Optimal trajectory planning for trains under a moving block signaling system

The optimal trajectory planning problem for trains under a moving block signaling system is considered. This optimal trajectory planning problem is significant for punctuality, energy consumption, passenger comfort, etc. In a moving block signaling system, the minimum distance between two successive trains is the instantaneous braking distance required by the following train plus a safety margin. The constraints caused by the moving block signaling system are described as nonlinear inequalities, which can be transformed into linear inequalities using piecewise affine approximations. The optimal trajectory planning problem is subsequently recast as a mixed integer linear programming problem, which can be solved efficiently by existing solvers. A case study is used to demonstrate the performance of the proposed approach.