience publication, USA, 1999. [9] J.Robert Schilling, Fundamentals of robotics analysis and control, Prenticehall of india, New delhi, India 2003. [10] S.S.Oho et.al, ˝Simulation of multifinger robotic gripper for dynamic analysis of dexterous grasping”, Proceedings of the world congress on engineering and computer science , ISBN:978 988-98671-0-2,pp.135-142,(2008).
Organized by Department of Mechanical Engineering, Bannari Amman Institute of Technology, Sathyamangalam, TamilNadu.
