Blind Manipulation of Deformable Linear Objects Based on Force
Information from Environmental Contacts
Rita Laezza1 , Finn Süberkrüb, and Yiannis Karayiannidis1
Abstract— Humans have the ability to manipulate Deformable Linear Objects (DLOs) such as cables, with little orno visual information by relying on force torque (FT) sensing.
In this work, we propose a simplified graph representation ofa DLO which enables such blind manipulation by keeping theobject under tension. We show that our representation can be
estimated online by a Kalman filter using FT data, which canthen be used to define a set of sliding and clipping manipulation
primitives. Both the estimation and manipulation primitives
were tested, demonstrating that force-based perception can besufficient for robotic tasks such as cable harness production.

I. I NTRODUCTION
Force Torque (FT) sensing has been extensively usedin robotic contact and interaction tasks both for feedback
control schemes and for estimating important propertiesof the objects being manipulated [1]–[4]. However, mostresearch has been limited to rigid objects, whose state canbe summarized by their pose. Deformable objects constitutea still under-explored class of objects that often require
more complex state representations, since such objects may
also change in shape. Research on FT-based deformableobject manipulation has been limited due to challenges insensing, since FT measurements require the object to provide
sufficient resistance to an applied force. This work focuseson objects much larger along one dimension than the othertwo dimensions, namely Deformable Linear Objects (DLOs)[5]. When manipulating a DLO, it will not offer resistanceto deformation in any direction, unless it is under tension.
This property is exploited to formulate our simplified graphrepresentation and nine manipulation primitives.
Although visual and tactile sensing are also important insuch contexts, here we aim to explore how far one can getwith FT information alone. Sanchez et al. [6] proposed sucha deformable object manipulation approach, but with a more
complex model and for a problem without environmentalcontacts. Here we focus on tasks where the environment
provides contacts which constrain the Degrees of Freedom(DOFs) of the DLO, such as cable harness problems. There
have been few works exploring DLO manipulation withenvironmental contacts [7], [8], and these did not make useof FT sensing. Most notably, Zhu et al. [9] proposed a motion
planning framework, using two motion primitives designed
for a robot to shape a DLO through circular contacts.
While they use a vision-based contact detector, we attempt
to estimate contacts through FT information and make noassumptions on the shape of the contact surface.
1 Division of Systems and Control, Department of Electrical Engineering, Chalmers University of Technology, Sweden {laezza , yiannis}@chalmers.sev3

e3

e2
v4
e1

v2
v1

Fig. 1: Illustration of DLO model constrained by two YuMi SmartGrippers
with four feature points v1 to v4 represented by red spheres and three edges
e1 to e3 , represented as black lines.

II. P ROBLEM S TATEMENT
We address force-based manipulation of DLOs withoutcomplementary visual information, therefore the robot isassumed to be equipped with at least one wrist FT sensor
capable of measuring the tension of the DLO. Furthermore,the problem is formulated assuming that once a DLO isgripped, its local pose is known. Consequently, the grippers
must prevent involuntary slipping of the DLO along the x(red) and z (blue) axes, while also allowing a controlled
sliding motion along x when desired. This can be achieved
mechanically through specialized parallel grippers, shown inFig. 2, which guide the DLO to a known location on thefingers and stop any further displacement along z.
In order to overcome the blindness of the robot, theworkspace must satisfy one key condition, namely it must
provide sufficient contact points in the form of fixtures orpivoting points, which restrict the DOFs of the DLO, thus
enabling tensioning. This is imperative, since when a DLO isfully stretched between two points, the shape between themcan be assumed linear. Note that gravity itself can be used torestrict the DOFs of the DLO. Once an end-effector equippedwith a FT sensor is gripping the object by holding it limp
in the air, the shape of the DLO segment below the gripper
can be inferred to be vertical, assuming quasi-static motion.
III. DLO R EPRESENTATION
We propose a model {G, ρ} to represent the state of a
uniformly weighted DLO. While ρ is a known constant thatdenotes the DLO’s weight per unit length, its state is modeled
as a path graph G = (V, E) where: V is a set of feature points
on the DLO which can be listed in the order v1 , v2 , . . . , v|V | ;and E is a set of edges connecting adjacent feature points,(vi , vi+1 ) for i = 1, 2, . . . , |V | − 1. Note that the cardinalityof V , denoted by |V |, is not constant, and will change as themanipulator interacts with the DLO and indirectly with theenvironment.

pi+1 , mi+1

digpi , mi
di-1

fi-1

DLO hsifiafsens

pi-1 , mi-1

Fig. 3: Sag for edge with length di is denoted by si . The force measured by
an FT sensor in rigid contact with feature point vi is shown as fsens . The
position pi−1 and mass mi−1 can be determined using knowledge of pi
and the measured force fsens . Force fi is a s result of the tension between
pi and pi+1 , while the force fi−1 is caused by the mass mi−1 .

Fig. 2: Robotic setup of a YuMi equipped with specialized parallel grippers
and one fixture attached to a pegboard. Relevant frames are indicated as:{hF T } - FT sensing frame, {hl }/{hr }- left/right gripper tool tip frame,{hf ix } - fixture frame, {hworld } - world frame. Red, green and blue arrows
indicate x-, y- and z-axes, respectively.

A. Feature Points, VThe i-th feature point describing the state of the DLO isdefined as a tuple vi = (pi , Qi , mi ), where pi ∈ R3 is theposition, Qi represents the orientation as a unit quaternion
and mi ∈ R is the mass.
If the feature point is the result of a perceived tension, it
may be due to an unknown contact with the environment or
another gripper. While in the first case pi must be estimated,in the latter it can be obtained directly through forward
kinematics. Furthermore, if an additional feature point vk
is introduced to define a goal, it can be determined bylinear interpolation between two neighboring points, vk−1
and vk+1 . The index k will depend on the location of theadded point relative to the existing points in the model. The
position is then calculated by interpolation as:
pk = pk−1 + δ(pk+1 − pk−1 ), with δ ∈ [0, 1](1)

Since the orientation cannot be accurately estimated, it
is only inferred from the pose of the gripper. For estimatedpoints, the orientation is set so that the x-axis is aligned withthe length of the DLO, without twist i.e. the orientation oftwo adjacent points is the same. When a point vk is added todescribe a goal, a linear interpolation between two quaternion
orientations is computed by spherical linear interpolation,
analogously to the position.
Finally, the mass of the DLO is equally distributed between the feature points, leading to mi . Depending on therelative location of a feature point with respect to otherpoints, the mass is computed as:(diρ, i is an end-point of the DLO(2)
mi = d2i−1 +diρ
, i is between feature points
2
where di is a property of the edges to be described next.
B. Edges, E
The i-th edge, connecting two adjacent feature points(vi , vi+1 ) is defined as a tuple ei = (di , si , fi , ki ), wheredi ∈ R describes the length, si ∈ R is the sag, fi ∈ R thetension and ki ∈ R the spring constant of the DLO between
feature point vi and an adjacent feature point vi+1 .
The sag si between two feature points, illustrated in Fig. 3,
is a measure used to determine whether the tensioning of theDLO is sufficient for the assumption of a linear connection.
If two feature points are not on the same horizontal line andthe sag-to-span ratio (s/a  1) is small enough, no partof the DLO is below the lower feature point. In such cases,
the sag can be approximated [10], unless one of the featurepoints is the extremity of the DLO, constrained by gravity
alone, in which case the sag is set to 0.
The weight compensated DLO tension fi between an endeffector at feature point vi equipped with a FT sensor and asecond feature point vi+1 can be calculated from the force
measurements fsens and the preceding edge’s tension fi−1according to: 0(3)p̂i fi = fsens − 0 mi + p̂i−1 fi−1gwhere g denotes the gravitational acceleration, and the unit
vectors p̂i−1 and p̂i denote the normalized force directions:p̂i =(pi+1 − pi )||pi+1 − pi ||(4)With only one FT sensor, the force fi−1 can only be taken
into account under the assumption that it results from themass of the rope (a free hanging feature point). In order tosense a second tension e.g. if the DLO is tensioned on bothsides of the gripper, another FT sensor would be necessary.
IV. M ANIPULATION P RIMITIVESIn this section we present a set of manipulation primitives
for DLOs, which can be executed based on FT sensing alone,
and limited knowledge about the environment. These areillustrated in Fig. 4, together with their description.
Each primitive specifies a desired force fd ∈ R, position
xd ∈ R3 and quaternion orientation Qd as well as aprojection matrix P ∈ R12×12 to define in which dimensions
a force control is active. The primitives are divided into
individual control primitives, where the two end-effectors
are controlled separately, and coordinated control primitives,
where the absolute and relative end-effector position iscontrolled. In both cases, a hybrid motion-force controller
is used to compute the task space velocities [11].

A - Parallel DLO Tensioning

D - Single Arm DLO TensioningG - Gripper Alignment

B - Parallel DLO Sliding

E - Single Arm DLO Sliding

H - Grasping a Tensioned DLO

C - Parallel DLO Clipping

F - Single Arm DLO Clipping

I - Rotating Around Feature PointFig. 4: FT-based manipulation primitives for DLO manipulation. These constitute diverse actions such as tensioning, clipping, sliding, grasping and rotating.
Motion primitives are divided into individual and coordinated control, depending on whether or not the robot arms are controlled separately. The numberof successful trials (green) from randomized states is shown for each primitive. Since tensioning primitives (A and D) are essential for the proposed DLO
representation, these were tested for 25 trials, while the rest were tested for 15 trials.

V. E VALUATIONA dual-arm YuMi robot equipped with an ATI Mini40
6-axis FT sensor, was used in the real-world experiments.
For a global evaluation of our approach, a cable harness
production scenario was designed which involved routing
two cables through different fixtures. A winding motion
was also demonstrated by combining different manipulation
primitives in a sequence. The video can be found here:
https://youtu.be/3Y5HFzrlxds.
A. Contact Point Estimation

estimation error (mm)The accuracy of the DLO state representation relies on
the identification of contact points through a Kalman filter.
Therefore, we evaluate the uncertainty of this estimate formanipulation primitive D. To that end, the gripper equippedwith the FT sensor was made to execute circular motions overthe contact point to be estimated, and after a while a second
fixture was placed in the path of the DLO, thus changing
the contact point. Fig. 5 shows the position estimation error
along the three dimensions.
8x dimension
y dimension
z dimension
contact point change

64200200

400

600

800

1000

estimation stepFig. 5: The estimation error of the contact point along each axis. The verticaldashed line shows the moment when the contact point changes. For every
125 steps of the estimator, one full circle trajectory is executed.

Initially, the first contact point is accurately estimatedalready after half a circle. Once the contact point changes(at the dashed line), the estimate of the new contact point
converges again after an initial spike in the error.
B. Manipulation Primitive Reliability
To evaluate the reliability of the proposed manipulation
primitives, all were executed multiple times for randomized
placement of the fixtures, initial position of the end effectors,
as well as elasticity and length of the DLOs. The result of
this evaluation is summarized in Fig. 4.
Most primitives had a perfect success rate, with a few
exceptions. Primitives A and D had a combined total of threefailures, due to a problem with the tension controller which
also requires correct estimation of an elasticity parameter.
This parameter is needed to maintain a constant tension on
the DLO without triggering the YuMi’s safety stop. In thefirst moment, the DLO was estimated to be significantly
more elastic than it actually was, which caused a movementthat quickly built up tension, reaching the limit of the robot.
The failure of primitive C was due to an excessive distance
between grippers which prevented the YuMi to be able toapply sufficient force and overcome the clipping resistance.
VI. C ONCLUSION
We presented a DLO manipulation approach relying on FT
sensing alone. This is feasible in applications which provide
environmental contacts which limit the DLO’s DOFs andenable tensioning. By keeping the DLO under tension, itis possible to estimate the location of these contacts, andtherefore to keep a simplified path graph representation of theobject’s state. This representation was successfully employed
to solve a cable harness problem. Future work will aim tocomplement FT sensing with visual information.

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