  Safety-guaranteed motion planning is critical for self-driving cars to
generate collision-free trajectories. A layered motion planning approach with
decoupled path and speed planning is widely used for this purpose. This
approach is prone to be suboptimal in the presence of dynamic obstacles.
Spatial-temporal approaches deal with path planning and speed planning
simultaneously; however, the existing methods only support simple-shaped
corridors like cuboids, which restrict the search space for optimization in
complex scenarios. We propose to use trapezoidal prism-shaped corridors for
optimization, which significantly enlarges the solution space compared to the
existing cuboidal corridors-based method. Finally, a piecewise B\'{e}zier curve
optimization is conducted in our proposed corridors. This formulation
theoretically guarantees the safety of the continuous-time trajectory. We
validate the efficiency and effectiveness of the proposed approach in numerical
and CommonRoad simulations.
