Kinematics of continuum planar grasping

TL;DR

This paper develops an analytical framework for understanding and optimizing the kinematics of soft continuum arms grasping planar objects, introducing geometric modeling, optimal control, and grasp quality metrics.

Contribution

It introduces a novel geometric and control-based approach to analyze and optimize continuum arm grasping of planar objects, including new metrics and simulation validation.

Findings

Derived reduced kinematic equations for continuum grasping.

Formulated an optimal control problem for feasible arm shapes.

Proposed new grasp quality metrics based on algebraic properties.

Abstract

This paper presents an analytical framework to study the geometry arising when a soft continuum arm grasps a planar object. Both the arm centerline and the object boundary are modeled as smooth curves. The grasping problem is formulated as a kinematic boundary following problem, in which the object boundary acts as the arm's 'shadow curve'. This formulation leads to a set of reduced kinematic equations expressed in terms of relative geometric shape variables, with the arm curvature serving as the control input. An optimal control problem is formulated to determine feasible arm shapes that achieve optimal grasping configurations, and its solution is obtained using Pontryagin's Maximum Principle. Based on the resulting optimal grasp kinematics, a class of continuum grasp quality metrics is proposed using the algebraic properties of the associated continuum grasp map. Feedback control aspects in the dynamic setting are also discussed. The proposed methodology is illustrated through systematic numerical simulations.