A survey on optimal trajectory planning for train operations

Because of the rising energy prices and environmental concerns, the calculation of energy-optimal reference trajectories for trains is significant for energy saving. On the other hand, with the development automatic train operation (ATO), the optimal trajectory planning is significant to the performance of train operation. In this paper, we present an integrated survey of this field. First, a nonlinear continuous-time train model and a continuous-space model of train operations are described, after which the optimal trajectory planning problem is formulated based on these two models. The various approaches in the literature to calculate the reference trajectory are reviewed and categorized into two groups: analytical solutions and numerical optimization. Finally, a short discussion of some open topics in the field of optimal trajectory planning for train operations are given.

[1]  Hirokazu Ihara,et al.  FUZZY CONTROL FOR AUTOMATIC TRAIN OPERATION SYSTEM , 1984 .

[2]  M. Meyer,et al.  An algorithm for the optimal control of the driving of trains , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[3]  Peter Terwiesch,et al.  Optimal Control of the Driving of Trains (Optimale Steuerung der Fahrweise von Zügen) , 2002 .

[4]  Hyun Jun Park,et al.  An optimal automatic train operation (ATO) control using genetic algorithms (GA) , 1999, Proceedings of IEEE. IEEE Region 10 Conference. TENCON 99. 'Multimedia Technology for Asia-Pacific Information Infrastructure' (Cat. No.99CH37030).

[5]  Ted K. Ralphs,et al.  Noncommercial Software for Mixed-Integer Linear Programming , 2005 .

[6]  Clive Roberts,et al.  Optimal driving strategy for traction energy saving on DC suburban railways , 2007 .

[7]  C. S. Chang,et al.  Differential evolution based tuning of fuzzy automatic train operation for mass rapid transit system , 2000 .

[8]  Eugene Khmelnitsky,et al.  On an optimal control problem of train operation , 2000, IEEE Trans. Autom. Control..

[9]  P. Howlett.  A Restricted Variation Argument to Derive Necessary Conditions for the Optimal Control of a Train , 2000 .

[10]  A. E. Vardy,et al.  Estimation of train resistance coefficients in tunnels from measurements during routine operation , 1999 .

[11]  Phil Howlett,et al.  The Optimal Control of a Train , 2000, Ann. Oper. Res..

[12]  Felix Schmid,et al.  A review of methods to measure and calculate train resistances , 2000 .

[13]  Phil Howlett,et al.  Optimal driving strategies for a train journey with speed limits , 1994 .

[14]  Phil Howlett,et al.  Application of critical velocities to the minimisation of fuel consumption in the control of trains , 1992, Autom..

[15]  K. Ichikawa.  Application of Optimization Theory for Bounded State Variable Problems to the Operation of Train , 1968 .

[16]  Martin W. P. Savelsbergh,et al.  Integer-Programming Software Systems , 2005, Ann. Oper. Res..

[17]  Masafumi Miyatake,et al.  Application of dynamic programming to the optimization of the running profile of a train , 2004 .

[18]  Iakov M. Golovitcher.  Energy efficient control of rail vehicles , 2001, 2001 IEEE International Conference on Systems, Man and Cybernetics. e-Systems and e-Man for Cybernetics in Cyberspace (Cat.No.01CH37236).

[19]  Rongfang Rachel Liu,et al.  Energy-efficient operation of rail vehicles , 2003 .

[20]  S. A. Lechelle,et al.  OptiDrive: A practical approach for the calculation of energy-optimised operating speed profiles , 2010 .

[21]  P. Howlett.  An optimal strategy for the control of a train , 1990, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[22]  Rudiger Franke,et al.  Optimal control of the driving of trains , 2002 .

[23]  Mato Baotic,et al.  Optimal rail route energy management under constraints and fixed arrival time , 2009, 2009 European Control Conference (ECC).

[24]  Chung-Fu Chang,et al.  Optimising train movements through coast control using genetic algorithms , 1997 .

[25]  Mehmet Turan Soylemez,et al.  Coasting point optimisation for mass rail transit lines using artificial neural networks and genetic algorithms , 2008 .

[26]  Thomas Schank,et al.  A Fast Algorithm for Computing the Running-Time of Trains by Infinitesimal Calculus , 2011 .

[27]  Phil Howlett,et al.  Energy-efficient train control , 1994 .

[28]  Anil V. Rao,et al.  Algorithm 902: GPOPS, A MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method , 2010, TOMS.

[29]  Masafumi Miyatake,et al.  Optimization of Train Speed Profile for Minimum Energy Consumption , 2010 .

[30]  Phil Howlett,et al.  Optimal driving strategies for a train on a track with continuously varying gradient , 1997, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.