Classical And Learning-Based Multi-Goal Ordering And Path Planning For Mobile Robots

In the field of autonomous mobile robotics, efficient and scalable solutions to themulti-goal ordering and path planning problem—where a robot must visit a set ofspatially distributed goal nodes in the most optimal sequence—remain a significantchallenge. In this study, we develop two approaches to tackle this importantproblem. The first one is a classical geometry-based approach and the second oneis a learning-based approach that addresses the problem using either a traditionalmachine learning technique or a transformer-based method.In the classical approach, we propose a novel ordering strategy based on a onedistance-two-angles paradigm, which reduces reliance on traditional distance metricsby incorporating geometric considerations to infer optimal visiting sequences.This ordering procedure is paired with an improved version of the A* algorithm thatintegrates principles from computer graphics to eliminate redundant zigzags and intermediatepoints often present in grid-based environments, resulting in smoother and more cost-effective paths without compromising computational efficiency. Additionally,we introduce two learning-based frameworks to predict goal visiting orders.The first is a traditional machine learning model trained on hand-crafted featuresderived from brute-force optimal solutions, capturing geometric patterns such as distances,angles, and spatial relationships. The second is a transformer model trainedon features extracted using CNNs and Relational Transformers, along with geometriccontext-based features from optimal paths. Our experiments demonstrate thatboth models generalise effectively to unseen environments and large-scale scenarios,achieving high accuracy in reproducing near-optimal orders.We conducted extensive evaluations on a variety of publicly available datasets andsynthetic environments, benchmarking our proposed approaches against state-ofthe-art algorithms. Results demonstrate that both the classical and learning-basedmethods outperform existing solutions in terms of distance cost, path smoothness,and computational runtime. The proposed methods also show strong scalability andreproducibility across diff