  The optimal control problem for the kinematic bicycle model is considered
where the trajectories are required to satisfy the safety constraints in the
continuous-time sense. Based on the differential flatness property of the
model, necessary and sufficient conditions in the flat space are provided to
guarantee safety in the state space. The optimal control problem is relaxed to
the problem of solving three second-order cone programs (SOCPs) sequentially,
which find the safe path, the trajectory duration, and the speed profile,
respectively. Solutions of the three SOCPs together provide a sub-optimal
solution to the original optimal control problem. Simulation examples and
comparisons with state-of-the-art optimal control solvers are presented to
demonstrate the effectiveness of the proposed approach.
