Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T18:29:59.614Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal Motion Planning for Differential Drive Mobile Robots based on Multiple-Interval Chebyshev Pseudospectral Methods

Published online by Cambridge University Press:  29 May 2020

Run Mao ,
Hongli Gao Open the ORCID record for Hongli Gao [Opens in a new window]  and
Liang Guo
Run Mao
Affiliation:
Department of Electromechanical Measuring and Controlling, School of Mechanical Engineering, Southwest Jiaotong University, 610036 Chengdu, Sichuan, People’s Republic of China.
Hongli Gao*
Affiliation:
Department of Electromechanical Measuring and Controlling, School of Mechanical Engineering, Southwest Jiaotong University, 610036 Chengdu, Sichuan, People’s Republic of China.
Liang Guo
Affiliation:
Department of Electromechanical Measuring and Controlling, School of Mechanical Engineering, Southwest Jiaotong University, 610036 Chengdu, Sichuan, People’s Republic of China.
*
*Corresponding author. E-mail: hongli_gao@swjtu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Summary

This paper presents a Chebyshev Pseudospectral (PS) method for solving the motion planning problem of nonholonomic mobile robots with kinematic and dynamic constraints. The state and control variables are expanded in the Chebyshev polynomial of order N, and Chebyshev–Gauss–Lobatto (CGL) nodes are provided for approximating the system dynamics, boundary conditions, and performance index. For the lack of enough nodes nearby the obstacles, the interpolation of trajectory may violate the obstacles and the multiple-interval strategy is proposed to deal with the violation. Numerical examples demonstrate that multiple-interval strategy yields more accurate results than the single-interval Chebyshev PS method.

Keywords

Chebyshev pseudospectralMotion planningObstacle avoidanceCGLNonholonomic
Type
Articles
Information
Robotica , Volume 39 , Issue 3 , March 2021 , pp. 391 - 410
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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

Siegwart, R., Nourbakhsh, I. R., Scaramuzza, D. and Arkin, R. C., Introduction to Autonomous Mobile Robots (MIT Press, Cambridge, MA, 2011).Google Scholar
Martins, F. N., Sarcinelli-Filho, M. and Carelli, R., “A velocity-based dynamic model and its properties for differential drive mobile robots,” J. Intell. Robot. Syst. 85(2), 277–292 (2017).CrossRefGoogle Scholar
Milella, A., Cicirelli, G. and Distante, A., “RFID-assisted mobile robot system for mapping and surveillance of indoor environments,” Ind. Robot. 35(2), 143–152 (2008).CrossRefGoogle Scholar
Dubey, S., Chinnaaiah, M. C., Kiran, C. S., Priyanka, B. S. and Rao, P. P., “An FPGA Based Service Robot for Floor Cleaning with Autonomous Navigation,” In: International Conference on Research Advances in Integrated Navigation Systems, Bangalore (2016) pp. 1–6.Google Scholar
Lu, S. P., Chen, X. and Zhong, R. Y., “An active RFID tag-enabled locating approach with multipath effect elimination in AGV,” IEEE T. Autom. Sci. Eng. 13(3), 1333–1342 (2016).CrossRefGoogle Scholar
Schwesinger, D., Shariati, A., Montella, C. and Spletzer, J., “A smart wheelchair ecosystem for autonomous navigation in urban environments,” Auton. Robot. 41(3), 519–538 (2017).CrossRefGoogle Scholar
Mo, H. W. and Xu, L. F., “Research of biogeography particle swarm optimization for robot path planning,” Neurocomputing 148, 91–99 (2015).CrossRefGoogle Scholar
Gasparetto, A., Boscariol, P., Lanzutti, A. and Vidoni, R., “Path Planning and Trajectory Planning Algorithms: A General Overview,” Mech. Mach. Sci. 29, 3–27 (2015).CrossRefGoogle Scholar
Ni, X. H., Jiang, Z. Q. and Zhou, W. X., “Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks,” Phys. Lett. A. 373(42), 3822–3826 (2009).CrossRefGoogle Scholar
Canny, J., “A Voronoi Method for the Piano-Movers Problem,” In: IEEE International Conference on Robotics & Automation (1985) pp. 530–535.Google Scholar
Shewchuk, J. R., “Delaunay refinement algorithms for triangular mesh generation,” Comp. Geom. 22(1–3), 21–74 (2002).CrossRefGoogle Scholar
Elbanhawi, M., Simic, M. and Jazar, R., “Autonomous robots path planning: An adaptive roadmap approach,” Appl. Mech. Mater. 373–375, 246–254 (2013).CrossRefGoogle Scholar
Dijkstra, E. W., “A note on two problems in connection with graphs,” Numer. Math. 1(1), 269–271 (1959).Google Scholar
Jeddisaravi, K., Alitappeh, R. J. and Guimaraes, F. G., “Multi-Objective Mobile Robot Path Planning Based on A* Search,” In: 2016 6th International Conference on Computer and Knowledge Engineering (ICCKE) (IEEE, 2016) pp. 7–12.CrossRefGoogle Scholar
Likhachev, M., Ferguson, D., Gordon, G., A. Stentz and S. Thrun “Anytime search in dynamic graphs,” Artif. Intell. 172(14), 1613–1643 (2008).CrossRefGoogle Scholar
Pivtoraiko, M. and Kelly, K., “Kinodynamic Motion Planning with State Lattice Motion Primitives,” In: 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE, 2011) pp. 2172–2179.CrossRefGoogle Scholar
Pivtoraiko, M., Knepper, R. A. and Kelly, A., “Differentially constrained mobile robot motion planning in state lattices,” J. Field. Robot. 26(3), 308–333 (2009).CrossRefGoogle Scholar
Yang, S. X. and Meng, M., “Neural network approaches to dynamic collision-free trajectory generation,” IEEE T. Syst. Man. Cy. B. 31(3), 302–318 (2001).Google ScholarPubMed
Duan, H. B. and Huang, L. Z., “Imperialist competitive algorithm optimized artificial neural networks for ucav global path planning,” Neurocomputing 125, 166–171 (2014).CrossRefGoogle Scholar
Tian, L. F. and Collins, C. “An effective robot trajectory planning method using a genetic algorithm,” Mechatronics. 14(5), 455–470 (2004).CrossRefGoogle Scholar
Wang, M. M., Luo, J. J. and Walter, U., “Trajectory planning of free-oating space robot using Particle Swarm Optimization (PSO),” Acta Astronaut. 112, 77–88 (2015).CrossRefGoogle Scholar
Duan, H. B., Liu, S. Q. and Wu, J., “Novel intelligent water drops optimization approach to single ucav smooth trajectory planning,” Aerosp. Sci. Technol. 13(8), 442–449 (2009).CrossRefGoogle Scholar
Khatib, O., “Real-Time Obstacle Avoidance for Manipulators and Mobile Robots,” In: Autonomous Robot Vehicles (Springer, New York, NY, 1986) pp. 396–404.Google Scholar
Pettersson, P. O. and Doherty, P., “Probabilistic roadmap based path planning for an autonomous unmanned helicopter,” J. Intell. Fuzzy. Syst. 17(4), 395–405 (2006).Google Scholar
Cui, R. X., Li, Y. and Yan, W. S., “Mutual information-based multi-auv path planning for scalar field sampling using multidimensional rrt,” IEEE T. Syst. Man. Cy. B. 46(7), 993–1004 (2016).CrossRefGoogle Scholar
Elbanhawi, M. and Simic, M. “Sampling-based robot motion planning: A review,” IEEE Access. 2, 56–77 (2014).CrossRefGoogle Scholar
Su, Z. K., Wang, H. L. and Yao, P., “A hybrid backtracking search optimization algorithm for nonlinear optimal control problems with complex dynamic constraints,” Neurocomputing. 186, 182–194 (2016).CrossRefGoogle Scholar
Korayem, M. H., Nazemizadeh, M. and Nohooji, H. R., “Optimal point-to-point motion planning of non-holonomic mobile robots in the presence of multiple obstacles,” J. Braz. Soc. Mech. Sci. 36(1), 221–232 (2014).CrossRefGoogle Scholar
Korayem, M. H., Nohooji, H. R. and Nikoobin, A., “Path planning of mobile elastic robotic arms by indirect approach of optimal control,” Int. J. Adv. Robot. Syst. 8(1), 10 (2011).CrossRefGoogle Scholar
Su, Z. K. and Wang, H. L., “A novel robust hybrid gravitational search algorithm for reusable launch vehicle approach and landing trajectory optimization,” Neurocomputing. 162, 116–127 (2015).CrossRefGoogle Scholar
Betts, J. T., “Survey of numerical methods for trajectory optimization,” J. Guid. Contol Dynam. 21(2), 193–207 (1998).CrossRefGoogle Scholar
Lin, Q., Loxton, R. and Teo, K. L., “The control parameterization method for nonlinear optimal control: a survey,” J. Ind. Manag. Optim. 10(1), 275–309 (2014).Google Scholar
Albert, A., Imsland, L. and Haugen, J., “Numerical optimal control mixing collocation with single shooting: A case study,” IFAC Papersonline. 49(7), 290–295 (2016).CrossRefGoogle Scholar
Drozdova, E., Hopfgarten, S., Lazutkin, E. and Pu, L., “Autonomous driving of a mobile robot using a combined multipleshooting and collocation method,” IFAC Papersonline. 49(15), 193–198 (2016).CrossRefGoogle Scholar
Kelly, M. P., “Transcription Methods for Trajectory Optimization,” Tutorial (Cornell University, Ithaca, NY, 2015).Google Scholar
Fahroo, F. and Ross, M. I., “Direct trajectory optimization by a chebyshev pseudospectral method,” J. Guid. Control Dynam. 25(1), 160–166 (2002).CrossRefGoogle Scholar
Betts, J. T., Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, vol. 19 (SIAM, Philadelphia, PA, 2010).CrossRefGoogle Scholar
Dhaouadi, R. and Hatab, A. A., “Dynamic modelling of differential-drive mobile robots using lagrange and newton-euler methodologies: A unified framework,” Adv. Robot. Autom. 2(2), 1–7 (2013).Google Scholar
Kelly, M. “An introduction to trajectory optimization: how to do your own direct collocation,” SIAM Rev. 59(4), 849–904 (2017).Google Scholar
Herber, D. R., Dynamic System Design Optimization of Wave Energy Converters Utilizing Direct Transcription. M.S. Thesis (University of Illinois at Urbana-Champaign, Urbana, IL, USA, May 2014).Google Scholar
Fahroo, F. and Ross, M. I., “Direct trajectory optimization by a chebyshev pseudospectral method,” Proceedings of the 2000 American Control Conference, ACC (IEEE Cat. No.00CH36334), Chicago, IL, vol. 6, (June 2000) pp. 3860–3864.Google Scholar
Garg, D., Patterson, M., Hager, W. W., Rao, A. V., Benson, D. A. and Huntington, G. T., “A unified framework for the numerical solution of optimal control problems using pseudospectral methods,” Automatica. 46(11), 1843–1851 (2010).CrossRefGoogle Scholar
Gong, Q., Lewis, R. and Ross, M., “Pseudospectral motion planning for autonomous vehicles,” J. Guid. Control Dynam. 32(3), 1039–1045 (2009).CrossRefGoogle Scholar