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

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.