IEEE Robotics & Automation Magazine - December 2018 - 80

z 2
0
3

z 2
0
3
0

y -3

-2

2

0
x

z 2
0
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0

y -3

-2

2

0
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Global Optimal Planning
(RRT*)

z 2
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-2

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0

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-2

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Offline
Environmental
Parameters

Explicit Relationship

Style
Parameters

Motion Learning
(DMPs)

Regression
(GPR)

2
0
y -2

z2

Environmental
Parameters
(Online Sensing)

z2
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-2

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Featured
Motion Styles

Style
Parameters

0
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x

y -2

Online

New Environment

-2

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Figure 3. An overview of the proposed learning-based motion-planning algorithm for cooperative aerial manipulation.

and w is the weight to be learned. In the particular cooperative aerial transportation scenario considered here, our purpose is to avoid encountered obstacles in a safe and
optimized way. Hence, we place obstacles of different dimensions near the aerial manipulators and gather the planning
results from the RRT*. For the RRT*, the performance index
of the combined system is defined as the total travel distance
of the body of multirotors.
The difference between PDMPs and DMPs lies in formulating the attractor function f (|; w). In DMPs, the attractor
function is formulated by supervised learning of the target
attractor function, where the target attractor functions are
computed by substituting q with the demonstrated states q d
in (1). With respect to PDMPs, on the other hand, to consider
the multiple demonstrations in a unified framework, the style
parameters and basis functions are introduced to the attractor
function as
fn (|, s n; w n) = s 


IEEE Robotics & Automation Magazine - December 2018

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