Designing Underactuated Graspers with Dynamically Variable Geometry Using Potential Energy Map Based Analysis

TL;DR

The paper presents a friction-aware potential energy map framework for designing underactuated graspers with dynamically variable geometry, focusing on a two-phalanx tendon-pulley configuration. By including palm width, link lengths, and transmission ratios in the energy-based analysis, the authors show how object size and surface friction shape caging and in-hand manipulation performance. Through extensive simulations across thousands of designs and multiple objects, the work demonstrates that real-time morphing of palm and pulley radii can outperform fixed-geometry variants in many scenarios, albeit at the cost of additional actuation. The findings offer a path toward more capable, hardware-efficient grasps and manipulation strategies, with future work aiming to prototype and extend these energy-map–driven control approaches to non-symmetric and stop-oriented tasks.

Abstract

In this paper we present a potential energy map based approach that provides a framework for the design and control of a robotic grasper. Unlike other potential energy map approaches, our framework is able to consider friction for a more realistic perspective on grasper performance. Our analysis establishes the importance of including variable geometry in a grasper design, namely with regards to palm width, link lengths, and transmission ratio. We demonstrate the use of this method specifically for a two-phalanx tendon-pulley underactuated grasper, and show how various design parameters - palm width, link lengths, and transmission ratios - impact the grasping and manipulation performance of a specific design across a range of object sizes and friction coefficients. Optimal grasping designs have palms that scale with object size, and transmission ratios that scale with the coefficient of friction. Using a custom manipulation metric we compared a grasper that only dynamically varied its geometry to a grasper with a variable palm and distinct actuation commands. The analysis revealed the advantage of the compliant reconfiguration ability intrinsic to underactuated mechanisms; by varying only the geometry of the grasper, manipulation of a wide range of objects could be performed.

Figures (8)

• Figure 1: Subset of the possible benefits of dynamically variable geometry for grasping and in-hand manipulation. In (1), the palm width is decreased in order to move the object toward the fingertips during a "place" task. The underactuated fingers keep the object caged for as long as possible during this operation. In (2), the left side shows the link lengths decreasing to move the object away from the palm, and on the right the link lengths are increased to pull the object up to the palm. In (3), increasing the transmission ratio causes the object-grasper system to reconfigure from a tip prehension to a power grasp. Note that the tendon (shown in red) wraps around a larger distal pulley on the right side of (3). The thickness of the links is shown in this case so the changing distal pulley diameter can more easily be visualized.
• Figure 2: (a) Description of the terms used in the grasper analysis, including geometric and contact parameters. (b) The frames for each link, the palm, and the object.
• Figure 3: Potential energy map. Hatched regions indicate static equilibrium, i.e., \ref{['eq: contactWrenchHull']} is satisfied. Objects will tend to move from high potential energy to low potential energy configurations as indicated by the red arrows. Friction may prevent the lowest possible energy state from being reached. Note that the grasper and object are not to scale with the energy map, but are there to illustrate the evolution of the grasp.
• Figure 4: Best graspers at evolving the given object, defined by $r$ and $\mu_{s}$, into a caging grasp. Each grasper is shown to scale on top of its corresponding energy map for the given object. Darker colors represent lower energy states for the system, and hence the object will tend to be pulled into these regions.
• Figure 5: Contact point evolution on the distal link. If the transmission ratio $R$ is sufficiently large, the contact point will slide toward the fingertip of the distal link (going from (1) to (2)), causing the contact normal to point more toward the palm.