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G2 Continuity Smooth Path Planning using Cubic Polynomial Interpolation with Membership Function
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 Title & Authors
G2 Continuity Smooth Path Planning using Cubic Polynomial Interpolation with Membership Function
Chang, Seong-Ryong; Huh, Uk-Youl;
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Path planning algorithms are used to allow mobile robots to avoid obstacles and find ways from a start point to a target point. The general path planning algorithm focused on constructing of collision free path. However, a high continuous path can make smooth and efficiently movements. To improve the continuity of the path, the searched waypoints are connected by the proposed polynomial interpolation. The existing polynomial interpolation methods connect two points. In this paper, point groups are created with three points. The point groups have each polynomial. Polynomials are made by matching the differential values and simple matrix calculation. Membership functions are used to distribute the weight of each polynomial at overlapped sections. As a result, the path has continuity. In addition, the proposed method can analyze path numerically to obtain curvature and heading angle. Moreover, it does not require complex calculation and databases to save the created path.
Continuous-curvature path;Geometric continuity;Interpolation;Path planning;Cubic polynomial;Mobile robot;Robot motion;Smooth path;Spline interpolation;Vehicles navigation;
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Discrete-Time Circular Walking Pattern for Biped Robots, Journal of Electrical Engineering and Technology, 2016, 11, 5, 1395  crossref(new windwow)
Y. K. Hwang and N. Ahuja, “A potential field approach to path planning,” Robotics and Automation, IEEE Transactions on, vol. 8, pp. 23-32, 1992. crossref(new window)

S. S. Ge and Y. J. Cui, “New potential functions for mobile robot path planning,” Robotics and Automation, IEEE Transactions on, vol. 16, pp. 615-620, 2000. crossref(new window)

Y. Wang and G. S. Chirikjian, “A new potential field method for robot path planning,” in Robotics and Automation, 2000. Proceedings. ICRA'00. IEEE International Conference on, 2000, pp. 977-982.

P. E. Hart, N. J. Nilsson, and B. Raphael, “A formal basis for the heuristic determination of minimum cost paths,” Systems Science and Cybernetics, IEEE Transactions on, vol. 4, pp. 100-107, 1968. crossref(new window)

A. Stentz, “The focussed D* algorithm for real-time replanning,” in International Joint Conference on Artificial Intelligence, 1995, pp. 1652-1659.

S. Koenig and M. Likhachev, “D* Lite,” in Proceedings of the national conference on artificial intelligence, 2002, pp. 476-483.

J. J. Kuffner Jr and S. M. LaValle, “RRT-connect: An efficient approach to single-query path planning,” in Robotics and Automation, 2000. Proceedings. ICRA'00. IEEE International Conference on, 2000, pp. 995-1001.

S. M. LaValle, Planning algorithms: Cambridge university press, 2006.

G. E. Farin, Curves and surfaces for CAGD [electronic resource]: a practical guide: Morgan Kaufmann, 2002.

B. A. Barsky and A. D. DeRose, “Geometric continuity of parametric curves,” 1984.

Y. Kanayama and B. I. Hartman, “Smooth local path planning for autonomous vehicles,” in Robotics and Automation, 1989. Proceedings., 1989 IEEE International Conference on, 1989, pp. 1265-1270.

T. Fraichard and J.-M. Ahuactzin, “Smooth path planning for cars,” in Robotics and Automation, 2001. Proceedings 2001 ICRA. IEEE International Conference on, 2001, pp. 3722-3727.

F. Lamiraux and J.-P. Lammond, “Smooth motion planning for car-like vehicles,” Robotics and Automation, IEEE Transactions on, vol. 17, pp. 498-501, 2001. crossref(new window)

T. Kito, J. Ota, R. Katsuki, T. Mizuta, T. Arai, T. Ueyama, et al., “Smooth path planning by using visibility graph-like method,” in Robotics and Automation, 2003. Proceedings. ICRA'03. IEEE International Conference on, 2003, pp. 3770-3775.

K. Yang and S. Sukkarieh, “An analytical continuous-curvature path-smoothing algorithm,” Robotics, IEEE Transactions on, vol. 26, pp. 561-568, 2010. crossref(new window)

J. Villagra, V. Milanés, J. Pérez, and J. Godoy, “Smooth path and speed planning for an automated public transport vehicle,” Robotics and Autonomous Systems, vol. 60, pp. 252-265, 2012. crossref(new window)

N. A. Melchior and R. Simmons, “Particle RRT for path planning with uncertainty,” in Robotics and Automation, 2007 IEEE International Conference on, 2007, pp. 1617-1624.

H. Choset, K. M. Lynch, S. Hutchinson, G. Kantor, W. Burgard, L. E. Kavraki, et al., Principles of robot motion: theory, algorithms, and implementations: MIT press, 2005.

J. Stoer, R. Bulirsch, R. Bartels, W. Gautschi, and C. Witzgall, Introduction to numerical analysis vol. 2: Springer New York, 1993.

A. Gilat and V. Subramaniam, Numerical methods for engineers and scientists: Wiley, 2007.

J. F. Epperson, “On the Runge example,” Amer. Math. Monthly, vol. 94, pp. 329-341, 1987. crossref(new window)

A. Piazzi, C. Lo Bianco, M. Bertozzi, A. Fascioli, and A. Broggi, “Quintic G2-splines for the iterative steering of vision-based autonomous vehicles,” Intelligent Transportation Systems, IEEE Transactions on, vol. 3, pp. 27-36, 2002. crossref(new window)

A. Piazzi, C. Guarino Lo Bianco, and M. Romano, “η3 Splines for the Smooth Path Generation of Wheeled Mobile Robots,” IEEE TRANSACTIONS ON ROBOTICS, vol. 23, pp. 1089-1095, 2007. crossref(new window)

A. Piazzi, C. G. L. Bianco, and M. Romano, “Smooth path generation for wheeled mobile robots using η3-splines,” Motion Control, pp. 75-96, 2010.

A. Piazzi, M. Romano, and C. G. L. Bianco, “G3-splines for the path planning of wheeled mobile robots,” in European Control Conference, 2003.

K. Yang, D. Jung, and S. Sukkarieh, “Continuous curvature path-smoothing algorithm using cubic B zier spiral curves for non-holonomic robots,” Advanced Robotics, vol. 27, pp. 247-258, 2013. crossref(new window)