Collision-Free Navigation of Mobile Robots via Quadtree-Based Model Predictive Control

TL;DR

The paper addresses the challenge of safe, real-time navigation for AMRs in cluttered environments where non-convex obstacles hinder traditional MPC approaches. It introduces a quadtree-based safe-area decomposition that converts obstacle avoidance into convex linear constraints, while generating collision-free trajectories via waypoint selection, arc-length interpolation, and B-spline smoothing; the MPC is solved in a receding-horizon fashion using a unicycle model. Key contributions include (1) a safe-area MPC framework that tightly couples perception, mapping, trajectory generation, and control, (2) quadtree-derived convex constraint embedding for tractable optimization, and (3) a dual-layer cost combining hard safety with soft margins to enhance robustness. The method demonstrates recursive feasibility, computational efficiency, and robust performance across complex, non-convex environments, outperforming baseline MPC and other learning/sampling-based methods. This framework offers a practical, interpretable, and verifiable navigation pipeline suitable for real-world AMR deployment without explicitly modeling obstacles.

Abstract

This paper presents an integrated navigation framework for Autonomous Mobile Robots (AMRs) that unifies environment representation, trajectory generation, and Model Predictive Control (MPC). The proposed approach incorporates a quadtree-based method to generate structured, axis-aligned collision-free regions from occupancy maps. These regions serve as both a basis for developing safe corridors and as linear constraints within the MPC formulation, enabling efficient and reliable navigation without requiring direct obstacle encoding. The complete pipeline combines safe-area extraction, connectivity graph construction, trajectory generation, and B-spline smoothing into one coherent system. Experimental results demonstrate consistent success and superior performance compared to baseline approaches across complex environments.

Figures (6)

• Figure 1: The proposed framework integrates quadtree-based safe-area generation from occupancy grid map perception with local planning and control.
• Figure 2: Illustration of the safe area generation: From the real-world map to occupancy map generation, quadtree decomposition (nodes are indexed with different colors representing their states), and merged safe areas enabling efficient trajectory planning.
• Figure 3: Trajectory generation. Green rectangles are safe regions, and red blocks are obstacles. The dark dashed line is the original reference path. Large purple points are waypoints from greedy search, and small ones are interpolated. The yellow polyline forms the new reference path, and the blue curve is the B-spline-smoothed trajectory.
• Figure 4: SA-MPC navigation across test scenarios with quadtree-derived safe areas (green)
• Figure 5: Baseline MPC performance showing failures in non-convex and complex scenarios