Enhancing Robustness in Manipulability Assessment: The Pseudo-Ellipsoid Approach

TL;DR

The paper addresses robustness gaps in directional manipulability analysis caused by noisy or incomplete body configuration data. It introduces a manipulability pseudo-ellipsoid that replaces the conventional radius with a direction-projected metric $l$ via $l = sqrt(sum r_i^2 cos^2(theta_i))$, reducing sensitivity to estimation errors. Through a theoretical sensitivity analysis, simulations, and RGB-D/Vicon experiments, it demonstrates that $l$ is markedly more robust than the standard ellipsoid radius $r$, especially near singular configurations. This robustness is particularly beneficial for human-centered robotics and assistive devices, where reliable manipulability cues are critical for control and task planning.

Abstract

Manipulability analysis is a methodology employed to assess the capacity of an articulated system, at a specific configuration, to produce motion or exert force in diverse directions. The conventional method entails generating a virtual ellipsoid using the system's configuration and model. Yet, this approach poses challenges when applied to systems such as the human body, where direct access to such information is limited, necessitating reliance on estimations. Any inaccuracies in these estimations can distort the ellipsoid's configuration, potentially compromising the accuracy of the manipulability assessment. To address this issue, this article extends the standard approach by introducing the concept of the manipulability pseudo-ellipsoid. Through a series of theoretical analyses, simulations, and experiments, the article demonstrates that the proposed method exhibits reduced sensitivity to noise in sensory information, consequently enhancing the robustness of the approach.

Figures (10)

• Figure 1: Downscaled visualization of the velocity manipulability ellipsoid and the principal radii for a right arm 12-DoF kinematics model, based on the VHP dataset Garner1999 with the following joint values (in radian): sternoclavicular [-0.31, 0.33], acromioclavicular [0.47, 0.1, -0.02], glenohumeral [0.52, 0.37, -0.98], humeroulnar [0.17], radioulnar [1.86] and radiocarpal [-0.11, -0.25].
• Figure 2: Ellipsoid's principal radii in Fig. \ref{['fig:skeleton_side']} projected onto the direction $\boldsymbol{\nu}$, and the resulting projection norm $l$.
• Figure 3: Ellipsoids on the left, and their corresponding pseudo-ellipsoids on the right. The principal radii with the lengths $r_1$, $r_2$ and $r_3$ are along the axes $x$, $y$ and $z$, respectively.
• Figure 4: Simulation scenario -- A 2-DoF arm kinematics model in three different configurations with their associated manipulability ellipses.
• Figure 5: Simulation results -- Maximum deviation of the estimated metrics: manipulability ellipsoid radius $r$ (left) and manipulability pseudo-ellipsoid radius $l$ (right) for changes in values $q_{h,1}$ and $q_{h,2}$ associated with different body configurations; see Fig. \ref{['fig:threeArms']}.