IEEE Robotics & Automation Magazine - September 2018 - 89

driving the hand to a desired angular set point. This problem
is solved using passivity-based control (PBC) for port-Hamiltonian (pH) systems. In its standard form, this approach
applied to nonprehensile rolling aims to find a control law for
system (1a) and (1b) such that the closed-loop dynamics can
be written as
qo
0
B -1 B d
; E==
G dH d (q, p),
1
po
- B d B J 2 (q, p) - R d (q, p)

(2)

where q ! R 2 and p ! R 2 are the generalized coordinate
and moment vectors, H d = (1/2) p < B -d 1 (q) p + Vd (q) ! R
is the desired total energy of the closed-loop system,
B d ! R 2 # 2 and Vd ! R are the desired mass matrix and
potential energy, respectively, and J 2 ! R 2 # 2 and R d ! R 2 # 2
represent the gyroscopic forces and damping injection of
the closed loop, respectively. The objective is to shape the
desired energy of the closed-loop dynamics to produce a
minimum potential energy at the desired equilibrium.
The asymptotic stability of the closed loop is ensured by
using the desired energy as the Lyapunov function and
the detectability of the passive output. The full development of the control design for the DoD example is
reported in [11].
Within the RoDyMan project, control laws related to the
nonprehensile rolling primitive have also been developed for
the 3-D case, such as the stabilization of a ball on a flat plate
and the control of a robotic hula-hoop [19]. As a milestone, it
is affirmed that nonprehensile rolling can be successfully
modeled through the pH formalism and, consequently, controlled with PBC approaches. This means that a unified
framework exists at least for this class of nonprehensile
manipulation primitive.
Friction-Induced Manipulation Primitive
As a case study, to uniformly cook a pizza, the dough must
be rotated through a peel inside a wooden oven, where the
heat source is present only on one side of the structure.
Similar actions are performed by chefs when food must be
browned or rotated in a pan.
From a dynamic point of view, friction plays a key role
because of the sliding manipulation primitive between the
tool and the manipulated part. In the literature, frictioninduced manipulation was extensively studied to create virtual velocity fields on a vibrating plate actuated by a mechanical
system equal or similar to a Stewart platform [10]. A similar
concept was suitably modified for the pizza case [20].
The RoDyMan platform has successfully achieved a
bimanual nonprehensile manipulation task through sliding by
handling a peel to rotate the pizza placed on it. With reference
to Figure 1, the peel is chosen to only be translated (and rotated) along (and around) its longitudinal direction. A suitable
combination of these two movements creates the desired
motion of the object on the peel: acceleration along the longitudinal direction moves the object back and forth on the peel
once static friction is overcome, while an angular acceleration

around the same axis creates a nonuniform pressure distribution on the object. This, together with the linear acceleration,
creates a rotation of the object. The object rotation is not
decoupled from a linear displacement on the peel. Adaptations from [20] have been necessary to apply the concepts on
the RoDyMan platform. Two suitable smooth sinusoidal
accelerations with the same tunable frequency and different
tunable amplitudes and phases are planned for the linear and
angular accelerations of the peel. The motion of the RoDyMan joints is then retrieved by means of a standard closedloop inverse kinematic algorithm. The previously described
tracking of deformable objects is employed to control the center of mass of the pizza toward the center of the peel through
a simple proportional-integral controller while a complete
rotation of the circular shape is requested.
Friction estimation is crucial within this task, and several
tests have been performed to suitably tune all of the parameters of the control model to fit the real setup. Current work
aims at finding structural properties for the controller, such as
the design of orbital stabilization for the object on the peel
(i.e., to reach a desired rotational velocity).
Tossing Task
Tossing and catching a deformable object, like pizza dough, is
a procedure that is frequently dexterously performed by
human pizza chefs. There are at least three reasons why tossing the dough during the preparation of the pizza is attractive:
1) the dough is stretched to a desired size, 2) the dough

θh

Figure 6. The RoDyMan platform actuating the BoD system. The
disk is actuated by the movement of the RoDyMan joints. The
displayed structure, made by three connected bars, is employed
to start the experiments with the ball in a position that is
different from the desired equilibrium on the top of the disk. The
world frame is depicted in red, the one attached to the rotating
wheel is in green, i h represents the angle between the two, and
s h measures the contact position of the ball on the wheel.
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IEEE ROBOTICS & AUTOMATION MAGAZINE

IEEE Robotics & Automation Magazine - September 2018

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