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Multi Graph Search for High-Dimensional Robot Motion Planning

Itamar Mishani, Maxim Likhachev

TL;DR

This work introduces Multi-Graph Search (MGS), a search-based motion planning algorithm that generalizes classical unidirectional and bidirectional search to a multi-graph setting and proves that MGS is complete and bounded-suboptimal.

Abstract

Efficient motion planning for high-dimensional robotic systems, such as manipulators and mobile manipulators, is critical for real-time operation and reliable deployment. Although advances in planning algorithms have enhanced scalability to high-dimensional state spaces, these improvements often come at the cost of generating unpredictable, inconsistent motions or requiring excessive computational resources and memory. In this work, we introduce Multi-Graph Search (MGS), a search-based motion planning algorithm that generalizes classical unidirectional and bidirectional search to a multi-graph setting. MGS maintains and incrementally expands multiple implicit graphs over the state space, focusing exploration on high-potential regions while allowing initially disconnected subgraphs to be merged through feasible transitions as the search progresses. We prove that MGS is complete and bounded-suboptimal, and empirically demonstrate its effectiveness on a range of manipulation and mobile manipulation tasks. Demonstrations, benchmarks and code are available at https://multi-graph-search.github.io/.

Multi Graph Search for High-Dimensional Robot Motion Planning

TL;DR

This work introduces Multi-Graph Search (MGS), a search-based motion planning algorithm that generalizes classical unidirectional and bidirectional search to a multi-graph setting and proves that MGS is complete and bounded-suboptimal.

Abstract

Efficient motion planning for high-dimensional robotic systems, such as manipulators and mobile manipulators, is critical for real-time operation and reliable deployment. Although advances in planning algorithms have enhanced scalability to high-dimensional state spaces, these improvements often come at the cost of generating unpredictable, inconsistent motions or requiring excessive computational resources and memory. In this work, we introduce Multi-Graph Search (MGS), a search-based motion planning algorithm that generalizes classical unidirectional and bidirectional search to a multi-graph setting. MGS maintains and incrementally expands multiple implicit graphs over the state space, focusing exploration on high-potential regions while allowing initially disconnected subgraphs to be merged through feasible transitions as the search progresses. We prove that MGS is complete and bounded-suboptimal, and empirically demonstrate its effectiveness on a range of manipulation and mobile manipulation tasks. Demonstrations, benchmarks and code are available at https://multi-graph-search.github.io/.
Paper Structure (30 sections, 3 theorems, 4 equations, 12 figures, 1 table, 3 algorithms)

This paper contains 30 sections, 3 theorems, 4 equations, 12 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Classical Planning Approaches and Their Limitations
  4. Bidirectional and Multi-Directional Search Strategies
  5. Subgoal-Guided and Region-Based Planning
  6. Preliminaries
  7. Problem Formulation
  8. Focal Search for Sub-graph Exploration
  9. Attractor-Based Methods for Root Selection
  10. Multi-Graph Search
  11. Multi-Directional Problem Formulation
  12. Search Heuristics
  13. Multi-Graph Search Algorithm
  14. Workspace-Aware Root Selection via Backward BFS
  15. Theoretical Properties
  16. ...and 15 more sections

Key Result

Theorem 1

Let $h: \mathcal{C} \to \mathbb{R}_{\geq 0}$ be an admissible heuristic (i.e., $h(q) \leq c^*(q, q_{\text{goal}})$ for all $q \in \mathcal{C}$). If Mgs returns a solution path $\pi$, then $\text{cost}(\pi) \leq \epsilon \cdot c^*$, where $c^*$ is the optimal solution cost and $\epsilon \geq 1$ is th

Figures (12)

  • Figure 1: Left: Mobile manipulators in warehouse settings demand efficient, predictable motion planning. Middle: Mgs anchors search at key states and grows multiple subgraphs simultaneously, yielding a solution with a substantial reduction in search efforts. Right: Weighted-A* expands significantly more states to solve the same problem. Both searches operate on an 8-connected 2D grid with bounded suboptimality of 10.
  • Figure 2: Illustration of attractor states ($\text{A}_i$) and their regions of trivial connectivity. States within each region can reach the corresponding attractor through greedy tracing. The red cell is the state from which we expand the BFS wavefront. The grid is 8-connected with cardinal cost 1, diagonal cost $\sqrt{2}$, and Euclidean distance as the potential.
  • Figure 3: Experimental environments for manipulation (left three: shelf pick-and-place, bin picking, cage extraction) and mobile manipulation (right four: low-clearance passage, deep shelf reach, cluttered table, combined warehouse).
  • Figure 4: Path cost consistency for manipulation (left) and mobile manipulation (right) tasks. Each planner was executed 5 times per query; bars show the coefficient of variation (CV) of path costs across runs.
  • Figure 5: Consistency analysis under start/goal perturbations for manipulation (top) and mobile manipulation (bottom) tasks. Each planner was tested on 10 perturbed versions of each base query; bars show the coefficient of variation (CV) of path costs and planning times across perturbations.
  • ...and 7 more figures

Theorems & Definitions (8)

  • Definition 1: Greedy Predecessor
  • Definition 2: Greedy Tracing
  • Theorem 1: Bounded Suboptimality
  • proof : Proof Sketch
  • Theorem 2: Bounded Re-Expansions
  • proof : Proof Sketch
  • Theorem 3: Completeness
  • proof : Proof Sketch