Abstract
This paper presents a path planning algorithm that can efficiently check for interference with potential obstacles while piecewise continuously computing the required space of moving car-like vehicles using cubic Bezier curves. Our collision-checking algorithm uses trajectories generated from a vehicle’s front outer corner and rear inner axle, as well as partially overlapped rectangles. These outer and inner trajectories are computed from the trajectory generated by the center of the rear axle of the vehicle, which considers the dimensions of the vehicle, and the tangential and normal vectors of the trajectory. To validate the continuity and efficacy of our collision-checking algorithm, the collision-checking algorithm is applied to a spline-based RRT∗, where the kinematics (or minimum turning radius) of car-like vehicles is satisfied using cubic Bezier curves. We show the benefits of our method through simulations and experimental results by using an autonomous ground vehicle.
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Likhachev, M., Ferguson, D.: Planning long dynamically feasible maneuvers for autonomous vehicles. Int. J. Robot. Res. 28(8), 933–945 (2009)
Dolgov, D., Thrun, S., Montemerlo, M., Diebel, J.: Path planning for autonomous vehicles in unknown semi-structured environments. Int. J. Robot. Res. 29(5), 485–501 (2010)
Yoon, S., Yoon, S. E., Lee, U., Shim, D.H.: Recursive path planning using reduced states for car-like vehicles on grid maps. IEEE Trans. Intell. Transp. Syst. 16(5), 2797–2813 (2015)
Koenig, S., Likhachev, M., Furcy, D.: Lifelong planning A∗. Artif. Intell. 155, 93–146 (2004)
Yoon, S., Shim, D.H.: SLPA,∗: Shape-aware lifelong planning A∗ for differential wheeled vehicles. IEEE Trans. Intell. Transp. Syst. 16(2), 730–740 (2015)
Svestka, P., Overmars, M.H.: Coordinated motion planning for multiple car-like robots using probabilistic roadmaps. In: ICRA, pp 1631–1636 (1995)
LaValle, S. M., James, J., Kuffner, J.: Randomized kinodynamic planning. Int. J. Robot. Res. 20(5), 378–400 (2001)
Kuwata, Y., Teo, J., Fiore, G., Karaman, S., Frazzoli, E., How, J.P.: Real-time motion planning with applications to autonomous urban driving. IEEE Trans. Control Syst. Technol. 17(5), 1105–1118 (2009)
Goretkin, G., Perez, A., Platt, R, Konidaris, G.: Optimal sampling-based planning for linear-quadratic kinodynamic systems. In: ICRA, pp. 2429–2436 (2013)
Karaman, S., Frazzoli, E.: Optimal kinodynamic motion planning using incremental sampling-based methods. In: IEEE Conference on Decision and Control, pp. 7681–7687 (2010)
Yang, K., Moon, S., Yoo, S., Kang, J., Doh, N. L., Kim, H. B., Joo, S.: Spline-based RRT path planner for non-holonomic robots. J. Intell Robot Syst. 1–20 (2013)
Yang, K., Gan, S. K., Huh, J., Joo, S.: Optimal spline-based RRT path planning using probabilistic map. In: International Conference on Control, Automation and Systems (ICCAS), pp. 643–646 (2014)
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)
Connors, J., Elkaim, G.: Analysis of a spline based, obstacle avoiding path planning algorithm. In: IEEE Vehicular Technology Conference, pp. 2565–2569 (2007)
Perez, A., Platt, R, Konidaris, G., Kaelbling, L., Lozano-Perez, T.: LQR-RRT∗: Optimal sampling-based motion planning with automatically derived extension heuristics. In: ICRA, pp. 2537–2542 (2012)
Webb, D. J., van den Berg, J.: Kinodynamic RRT∗: Asymptotically optimal motion planning for robots with linear dynamics. In: ICRA, pp. 5054–5061 (2013)
Palmieri, L., Arras, K.O.: A novel RRT extend function for efficient and smooth mobile robot motion planning. In: IROS, pp. 205–211 (2014)
Yershova, A., Jaillet, L., Siméon, T., LaValle, S.M.: Dynamic-domain RRTs: Efficient exploration by controlling the sampling domain. In: ICRA, pp. 3856–3861 (2005)
Lee, J., Kwon, O., Zhang, L., Yoon, S.E.: A selective retraction-based RRT planner for various environments. IEEE Trans. Robot. 30(4), 1002–1011 (2014)
Pruski, A., Rohmer, S.: Robust path planning for non-holonomic robots. J. Intell. Robot. Syst. 18(4), 329–350 (1997)
Varadhan, G., Sriram, S. K. T. V. N., Manocha, D.: A simple algorithm for complete motion planning of translating polyhedral robots. Int. J. Robot. Res. 24(11), 983–995 (2005)
Wise, K. D., Bowyer, A.: A survey of global configuration-space mapping techniques for a single robot in a static environment. Int. J. Robot. Res. 19(8), 762–779 (2000)
Minguez, J., Montano, L.: Extending collision avoidance methods to consider the vehicle shape, kinematics, and dynamics of a mobile robot. IEEE Trans. Robot. 25(2), 367–381 (2009)
Yang, K., Sukkarieh, S.: An analytical continuous-curvature path-smoothing algorithm. IEEE Trans. Robot. 26(3), 561–568 (2010)
Bicchi, A., Casalino, G., Santilli, C.: Planning shortest bounded-curvature paths for a class of nonholonomic vehicles among obstacles. J. Intell. Robot. Syst. 16, 387–405 (1996)
Geraerts, R., Overmars, M.H.: The corridor map method: a general framework for real-time high-quality path planning. Comput. Anim. Virt. Worlds 18, 107–119 (2007)
Maekawa, T., Noda, T., Tamura, S., Ozaki, T., Ichiro Machida, K.: Curvature continuous path generation for autonomous vehicle using B-spline curves. Comput. Aided Des. 42, 350–359 (2010)
Gómez-Bravo, F., Cuesta, F., Ollero, A.: Parallel and diagonal parking in nonholonomic autonomous vehicles. Eng. Appl. Artif. Intel. 14(4), 419–434 (2001)
Jazar, R.N.: Vehicle Dynamics: Theory and Applications. Springer (2008)
Luca, A. D., Oriolo, G., Samson, C., Laumond, J.P.: Feedback control of a nonholonomic car-like robot. In:Robot motion planning and control, pp. 171–253. Springer (1998)
Anand, V.B.: Computer Graphics and Geometric Modeling for Engineers, 1st edn. Wiley (1993)
Zill, D. G., Cullen, M.R.: Advanced Engineering Mathematics PWS. Publishing Company (1992)
Karaman, S., Frazzoli, E.: Sampling-based algorithms for optimal motion planning. Int. J. Robot. Res. 30 (7), 846–894 (2011)
Karaman, S., Frazzoli, E.: Sampling-based optimal motion planning for non-holonomic dynamical systems. In: ICRA, pp. 5041–5047 (2013)
Lee, U., Jung, J., Shin, S., Jeong, Y., Park, K., Shim, D. H., So Kwon, I.: EureCar turbo: A self-driving car that can handle adverse weather conditions. In: The International Conference of Intelligent Robots and Systems (IROS), pp. 2301–2306 (2016)
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Yoon, S., Lee, D., Jung, J. et al. Spline-based RRT∗ Using Piecewise Continuous Collision-checking Algorithm for Car-like Vehicles. J Intell Robot Syst 90, 537–549 (2018). https://doi.org/10.1007/s10846-017-0693-4
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DOI: https://doi.org/10.1007/s10846-017-0693-4