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COAD: Constant-Time Planning for Continuous Goal Manipulation with Compressed Library and Online Adaptation

Adil Shiyas, Zhuoyun Zhong, Constantinos Chamzas

Abstract

In many robotic manipulation tasks, the robot repeatedly solves motion-planning problems that differ mainly in the location of the goal object and its associated obstacle, while the surrounding workspace remains fixed. Prior works have shown that leveraging experience and offline computation can accelerate repeated planning queries, but they lack guarantees of covering the continuous task space and require storing large libraries of solutions. In this work, we present COAD, a framework that provides constant-time planning over a continuous goal-parameterized task space. COAD discretizes the continuous task space into finitely many Task Coverage Regions. Instead of planning and storing solutions for every region offline, it constructs a compressed library by only solving representative root problems. Other problems are handled through fast adaptation from these root solutions. At query time, the system retrieves a root motion in constant time and adapts it to the desired goal using lightweight adaptation modules such as linear interpolation, Dynamic Movement Primitives, or simple trajectory optimization. We evaluate the framework on various manipulators and environments in simulation and the real world, showing that COAD achieves substantial compression of the motion library while maintaining high success rates and sub-millisecond-level queries, outperforming baseline methods in both efficiency and path quality. The source code is available at https://github.com/elpis-lab/CoAd.

COAD: Constant-Time Planning for Continuous Goal Manipulation with Compressed Library and Online Adaptation

Abstract

In many robotic manipulation tasks, the robot repeatedly solves motion-planning problems that differ mainly in the location of the goal object and its associated obstacle, while the surrounding workspace remains fixed. Prior works have shown that leveraging experience and offline computation can accelerate repeated planning queries, but they lack guarantees of covering the continuous task space and require storing large libraries of solutions. In this work, we present COAD, a framework that provides constant-time planning over a continuous goal-parameterized task space. COAD discretizes the continuous task space into finitely many Task Coverage Regions. Instead of planning and storing solutions for every region offline, it constructs a compressed library by only solving representative root problems. Other problems are handled through fast adaptation from these root solutions. At query time, the system retrieves a root motion in constant time and adapts it to the desired goal using lightweight adaptation modules such as linear interpolation, Dynamic Movement Primitives, or simple trajectory optimization. We evaluate the framework on various manipulators and environments in simulation and the real world, showing that COAD achieves substantial compression of the motion library while maintaining high success rates and sub-millisecond-level queries, outperforming baseline methods in both efficiency and path quality. The source code is available at https://github.com/elpis-lab/CoAd.
Paper Structure (26 sections, 1 theorem, 13 equations, 5 figures, 2 tables, 2 algorithms)

This paper contains 26 sections, 1 theorem, 13 equations, 5 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Classical Motion Planning
  4. Experience-Based Motion Planning
  5. Constant-Time and Precomputation-Based Planning
  6. Notations and Problem Statement
  7. Motion Planning Problem
  8. Goal-varying motion planning problem
  9. Methodology
  10. Task Space Discretization
  11. Task Space Region
  12. Shared goals across object poses
  13. Task Coverage Regions
  14. Finite coverage of the task space
  15. Offline Library Building with Compression
  16. ...and 11 more sections

Key Result

Theorem 1

Let $\Delta(\mathbf{B}) \subset SE(3)$ be the bounded displacement set of $\mathrm{TSRs}$. If $\Delta(\mathbf{B})$ has non-empty interior, then for any fixed $\mathbf{T}\xspace_e, \mathbf{T}\xspace_{s} \in SE(3)$, $\mathrm{TCR}(\mathbf{T}\xspace_e)$ also has non-empty interior and contains an axis-a

Figures (5)

  • Figure 1: A physical UR10 robot repeatably solves motion-planning problems to grasp an object whose pose continuously varies across queries, while the rest of the workspace remains unchanged.
  • Figure 2: CoAd consists of an offline library-building stage and an online query stage. 1) The continuous task space is discretized into a finite set of TCRs, each indexed for constant-time lookup. 2) During offline preprocessing, an uncovered region is selected, a motion planner finds a root motion for that region, and the resulting path is stored in the root-motion library. 3) The same root motion is then adapted and verified on neighboring regions; successful adaptations are recorded in an adaptation map that links each covered region index to a root-motion index. 4) During the online query stage, the sensed Goal pose is mapped to its region index, the corresponding root motion is retrieved in constant time, and the motion is adapted to satisfy the queried goal condition using an adaption algorithm. This process yields a compressed library that provides constant plans and covers the full task space.
  • Figure 3: 2D illustration of TSRs and TCRs.
  • Figure 4: Fetch (top) and Panda (bottom) manipulators planning in Table (left), Shelf (middle) and Cage (right) environments adapted from chamzas2022-motion-bench-maker.
  • Figure 5: Comparison of Planning Times for all methods. Y-axis is in log-scale milli-seconds. RRT-connect has a 3.0 second timeout. The library baseline has the same number of paths as the uncompressed CoAd.

Theorems & Definitions (3)

  • Definition 1: Task Coverage Region
  • Theorem 1
  • proof : Proof Sketch