Statics of continuum planar grasping
For continuum robotics researchers, it provides a theoretical foundation and optimization tools for static grasping, though it is an incremental extension of rigid-body grasp theory.
This paper develops a control-theoretic framework for analyzing static equilibrium of continuum planar grasping, formulating it as a linear control system and using optimal control to minimize contact forces. It generalizes rigid-body grasp quality metrics to continuum robots and provides numerical results.
Continuum robotic grasping, inspired by biological appendages such as octopus arms and elephant trunks, provides a versatile and adaptive approach to object manipulation. Unlike conventional rigid-body grasping, continuum robots leverage distributed compliance and whole-body contact to achieve robust and dexterous grasping. This paper presents a control-theoretic framework for analyzing the statics of continuous contact with a planar object. The governing equations of static equilibrium of the object are formulated as a linear control system, where the distributed contact forces act as control inputs. To optimize the grasping performance, a constrained optimal control problem is posed to minimize contact forces required to achieve a static grasp, with solutions derived using the Pontryagin Maximum Principle. Furthermore, two optimization problems are introduced: (i) for assigning a measure to the quality of a particular grasp, which generalizes a (rigid-body) grasp quality metric in the continuum case, and (ii) for finding the best grasping configuration that maximizes the continuum grasp quality. Several numerical results are also provided to elucidate our methods.