Deformable Linear Object Surface Placement Using Elastica Planning and Local Shape Control

TL;DR

A two-layered approach for placing DLOs on a flat surface using a single robot hand based on Euler's elastica solutions that can recover from states where the high-level manipulation planner has failed as required by practical robot manipulation systems.

Abstract

Manipulation of deformable linear objects (DLOs) in constrained environments is a challenging task. This paper describes a two-layered approach for placing DLOs on a flat surface using a single robot hand. The high-level layer is a novel DLO surface placement method based on Euler's elastica solutions. During this process one DLO endpoint is manipulated by the robot gripper while a variable interior point of the DLO serves as the start point of the portion aligned with the placement surface. The low-level layer forms a pipeline controller. The controller estimates the DLO current shape using a Residual Neural Network (ResNet) and uses low-level feedback to ensure task execution in the presence of modeling and placement errors. The resulting DLO placement approach can recover from states where the high-level manipulation planner has failed as required by practical robot manipulation systems. The DLO placement approach is demonstrated with simulations and experiments that use silicon mock-up objects prepared for fresh food applications.

Figures (11)

• Figure 1: A single robot arm has to place a strip-like fresh food item whose median axis is modeled as a DLO on a tray in a stable and non-self-intersecting manner. The DLO placement combines high-level planning with low-level feedback controller: $S(t)$ is the DLO high-level planned shape, $\hat{S}(t)$ is the ResNet measurement DLO observed shape. $||S(t) \!-\! \hat{S}(t)||$ is the DLO shape estimation error fed to the low-level controller.
• Figure 2: Top view of full period elastica shape with the physical flexible cable of length $L$ embedded in its periodic elastica solution of full-period length $\tilde{L}$. The elastica axis with angle $\phi_0$ passes through the zero curvature points and is parallel to the opposing forces of magnitude $\lambda_r$ applied at cable endpoints.
• Figure 3: (a) Stage I: contact free transport until the DLO tip touches the placement surface. (b) Stage II: non-slip rolling of the DLO tip against the surface until $\phi(0) \!=\! 0$. (c) Stage III: non-slip rolling placement of the entire DLO under surface friction conditions.
• Figure 4: (a) The DLO shape when the robot arm grasps the DLO at the red endpoint where $s = L$ while the DLO is supported by the surface at the tip where $s \!=\! 0$. When $s_0 \!=\! \tfrac{\Tilde{L}}{4}$, the DLO rotates clockwise around the surface attachment point. (b) The DLO shape when the robot arm grasps the DLO at the red endpoint where $s \!=\! L$ with a surface-contacting segment of length $l$.
• Figure 5: The DLO non-slip constraint under Coulomb's friction law in (a) stage II, and (b) stage III of the three-stage placement scheme.