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Time-optimal cornering trajectory planning for car-like mobile robots containing actuator dynamics

Published online by Cambridge University Press:  12 November 2021

Yong Jin Byeon Open the ORCID record for Yong Jin Byeon [Opens in a new window]  and
Byung Kook Kim
Yong Jin Byeon
Affiliation:
School of Electrical Engineering, Korea Advanced Institute of Science and Technology(KAIST), Daejeon, Korea
Byung Kook Kim*
Affiliation:
School of Electrical Engineering, Korea Advanced Institute of Science and Technology(KAIST), Daejeon, Korea
*
*Corresponding author. E-mails: daybreakey@kaist.ac.kr, bkkim@kaist.ac.kr
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Abstract

We establish a highly feasible algorithm for time-optimal cornering trajectory planning (TP) for car-like mobile robots (CLMRs) based on a dynamic model that contains actuator dynamics. First, we formulate an accurate dynamic model of a robot that contains DC motor actuators; this includes steering braking (caused by the lateral force of the front steering wheel) and two types of friction (viscous and Coulomb) under a nonslip condition. Our TP algorithm can utilize the full power of the DC motor actuators within proper pulse width modulation bounds and generated torque limits. Then, we establish an algorithm for a time-optimal cornering trajectory planning for CLMRs (TOCTP-CLMR). Our algorithm divides the trajectory into five sections comprising three turnings and two translations to minimize the travel distance. Then, we utilize the quickest rotation when turning to construct the time-optimal trajectory that satisfies the bang-bang principle. In addition, simulations are performed to demonstrate the validity of this method. Finally, we conduct open-loop experiments to validate our dynamic model and a trajectory tracking experiment to demonstrate the feasibility of the TOCTP-CLMR trajectory.

Keywords

time-optimal trajectory planningcar-like mobile robot dynamicsDC motor actuator dynamicstorque constraintPWM constraint
Type
Research Article
Information
Robotica , Volume 40 , Issue 5 , May 2022 , pp. 1627 - 1649
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Huang, X. and Wang, J., “Lightweight vehicle control-oriented modeling and payload parameter Sensitivity Analysis,” IEEE Trans. Veh. Technol. 60(5), 1999–2011 (2011).CrossRefGoogle Scholar
Di Cairano, S., Tseng, H. E., Bernardini, D. and Bemporad, A., “Vehicle yaw stability control by coordinated active front steering and differential braking in the tire sideslip angles domain,” IEEE Trans. Control Syst. Technol. 21(4), 1236–1248 (2013).CrossRefGoogle Scholar
Rucco, A., Hauser, J. and Notarstefano, G., “Optimal control of steer-braking systems: Non-existence of minimizing trajectories,” Optim. Control Appl. Methods 37(5), 965–979 (2016).CrossRefGoogle Scholar
Siegwart, R. and Nourbakh, I. R., Introduction to Autonomous Mobile Robot (MIT Press, Cambridge, MA, 2004).Google Scholar
Choset, H., Lynch, K. M., Hutchinson, S., Kantor, G., Burgard, W., Kavraki, L. E. and S. Thrun et al. , Principle of Robot Motion: Theory Algorithms and Implementations (MIT Press, Cambridge, MA, 2005).Google Scholar
Gillespie, T. D., Fundamentals of Vehicle Dynamics (Society of Automotive Engineers, Warrendale, PA, 1992).CrossRefGoogle Scholar
Edquist, J., Rudin-Brown, C. M. and Lenné, M. G., “The effects of on-street parking and road environment visual complexity on travel speed and reaction time,” Accid. Anal. Prev. 45, 759–765 (2012). https://doi.org/10.1016/j.aap.2011.10.001.CrossRefGoogle ScholarPubMed
Lee, M. H. and T.-H. S. Li, “Kinematics, dynamics and control design of 4WIS4WID mobile robots,” J. Eng. 2015(1), 6–16 (2015).CrossRefGoogle Scholar
Yeh, Y.-C., Li, T.-H. S. and Chen, C.-Y., “Adaptive fuzzy sliding-mode control of dynamic model based car-like mobile robot,” Int. J. Fuzzy Syst. 11(4), 272–286 (2009).Google Scholar
Hwang, C., “Comparison of path tracking control of a car-like mobile robot with and without motor dynamics,” IEEE/ASME Trans. Mechatron. 21(4), 1801–1811 (2016).CrossRefGoogle Scholar
Zhou, S., Liu, Z., Suo, C., Wang, H., Zhao, H. and Liu, Y., “Vision-based Dynamic Control of Car-like Mobile Robots,” International Conference on Robotics and Automation (ICRA) (2019) pp. 6631–6636.Google Scholar
Choi, J. S. and Kim, B. K., “Near-time-optimal trajectory planning for wheeled mobile robots with translational and rotational sections,” IEEE Trans. Rob. Autom. 17(1), 85–90 (2001).CrossRefGoogle Scholar
Dubins, L. E., “On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents,” Am. J. Math. 79(3), 497–516 (1957).CrossRefGoogle Scholar
Reeds, J. A. and Sheep, L. A., “Optimal paths for a car that goes both forwards and backwards,” Pac. J. Math. 145(2), 367–393 (1990).CrossRefGoogle Scholar
Laumond, J.-P., Jacobs, P. E., Taix, M. and Murray, R. M., “A motion planner for nonholonomic mobile robots,” IEEE Trans. Rob. Autom. 10(5), 577–593 (1994).CrossRefGoogle Scholar
Ravankar, A., Ravankar, A. A., Kobayashi, Y. and Emaru, T., “Path Smoothing Extension for Various Robot Path Planners,” International Conference on Control, Automation and Systems (ICCAS) (2016) pp. 263–268.Google Scholar
Valero, F., Rubio, F. and Llopis-Albert, C., “Assessment of the effect of energy consumption on trajectory improvement for a car-like robot,” Robotica 37(11), 1998–2009 (2019).CrossRefGoogle Scholar
Hu, Y., Li, D., He, Y. and Han, J., “Path planning of UGV based on Bézier curves,” Robotica 37(6), 969–997 (2019).CrossRefGoogle Scholar
Bakdi, A., Hentout, A., Boutami, H., Maoudj, A., Hachour, O. and Bouzouia, B., “Optimal path planning and execution for mobile robots using genetic algorithm and adaptive fuzzy-logic control,” Rob. Auton. Syst. 89, 95–109 (2017). https://doi.org/10.1016/j.robot.2016.12.008.CrossRefGoogle Scholar
Sung, I., Choi, B. and Nielsen, P., “On the training of a neural network for online path planning with offline path planning algorithms,” Int. J. Inf. Manage. 57, 102142–102150 (2019). https://doi.org/10.1016/j.ijinfomgt.2020.102142.CrossRefGoogle Scholar
Song, P., Pan, J. and Chu, S.-C., “A parallel compact cuckoo search algorithm for three-dimensional path planning,” Appl. Soft Comput. 94, 106443–106459 (2020).CrossRefGoogle Scholar
Wang, J. and Meng, M. Q.-H., “Optimal path planning using generalized voronoi graph and multiple potential functions,” IEEE Trans. Ind. Electron. 67(12), 10621–10630 (2020).CrossRefGoogle Scholar
Verscheure, D., Demeulenaere, B., Swevers, J., Schutter, J. D. and Diehl, M., “Time-optimal path tracking for robots: A convex optimization approach,” IEEE Trans. Autom. Control 44(10), 2318–2327 (2009).CrossRefGoogle Scholar
Lipp, T. and Boyd, S., “Minimum-time speed optimization over a fixed path,” Int. J. Control 87(6), 1297–1311 (2014).CrossRefGoogle Scholar
Luo, X., Li, S., Liu, S. and Liu, G., “An optimal trajectory planning method for path tracking of industrial robots,” Robotica 37(3), 502–520 (2019).CrossRefGoogle Scholar
Walambe, R., Agarwal, N., Kale, S. and Joshi, V., “Optimal trajectory generation for car-type mobile robot using spline interpolation,” IFAC-PapersOnLine 49(1), 601–606 (2016).CrossRefGoogle Scholar
Kim, J., “Trajectory generation of a two-wheeled mobile robot in an uncertain environment,” IEEE Trans. Ind. Electron. 67(7), 5586–5594 (2020).CrossRefGoogle Scholar
Haddad, M., Khalil, W. and Lehtihet, H. E., “Trajectory planning of unicycle mobile robots with a trapezoidal-velocity constraint,” IEEE Trans. Rob. 26(5), 954–962 (2010).CrossRefGoogle Scholar
LaValle, S. M., “Rapidly-exploring random trees: A new toll for path planning, TR 98-11 Computer Science Department,” Iowa State University (1998).Google Scholar
Ghosh, D., Nandakumar, G., Narayanan, K., Honkote, V. and Sharma, S., “Kinematic Constraints Based Bi-directional RRT (KB-RRT) with Parameterized Trajectories for Robot Path Planning in Cluttered Environment,” International Conference on Robotics and Automation (ICRA) (2019) pp. 8627–8633.Google Scholar
Balkcom, D. J. and Mason, M. T., “Time optimal trajectories for bounded velocity differential drive vehicles,” Int. J. Rob. Res. 21(3), 199–217 (2002).CrossRefGoogle Scholar
Red, E., “A dynamic optimal trajectory generator for cartesian path following,” Robotica 18(5), 451–458 (2000).CrossRefGoogle Scholar
Sathiya, V. and Chinnadurai, M., “Evolutionary algorithms-based multi-objective optimal mobile robot trajectory planning,” Robotica 37(8), 1363–1382 (2019).CrossRefGoogle Scholar
Penin, B., Giordano, P. R. and Chaumette, F., “Minimum-time trajectory planning under intermittent measurements,” IEEE Rob. Autom. Lett. 4(1), 153–160 (2019).CrossRefGoogle Scholar
Xue, X., Li, Z., Zhang, D. and Yan, Y., “A Deep Reinforcement Learning Method for Mobile Robot Collision Avoidance based on Double DQN,” IEEE 28th International Symposium on Industrial Electronics (ISIE) (2019) pp. 2131–2136.Google Scholar
Zhang, F., Xia, R. and Chen, X., “An optimal trajectory planning algorithm for autonomous trucks: architecture, algorithm, and experiment,” J. Field Rob. 17(2), 1–11 (2020).Google Scholar
Shen, P., Zhang, X., Fang, Y. and Yuan, M., “Real-time acceleration-continuous path-constrained trajectory planning with built-in tradeoff between cruise and time-optimal motions,” IEEE Trans. Autom. Sci. Eng. 17(4), 1911–1924 (2020).CrossRefGoogle Scholar
Okuyama, I. F., Maximo, M. R. O. A. and Afonso, R. J. M., “Minimum-time trajectory planning for a differential drive mobile robot considering non-slipping constraints,” J. Control, Autom. Electr. Syst. 32, 120–131 (2021). https://doi.org/10.1007/s40313-020-00657-x.CrossRefGoogle Scholar
Kim, Y. J. and Kim, B. K., “Time-optimal trajectory planning based on dynamics for differential-wheeled mobile robots with a geometric corridor,” IEEE Trans. Ind. Electron. 64(7), 5502–5512 (2017).CrossRefGoogle Scholar
Kim, J. and Kim, B. K., “Cornering trajectory planning avoiding slip for differential-wheeled mobile robots,” IEEE Trans. Ind. Electron. 64(4), 6698–6708 (2020).CrossRefGoogle Scholar
Armstrong-Hélouvry, B., Dupont, P. and de Wit, C. C., “A survey of models analysis tools and compensation methods for the control of machines with friction,” Automatica 30(7), 1083–1138 (1994).CrossRefGoogle Scholar
Bryson, A. E. and Ho, Y.-C., Applied Optimal Control, (Waltham:Ginn, London:Blaisdell, 1969).Google Scholar
Wong, J. Y., Theory of Ground Vehicles, 4th ed. (John Wiley & Sons, New York, 2008).Google Scholar
Wade Allen, R., Rosenthal, T. J., Klyde, D. H. and Chrstos, J. P., “Vehicle and tire modeling for dynamic analysis and real-time simulation,” SAE Trans. 109(6), 2020–2042 (2000).Google Scholar
Heidfeld, H., Schünemann, M. and Kasper, R., “UKF-based state and tire slip estimation for a 4WD electric vehicle,” Veh. Syst. Dyn. 58(10), 1479–1496 (2020).CrossRefGoogle Scholar
Reina, G., Ishigami, G., Nagatani, K. and Yoshida, K., “Vision-based Estimation of Slip Angle for Mobile Robots and Planetary Rovers,” IEEE International Conference on Robotics and Automation (2008) pp. 486–491.Google Scholar
Reina, G., Leanza, A. and Mantriota, G., “Model-based observers for vehicle dynamics and tyre force prediction,” Int. J. Veh. Mech. Mobility, 1–26 (2021). https://doi.org/10.1080/00423114.2021.1928245.CrossRefGoogle Scholar