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

Algorithm 2

Trap_TNLPPs(𝜀,𝐹,𝑚,𝑛).

Input: Admissible error between two consecutive values of path length function: 𝜀, number of the

interval [0,𝑡_𝑓𝑖] equal parts: 𝐹, and coefficient of polynomials: 𝑚 and 𝑛.

Output: Optimal path parameters of 𝐴_𝑖: 𝐴^𝑖,𝐵^𝑖,𝑇^𝑖_𝐴 and 𝑇^𝑖_𝐵, path length 𝑠_𝑖.

(1) Set 𝑚=1,𝑛=1.

(2) NLPP(𝜀,𝐹,𝑚,𝑛)

(3)  If NLPP is infeasible

(4)  then  𝑚++,𝑛++

(5)      Transfer to (2)

(6)  else optimal path parameters 𝐴^𝑖, 𝐵^𝑖, 𝑇^𝑖_𝐴 and 𝑇^𝑖_𝐵, path length 𝑠⁰_𝑖

(7)  end if

(8)  𝑚++,𝑛++

(9) NLPP(𝜀,𝐹,𝑚,𝑛)

(10)  Assign the results of (9) to 𝐴^𝑖,𝐵^𝑖,𝑇^𝑖_𝐴 and 𝑇^𝑖_𝐵, 𝑠¹_𝑖

(11)  if abs(𝑠⁰_𝑖,𝑠¹_𝑖) > 𝜀

(12)  then Transfer to (8)

(13)  else optimal path length value 𝑠_𝑖=𝑠¹_𝑖

(14)  return optimal path parameters 𝐴^𝑖, 𝐵^𝑖, 𝑇^𝑖_𝐴 and 𝑇^𝑖_𝐵, path length 𝑠_𝑖