Safe Interval Motion Planning for Quadrotors in Dynamic Environments

2024-09-16

arXiv.org

AI Summary

To address the spatiotemporal non-convexity and real-time requirements in quadrotor trajectory planning under dynamic environments, this paper proposes a two-stage framework based on *safe time intervals*. The front-end constructs a dynamically connected visibility graph to ensure topological completeness, while the back-end parameterizes trajectories within spatiotemporal corridors using B-splines and refines them via gradient-based optimization to achieve smooth, dynamically feasible, and near-optimal motion plans. Key innovations include the first formal modeling of *safe time intervals* and the *Uniform Time-Visibility Deformation (UTVD)* algorithm, which rigorously preserves spatiotemporal topological equivalence—thereby guaranteeing planning completeness, optimality, and global convergence. Extensive simulations and real-world flight experiments demonstrate >95% task success rate across multi-density dynamic obstacle scenarios, significantly outperforming state-of-the-art methods and validating practical deployability.

Technology Category

• Planning, Routing, and Scheduling: Temporal Planning
• Intelligent Robots: Motion and Path Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Trajectory generation in dynamic environments presents a significant challenge for quadrotors, particularly due to the non-convexity in the spatial-temporal domain. Many existing methods either assume simplified static environments or struggle to produce optimal solutions in real-time. In this work, we propose an efficient safe interval motion planning framework for navigation in dynamic environments. A safe interval refers to a time window during which a specific configuration is safe. Our approach addresses trajectory generation through a two-stage process: a front-end graph search step followed by a back-end gradient-based optimization. We ensure completeness and optimality by constructing a dynamic connected visibility graph and incorporating low-order dynamic bounds within safe intervals and temporal corridors. To avoid local minima, we propose a Uniform Temporal Visibility Deformation (UTVD) for the complete evaluation of spatial-temporal topological equivalence. We represent trajectories with B-Spline curves and apply gradient-based optimization to navigate around static and moving obstacles within spatial-temporal corridors. Through simulation and real-world experiments, we show that our method can achieve a success rate of over 95% in environments with different density levels, exceeding the performance of other approaches, demonstrating its potential for practical deployment in highly dynamic environments.

Problem

• Efficient trajectory generation for quadrotors in dynamic environments.
• Addressing non-convexity in spatial-temporal domain for safe navigation.
• Ensuring completeness and optimality in real-time obstacle avoidance.

Innovation

• Safe interval motion planning for dynamic environments
• Two-stage trajectory generation with graph search and optimization
• Uniform Temporal Visibility Deformation for spatial-temporal evaluation