Hendrikx, J. M., Meijlink, T., and Kriens, R. F. C., 1996, “Application of Optimal Control Theory to Inverse Simulation of Car Handling,” Vehicle System Dynamics, 26(6), pp. 449–461.

[CrossRef]Casanova, D., 2000, “On Minimum Time Vehicle Manoeuvring: The Theoretical Optimal Lap,” Ph.D. thesis, Cranfield University School of Engineering, Bedfordshire, UK.

Kelly, D. P., 2008, “Lap Time Simulation with Transient Vehicle and Tyre Dynamics,” Ph.D. thesis, Cranfield University School of Engineering, Bedfordshire, UK.

Cossalter, V., Lio, M. D., Lot, R., and Fabbri, L., 1999, “A General Method for the Evaluation of Vehicle Manoeuvrability With Special Emphasis on Motorcycles,” Veh. Syst. Dyn., 31(2), pp. 113–135.

[CrossRef]Perantoni, G., and Limebeer, D. J., 2014, “Optimal Control for a Formula One Car With Variable Parameters,” Veh. Syst. Dyn., 52(5), pp. 653–678.

[CrossRef]Timings, J. P., and Cole, D. J., 2013, “Minimum Maneuver Time Calculation Using Convex Optimization,” ASME J. Dyn. Syst., Meas., Control, 135(3), p. 031015.

[CrossRef]Koenderink, J. J., 1990, *Solid Shape* (Artificial Intelligence), MIT, Cambridge, MA.

White, J. H., and Bauer, W. R., 1986, “Calculation of the Twist and the Writhe for Representative Models of DNA,” J. Mol. Bio., 189(2), pp. 329–341.

[CrossRef]Panyukov, S., and Rabin, Y., 2000, “Fluctuating Filaments: Statistical Mechanics of Helices,” Phys. Rev. E, 62(5 Pt B), pp. 7135–46.

[CrossRef]Kessler, D. A., and Rabin, Y., 2003, “Effect of Curvature and Twist on the Conformations of a Fluctuating Ribbon,” J. Chem. Phys., 118(2), pp. 897–904.

[CrossRef]Rappaport, S. M., and Rabin, Y., 2007, “Differential Geometry of Polymer Models: Worm-Like Chains, Ribbons and Fourier Knots,” J. Phys. A: Math. Theor., 40(17), pp. 4455–4466.

[CrossRef]Behringer, R., van Holt, V., and Dickmanns, D., 1992, “Road and Relative Ego-State Recognition,” Proceedings of the Intelligent Vehicles '92 Symposium, Detroit, MI, June 29–July 7, pp. 385–390.

Dickmanns, E., and Mysliwetz, B., 1992, “Recursive 3-D Road and Relative Ego-State Recognition,” IEEE Trans. Patt. Anal. Mach. Intell., 14(2), pp. 199–213.

[CrossRef]Behringer, R., 1995, “Detection of Discontinuities of Road Curvature Change by GLR,” Proceedings of the Intelligent Vehicles '95 Symposium, Detroit, MI, Sept. 25–26, pp. 78–83.

Khosla, D., 2002, “Accurate Estimation of Forward Path Geometry Using Two-Clothoid Road Model,” IEEE Intelligent Vehicle Symposium, Versailles, France, June 17–21, Vol. 1, pp. 154–159.

Loose, H., and Franke, U., 2010. “B-Spline-Based Road Model for 3D Lane Recognition,” 13th International IEEE Conference on Intelligent Transportation Systems (ITSC), Funchal, Madeira Island, Portugal, Sept. 19–22, pp. 91–98.

Cong, S., Shen, S., and Hong, L., 2009, “Road Curvature Estimation System,” U.S. Patent No. 7,626,533.

Shen, T., and Ibrahim, F., 2012, “Interacting Multiple Model Road Curvature Estimation,” 15th International IEEE Conference on Intelligent Transportation Systems (ITSC), Anchorage, AK, Sept. 16–19, pp. 710–715.

Eidehall, A., and Gustafsson, F., 2006 “Obtaining Reference Road Geometry Parameters From Recorded Sensor Data,” IEEE Intelligent Vehicles Symposium, Tokyo, Japan, June 13–15, pp. 256–260.

Mena, J., 2003, “State of the Art on Automatic Road Extraction for GIS Update: A Novel Classification,” Pattern Recognit. Lett., 24(16), pp. 3037–3058.

[CrossRef]Lin, X., Zhang, J., Liu, Z., Shen, J., and Duan, M., 2011, “Semi-Automatic Extraction of Road Networks by Least Squares Interlaced Template Matching in Urban Areas,” Int. J. Remote Sens., 32(17), pp. 4943–4959.

[CrossRef]Willemsen, P., Kearney, J., and Wang, H., 2003, “Ribbon Networks for Modeling Navigable Paths of Autonomous Agents in Virtual Urban Environments,” IEEE Virtual Reality, Los Angeles, CA, Mar. 22–26, pp. 79–86.

Kreyszig, E., 1991, *Differential Geometry*, Dover Publications, New York.

Struik, D. J., 1988, *Lectures on Classical Differential Geometry*, 2nd ed., Dover, New York.

Gear, C. W., 1971, *Numerical Initial Value Problems in Ordinary Differential Equations* (Prentice-Hall Series in Automatic Computation), Prentice-Hall, Englewood Cliffs, NJ.

Brenan, K. E., Campbell, S. L., and Petzold, L. R., 1996, *Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations* (SIAM's Classics in Applied Mathematics), SIAM, Philadelphia, PA.

Griffiths, D., and Higham, D., 2010, *Numerical Methods for Ordinary Differential Equations: Initial Value Problems*, Springer, New York.

Betts, J. T., 2001, *Practical Methods for Optimal Control and Estimation Using Nonlinear Programming*, 2nd ed., SIAM, Philadelphia, PA.

Darby, C. L., Hager, W. W., and Rao, A. V., 2011, “An Hp-Adaptive Pseudospectral Method for Solving Optimal Control Problems,” Optim. Control Appl. Methods, 32(4), pp. 476–502.

[CrossRef]Limebeer, D. J. N., and Perantoni, G., 2013, “Optimal Control of a Formula One Car on a Three-Dimensional Track Part 2: Optimal Control,” ASME J. Dyn. Syst., Meas., Control,(submitted).

Patterson, M. A., and Rao, A. V., 2013, “GPOPS—II: A Matlab Software for Solving Multiple-Phase Optimal Control Problems Using Hp-Adaptive Gaussian Quadrature Collocation Methods and Sparse Nonlinear Programming,” ACM Trans. Math. Soft., 39(3), 41 pages.

Patterson, M. A., and Rao, A. V., 2011, “Exploiting Sparsity in Direct Collocation Pseudospectral Methods for Solving Optimal Control Problems,” J. Spacecr. Rockets, 49(2), pp. 364–377.

Lawrence, J. D., 1972, *A Catalog of Special Plane Curves*, Dover Publications, New York.