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

**Authors:** Zhefan Xu, Kenji Shimada  
**arXiv:** [2309.08544](https://arxiv.org/abs/2309.08544)  
**Date:** 2023-09-15  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2309.08544v1/

## Key points

- Robots in autonomous navigation must generate trajectories for efficient collision avoidance
- Previous solutions lack time efficiency and safety under uncertainties related to perception and control
- The Robust Optimal Time Allocation (ROTA) framework optimizes trajectory progress for improved time efficiency and safety
- ROTA formulates a non-convex optimization problem to minimize trajectory execution time while considering collision probability constraints near obstacles
- Introduces the concept of a "trajectory braking zone" and uses chance-constrained formulation for robust collision avoidance within these zones
- Transforms the optimization problem into a second-order cone programming problem for real-time performance
- Authors Zhefan Xu and Kenji Shimada demonstrated through simulations and physical flight experiments that the approach reduces trajectory execution time while enabling robust collision avoidance

## Summary

In the realm of autonomous navigation, robots must be able to generate trajectories that allow for efficient collision avoidance. Previous research has shown success in creating smooth and spatially collision-free trajectories. However, these solutions often lack time efficiency and safety when considering uncertainties related to robot perception and control. To address this challenge, a new framework known as Robust Optimal Time Allocation (ROTA) has been introduced. This framework focuses on optimizing trajectory progress to improve both time efficiency and safety under uncertain conditions. The ROTA framework formulates a non-convex optimization problem with the goal of minimizing trajectory execution time while also incorporating constraints on collision probability near obstacles. It also introduces the concept of a "trajectory braking zone" and adopts a chance-constrained formulation for robust collision avoidance within these zones. To ensure real-time performance, the non-convex optimization problem is transformed into a second-order cone programming problem. Through simulations and physical flight experiments, authors Zhefan Xu and Kenji Shimada have demonstrated that the proposed approach effectively reduces trajectory execution time while enabling robust collision avoidance in complex environments. Their work addresses key challenges in autonomous navigation and paves the way for more efficient and safer robotic operations in dynamic environments.