IEEE Robotics & Automation Magazine - June 2020 - 29
Success Rate
0.84
Learning From 100 Demonstrations
0.8
0.76
0.72
1,500
3,000
Epochs
(a)
4,500
6,000
Learning From 300 Demonstrations
Success Rate
For the demonstrations, we used a random trajectory generator based on a fifth-order polynomial with which the position and velocity at the end of the trajectory can be specified.
The initial ball location on the table is fixed. The end velocities of the trajectories are randomly sampled from a uniform
distribution. With different hitting velocities, the ball stops at
different locations. We collected the final locations of the ball
q and MP parameters w in a training data set.
As shown in Figure 7, the ball can bounce off the borders
of the table, which realizes multiple modes for one specific
target location in the collected demonstrations. The table
measures 260 # 200 cm, and the ball has a radius of 5 cm.
Successful task execution means that the ball is no more than
10 cm from the target location.
We use K = 3 mixture components and train the MDN
with 50 random demonstrations and test it on 100 new ball
locations. When selecting the most probable mode, we get an
average success rate of approximately 15%. This poor performance might be because the task requires an accurate trajectory. With a randomly small perturbation of the MP parameters
that correspond to the original 50 demonstrations, the success
rate can drop rapidly. As mentioned previously to improve the
task performance, we draw several samples from the output
distribution. In this case, a successful MP generalization means
that there exists at least one of these samples that leads to
0.85
0.84
0.83
lNLL
lNLL + lmodel
lNLL + lmodel + lneg
1,500
3,000
Epochs
(b)
4,500
6,000
Figure 5. A comparison between the original and entropy MDNs,
showing the results with (a) 100 and (b) 300 demonstrations.
Figure 6. Three obstacles are randomly placed in the 2D space. The solid curves correspond to the most probable mode, and the
dashed curves are generated by the two other modes that are not selected by the MDN.
JUNE 2020
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IEEE ROBOTICS & AUTOMATION MAGAZINE
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29
IEEE Robotics & Automation Magazine - June 2020
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