[Paper Review] Multi-query Robotic Manipulator Task Sequencing with Gromov-Hausdorff Approximations

Fouad Sukkar, Jennifer Wakulicz+3 more|arXiv (Cornell University)|Sep 11, 2022

Robotic Path Planning Algorithms4 citations

TL;DR

This paper proposes a motion planning framework for robotic manipulators that uses $ \epsilon$-Gromov-Hausdorff approximations to establish task-space-to-configuration-space isometries, enabling efficient, bounded-suboptimal trajectory sequencing in real time. By constructing a trajectory library offline and querying it online, the method ensures smooth concatenation of paths and achieves suboptimal but feasible solutions for multi-query task sequencing under tight computational constraints.

ABSTRACT

Robotic manipulator applications often require efficient online motion planning. When completing multiple tasks, sequence order and choice of goal configuration can have a drastic impact on planning performance. This is well known as the robot task sequencing problem (RTSP). Existing general-purpose RTSP algorithms are susceptible to producing poor-quality solutions or failing entirely when available computation time is restricted. We propose a new multi-query task sequencing method designed to operate in semi-structured environments with a combination of static and non-static obstacles. Our method intentionally trades off workspace generality for planning efficiency. Given a user-defined task space with static obstacles, we compute a subspace decomposition. The key idea is to establish approximate isometries known as $ε$-Gromov-Hausdorff approximations that identify points that are close to one another in both task and configuration space. Importantly, we prove bounded suboptimality guarantees on the lengths of paths within these subspaces. These bounding relations further imply that paths within the same subspace can be smoothly concatenated, which we show is useful for determining efficient task sequences. We evaluate our method with several kinematic configurations in a complex simulated environment, achieving up to 3x faster motion planning and 5x lower maximum trajectory jerk compared to baselines.

Motivation & Objective

• To address the challenge of real-time, high-frequency motion planning for robotic manipulators in dynamic environments with static and non-static obstacles.
• To reduce computational overhead in online planning by operating in a user-defined task space rather than full configuration space.
• To automatically generate a reusable trajectory library that supports fast, bounded-suboptimal path queries for multiple goals.
• To ensure smooth trajectory concatenation through approximate isometries that preserve proximity in task and configuration spaces.
• To enable practical deployment in cobot and advanced manufacturing applications requiring rapid reconfiguration and reliable online planning.

Proposed method

• The framework constructs a graph over task-space poses and uses $ \epsilon$-Gromov-Hausdorff approximations to define approximate isometries between task-space proximity and configuration-space distance.
• It employs a modified Dijkstra’s algorithm to compute unique inverse kinematics solutions that minimize path cost while satisfying the $ \epsilon$-GHA constraint.
• Trajectory libraries are generated by sampling root nodes and computing shortest paths across the graph using the $ \epsilon$-GHA mappings.
• The method ensures bounded suboptimality by minimizing the sum of path costs across all goal sequences, with coverage prioritized in early iterations.
• A candidate IK solution selection process evaluates neighboring nodes using a priority queue, updating mappings only if a lower-cost, valid path is found.
• The algorithm runs iteratively to explore multiple $ \epsilon$-GHA maps, selecting the one that minimizes the total cost function $J(\theta^i, t_0)$.

Experimental results

Research questions

• RQ1 Can a motion planning framework achieve real-time performance for multi-query robotic task sequencing while maintaining bounded suboptimality?
• RQ2 How can approximate isometries between task space and configuration space be constructed to enable efficient trajectory library generation?
• RQ3 To what extent can $ \epsilon$-Gromov-Hausdorff approximations reduce online planning time without sacrificing trajectory quality?
• RQ4 How does the proposed method compare to naive planners in terms of trajectory length and execution efficiency in dynamic environments?
• RQ5 Can the framework be extended to handle manipulators with kinematic redundancy and mobile bases in practical industrial applications?

Key findings

• The framework achieves feasible real-time performance in simulation across multiple kinematic configurations, including manipulators on mobile bases.
• Trajectory libraries generated via $ \epsilon$-Gromov-Hausdorff approximations enable bounded suboptimality guarantees on total path length.
• The method outperforms naive planners by selecting shorter, smoother trajectories through intelligent task-space sequencing.
• The use of approximate isometries ensures that nearby task-space goals are mapped to nearby configuration-space poses, enabling smooth path concatenation.
• The algorithm successfully handles kinematic redundancy by selecting inverse kinematics solutions that minimize path cost under $ \epsilon$-GHA constraints.
• The framework demonstrates scalability and reusability, supporting rapid redeployment for new tasks and environmental changes.