General Optimal Trajectory Planning: Enabling Autonomous Vehicles with the Principle of Least Action
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Summary
This paper introduces a General Optimal Trajectory Planning (GOTP) framework designed to enable autonomous vehicles (AVs) to navigate dynamic environments safely and efficiently. The research addresses the challenge of generating trajectories that simultaneously satisfy feasibility, optimality, and adaptability in complex traffic scenarios involving multiple interactive participants. Existing methods often struggle with high computational costs, discontinuous curvature, or the difficulty of weighting multiple performance objectives like safety, comfort, and efficiency. To overcome these limitations, the authors propose a unified approach inspired by the principle of least action, aiming to simulate human driving behavior characterized by "seeking benefits and avoiding losses." The methodology employs a multi-stage process. First, a reference path is generated along the road centerline using fifth-order Bezier curves to ensure curvature continuity and smoothness. Cartesian coordinates are then transformed into a curvilinear coordinate system to generate a cluster of feasible candidate trajectories. These candidates are constructed using cubic polynomials that satisfy vehicle kinematic constraints, including limits on curvature and acceleration, ensuring physical feasibility. Speed profiles are generated using smoothed trapezoidal curves to maintain continuous velocity and acceleration. The core innovation lies in the selection of the optimal trajectory from this cluster. The authors develop a unified, auto-tuning objective function based on the principle of least action, which integrates kinetic and potential energy concepts to quantify driving expectations. This function eliminates the need for manual weighting of individual objectives. Finally, receding-horizon optimization is applied to dynamically adjust the trajectory in real-time, ensuring adaptability to changing environmental conditions. Extensive simulations and experiments demonstrate the framework's effectiveness in avoiding both static and dynamic obstacles across various scenarios. The results indicate that the GOTP framework successfully coordinates multi-performance objectives, providing trajectories that are feasible, optimal, and adaptable. The study proves that the method guarantees real-time planning capabilities and meets safety requirements comparable to human driver manipulation. By unifying the objective function through the principle of least action, the approach achieves a balance between safety and efficiency without the inconsistencies associated with traditional multi-objective weighting methods. The significance of this work lies in its ability to provide a generalizable solution for AV trajectory planning that mimics human-like decision-making processes. By grounding the optimization in physical principles rather than arbitrary heuristic weights, the framework offers improved interpretability and robustness in complex, interactive traffic environments. This contributes to the development of more reliable and human-centered autonomous driving systems capable of handling diverse and uncertain scenarios.
Key finding
The proposed trajectory planning framework successfully integrates the principle of least action to create a unified objective function that ensures safe, efficient, and real-time autonomous driving in complex dynamic environments without requiring manual parameter tuning.
Methodology
simulation_modeling
Provenance
The full processing record for this entry. Every stage of this paper's journey through the pipeline is logged — what ran, with which tool and model, how many attempts it took, and when it last completed. Discovered via author_sweep_intake on 2026-05-27 (2 acquisition events logged).
| Stage | Outcome | Tool | Model | Prompt | Attempts | Completed |
|---|---|---|---|---|---|---|
| discover | success | author_sweep | — | — | 3 | 2026-05-28 |
| archive | success | canonical_url | — | — | 5 | 2026-06-06 |
| extract | success | cached | — | — | 3 | 2026-06-10 |
| clean | success | clean | — | — | 1 | 2026-06-07 |
| chunk | success | chunk | — | — | 1 | 2026-06-07 |
| embed | success | embed | Qwen/Qwen3-Embedding-8B | — | 1 | 2026-06-07 |
| enrich | skipped | — | — | — | 4 | 2026-07-02 |
| promote | success | — | — | — | 1 | 2026-06-04 |
| summarize | success | llm | qwen3.6-27b-prismaquant | summ-v5 | 2 | 2026-06-10 |
| tag | success | vector_similarity | — | — | 15 | 2026-06-11 |
| verify | success | — | — | — | 2 | 2026-06-10 |
Summary generated by qwen3.6-27b-prismaquant on 2026-06-10; verification: verified.
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- Theoretical Contribution: computational model