![](bg6.png)
values over all trials for the first found admissible tra-
jectories are shown in Fig. 3.
Also in this case, SOM RRG requires less num-
ber of RRG expansions to find a feasible solution.
Such a solution can be then improved by the RRG ex-
pansions in a similar way as the reference algorithm
works, which is demonstrated in Fig. 5.
5.3 Discussion
Despite of the relatively simple problems considered,
the presented early results validate a feasibility of the
proposed approach for steering the randomized sam-
pling in the RRG. The results indicate SOM for the
TSP can be applied directly in C and thus a construc-
tion of the motion planning roadmap prior sequenc-
ing part of the MGMP can be avoided. The SOM
RRG provides first feasible solutions of the MGMP
in fewer expansions steps albeit the quality of such a
solution is worse than for reference algorithm utiliz-
ing the known sequence of the goals.
The SOM based approach seems to be faster than
the reference algorithm in finding the first feasible so-
lution; however, we found out that the selection of the
winner node is computationally more demanding with
increasing learning epoch and the number of goals,
see Fig. 3(d). It is because the graph G
RRG
becomes
denser, which increases computational burden of the
determination of the vertex v
ν,g
by (1). This issue may
be addressed by removing non-perspective roadmap’s
vertices or by building an additional structure to sup-
port path queries in the roadmap.
6 CONCLUSION
In this paper, we address multi-goal trajectory plan-
ning with motion primitives and we introduce a new
steering strategy for randomized sampling in RRG to
improve its performance for a hexapod walking robot.
The proposed approach is based on principles of un-
supervised learning of self-organizing maps that al-
low to simultaneously solve the sequencing part of the
MGMP together with determination of the particular
trajectories. The presented early results of the pro-
posed idea in simple case studies provide a ground
work for a further research. Despite of the simple
problems considered, a straightforward MGMP plan-
ner based on a priori known sequence of goals visits
and the standard RRG algorithm requires more expan-
sion steps to find a feasible solution than the proposed
approach. This indicates that the proposed steering of
the randomized sampling in the RRG can improve the
performance of the planner significantly.
The encouraging results motives us to evaluate the
proposed idea in more complex problems and to com-
pare the performance regarding the solution quality
of the final multi-goal trajectory provided by other
approaches based on postponed distance evaluation
techniques.
ACKNOWLEDGEMENTS
The presented work is supported by the Czech Sci-
ence Foundation (GA
ˇ
CR) under research project No.
13-18316P. The work of Petr Van
ˇ
ek was supported by
the Grant Agency of the Czech Technical University
in Prague, grant No. SGS14/203/OHK3/3T/13.
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