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We will first start with task space planning. Therefore we add an 'mental observation' of reaching the
th discrete position in task space
at time
to our Bayesian network (see Figure 10). We will set our desired target position to be
, the index
denotes the discrete index of this position. In addition, we also observe our current state
which is
. Our task is to estimate a trajectory
using Gibbs-sampling.
- Your main task is to generate the state transition probabilities
as well as the kinematic task mapping
as described in the text.
- Initialize your trajectory
with random discrete indices. Use 5000 Gibbs sampling steps to estimate the true distribution. Plot 5 independent samples of
from the sampling process. We assume that two samples are independent at least after 100 Gibbs Sampling steps.
- Now we want to calculate the marginals
for all
and
. Therefore count the number of of times in which the variable
equals
during the last 3000 Gibbs sampling steps. Plot the marginals for each time step, use a visualization which you find appropriate. How does the estimated solution look like?
- Repeat the experiment at least 10 times using different initial positions for the Gibbs sampler. Are the marginals always similar (up to a certain noise level...)? If not, why not?
Next: Task Space Planning with
Up: Planning with Approximate Inference
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Haeusler Stefan
2011-01-25