Characterizing Manipulation Robustness through Energy Margin and Caging Analysis

TL;DR

This paper introduces an approach for evaluating manipulation robustness through energy margins and caging-based analysis and extends traditional caging concepts for dynamic manipulation by measuring the energy margin to failure and extending traditional caging concepts for dynamic manipulation.

Abstract

To develop robust manipulation policies, quantifying robustness is essential. Evaluating robustness in general manipulation, nonetheless, poses significant challenges due to complex hybrid dynamics, combinatorial explosion of possible contact interactions, global geometry, etc. This paper introduces an approach for evaluating manipulation robustness through energy margins and caging-based analysis. Our method assesses manipulation robustness by measuring the energy margin to failure and extends traditional caging concepts for dynamic manipulation. This global analysis is facilitated by a kinodynamic planning framework that naturally integrates global geometry, contact changes, and robot compliance. We validate the effectiveness of our approach in simulation and real-world experiments of multiple dynamic manipulation scenarios, highlighting its potential to predict manipulation success and robustness.

Figures (5)

• Figure 1: Examples of manipulation primitives. The capture sets $\mathcal{Z}_{\text{cap}}$ (blue) and task success sets $\mathcal{Z}_{\text{suc}}$ (gray) are marked.
• Figure 2: Qualitative evaluation for the planar pushing example. Data in the subfigures indicate $(\Omega_{\text{suc}}, \Omega_{\text{cap}})$. (i) and (ii) refer to a failed and a successful trajectory of pushing a rectangular box (yellow) to the wall (black). Three screenshots are taken along each trajectory, for which we run Algo. \ref{['algo-likelihood']} and visualize the expansive tree after running 100 iterations. The nodes on the tree are shown in colored dots (CoM position of the box) ranging from blue to red, implying the energy cost field. More reddish dots indicate nodes with higher cost-to-come $c$. Box and circular end-effector (green) configurations of three random nodes on the tree are visualized in partial transparency. Note the capture set $\mathcal{Z}_{\text{cap}}$ (light blue) and the task success set $\mathcal{Z}_{\text{suc}}$ (gray).
• Figure 3: Time efficiency and performance (AUC/AP values for $\Omega_{\text{suc}}(\boldsymbol{z}, {\Bar{k}})$) of Algo. \ref{['algo-likelihood']} in a planar pushing task.
• Figure 4: Robustness evaluation of Algo. \ref{['algo-likelihood']} under various modeling errors: This plot shows the algorithm performance against different estimation errors of various types, including friction coefficient ($\mu$), velocity ($\dot{\boldsymbol{x}}, \dot{\boldsymbol{y}}$), relative position (${\boldsymbol{r}_x}, {\boldsymbol{r}_y}$), and contact forces ($\lambda_{\mathbin{\!/\mkern-5mu/\!}}, \lambda_{\perp}$). The graph demonstrates how AP values for the capture score $\Omega_{\text{cap}}$ (blue, orange and green) and the force-based baseline (BL) score $\Omega_{\text{force}}$ (red) vary given increasing maximal error thresholds ($\Bar{e}_{\text{max}}$).
• Figure 5: Real-world experiments settings. (i) The planar pushing task using an Interbotix WidowX-200 robot arm with a top-view camera. (ii) 5 3D-printed objects and 2 end-effectors. (iii) Replication in the simulation of the scene in (i) for computing the energy margins. (iv,v) Screenshots of a failed/successful trajectory from the camera view.

Theorems & Definitions (4)

• Definition 1
• Definition 2
• Definition 3
• Definition 4