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Page 326 Lei et al. Intell Robot 2022;2(4):313­32 I http://dx.doi.org/10.20517/ir.2022.18

where V is the set of number of target points. The first set of equalities is a go-to constraint, which requires
that each target point is visited only once and is different from the others. The second set of equalities is a
come-from constraint, which requires that the departure of each target point also occurs once and is different
from the other ones.

Equations (12) and (13) may form multiple enclosed paths for all target points, with the formation of subtours.
The MTZ constraints are utilized to eliminate unnecessary subtours and ensure a single enclosed path with the
shortest length [Equation (14)]. Each visited node is labeled, resulting in the uniqueness of each visit.

( )
U + ℭ ≤ U + ( − 1) × 1 − ℭ 2 ≤ ≤ (14)

where U is the sequence of each target point visited and is the number of target points. When ℭ = 1, the
equality holds (U + 1 = U ).

Based on the MTZ algorithm, we finally obtain a visiting sequence of dead broilers. The robot with that
sequence starts and ends at the gate of the broiler barn with the shortest collision-free paths.

Algorithm 2: Hub-based multi-target routing (HMTR) scheme
Load N obtained broiler locations as T 1 , ...,T and robot initial location as T 0.
N
Initialize the connection variable matrix ℭ;
for = 0 : N do
for = 0 : N do
if T can direct connect to T then
√
2
2
= ( − ) + ( − ) ;
T T T T
else
if (F + F ) > (F + F ) then
Select corresponding right-side hub grids;
else
Select corresponding left-side hub grids;
end
Select the best ports in the hub grids;

Use Dijkstra algorithm to obtain
end
end
end
Use MTZ method to find the optimal visiting sequence.

4. SIMULATION AND COMPARATIVE STUDIES
Simulationandcomparativestudieswerecarriedouttovalidatetheeffectivenessandefficiencyoftheproposed
path planning methods of real-time autonomous mobile robots. The environments referred to are those in a
typical broiler barn. The robotwas parameterized as described in Section 2.1 based oncommercialized poultry
robots. Thesesettingsweretakentoexemplifyourproposedmethodandcouldbetailoredaccordingtospecific
applications.