Time Optimal Trajectory Generation with Obstacle Avoidance by Using Optimal Control Theory for a Wheeled Mobile Robot

Year 2023, Volume: 36 Issue: 1, 430 - 439, 01.03.2023

Masoud Mosayebi , Pouya Mallahi Kolahi

https://doi.org/10.35378/gujs.944300

Cited By: 2

Abstract

The design of the mobile robot path is important when obstacles are present in the environment. In the present study, the theory of optimal control for path design and obstacle avoidance via simultaneous minimization of the time and kinetic energy is proposed. Nonlinear equations of robot motion without simplification are considered in optimum control problems, and in order to prevent collisions, the potential functions are utilized. In the next phase, the cost function is proposed that includes velocity inputs, time, and the potential function for obstacle avoidance, in which the nonlinear equation of the motion of the mobile robot is deemed as a constraint. The final equations are numerically solved, and the capability and effectiveness of the presented method will be presented via different simulations on the mobile robot.

Keywords

Wheeled mobile robot, Optimal control, Optimal time, Trajectory planning

References

• [1] Pandey, A., Pandey, S., Parhi, D.R., “Mobile robot navigation and obstacle avoidance techniques: A review”, International Robotics & Automation Journal, 2(3): 00022, (2017).
• [2] Spong, M. W., Hutchinson, S., Vidyasagar, M., Robot modeling and control, John Wiley & Sons, United States, (2020).
• [3] Cui, M., Sun, D., Liu, W., Zhao, M., Liao, X., “Adaptive tracking and obstacle avoidance control for mobile robots with unknown sliding”, International Journal of Advanced Robotic Systems, 9(5): 171, (2012).
• [4] Nazemizadeh, M., Rahimi, H. N., Khoiy, K.A., “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, (2012).
• [5] Yen, C.T., Cheng, M.F., “A study of fuzzy control with ant colony algorithm used in mobile robot for shortest path planning and obstacle avoidance”, Microsystem Technologies, 24(1): 125-135, (2018).
• [6] Liu, J., Yang, J., Liu, H., Tian, X., Gao, M., “An improved ant colony algorithm for robot path planning”, Soft Computing, 21(19): 5829-5839, (2017).
• [7] Nazemizadeh, M., Mallahi Kolahi, P., “Trajectory Tracking of an Intelligent Mobile Robot on a Slope Surface using the Nonlinear Sliding Mode Control”, Mechanic of Advanced and Smart Materials, 1(1): 1-14, (2021).
• [8] Korayem, M.H., Ghobadi, N., Fathollahi Dehkordi, S., “Designing an optimal control strategy for a mobile manipulator and its application by considering the effect of uncertainties and wheel slipping”, Optimal Control Applications and Methods, 1-25, (2021).
• [9] Mallahi Kolahi, P., Mosayebi, M., “Optimal Trajectory Planning for an Industrial Mobile Robot using Optimal Control Theory”, Journal of Modern Processes in Manufacturing and Production, 10(3), 25-34, (2021).
• [10] Korayem, M.H., Nazemizadeh, M., Nohooji, H.R., “Optimal point-to-point motion planning of nonholonomic mobile robots in the presence of multiple obstacles”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 36(1): 221-232, (2014).
• [11] Wu, Y., Liu, L., Yang, Y., Dai, S., “Optimal Control Method for Robot-Tracking Based on Control-Lyapunov-Function”, IEEE Access, 7: 90565-90573, (2019).
• [12] Klancar, G., Zdesar, A., Blazic, S., Skrjanc, I., “Wheeled mobile robotics: from fundamentals towards autonomous systems”, Butterworth-Heinemann, United Kingdom, (2017).
• [13] Kirk, D.E., “Optimal control theory: an introduction”, Courier Corporation, Prentice Hall, New York, (1994).
• [14] Wang, X., “Solving optimal control problems with MATLAB: Indirect methods”, Industrial and Systems Engineering Department., NCSU, Raleigh, NC, 27695, (2009).