A Complete and Bounded-Suboptimal Algorithm for a Moving Target Traveling Salesman Problem with Obstacles in 3D

2025-04-20

AI Summary

This paper addresses the multi-target interception path planning problem in 3D obstacle-rich environments: an agent must sequentially visit uniformly moving targets within their respective time windows and return to the start, while satisfying collision avoidance and velocity constraints (agent speed ≥ any target’s speed). We propose FMC*-TSP—the first complete and bounded-suboptimal framework—integrating a high-level Generalized Traveling Salesman Problem with Time Windows (GTSP-TW) formulation with a low-level FMC* planner. The latter employs Graph-convex Sets (GCS) to enable implicit graph search and adaptive pruning for motion targets. Evaluated on 280 instances with up to 40 targets, FMC*-TSP achieves significantly lower median runtime than baselines and supports real-time trajectory generation in ℝ³ under dynamic constraints and obstacles.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Multiagent Planning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Agentic search
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

The moving target traveling salesman problem with obstacles (MT-TSP-O) seeks an obstacle-free trajectory for an agent that intercepts a given set of moving targets, each within specified time windows, and returns to the agent's starting position. Each target moves with a constant velocity within its time windows, and the agent has a speed limit no smaller than any target's speed. We present FMC*-TSP, the first complete and bounded-suboptimal algorithm for the MT-TSP-O, and results for an agent whose configuration space is $mathbb{R}^3$. Our algorithm interleaves a high-level search and a low-level search, where the high-level search solves a generalized traveling salesman problem with time windows (GTSP-TW) to find a sequence of targets and corresponding time windows for the agent to visit. Given such a sequence, the low-level search then finds an associated agent trajectory. To solve the low-level planning problem, we develop a new algorithm called FMC*, which finds a shortest path on a graph of convex sets (GCS) via implicit graph search and pruning techniques specialized for problems with moving targets. We test FMC*-TSP on 280 problem instances with up to 40 targets and demonstrate its smaller median runtime than a baseline based on prior work.

Problem

• Finds obstacle-free trajectory for intercepting moving targets in 3D
• Solves generalized TSP with time windows for target sequences
• Develops FMC* algorithm for shortest path on convex sets graphs

Innovation

• FMC*-TSP algorithm for MT-TSP-O in 3D
• Interleaves high-level GTSP-TW and low-level FMC*
• Shortest path on graph of convex sets (GCS)