ERK'2022, Portorož, 212-215 212
Human-inspired robotic levering using Periodic Dynamic
Movement Primitives
Boris Kuster, Matevˇ z Majcen Horvat
Humanoid and Cognitive Robotics Lab, Dept. of Automatics, Biocybernetics
and Robotics, Joˇ zef Stefan Institute, Jamova cesta 39, 1000 Ljubljana
E-mail: boris.kuster@ijs.si, matevz.majcen@ijs.si
Abstract
Autonomous robotic disassembly (recycling) of elec-
tronics requires a variety of skills. One of these is lev-
ering, which allows the robot to apply greater forces us-
ing a fulcrum, providing a mechanical advantage. While
such tasks can be accomplished in some cases using pre-
recorded robot trajectories obtained by demonstration,
a more general approach to levering is preferred. The
issue is an automatic adaptation to the different object
shapes. This work presents an algorithm for perform-
ing human-inspired robotic levering exploiting periodic
dynamic movement primitives and force/torque feedback-
based control for contact point determination. The algo-
rithm autonomously adapts to the different object shapes
and provides for the successful accomplishment of the
levering task.
1 Introduction
With the recent shift towards environmentalist policies,
robotic disassembly of items for waste reduction by re-
cycling has received increased attention. Humanity pro-
duces a great deal of electronic waste [1]. The applica-
tion of intelligent and flexible robots to replace human
workers can decrease recycling costs in the long term.
On the other hand, recycling faces the problem of small
batches and a great variety of recycled items. In such cir-
cumstances, the effort for robot programming to perform
autonomous disassembly of generic electronics is one of
the reasons for the slow deployment of robotics-based so-
lutions. During the disassembly of electronics and other
items, various robotic skills are needed, one of which is
levering. It is a process whereby mechanical advantage
can be gained using a rigid beam (lever) and a fixed hinge
(fulcrum), allowing a greater force to be exerted on the
load (the levered object). Some operations where lever-
ing is needed include removing pins and nails or separat-
ing different device parts. While this is an easy task for
humans, as they can rely on vision, force, and pressure
sensing supported by previous experience and general-
isation capability, robotic disassembly applications still
commonly use pre-recorded trajectories. These trajec-
tories, however, need to be carefully adapted and repro-
grammed for each disassembled object. Dynamic move-
ment primitives were shown to be applicable to assembly
and disassembly tasks [2] as well as to the task of motor
control in humanoid robots [3]. In this paper, we propose
to improve the generalisation of the levering movement
using Periodic Dynamic Movement Primitives (PDMPs)
and combine them with external forces and torques esti-
mation, acting on the end-effector. One of the benefits
of the proposed framework is adaptation without addi-
tional vision information, which can be unreliable due to
the poor lighting conditions and occlusions often encoun-
tered in recycling processes. The proposed algorithm for
performing human-inspired robotic levering was imple-
mented on a collaborative Franka Emika Panda robot and
applied to disassembling heat cost allocators (electronic
devices).
2 Preliminaries and related work
Dynamic movement primitives (DMPs) were proposed
as an efficient way for learning and control of complex
robot behaviors [4]. The basic form of DMPs consists
of a differential equation (a linear second order damped
spring attractor system) along with an added nonlinear
forcing term, which allows the adaptation of the simple
second order attractor dynamics to a specific robot move-
ment [5]. Eq. (1) is the nonlinear differential equation
defining a DMP. This model can be written in first-order
notation, as shown in Eqns. (2, 3). Here, τ is a time
constant, whileα z
andβ z
are positive constants that rep-
resent the damping and proportional terms, respectively.
With the appropriate choice ofα z
andβ z
, the system will
be critically damped and y will monotonically converge
towardsg. In the context of robotics, ¨y, ˙y andy represent
the acceleration, velocity and position of a joint, respec-
tively. g represents the goal, the desired final position of
the movement. If the forcing term f is set to zero, these
equations represent a globally stable second-order linear
system with (z,y) = (0,g) as a point attractor.
τ ¨y =α z
(β z
(g− y)− ˙ y ) +f (1)
τ ˙y =z (2)
τ ˙z =α z
(β z
(g− y)− z) +f (3)
To avoid explicit time dependency, the phase x has
been introduced. It follows the first order linear dynamics

213
shown in Eq. (4). The advantage of this approach is that,
for example, we can stop the evolution of time to account
for perturbations during trajectory execution.
τ ˙x = − α x
x (4)
Periodic dynamic movement primitives can be mod-
eled in a similar fashion as discrete DMPs, shown in Eqns.
(5, 6). Ude et al. [6] presented an implementation of
PDMPs. In this work, we follow their implementation.
˙ z = Ω( α z
(β z
(g− y)− z) +f(ϕ,r )) (5)
˙ y = Ω z (6)
The phase variable ϕ is introduced to avoid explicit
time dependency. The phase is assumed to move with
constant speed, as shown in Eqns. (7, 8). The frequency
of oscillation is defined as Ω .
τ =
1
Ω (7)
˙ ϕ = Ω (8)
The forcing termf can be used to create more versa-
tile point attractor dynamics, so that a more specific path
can be followed from the current position to the goal, for
example avoiding an obstacle between the current posi-
tion and the goal. The forcing term usually takes the
form shown in Eq. (9) for PDMPs, where ψ i
are fixed
basis functions, whilew
i
are adjustable weights [7].
f(ϕ,r ) =
N
P
i=1
ψ i
(ϕ )· w
i
N
P
i=1
ψ i
(ϕ )
r (9)
In general, a demonstrated robot trajectory y
demo
is
recorded in joint or Cartesian space. Velocities and accel-
erations can be calculated as derivatives of the recorded
positions or recorded directly. Then, the trajectory is
encoded into a DMP by setting the goal to be the last
recorded position. For PDMPs, the goal is set as shown
in Eq. (10). Eq. (1) can be reformulated as Eq. (11).
g = 0. 5· (min(y) +max(y)) (10)
f
target
=τ 2
¨ y
demo
− α z
(β z
(g− y
demo
)− τ ˙ y
demo
) (11)
For PDMPs, this equation takes the form of Eq. (12),
wherer is the amplitude of the oscillator.
f(ϕ (t),r) =
¨ y
Ω 2
− α z
(β z
(g− y)− ˙ y
Ω ) (12)
The forcing function values are approximated by a
linear combination of weight functions, shown in Eq. (9).
Weight functions for Periodic DMPs are shown in Eq.
(13). The weightsw
i
are calculated by applying standard
regression techniques [7]. Centers of the weight func-
tions,c
i
, are evenly distributed along the trajectory, while
h
i
> 0.
ψ i
(ϕ ) =exp(h
i
(cos(ϕ − c
i
)− 1)) (13)
Various improvements have been proposed for DMPs.
Ude et al. propose defining DMPs for non minimal, sin-
gularity free representations of orientation, with rotation
matrices and quaternions [7]. Nemec et al. [2] propose
extensions, which enable the generalization of movement
back and forth for Cartesian Dynamic Movement primi-
tives, while also encoding the robot end-effector quater-
nion orientation. Saveriano et al. [4] describe the various
existing DMP formulations and discuss their advantages
and disadvantages. Ijspeert et al. [5] show how to op-
timize DMP parameters to minimize various costs, for
example the total jerk of the trajectory or the end-point
variance. Deniˇ sa et al. [8] propose compliant movement
primitives (CMPs), which encode both the kinematic tra-
jectory as well as the corresponding joint torques. This
allows for compliant robot behavior, which is advanta-
geous when operating in unstructured environments along-
side humans.
3 Levering setup
Fig. 1 shows the typical levering setup. The lever is at-
tached to the robot flange, therefore the terms lever and
tool can be used interchangeably. The used tool in this
task is a screwdriver. The levered part lies within the ob-
ject. Subsequently, we will refer to the levered part as
part. To increase mechanical advantage, the lever is posi-
tioned against the fulcrum.
Figure 1: Elements of a levering process.
In Fig. 2, object coordinate system(c.s.) (X, Y , Z
axes), the robot flange c.s. (X
0
, Y
0
, Z
0
), the nominal
tool c.s. (X
1
,Y
1
,Z
1
) and the tool c.s. (X
2
,Y
2
,Z
2
) are
shown. The Tool Center Point (TCP) is located at the tool
c.s. Initially, the nominal tool c.s. and the tool c.s. are
identical, the tool c.s. is changed only after the location
of the fulcrum is known. In our work, we make use of
force-torque (FT) measurements (F
x0
, F
y0
, F
z0
, M
x0
,
M
y0
,M
z0
), which are calculated in the robot flange c.s.
The lever (tool) angleα is shown in Fig. 2.

214
Figure 2: The object, robot flange, nominal tool and tool coor-
dinate systems.
4 Fulcrum and part contact point search al-
gorithm
Our search algorithm is parameterized with the following
input parameters:
• initial Cartesian position (x,y,z) in robot coordi-
nate system.
• the c.s. rotation angleβ .
• torque threshold to detect the part and fulcrum,M
thr
.
• forceF
z0
threshold to detect the part,F
thr
The robot TCP must be initially positioned above the
part and the approximate location of the part and fulcrum
must be known in advance. This approximate informa-
tion can be obtained, for example, by a vision system, or
by pre-positioning the part within a holder with a known
pose. The input parameters for the algorithm are the ini-
tial Cartesian position (x,y,z) between the fulcrum and
part (in the robot c.s.) and the angle of rotation around
thez axis,β . This position and the angle define the plane
in which we will perform the levering, as shown in Fig.
1). The initial Cartesian position must be located between
the fulcrum and the part.
To detect the part, we can take advantage of the fact
that our object has a flat lower plane, which we detect by
moving in the negativez direction until determining con-
tact by measuringF
z0
. The location of the levered part
(load) can be trivially determined by moving along the
positivex axis until detecting contact by measuringM
x
.
After the threshold valueM
thr
is reached, the current po-
sition is recorded as the part position.
To contact the fulcrum, the tool angleα is decreased
until contact is detected by measuringM
x0
. The TCP is
recorded. For approximately detecting the location of the
fulcrum, we can take advantage of the fact that we know
both the robot flange and TCP positions. After slightly
increasing the threshold value M
thr
, further rotation is
performed and the position is again recorded. In a 2D
plane, the approximate position of the fulcrum can be de-
termined by the intersection of the two lines connecting
the robot flange to the TCP.
The robot’s TCP, which was previously located at the
end of the lever, is moved to the position of the fulcrum,
as seen in Fig. 2 (the TCP is reduced in the negativez
0
axis). This ensures that, when changing the tool angleα ,
the lever is rotated around the fulcrum and always stays
in contact with it.
5 Executing the levering
We have observed that humans often use periodic move-
ments when levering, especially when they do not know
the force required to dislodge an object with the lever. In
doing so, they slightly increase the force on the lever in
each period.
Our levering algorithm is parameterized with the fol-
lowing input parameters:
• initial amplitude of the sinusoidal cycle, set toA =
10
◦ in our experiments.
• duration of the sinusoidal cycle, set tot
c
= 10s.
• number of weights for encoding the PDMP, set to
n = 25.
• goal scaling for each iteration, set tog =g+0. 2·A.
• initial radius of the PDMP, set tor = 1.
To mimic this behavior, we generate a single degree-
of-freedom (DOF) sinusoidal cycle with an amplitudeA
and cycle timet
c
, which represents the angle of the end-
effector relative to the initial angleα at which the robot
is in contact with the fulcrum and part. This angle is the
most important parameter in levering.
The specified sinusoidal pattern is encoded into the
PDMP as per section 2. We usen weights.
After the lever is in the initial position, touching both
the part and the fulcrum, the execution of the PDMP be-
gins.
While the PDMP is being executed, the measured force-
torque signals are used to detect when the levering was
successful, as per Section 6. If the entire trajectory is
completed without encountering a success signal, the PDMP
goal value is increased as specified by the input parame-
ters of the algorithm. This effectively increases the force
applied to the levered part during each iteration. The orig-
inal generated trajectory (lever angle) is shown in Fig. 3,
along with the decoded PDMP trajectory. Here, three it-
erations are shown, and after each iteration the goal angle
is increased.
6 Detecting levering completion using force-
torque measurement
To detect when levering is successful without using vi-
sion or other feedback signals, we can use force-torque
(FT) measurements (F
x0
,F
y0
,F
z0
,M
x0
,M
y0
,M
z0
) on
the robot end effector.
The algorithm for detecting levering success is pa-
rameterized with the following input parameters:
• component of the FT measurement, in our casei =
4, which corresponds toM
x
.

215
Figure 3: Three iterations of decoded PDMP with an increasing
goal.
• torque value used as a threshold,M
max
= 2Nm.
• time window in which the threshold condition is
calculated,t
w
= 1s.
• the secondary cut-off condition,α max
, set to 0°.
We observe that M
x
shows a sharp drop-off at the
point in time when the part (load) is dislodged, as shown
in Fig. 4. There are two possible conditions for lever-
ing success. Firstly, the levering is successful if the dif-
ference between the maximal and minimal torque value
within the width of the signal observation window,t
w
, is
greater than the parameterM
max
, as shown in Eq. (14).
The current sample time is denoted ast
k
. The measured
torques, as well as the value of this threshold condition
cond are shown in Fig. 4. An additional constraint is that
this condition can only be triggered while the lever angle
α is increasing, meaning it’s applying force to the part.
max(M
x
(t))− min(M
x
(t))>M
max
,t =t
k
− t
w
,...,t
k
,
(14)
When recycling old electronics, it can sometimes hap-
pen that the levered part is very loose and does not pro-
vide a large resistance force, so a drop in M
x
will not
be detected. Therefore, the secondary condition for lev-
ering success is if the lever angle α is higher than the
parameter of the second cut-off conditionα max
. In our
specific case, shown in Fig. 1, the contact point with the
part is always lower than the fulcrum in the objectz axis.
Therefore, if the lever’s angle is greater than horizontal
(α> 0°), the levering stops.
7 Conclusion and further work
We presented a human-inspired levering algorithm, com-
posed of two sub-tasks: searching and levering. The search
algorithm automatically detects contact points after be-
ing roughly pre-positioned between and above the part
and fulcrum locations. The levering algorithm is accom-
plished using periodic dynamic motion primitives frame-
work. Both algorithms are parametrized to quickly adapt
Figure 4: Measured torques and the condition variable.
to different use-cases. The success of the levering ac-
tion is detected based on a pre-defined criteria of a torque
measurement drop-off. However, this value needs fine
tuning. To overcome this problem, we propose to analyze
the force torque signals using the dynamic time warping
(DTW), which compares a reference signal of successful
levering torques with the observed torques in the current
levering iteration.
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