Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-05T13:14:17.216Z Has data issue: false hasContentIssue false

Optimal Control and Path Planning of a 3PRS Robot Using Indirect Variation Algorithm

Published online by Cambridge University Press:  25 July 2019

H. Tourajizadeh*
Affiliation:
Mechanical Engineering Department, Faculty of Engineering, Kharazmi University, Tehran, Iran
O. Gholami
Affiliation:
Mechanical Engineering Department, Faculty of Engineering, Kharazmi University, Tehran, Iran
*
* Corresponding author. Email: [email protected]

Summary

In this paper, optimal control of a 3PRS robot is performed, and its related optimal path is extracted accordingly. This robot is a kind of parallel spatial robot with six DOFs which can be controlled using three active prismatic joints and three passive rotary ones. Carrying a load between two initial and final positions is the main application of this robot. Therefore, extracting the optimal path is a valuable study for maximizing the load capacity of the robot. First of all, the complete kinematic and kinetic modeling of the robot is extracted to control and optimize the robot. As the robot is categorized as a constrained robot, its kinematics is studied using a Jacobian matrix and its pseudo inverse whereas its kinetics is studied using Lagrange multipliers. The robot is then controlled using feedforward term of the inverse dynamics. Afterward, the extracted dynamics equation of the robot is transferred to state space to be employed for calculus of variations. Considering the constrained entity of the robot, null space of the robot is employed to eliminate the Lagrange multipliers to provide the applicability of indirect variation algorithm for the robot. As a result, not only are the optimal controlling signals calculated but also the corresponding optimal path of the robot between two boundary conditions is extracted. All the modeling, controlling, and optimization process are verified using MATLAB simulation. The profiles are then double-checked by comparing the results with SimMechanics. It is proved that with the aid of the proposed controlling and optimization method of this article, the robot can be controlled along its optimal path through which the maximum load can be carried.

Type
Articles
Copyright
© Cambridge University Press 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Stewart, D., “A Platform with Six Degrees of Freedom,” Proceedings of the Institution of Mechanical Engineers, Thousand Oaks, California (1965) pp. 371386.Google Scholar
Ruiz, A., Campa, F., Roldán-Paraponiaris, C. and Altuzarra, O., “Dynamic Model of a Compliant 3PRS Parallel Mechanism for Micromilling,” In: Microactuators and Micromechanisms (Springer, New York City, 2017) pp. 153164.CrossRefGoogle Scholar
Li, Y. and Xu, Q., “Kinematics and inverse dynamics analysis for a general 3-PRS spatial parallel mechanism,Robotica 23(2), 219229 (2005).CrossRefGoogle Scholar
Pond, G. and Carretero, J. A., “Architecture optimisation of three 3-RS variants for parallel kinematic machining,Robot. Comput.-Integr. Manuf. 25(1), 6472 (2009).CrossRefGoogle Scholar
Tsai, M.-S. and Yuan, W.-H., “Inverse dynamics analysis for a 3-PRS parallel mechanism based on a special decomposition of the reaction forces,” Mech. Mach. Theory 45(11), 14911508 (2010).CrossRefGoogle Scholar
Tsai, M.-S. and Yuan, W.-H., “Dynamic modeling and decentralized control of a 3 PRS parallel mechanism based on constrained robotic analysis,J. Intell. Robotic Syst. 63(3–4), 525545 (2011).CrossRefGoogle Scholar
Yuan, W.-H. and Tsai, M.-S., “A novel approach for forward dynamic analysis of 3-PRS parallel manipulator with consideration of friction effect,Robot. Comput.-Integr. Manuf. 30(3), 315325 (2014).CrossRefGoogle Scholar
Staicu, S., “Matrix modeling of inverse dynamics of spatial and planar parallel robots,Multibody Syst. Dyn . 27(2), 239265 (2012).CrossRefGoogle Scholar
Li, Y. G., Xu, L. X. and Wang, H., “Dimensional Synthesis of 3PRS Parallel Mechanism Based on a Dimensionally Homogeneous Analytical Jacobian,” In: Applied Mechanics and Materials (Trans Tech Publ, 2014) pp. 354359.Google Scholar
Altuzarra, O., Gomez, F. C., Roldan-Paraponiaris, C. and Pinto, C., “Dynamic Simulation of a Tripod Based in Boltzmann-Hamel Equations,” In: ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (American Society of Mechanical Engineers, 2015) pp. V05CT08A022–V05CT08A022.Google Scholar
Ruiz, A., Campa, F., Roldán-Paraponiaris, C., Altuzarra, O. and Pinto, C., “Experimental validation of the kinematic design of 3-PRS compliant parallel mechanisms,Mechatronics 39, 7788 (2016).CrossRefGoogle Scholar
Korayem, M. and Shafei, A., “Application of recursive Gibbs–Appell formulation in deriving the equations of motion of N-viscoelastic robotic manipulators in 3D space using Timoshenko beam theory,Acta Astronaut . 83, 273294 (2013).CrossRefGoogle Scholar
Zhou, P., Wang, F.-Y., Chen, W. and Lever, P., “Optimal construction and control of flexible manipulators: a case study based on LQR output feedback,Mechatronics 11(1), 5977 (2001).CrossRefGoogle Scholar
Korayem, M., Zehfroosh, A., Tourajizadeh, H. and Manteghi, S., “Optimal motion planning of non-linear dynamic systems in the presence of obstacles and moving boundaries using SDRE: application on cablesuspended robot,Nonlinear Dyn . 76(2), 14231441 (2014).CrossRefGoogle Scholar
Korayem, M. and Nekoo, S., “Finite-time state-dependent Riccati equation for time-varying nonaffine systems: Rigid and flexible joint manipulator control,ISA Trans . 54, 125144 (2015).CrossRefGoogle Scholar
Chettibi, T., Lehtihet, H., Haddad, M. and Hanchi, S., “Minimum cost trajectory planning for industrial robots,Eur. J. Mech. A: Solids 23(4), 703715 (2004).CrossRefGoogle Scholar
Lee, J. and Bien, Z., “Collision-free trajectory control for multiple robots based on neural optimization network,Robotica 8(3), 185194 (1990).CrossRefGoogle Scholar
Omran, A., El-Bayiumi, G., Bayoumi, M. and Kassem, A., “Genetic algorithm based optimal control for a 6-dof non redundant stewart manipulator,Int. J. Mech. Syst. Sci. Eng. 2(2), 7379 (2008).Google Scholar
Korayem, M. H., Nikoobin, A. and Azimirad, V., “Maximum load carrying capacity of mobile manipulators: optimal control approach,Robotica 27(1), 147159 (2009).CrossRefGoogle Scholar
Gasparetto, A. and Zanotto, V., “Optimal trajectory planning for industrial robots,Adv. Eng. Software 41(4), 548556 (2010).CrossRefGoogle Scholar
Callies, R. and Rentrop, P., “Optimal control of rigid-link manipulators by indirect methods,GAMM-Mitt . 31(1), 2758 (2008).CrossRefGoogle Scholar
Sundar, S. and Shiller, Z., “Optimal obstacle avoidance based on the Hamilton-Jacobi-Bellman equation,IEEE Trans. Robot. Autom. 13(2), 305310 (1997).CrossRefGoogle Scholar
Cheng, T., Lewis, F. L. and Abu-Khalaf, M., “Fixed-final-time-constrained optimal control of nonlinear systems using neural network HJB approach,IEEE Trans. Neural Networks 18(6), 17251737 (2007).CrossRefGoogle Scholar
Korayem, M. H., Nikoobin, A. and Azimirad, V., “Trajectory optimization of flexible link manipulators in point-to-point motion,Robotica 27(6), 825840 (2009).CrossRefGoogle Scholar
Khardi, S., “Aircraft flight path optimization. The hamilton-jacobi-bellman considerations,” Appl. Math. Sci. 6(25), 12211249 (2012).Google Scholar
Korayem, M. and Irani, M., “New optimization method to solve motion planning of dynamic systems: application on mechanical manipulators,Multibody Syst. Dyn . 31(2), 169189 (2014).CrossRefGoogle Scholar
Korayem, A., Rahagi, M. I., Babaee, H. and Korayem, M. H., “Maximum load of flexible joint manipulators using nonlinear controllers,Robotica 35(1), 119142 (2017).CrossRefGoogle Scholar
Korayem, M., Ghariblu, H. and Basu, A., “Dynamic load-carrying capacity of mobile-base flexible joint manipulators,Int. J. Adv. Manuf. Technol. 25(1–2), 6270 (2005).CrossRefGoogle Scholar
Korayem, M. and Nikoobin, A., “Maximum payload path planning for redundant manipulator using indirect solution of optimal control problem,Int. J. Adv. Manuf. Technol. 44(7–8), 725 (2009).CrossRefGoogle Scholar
Spong, M. W., Hutchinson, S. and Vidyasagar, M., Robot Modeling and Control (John Wiley & Sons Inc., Hoboken, New Jersey, 2005) ISBN-100-471-649.Google Scholar
Liang, C. and Lance, G. M., “A differentiable null space method for constrained dynamic analysis,J. Mech. Transm. Autom Des. 109(3), 405411 (1987).CrossRefGoogle Scholar