Deformable Object Manipulation With Constraints Using Path Set Planning and Tracking

TL;DR

A systematic manipulation framework for DOM subject to constraints is presented by proposing a novel path set planning and tracking scheme and a control architecture combining path set tracking and constraint handling is designed for task execution.

Abstract

In robotic deformable object manipulation (DOM) applications, constraints arise commonly from environments and task-specific requirements. Enabling DOM with constraints is therefore crucial for its deployment in practice. However, dealing with constraints turns out to be challenging due to many inherent factors such as inaccessible deformation models of deformable objects (DOs) and varying environmental setups. This article presents a systematic manipulation framework for DOM subject to constraints by proposing a novel path set planning and tracking scheme. First, constrained DOM tasks are formulated into a versatile optimization formalism which enables dynamic constraint imposition. Because of the lack of the local optimization objective and high state dimensionality, the formulated problem is not analytically solvable. To address this, planning of the path set, which collects paths of DO feedback points, is proposed subsequently to offer feasible path and motion references for DO in constrained setups. Both theoretical analyses and computationally efficient algorithmic implementation of path set planning are discussed. Lastly, a control architecture combining path set tracking and constraint handling is designed for task execution. The effectiveness of our methods is validated in a variety of DOM tasks with constrained experimental settings.

Figures (25)

• Figure 1: Piece of cloth is intended to be led by the robot to pass the narrow passage $1$ or $2$ to reach the desired position. Which passage (1 is closer but narrower) to pass and how to pass it are unknown. Path set planning aims to find an appropriate spatial path for a DO in constrained environments.
• Figure 2: Block diagram illustrating the pipeline of the proposed manipulation framework for DOM with constraints.
• Figure 3: Robot needs to manipulate the DO to pass through a narrow passage. In this task, over-compression and collision with the environment have a high probability to happen.
• Figure 4: Path 1 is optimal under classical path optimization criterion, e.g., path length and execution time, but it admits a quite narrow passage $(\mathcal{E}_4, \mathcal{E}_5)$. Path 2 better trades off the path length and workspace along the path.
• Figure 5: Path 1 and 2 are path homotopic. The composed path set (suppose paths are processed to have the same path ends) is infeasible. On the right, the segment between point 1 and 2 collides with the obstacle. Their path set is not strong homotopic-like, but the shown pose is feasible in DOM.

Theorems & Definitions (1)

• Definition 1