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Autonomous navigation requires robots to generate trajectories for collisionavoidance efficiently. Although plenty of previous works have proven successfulin generating smooth and spatially collision-free trajectories, their solutionsoften 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 ofthe trajectories temporally, serving as a post-processing tool to enhancetrajectory time efficiency and safety under uncertainties. In this study, webegin by formulating a non-convex optimization problem aimed at minimizingtrajectory execution time while incorporating constraints on collisionprobability as the robot approaches obstacles. Subsequently, we introduce theconcept of the trajectory braking zone and adopt the chance-constrainedformulation for robust collision avoidance in the braking zones. Finally, thenon-convex optimization problem is reformulated into a second-order coneprogramming problem to achieve real-time performance. Through simulations andphysical flight experiments, we demonstrate that the proposed approacheffectively reduces trajectory execution time while enabling robust collisionavoidance in complex environments.

Quadcopter Trajectory Time Minimization and Robust Collision Avoidance via Optimal Time Allocation