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Two-Stage Path Following for Mobile Manipulators via Dimensionality-Reduced Graph Search and Numerical Optimization

Fuyu Guo, Yuting Mei, Yuyao Zhang, Qian Tang

TL;DR

A robust two-stage configuration planning framework that decouples the 8-DoF planning problem into a tractable 2-DoF base optimization under a yaw-fixed base planning assumption is presented.

Abstract

Efficient path following for mobile manipulators is often hindered by high-dimensional configuration spaces and kinematic constraints. This paper presents a robust two-stage configuration planning framework that decouples the 8-DoF planning problem into a tractable 2-DoF base optimization under a yaw-fixed base planning assumption. In the first stage, the proposed approach utilizes IRM to discretize the task-space path into a multi-layer graph, where an initial feasible path is extracted via a Dijkstra-based dynamic programming approach to ensure computational efficiency and global optimality within the discretized graph. In the second stage, to overcome discrete search quantization, feasible base regions are transformed into convex hulls, enabling subsequent continuous refinement via the L-BFGS algorithm to maximize trajectory smoothness while strictly enforcing reachability constraints. Simulation results demonstrate the theoretical precision of the proposed method by achieving sub-millimeter kinematic accuracy in simulation, and physical experiments on an omnidirectional mobile manipulator further validate the framework's robustness and practical applicability.

Two-Stage Path Following for Mobile Manipulators via Dimensionality-Reduced Graph Search and Numerical Optimization

TL;DR

A robust two-stage configuration planning framework that decouples the 8-DoF planning problem into a tractable 2-DoF base optimization under a yaw-fixed base planning assumption is presented.

Abstract

Efficient path following for mobile manipulators is often hindered by high-dimensional configuration spaces and kinematic constraints. This paper presents a robust two-stage configuration planning framework that decouples the 8-DoF planning problem into a tractable 2-DoF base optimization under a yaw-fixed base planning assumption. In the first stage, the proposed approach utilizes IRM to discretize the task-space path into a multi-layer graph, where an initial feasible path is extracted via a Dijkstra-based dynamic programming approach to ensure computational efficiency and global optimality within the discretized graph. In the second stage, to overcome discrete search quantization, feasible base regions are transformed into convex hulls, enabling subsequent continuous refinement via the L-BFGS algorithm to maximize trajectory smoothness while strictly enforcing reachability constraints. Simulation results demonstrate the theoretical precision of the proposed method by achieving sub-millimeter kinematic accuracy in simulation, and physical experiments on an omnidirectional mobile manipulator further validate the framework's robustness and practical applicability.
Paper Structure (20 sections, 10 equations, 11 figures, 4 tables, 3 algorithms)

This paper contains 20 sections, 10 equations, 11 figures, 4 tables, 3 algorithms.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORK
  3. Stage One: Discrete Graph Search on Inverse Reachability Maps
  4. Reachability Analysis for High-Dimensional Decoupling
  5. Reachability Mapping
  6. Inverse reachability map projection
  7. Configuration Planning Algorithm for Path Following
  8. Stage Two: Continuous Refinement via L-BFGS Optimization
  9. Geometric Region Representation of Feasible Base Configuration Sets
  10. Continuous Configuration Refinement via Numerical Optimization
  11. Cost Function and Gradient Derivation
  12. Configuration Planning Algorithm Based on L-BFGS
  13. EXPERIMENTS
  14. Comparative Evaluation with Holistic Reactive Control
  15. Comparative Analysis with CHOMP
  16. ...and 5 more sections

Figures (11)

  • Figure 1: Motion planning for path following of mobile manipulators
  • Figure 2: Reachability distribution map of the Z1 robotic arm, where red voxels indicate high pose redundancy and blue voxels signify limited reachability.
  • Figure 3: The results of the initial configuration planning method based on dynamic programming and Dijkstra's algorithm
  • Figure 4: Process of converting discrete point sets into geometric feasible regions
  • Figure 5: Schematic of secondary configuration optimization
  • ...and 6 more figures