Automatic Tool Design for Robotic Caging Using
Flexible Wires
Jake Ketchum ∗Joel Meyer ∗Todd Murphey

Northwestern University

Northwestern University

Northwestern University

Abstract—In this work we present a method for automated tool
design for robotic caging with flexible wires. We use computer
vision to determine the end points of the flexible wire thatwill be used by a pair of robot arms to manipulate an object
through a caging structure formed by the wire. We determine theconfiguration of the flexible wire (given its end points) througha geometric optimization scheme. We then deform the end point
positions of the wire’s configuration so that the wire can forma caging structure around the object. We discuss our work-inprogress and conclude with our plans for future work.

I. I NTRODUCTION
While there are many examples of prior work that examine
the role that contact plays in robotic manipulation, few works
have focused on robot tool formation, specifically automatically forming tools that leverage flexible contact with objects
in the environment to accomplish tasks. Surveys on various
techniques for robotic grasping have revealed robotic caging(constraining an object without force closure) to be an effective
method for in-hand manipulation and object transport—the actof enclosing an object relaxes the amount of contacts andforces that need to be tracked during manipulation and theenclosure bounds the position tracking error that can occur [2].
External caging configurations, from which the object cannot
escape given any perturbation, form pre-grasp cages and canbe converted to grasping configurations by squeezing the cage
points towards the object [4]. In this work we present a systempipeline to automatically design wire tool configurations for
manipulating various objects through robotic caging.
To design the tool configuration (in our case, the shape ofan elastic rod that a pair of robot manipulators will grasp),
we build off of work performed in [1] that planned elastic∗ These authors contributed equally to this work.

rod configurations for sets of robot manipulators maneuveringrods through obstacles. Using this work, we have designed ageometric optimization scheme that can determine the configuration of an elastic rod (with knowledge of the rod’s physicalproperties—bending stiffness, torsional stiffness, and whether
the rod is Kirchhoff elastic) based upon the end points of
the rod. Our system pipeline uses this optimization scheme toautomatically design flexible tools for manipulating objects inthe environment.
II. S YSTEM P IPELINE
Figure 1 gives a step-by-step overview of our systempipeline for the automated design of flexible wire tools for
robotic caging. Our system pipeline consists of two primary
components: 1) designing a tool and 2) caging an object.
A. Designing a ToolThe design of the tool starts starts with the selection of“start” and “end” points for the tool (flexible wire) on theobject face most accessible to the two manipulators. These
start and end points lie on the outer edge of the object, which
will be determined through computer vision. A path between
these two points is then traced over a 2-D top-down outline ofthe object to get a desired shape for the tool when “closed”.
That shape is then welded to two lever sections and pulled
open by 125% of the object’s longest chord perpendicular tothe tool use axis. Our geometric optimization scheme (whichbuilds off of work in [1]) then generates the post-expansion
tool shape from these lever positions. This is then used as thefinal design for the wire. In order to bend the wire into thetarget configuration, the design will be segmented into a seriesof curves, each with a position, arc length, and radius about

Fig. 1. Designing a Tool and Caging an Object: A breakdown of the steps involved in designing and using a tool based on the target object’s outline.
Once the object has been caged additional inward force can be applied to the wire “handles” (levers) to constrict the shape and achieve form closure.

A. Manipulation with Automated Tool Design vs. Arbitrary
CurvesFigure 2 shows a comparison of an arbitrary tool curve
shape and a tool designed by our optimization scheme (currently bent by hand for demonstration purposes). The tools
designed by our optimization scheme have more points ofcontact with the object than the arbitrary designs, which gives
the robot manipulators more control over the object.
B. Perturbing End Points for Caging DesignsThe tool designs output by our geometric optimization
scheme are perturbed at their end points during two different
steps in our system pipeline: first, after the outline of the target
object has been determined, and second after our optimization
scheme outputs the desired design. The magnitude of theperturbations during these steps is arbitrary (125% and 25%),
but may vary according to tool design and the material of thetool being used. These perturbations are needed so that therobot manipulators can fit the designed tool over the object(and adjust the design as needed once it is in contact).
IV. C ONCLUSION

Fig. 2. Real-World Tool Shapes for Caging: These photos compare anarbitrary tool design to the output from our optimization scheme (we manuallybent the wires here for demonstration purposes). The manipulators holding
the optimized tool designs have more control over the object due to increased
contact than the manipulators holding the arbitrary tool designs.

a centroid from the previous bend. Future work (covered inSection IV) will develop a method for performing this bending
in the real-world using a pair of robotic manipulators.
B. Caging an Object
The opening of the tool (the distance between the start andend positions of the tool) that is generated via our geometric
optimization scheme is able to fit around the target object fromeither the top or side. Once the object has been enclosed, therobot end effectors will then bring the two end points of therod “closer” together by 25% of the object’s longest chord
perpendicular to the tool use axis in order to cage the object.
For more precise control, the end effectors can further tighten
the tool to achieve form closure. The manipulators can now
move with fixed relative positions to change the position andorientation of the object without losing control over it.
III. D ISCUSSION
In this section, we discuss some of the finer points ofour system pipeline for automated tool design, as well aspreliminary results.

We have presented a method for automatically designing
robotic caging tools using flexible wires. Our method uses ageometric optimization scheme to solve for a desired configuration of a flexible wire based on an object’s outline. Robotmanipulators can then use the resulting tool to control anobject’s position and orientation through caging. We numerically perturb the wire endpoints after determining the outerboundary of the target object. This creates a caging tool for therobot manipulators to fit around the object. The tool endpoints
can then be brought together to cage the object.
In future work, we will design a trajectory planning pipeline
to enable a two-arm robot manipulator to bend the wire tools
according to our optimization scheme outputs. We are alsointerested making the bending planning pipeline closed-loop:
the robot manipulators will receive feedback on the realworld configuration of the wire (i.e., through a camera orforce/torque sensing [3]) during bending and adjust their planfor subsequent bends.
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[2] Satoshi Makita and Weiwei Wan. A survey of robotic
caging and its applications. Advanced Robotics, 31(1920):1071–1085, 2017.
[3] Itamar Mishani and Avishai Sintov. Real-time non-visualshape estimation and robotic dual-arm manipulation control of an elastic wire. IEEE Robotics and Automation
Letters, 7(1):422–429, 2022.
[4] Alberto Rodriguez, Matthew T Mason, and Steve Ferry.
From caging to grasping. The International Journal ofRobotics Research, 31(7):886–900, 2012.