IEEE Robotics & Automation Magazine - September 2020 - 41

Legend

Disturbance

QP
Actual
Planned

Start

vr

ve

va

0.45

0
x (m)

-0.3
0.1

0.2

-0.3 -0.2

0.3

-0.1

0.06

-0.5
-0.3

0
0.1
x (m)
(b)

0.2

)

-0.7
Start

(a)

0.3

QP
Actual

0.04
Velocity (rad/s)

-0.9

End

(m

-0.2 -0.1

-0.5

0.15

(m

End

0.30

y

0.15

)

-0.9
-0.7

(m)

-1.1

0.30

y

z (m)

0.45

-0.3

Occluded View
Camera 6

0.02
0
-0.02
-0.04
-0.06

Velocity (rad/s)

-0.08

1,150 1,200 1,250 1,300 1,350 1,400 1,450 1,500 1,550 1,600
Time (s)

0.02
0

-0.02
1,280

1,290

1,300
Time (s)

1,310

1,320

(c)

Figure 8. The results of experiment 1. This experiment concerns the online trajectory and OBS/collision avoidance of a
robotic end effector during the magnetic deflection of an endovascular catheter in seven targets. (a) The move from the
initial configuration to target 1 during trajectory 2. The end effector (orange) avoids a mockup arterial structure that is
displaced horizontally. This trajectory is shown in the 3D capture volume around the BB of the arterial structure, which is
enveloped in a safety hemisphere. The end effector first follows a planned trajectory obtained from (7), indicated in green,
after which the QP algorithm calculates the joint velocities to obtain the desired end-effector position (blue). (b) The move
from target 5 to 6. The end effector avoids the arterial structure during vertical motions. The left-side inset shows
the reactive planner that results from these motions due to the attractive-velocity vector (v a), repulsive velocity (v r), and
velocity vector of the end effector (v e). The right-side inset from camera 6 illustrates the consistent tracking of the end
effector despite an occlusion. (c) The joint velocity profile of joint 2 indicates the calculated (blue) versus the actual
(orange) velocities.

SEPTEMBER 2020

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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41



IEEE Robotics & Automation Magazine - September 2020

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