Mobile Robots Path Planning Using the Overall Conflict Resolution and Time Baseline Coordination

Algorithm 1

Time_Coor(𝑃_𝑖0,𝑃_𝑖𝑓,𝑥_𝑖(𝑡),𝑡_𝑓𝑖,𝛼_𝑘(𝑡),𝑡_𝑘,𝐹,𝑇_min).

Input: Start and end poses 𝑃_𝑖0 and 𝑃_𝑖𝑓, respectively. Unknown path 𝑥_𝑖(𝑡), a known path 𝛼_𝑘(𝑡), motion time 𝑡_fi and 𝑡_𝑘, and

number of divided time interval 𝐹, temporary time variable 𝑇_min.

Output: Parameters 𝐴^𝑖, 𝐵^𝑖, 𝑇^𝑖_𝐴 and 𝑇^𝑖_𝐵 which are used to represent the path of 𝐴_𝑖.

Begin

 𝑇_min = 0;

 foreach  𝑡_fi of 𝐴_𝑖  do

  𝑇_min=min𝑡_fi;

 end foreach

 foreach  𝐴_𝑖 in the set of multiple mobile robots

  Map motion time interval [0,𝑡_fi] of 𝐴_𝑖 into [0,𝑡_fi/𝑇_min] with the multiples of 1/𝑇_min.

  Map constraints of kinematics and obstacle-avoidance of 𝐴_𝑖 into corresponding forms with respect to [0, 𝑡_fi/𝑇_min].

 end foreach

 Modify the objective function with all the adjustments, then reach the newly TNLPPs named TNLPPs_{_new}.

 Call Trap_{_TNLPPs}(TNLPPs_{_new})

 foreach  𝐴_𝑖  do

  Multiples 𝐴^𝑖′, 𝐵^𝑖′, 𝑇_𝐴^𝑖′ and 𝑇_𝐵^𝑖′ with 𝑇_min.

 end foreach

 return  𝐴^𝑖, 𝐵^𝑖, 𝑇^𝑖_𝐴 and 𝑇^𝑖_𝐵.

End