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MeshA*: Efficient Path Planning With Motion Primitives

Marat Agranovskiy, Konstantin Yakovlev

TL;DR

MeshA* tackles kinodynamic path planning on grids by replacing primitive-centric search with a cell-centered mesh graph that tracks which motion primitives pass through each cell. It proves equivalence and optimality preservation with lattice-based A*, and demonstrates substantial practical speedups through cell-level pruning and a precomputed transition table. The approach yields a formal, reconstructable, and efficient alternative to traditional lattice search, with potential extension to 3D and additional discrete state components. These contributions offer a scalable, guaranteed-path planning framework for kinodynamic agents in grid-based environments.

Abstract

We study a path planning problem where the possible move actions are represented as a finite set of motion primitives aligned with the grid representation of the environment. That is, each primitive corresponds to a short kinodynamically-feasible motion of an agent and is represented as a sequence of the swept cells of a grid. Typically, heuristic search, i.e. A*, is conducted over the lattice induced by these primitives (lattice-based planning) to find a path. However, due to the large branching factor, such search may be inefficient in practice. To this end, we suggest a novel technique rooted in the idea of searching over the grid cells (as in vanilla A*) simultaneously fitting the possible sequences of the motion primitives into these cells. The resultant algorithm, MeshA*, provably preserves the guarantees on completeness and optimality, on the one hand, and is shown to notably outperform conventional lattice-based planning (x1.5-x2 decrease in the runtime), on the other hand.

MeshA*: Efficient Path Planning With Motion Primitives

TL;DR

MeshA* tackles kinodynamic path planning on grids by replacing primitive-centric search with a cell-centered mesh graph that tracks which motion primitives pass through each cell. It proves equivalence and optimality preservation with lattice-based A*, and demonstrates substantial practical speedups through cell-level pruning and a precomputed transition table. The approach yields a formal, reconstructable, and efficient alternative to traditional lattice search, with potential extension to 3D and additional discrete state components. These contributions offer a scalable, guaranteed-path planning framework for kinodynamic agents in grid-based environments.

Abstract

We study a path planning problem where the possible move actions are represented as a finite set of motion primitives aligned with the grid representation of the environment. That is, each primitive corresponds to a short kinodynamically-feasible motion of an agent and is represented as a sequence of the swept cells of a grid. Typically, heuristic search, i.e. A*, is conducted over the lattice induced by these primitives (lattice-based planning) to find a path. However, due to the large branching factor, such search may be inefficient in practice. To this end, we suggest a novel technique rooted in the idea of searching over the grid cells (as in vanilla A*) simultaneously fitting the possible sequences of the motion primitives into these cells. The resultant algorithm, MeshA*, provably preserves the guarantees on completeness and optimality, on the one hand, and is shown to notably outperform conventional lattice-based planning (x1.5-x2 decrease in the runtime), on the other hand.

Paper Structure

This paper contains 27 sections, 5 theorems, 10 equations, 6 figures, 3 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Statement
  4. Method
  5. The Search Space
  6. Successors
  7. Transition Costs
  8. MeshA*
  9. Theoretical Results
  10. On The Efficiency Of MeshA*
  11. Empirical Evaluation
  12. Conclusion
  13. Appendix A. Proofs of Theoretical Statements
  14. Lemma 1
  15. Theorem 2
  16. ...and 12 more sections

Key Result

Lemma 1

For any path on the mesh graph starting from an initial extended cell, the cost of each transition is uniquely defined.

Figures (6)

  • Figure 1: Example of the path planning problem. The workspace is discretized to a grid, where the green cells correspond to the obstacles and the white ones represent the free space. The green cell with an arrow denotes the start state (position and heading), while the red cell -- the goal one. The path is composed of the primitives (green and red segments). The swept cells are shown in blue.
  • Figure 2: Definition of cell successors during the construction of a collision trace.
  • Figure 3: Experimental setup: control set and MovingAI maps.
  • Figure 4: Median runtime of the evaluated algorithms (relative to the runtime of LBA*). The lower -- the better. 50% corresponds to x2 speed-up.
  • Figure 5: Median number of processed grid cells (sum over all collision traces) for MeshA* relative to LazyLBA*
  • ...and 1 more figures

Theorems & Definitions (21)

  • Definition 1: Extended cell
  • Definition 2: Initial Configuration
  • Definition 3: Initial Successor
  • Definition 4: Regular Successor
  • Definition 5: Transition Cost
  • Lemma 1: Uniqueness of Path Cost
  • proof : Proof Sketch
  • Theorem 2: From State Lattice to Mesh Graph
  • proof : Proof Sketch
  • Theorem 3: From Mesh Graph to State Lattice
  • ...and 11 more