A station-time (S-T) graph may be obtained in response to a first reference line representing a path from a first location to a second location associated with an autonomous driving vehicle (ADV). One or more kernels may be applied to the S-T graph. Each of the one or more kernels may indicate a plurality of points on the S-T graph. One or more constraints may be applied to the S-T graph. Each of the one or more constraints may indicate a condition for points in the S-T graph. A set of speeds for portions of the path is determined based on the one or more kernels and the one or more constraints.