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Incremental Generalized Hybrid A*

Sidharth Talia, Oren Salzman, Siddhartha Srinivasa

TL;DR

The paper tackles kinodynamic motion planning over very large trees in complex environments, introducing Incremental Generalized Hybrid A* (IGHA*), an anytime framework that decouples vertex discovery from dominance via Shift and Activate mechanisms. IGHA* generalizes HA* by enabling dynamic, multi-resolution search with information reuse, and it provides theoretical convergence guarantees. Empirical results show IGHA* reduces expansions by about 6x compared to an optimized HA* baseline, achieves real-time performance in simulation, and demonstrates effective closed-loop planning on a small off-road vehicle. The approach yields robust, domain-agnostic planning for both on-road kinematic and off-road kinodynamic problems and integrates well with model predictive control in real-time systems.

Abstract

We address the problem of efficiently organizing search over very large trees, which arises in many applications ranging from autonomous driving to aerial vehicles. Here, we are motivated by off-road autonomy, where real-time planning is essential. Classical approaches use graphs of motion primitives and exploit dominance to mitigate the curse of dimensionality and prune expansions efficiently. However, for complex dynamics, repeatedly solving two-point boundary-value problems makes graph construction too slow for fast kinodynamic planning. Hybrid A* (HA*) addressed this challenge by searching over a tree of motion primitives and introducing approximate pruning using a grid-based dominance check. However, choosing the grid resolution is difficult: too coarse risks failure, while too fine leads to excessive expansions and slow planning. We propose Incremental Generalized Hybrid A* (IGHA*), an anytime tree-search framework that dynamically organizes vertex expansions without rigid pruning. IGHA* provably matches or outperforms HA*. For both on-road kinematic and off-road kinodynamic planning queries for a car-like robot, variants of IGHA* use 6x fewer expansions to the best solution compared to an optimized version of HA* (HA*M, an internal baseline). In simulated off-road experiments in a high-fidelity simulator, IGHA* outperforms HA*M when both are used in the loop with a model predictive controller. We demonstrate real-time performance both in simulation and on a small-scale off-road vehicle, enabling fast, robust planning under complex dynamics. Website: https://personalrobotics.github.io/IGHAStar/

Incremental Generalized Hybrid A*

TL;DR

The paper tackles kinodynamic motion planning over very large trees in complex environments, introducing Incremental Generalized Hybrid A* (IGHA*), an anytime framework that decouples vertex discovery from dominance via Shift and Activate mechanisms. IGHA* generalizes HA* by enabling dynamic, multi-resolution search with information reuse, and it provides theoretical convergence guarantees. Empirical results show IGHA* reduces expansions by about 6x compared to an optimized HA* baseline, achieves real-time performance in simulation, and demonstrates effective closed-loop planning on a small off-road vehicle. The approach yields robust, domain-agnostic planning for both on-road kinematic and off-road kinodynamic problems and integrates well with model predictive control in real-time systems.

Abstract

We address the problem of efficiently organizing search over very large trees, which arises in many applications ranging from autonomous driving to aerial vehicles. Here, we are motivated by off-road autonomy, where real-time planning is essential. Classical approaches use graphs of motion primitives and exploit dominance to mitigate the curse of dimensionality and prune expansions efficiently. However, for complex dynamics, repeatedly solving two-point boundary-value problems makes graph construction too slow for fast kinodynamic planning. Hybrid A* (HA*) addressed this challenge by searching over a tree of motion primitives and introducing approximate pruning using a grid-based dominance check. However, choosing the grid resolution is difficult: too coarse risks failure, while too fine leads to excessive expansions and slow planning. We propose Incremental Generalized Hybrid A* (IGHA*), an anytime tree-search framework that dynamically organizes vertex expansions without rigid pruning. IGHA* provably matches or outperforms HA*. For both on-road kinematic and off-road kinodynamic planning queries for a car-like robot, variants of IGHA* use 6x fewer expansions to the best solution compared to an optimized version of HA* (HA*M, an internal baseline). In simulated off-road experiments in a high-fidelity simulator, IGHA* outperforms HA*M when both are used in the loop with a model predictive controller. We demonstrate real-time performance both in simulation and on a small-scale off-road vehicle, enabling fast, robust planning under complex dynamics. Website: https://personalrobotics.github.io/IGHAStar/

Paper Structure

This paper contains 16 sections, 3 theorems, 7 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. Complexity of searching over a tree
  4. Hybrid A*(HA*)
  5. Incremental Generalized Hybrid A* (IGHA*)
  6. Warmup: HA*M - Simple multi-resolution HA* search
  7. The IGHA* Framework
  8. IGHA* - Multi-resolution search with information reuse
  9. IGHA*-$\bar{H}$ - Dynamically Shift resolution up and down
  10. Questions to address
  11. Theoretical Analysis
  12. Experiments and Results
  13. $\mathbb{R}^2$ Environments
  14. $\mathbb{R}^3,\mathbb{R}^4$ Environments
  15. Closed Loop Experiments for Off-Road Autonomy
  16. ...and 1 more sections

Key Result

Theorem 6.1

When at least one solution to a planning query has been found, IGHA* will terminate with finite expansions when assumptions heuristic_assumption-positive_edge_assumption hold.

Figures (7)

  • Figure 1: HA* operating at different resolutions for the same planning query. Vertices found (Open list) are shown in gray, pruned vertices in light gray, invalid (collision) in red, the goal set is marked as the circular region on the bottom right, the path is shown in black, and the gray bar on top represents the number of expansions. When using HA*, we don't a priori know the resolution for the first or the best solution, as shown in \ref{['fig: main_2']}, \ref{['fig: main_3']}. As a result, if the discretization is too coarse, we can end up with no solution as shown in \ref{['fig: main_0']} and \ref{['fig: main_1']} respectively. If it is too fine, we expand more than necessary as shown in \ref{['fig: main_4']}, where the solution quality does not improve compared to \ref{['fig: main_3']} despite $\approx3\times$ the number of expansions in the former.
  • Figure 2: IGHA* decopules vertex dominance and activation. (\ref{['fig:ighastar-flow']}) Red arrows denote breaking a loop. (\ref{['fig:ighastar-activate-shift']}) Instantiations of Shift, Activate for IGHA*-$\bar{H}$, where $\bar{H}$ is a measure of the hysteresis in switching to a lower resolution
  • Figure 3: Here, the resolution is too low for HA* to find a solution for either the Single-Bottleneck (SB) scenario (\ref{['fig:single_bn_example']}, or the Multi-Bottleneck (MB) scenario \ref{['fig:multi_bn_example']}). In contrast to Fig. \ref{['fig: main']}, for figures corresponding to IGHA*, translucent blue vertices are deactivated. IGHA* variants like IGHA*-$\infty$ only increase resolution and spend more expansions after escaping a bottleneck (\ref{['fig:single_bn_drk']}) when a lower resolution could suffice IGHA*-$0$ (\ref{['fig:single_bn_dsrk']}), resulting in fewer expansions to the first path for IGHA*-$0$ (\ref{['fig:single_bn_rankplot']}). However, variants like IGHA*-$0$ can prematurely switch back in situations where staying at the higher resolution is necessary and spend extra expansions (\ref{['fig:multi_bn_dsrk']}) by comparison to IGHA*-$\infty$ (\ref{['fig:multi_bn_drk']}). In both scenarios, an intermediate value for $\bar{H}$ can provide intermediate behavior; doing better than IGHA*-$\infty$ in SB (\ref{['fig:single_bn_50']}), and better than IGHA*-$0$ in MB (\ref{['fig:multi_bn_50']}). This interpolation is also visible through the rank plots corresponding to either scenario. In the rank plot, cells show the percentage of times (darker $=$ higher) a planner achieved a rank for first-path; lower ranks (left) = faster solutions.
  • Figure 4: In some queries of the SB environment, IGHA*-$0$ can have more expansions than IGHA*-$\infty$ (Fig. \ref{['fig:single_bn_rankplot']}). Examples \ref{['fig:single_bn_drk_counter_example']} and \ref{['fig:single_bn_dsrk_counter_example']} show that this happens when the low resolution of IGHA*-$0$ prevents it from finding a straight-line path to the goal. In some queries of the SB environment, IGHA*-$\infty$ can have more expansions than IGHA*-$0$ (\ref{['fig:multi_bn_rankplot']}). Examples \ref{['fig:multi_bn_drk_counter_example']} and \ref{['fig:multi_bn_dsrk_counter_example']} show that this can happen when the tree produced by IGHA*-$0$ contains a path at a lower resolution that passes through the two other gaps.
  • Figure 5: Notice that in Table \ref{['tab:H1_H2_table']}, IGHA*-$\infty$ beats IGHA*-$0$ in the kinematic environments and IGHA*-$0$ beats IGHA*-$\infty$ in the off-road/kinodynamic environments. It goes to show that the urban city environments (\ref{['fig:kinematic_example']}) exhibit more clutter, similar to MB, and off-road environments (\ref{['fig:off_road_exp']}) appear sparser as in SB.
  • ...and 2 more figures

Theorems & Definitions (6)

  • Definition 6.1: Shift
  • Definition 6.2: Activate
  • Definition 6.3: Rule
  • Theorem 6.1
  • Theorem 6.2
  • Corollary 6.1