Kinematics of continuum planar grasping

2026-04-10

AI Summary

This study addresses the geometric and kinematic modeling challenges of soft continuum manipulators in planar grasping tasks by introducing a “shadow curve” approach. The method treats the object boundary as a constraint trajectory for the manipulator’s centerline, enabling a simplified kinematic model formulated through relative geometric variables with curvature as the control input. Leveraging differential geometry and the Pontryagin maximum principle, the authors establish a quality metric for continuum grasping and derive optimal grasp configurations. Numerical simulations demonstrate the effectiveness of this framework in optimizing grasp postures and quantitatively evaluating grasp performance, offering both theoretical foundations and a novel paradigm for continuum robot manipulation.

Technology Category

• Intelligent Robots: Manipulation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• continuum grasping
• kinematics
• planar object
• soft robotics
• geometric modeling

Innovation

• continuum robotics
• kinematic boundary following
• optimal control
• grasp quality metrics
• Pontryagin's Maximum Principle