Optimal Trajectory Planning for an Industrial Mobile Robot using Optimal Control Theory

Subject Areas :

Pouya Mallahi Kolahi ¹ , Masoud Mosayebi ²

1 - Department of Mechanical Engineering, Malek-Ashtar University of Technology, Iran
2 - Department of Mechanical Engineering, Malek-Ashtar University of Technology, Iran

Received: 2021-08-08 Accepted : 2021-10-13 Published : 2021-08-01

Keywords: Optimal Control, Trajectory planning, Industrial Mobile Robot, Optimal Time,

Abstract :

Optimal path planning with optimal journey time and the motor saturation limit are two main challenges in mobile industrial robot design. The motion speed and motor saturation limit are important factors determining the required torque. Calculating the optimal torque value reduces the construction and motor selection costs. This paper proposes the theory of optimal control open-loop base model for path planning by simultaneously minimizing the journey time, wheels’ torque for industrial robots. In this study, nonlinear equations of robot motion were considered as a constraint in optimal control problems. Next, the cost function was proposed, including the torque of the left and right wheels and time-related terminal conditions and disturbance, in which the nonlinear equations of the industrial robot motion are assumed as constraints. The final equations were numerically solved, and the effectiveness of the proposed method was demonstrated by simulating and path design for industrial robots' motions along with considering motor saturation limit.

References:

[1] https://en.wikipedia.org/wiki/Mobile_industrial_robots#cite_note-13

[2] Pandey, A., Pandey, S. and Parhi, D.R. 2017. Mobile robot navigation and obstacle avoidance techniques: A review. Int Rob Auto J. 2(3): 00022.

[3] Korayem, M.H., Nazemizadeh, M. and Nohooji, H.R. 2014. Optimal point-to-point motion planning of non-holonomic mobile robots in the presence of multiple obstacles. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 36(1): 221-232.

[4] Nazemizadeh, M., Rahimi, H.N. and Khoiy, K.A. 2012. Trajectory planning of mobile robots using indirect solution of optimal control method in generalized point-to-point task. Frontiers of Mechanical Engineering. 7(1): 23-28.

[5] Wu, Y., Wang, B. and Zong, G.D. 2005. Finite-time tracking controller design for nonholonomic systems with extended chained form. IEEE Transactions on Circuits and Systems II: Express Briefs. 52(11): 798-802.

[6] Cui, M., Sun, D., Liu, W., Zhao, M. and Liao, X. 2012. Adaptive tracking and obstacle avoidance control for mobile robots with unknown sliding. International Journal of Advanced Robotic Systems. 9(5): 171.

[7] Dos Santos, R.R., Steffen, V. and de FP Saramago, S. 2008. Robot path planning in a constrained workspace by using optimal control techniques. Multibody System Dynamics. 19(1): 159-177.

[8] Ramos, O.E. 2019. Optimal Control for Time and Energy Minimization in the Trajectory Generation of a Mobile Robot. IEEE XXVI International Conference on Electronics, Electrical Engineering and Computing. August 12-13. 1-4.

[9] Tuncer, A. and Yildirim, M. 2012. Dynamic path planning of mobile robots with improved genetic algorithm. Computers & Electrical Engineering. 38(6): 1564-1572.

[10] Perrier, C., Dauchez, P. & Pierrot, F, 1998. A global approach for motion generation of non-holonomic mobile manipulators. In Proceedings. IEEE International Conference on Robotics and Automation. May 20. 4: 2971-2976.

[11] Chettibi, T., Lehtihet, H. E., Haddad, M., & Hanchi, S. 2004. Minimum cost trajectory planning for industrial robots. European Journal of Mechanics-A/Solids. 23(4): 703-715.

[12] Korayem, M. H., Ghariblu, H., & Basu, A. 2005. Dynamic load-carrying capacity of mobile-base flexible joint manipulators. The International Journal of Advanced Manufacturing Technology. 25(1): 62-70.

[13] Mohri, A., Furuno, S., & Yamamoto, M. 2001. Trajectory planning of mobile manipulator with end-effector's specified path. IEEE/RSJ International Conference on Intelligent Robots and Systems. 29 Oct.-3 Nov. 4: 2264:2269

[14] Korayem, M. H., Nazemizadeh, M., & Azimirad, V. 2011. Optimal trajectory planning of wheeled mobile manipulators in cluttered environments using potential functions. Scientia Iranica. 18(5): 1138-1147.

[15] Korayem, M. H., Rahimi, H. N., & Nikoobin, A. 2012. Mathematical modeling and trajectory planning of mobile manipulators with flexible links and joints. Applied Mathematical Modelling. 36(7): 3229-3244.

[16] Korayem, M. H., Nohooji, H. R., & Nikoobin, A. 2011. Path planning of mobile elastic robotic arms by indirect approach of optimal control. International Journal of Advanced Robotic Systems. 8(1): 10.

[17] Klancar, G., Zdesar, A., Blazic, S. and Skrjanc, I. 2017. Wheeled mobile robotics: from fundamentals towards autonomous systems. United Kingdom: Butterworth-Heinemann.

[18] Kirk, D.E. 2004. Optimal control theory: an introduction. New York: Courier Corporation.

[19] Najafi, H. S., & Edalatpanah, S. A. 2013. Iterative methods with analytical preconditioning technique to linear complementarity problems: application to obstacle problems. RAIRO-Operations Research. 47(1): 59-71.