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allowed for easier imitation learning, better interpola-
tion of the learned trajectories, and significantly better
chances of a success of a grasp in cluttered environ-
ments than standard motor primitives. Although the
experiments were performed within a grasping task
scenario, the proposed methods can be beneficial for
other manipulation tasks, such as pressing buttons and
pushing objects.
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APPENDIX
Dynamical Systems Motor Primitives
The dynamical systems motor primitives (DMPs) pro-
posed by Ijspeert et al. (Ijspeert et al., 2003) were in-
spired by the simple, but highly adaptive,motions that
animals employ,and combine to obtain more complex
motions. The primitives are implemented as a passive
dynamical system with an external force, and repre-
sented as
¨y = α
z
(β
z
τ
−2
(g− y) − τ
−1
˙y) + aτ
−2
f(x), (1)
where α
z
and β
z
are constants, τ controls the duration
of the primitive, a is an amplitude, f(x) is a nonlinear
function, and g is the goal for the state variable y.
By selecting α
z
and β
z
appropriately, and setting
a = 0, the system reduces to ¨y = α
z
(β
z
τ
2
(g− y) − τ˙y)
and becomes a critically damped global attractor. It
can be visualized as a spring and damper system that
ensures state y will always end at the goal value g.
The function f(x) is a shaping function based on
the state, x ∈ [0,1], of the canonical system that syn-
chronizes the DMPs ˙x = −α
x
τx, where α
x
is a time
GRASPING WITH VISION DESCRIPTORS AND MOTOR PRIMITIVES
53