A Machine Learning Framework for Autonomous Path Planning in Unstructured Environments Using Kolmogorov-Arnold Networks

Introduction/Objective: This study aims to develop a learning-based framework that enables autonomous path planning and continuous control for multiple interacting vehicles in unstructured environments. In unstructured scenarios that lack lane markings and right-of-way constraints and exhibit irregular geometry, existing learning-based planners struggle to achieve safety, efficiency, and real-time performance simultaneously. They also fail to adequately characterize nonlinear edge interactions. To address this gap, this paper proposes the Graph Learning Planning and Control Framework (TEKM), geared towards engineering implementation and patent-related applications, aiming to achieve a robust trade-off between safety and efficiency. Method: This approach explicitly models the relationships between multiple agents and obstacles using a graph structure: TransformerConv captures global dependencies, while EdgeConv encodes local geometry. Learnable B-splines are introduced during the message passing phase to transfer nonlinearity from nodes to edges, enhancing expressiveness and interpretability. The decoder employs a dual-branch architecture, outputting Q and V from the attention mechanism, respectively, used to construct interaction weights and global aggregation representations. Supervision signals are generated by MPCs satisfying feasible constraints. Training utilizes a segmented, stepped learning rate and reweighting of difficult samples, with non-leaking partitioning and multi-random seed verification based on map and scenario conditions. Results: Under the unified protocol, TEKM exhibits faster convergence and lower steady-state loss compared to learning-based and classical baselines, achieving higher task success rates and lower collision rates in multi-scenario evaluations. Inference latency shows linearly controllable scalability with increasing agent and obstacle numbers. Sensitivity analysis reveals that the prediction step size is most sensitive to stability, and piecewise stepped learning rates significantly reduce dependence on the initial learning rate. Discussion: Moving the learnable splines forward to the interaction edges enhances the expressiveness and interpretability of unit parameters. Combined with safety-focused loss weights and backoff mechanisms such as speed and curvature tightening, robustness is maintained in high-density scenarios. Current work does not explicitly incorporate surface material and slope modeling, falling within the scope of method-level validation. Conclusion: TEKM unifies global attention and edge-level nonlinearity, achieving safety-priority and real-time planning and control in unstructured environments, demonstrating patent-related engineering deployment potential. Future work will introduce surface parameters such as material and slope, and extend to 2.5D and 3D terrain for broader cross-domain validation.