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2008). However, these approaches require computati-
onal time exponential in the dimension of the com-
posite configuration space, so they are appropriate
for small-sized problems only. This drawback leads
to the development of methods that prune the search
space. For instance, Berg et al. (van den Berg et al.,
2009) decompose any instance of the problem into
a sequence of sub-problems where each subproblem
can be solved independently from the others. The Bi-
ased Cost Pathfinding (Geramifard et al., 2006) em-
ploys generalized central decision maker that resol-
ves collision points on paths that were pre-computed
independently per unit, by replanning colliding units
around the highest priority unit. Another approach is
to design an algorithm based on a specific topology
describing the environment. (Peasgood et al., 2008)
present a multi-phase approach with linear time com-
plexity based on searching a minimum spanning tree
of the graph, while an approach for grid-like environ-
ments is introduced in (Wang and Botea, 2008). A
flow-annotated search graph inspired by two-way ro-
ads is built to avoid head-to-head collisions and to re-
duce the branching factor in search. Nevertheless, the
computational complexity is still high (e.g., (van den
Berg et al., 2009) solves a problem with 40 robots in
12 minutes, (Wang and Botea, 2008) needs approx.
30 seconds for 400 robots).
On the contrary, decoupled methods present a
coordination phase separated from the path planning
phase. These approaches provide solutions typically
in orders of magnitude faster times than coupled plan-
ners, but these solutions are sub-optimal. Moreover,
the decoupled methods are often not complete as they
may suffer from deadlocks. These approaches are di-
vided into two categories: path coordination techni-
ques and prioritized planning. Path coordination con-
siders tuning the velocities of robots along the pre-
computed trajectories to avoid collisions (LaValle and
Hutchinson, 1998), (Simeon et al., 2002), while pri-
oritized planning computes trajectories sequentially
for the particular robots based on the robots’ priori-
ties. Robots with already determined trajectories are
considered as moving obstacles to be avoided by ro-
bots with lower priorities (van den Berg and Over-
mars, 2005), (Bennewitz et al., 2001), (Cap et al.,
2015). A similar idea was presented in (ter Mors
et al., 2010), where adaptation of the A* algorithm
is sequentially planning on a graph augmented by in-
formation in which time intervals the particular nodes
are occupied by already processed robots.
Several computationally efficient heuristics have
been introduced recently enabling to solve problems
for tens of robots in seconds. Windowed Hierarchical
Cooperative A* algorithm (WHCA*) employs heu-
ristic search in a space-time domain based on hier-
archical A* limited to a fixed depth (Silver, 2005).
Chiew (Chiew, 2010) proposes an algorithm for n
2
vehicles on a n × n mesh topology of path network
allowing simultaneous movement of vehicles in a cor-
ridor in opposite directions with computational com-
plexity O(n
2
). Luna and Bekros (Luna and Bekris,
2011) present a complete heuristics for general pro-
blems with at most n − 2 robots in a graph with n
vertices based on the combination of two primitives
- “push” forces robots towards a specific path, while
“swap” switches positions of two robots if they are to
be colliding. An extension which divides the graph
into subgraphs within which it is possible for agents
to reach any position of the subgraph, and then uses
“push”, “swap”, and “rotate” operations is presen-
ted in (DeWilde et al., 2014). Finally, Wang and
Wooi (Wang and Goh, 2015) formulate multi-robot
path planning as an optimization problem and approx-
imate the objective function by adopting a maximum
entropy function, which is minimized by a probabilis-
tic iterative algorithm.
Although many of the approaches mentioned
above have nice theoretical properties, the most
practically usable algorithm is probably Context-
Aware Route Planning (CARP) presented in (ter Mors
et al., 2010) as it is fast, produces solutions of high
quality, and although it is not complete, it finds a so-
lution for a large number of practical setups.
(Kiril Solovey, 2014) presented MRdRRT algo-
rithm, which is a probabilistic approach for path
planning on predefined structures for relatively small
number of robots inspired by RRT algorithm (Lavalle,
1998). (Dobson et al., 2017) improves upon MR-
dRRT by presenting its optimal variant.
In this paper, we present a probabilistic appro-
ach which extends and improves a discrete version
of Rapidly-Exploring Random Tree (RRT) for mul-
tiple robots (Kiril Solovey, 2014). Our approach fo-
cuses mainly on scalability with increasing number
of agents as well as improving the quality of solu-
tion compared to (Dobson et al., 2017) that presents
the optimal version of the dRRT algorithm but keeps
the number of robots relatively low. We show that
the proposed extensions allow solving problems with
tens of robots in times comparable to CARP with a
slightly worse quality of results. On the other hand,
the proposed algorithm finds solutions also for setups
where CARP fails.
The rest of the paper is organized as follows. The
multi-agent path-finding problem is presented as well
as the used terms are defined in Section 2. The multi-
robot discrete RRT algorithm and the proposed im-
provements are described in Section 3, while perfor-
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