Realtime Robust Shape Estimation of Deformable Linear Object

TL;DR

The real-world experiments of tracking and estimating a heavy-load cable prove that the proposed approach to estimate the shape of linear deformable objects in realtime is robust under occlusion and complex entanglement scenarios.

Abstract

Realtime shape estimation of continuum objects and manipulators is essential for developing accurate planning and control paradigms. The existing methods that create dense point clouds from camera images, and/or use distinguishable markers on a deformable body have limitations in realtime tracking of large continuum objects/manipulators. The physical occlusion of markers can often compromise accurate shape estimation. We propose a robust method to estimate the shape of linear deformable objects in realtime using scattered and unordered key points. By utilizing a robust probability-based labeling algorithm, our approach identifies the true order of the detected key points and then reconstructs the shape using piecewise spline interpolation. The approach only relies on knowing the number of the key points and the interval between two neighboring points. We demonstrate the robustness of the method when key points are partially occluded. The proposed method is also integrated into a simulation in Unity for tracking the shape of a cable with a length of 1m and a radius of 5mm. The simulation results show that our proposed approach achieves an average length error of 1.07% over the continuum's centerline and an average cross-section error of 2.11mm. The real-world experiments of tracking and estimating a heavy-load cable prove that the proposed approach is robust under occlusion and complex entanglement scenarios.

Figures (8)

• Figure 1: Experiment setup for robot-assisted TMS with optical tracking system (OTS) liu2022inside. The cable is connected to the TMS coil and held by the robot. Optical markers highlighted with white circles are evenly placed on the cable. In robot-assisted TMS, estimating the shape of the cable is crucial for external force compensation and safety concerns.
• Figure 2: Simulated DLO with nodes highlighted. The nodes are represented with circles in all three panels. A weighted graph in the middle panel is used to describe the connectivity of the nodes. The nodes are located at the same intervals along the center line of the DLO. The graph edges are initialized based on the Euclidean distances between the nodes. The right panel depicts the labeled nodes after pruning the edges.
• Figure 3: An illustration of two subsequent segments of a DLO $s$. Two segments are tangential at $p_i$ and the tangent vector is $\frac{\partial p}{\partial s}$. $p_{i+1}^j$ and $p_{i+1}^k$ are potential adjacent nodes with $p_i$. Plane $\bf{Q}_{i,j}$ is defined by the points $p_{i+1}^j$, $p_i$, and $\frac{\partial p}{\partial s}$; Plane $\bf{Q}_{i,k}$ is defined by the points $p_{i+1}^k$, $p_i$, and $\frac{\partial p}{\partial s}$. The dashed line represents the center line of the DLO.
• Figure 4: (a)-(d) are four examples that illustrate the noisy measured points versus the simulated ground truth of the DLO segments. Blue crosses are the noisy measured value $\tilde{p}_{i+1}^j$. Green dots represent the ideal value $p_{i+1}^j$. Orange dots are the base point $p_i$. The ideal arc connecting $p_i$ and $p_{i+1}^j$ is represented by green dashed lines. The orange lines are the previous segment. (e) depicts how the tangent circle $\mathbf{c}$ and the current segment are defined on a DLO. The center of the $\mathbf{c}$ is the blue dot in (a)-(e). Blue dashed lines define the radius of $\mathbf{c}$.
• Figure 5: Eight possible configurations are overlaid on the planar probability distribution field, which evaluates the likelihood of a node being the next adjacent node. The preset distance between nodes is 10mm in this example. The nodes are shown with orange dots. Arcs that connect the adjacent nodes are plotted as green dashed lines. The orange solid line denotes the previous segment.