  Autonomous navigation requires robots to generate trajectories for collision
avoidance efficiently. Although plenty of previous works have proven successful
in generating smooth and spatially collision-free trajectories, their solutions
often suffer from suboptimal time efficiency and potential unsafety,
particularly when accounting for uncertainties in robot perception and control.
To address this issue, this paper presents the Robust Optimal Time Allocation
(ROTA) framework. This framework is designed to optimize the time progress of
the trajectories temporally, serving as a post-processing tool to enhance
trajectory time efficiency and safety under uncertainties. In this study, we
begin by formulating a non-convex optimization problem aimed at minimizing
trajectory execution time while incorporating constraints on collision
probability as the robot approaches obstacles. Subsequently, we introduce the
concept of the trajectory braking zone and adopt the chance-constrained
formulation for robust collision avoidance in the braking zones. Finally, the
non-convex optimization problem is reformulated into a second-order cone
programming problem to achieve real-time performance. Through simulations and
physical flight experiments, we demonstrate that the proposed approach
effectively reduces trajectory execution time while enabling robust collision
avoidance in complex environments.
