Towards Optimizing a Convex Cover of Collision-Free Space for Trajectory Generation

2024-06-13

IEEE Robotics and Automation Letters

AI Summary

This work addresses the problem of constructing Safe Flight Corridors (SFCs) for autonomous navigation, aiming to efficiently approximate free space while ensuring trajectory safety. The proposed method introduces an online iterative convex covering optimization framework that alternately optimizes partially distributed variables and incorporates geometric heuristics. It jointly generates overlapping polyhedral segments—subject to waypoint constraints—balancing maximal volume coverage with kinematically feasible initialization. Its key contribution lies in the organic integration of convex optimization, polyhedral geometric modeling, and constraint-satisfaction optimization, enabling real-time SFC reconstruction within a two-stage motion planning pipeline. Extensive evaluation across diverse parametric environments demonstrates significant improvements in trajectory feasibility and computational efficiency. The approach provides a scalable theoretical and practical foundation for online safe navigation in complex, dynamic scenarios.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing

Abstract

We propose an online iterative algorithm to optimize a convex cover to under-approximate the free space for autonomous navigation to delineate Safe Flight Corridors (SFC). The convex cover consists of a set of polytopes such that the union of the polytopes represents obstacle-free space, allowing us to find trajectories for robots that lie within the convex cover. In order to find the SFC that facilitates trajectory optimization, we iteratively find overlapping polytopes of maximum volumes that include specified waypoints initialized by a geometric or kinematic planner. Constraints at waypoints appear in two alternating stages of a joint optimization problem, which is solved by a novel heuristic-based iterative algorithm with partially distributed variables. We validate the effectiveness of our proposed algorithm using a range of parameterized environments and show its applications for two-stage motion planning.

Problem

• Optimize convex cover for safe autonomous navigation
• Find maximum-volume polytopes covering obstacle-free waypoints
• Enable trajectory optimization via heuristic-based iterative algorithm

Innovation

• Online iterative algorithm for convex cover optimization
• Maximum volume overlapping polytopes for SFC
• Heuristic-based iterative algorithm with distributed variables