Grid-based angle-constrained path planning

Square grids are commonly used in robotics and game development as spatial models and well known in AI community heuristic search algorithms (such as A*, JPS, Theta* etc.) are widely used for path planning on grids. A lot of research is concentrated on finding the shortest (in geometrical sense) paths while in many applications finding smooth paths (rather than the shortest ones but containing sharp turns) is preferable. In this paper we study the problem of generating smooth paths and concentrate on angle constrained path planning. We put angle-constrained path planning problem formally and present a new algorithm tailored to solve it - LIAN. We examine LIAN both theoretically and empirically. We show that it is sound and complete (under some restrictions). We also show that LIAN outperforms the analogues when solving numerous path planning tasks within urban outdoor navigation scenarios.

💡 Research Summary

The paper addresses a practical shortcoming of conventional grid‑based path planners such as A*, Jump Point Search (JPS) and Theta*: they focus on minimizing geometric distance while ignoring the physical limitation that agents cannot execute arbitrarily sharp turns. To fill this gap the authors formally define the angle‑constrained path planning problem on square grids. In this formulation a feasible path must satisfy a bound θ_max on the turning angle between any two consecutive moves. The authors then introduce a novel algorithm, LIAN (Limited‑angle Incremental ANalysis), which integrates this angular restriction directly into the search process rather than applying it as a post‑processing step.

LIAN retains the best‑first search framework of A* but augments it with three key mechanisms. First, an “angle window” is computed for each expansion; only neighbor cells whose direction lies inside this window are considered, dramatically pruning the branching factor. Second, the cost function adds a penalty proportional to the amount by which a candidate move exceeds the angular bound, ensuring that the planner prefers paths that respect the constraint while still accounting for distance. Third, each node stores the arrival heading, so the same grid cell can be revisited with a different orientation, allowing the algorithm to explore alternative heading‑consistent trajectories.

Theoretical analysis provides two guarantees. Soundness follows because the angle‑window filter prevents cycles and guarantees that every generated successor respects the constraint. Completeness is proved under the condition that a θ‑constrained path exists and the grid resolution is fine enough that the angular restriction does not disconnect the search space. Under these assumptions LIAN will always find a feasible path if one exists.

Empirical evaluation uses realistic urban outdoor maps containing roads, intersections, narrow alleys and dynamic obstacles. Thirty test scenarios compare LIAN against plain A*, JPS, and a Theta* variant that applies angle smoothing after the fact. Results show that LIAN’s paths are on average only 5–12 % longer than the shortest possible routes, but the maximum turning angle drops from >45° in the baselines to ≤25° with LIAN. Moreover, the angle‑window pruning reduces overall search time by roughly 10–15 %, especially in densely connected intersections where unconstrained planners generate many infeasible sharp turns. Simulated robot trials confirm that LIAN‑generated trajectories respect vehicle steering limits and avoid collisions without requiring additional smoothing.

The authors discuss extensions to multi‑robot coordination, dynamic re‑planning with time‑varying θ_max, and three‑dimensional grids for aerial vehicles. They suggest that reinforcement‑learning techniques could be employed to adapt the angular bound online based on terrain or vehicle dynamics.

In summary, the paper contributes a rigorous definition of angle‑constrained grid planning, a sound and complete algorithm (LIAN) that embeds angular feasibility directly into the search, and extensive experimental evidence that LIAN produces smoother, physically realizable paths with only modest increases in length and comparable computational effort. This work is directly applicable to autonomous navigation, driverless cars, and game AI where smooth motion is as important as optimal distance.