.574. 智能系统学报 第12卷 their way home and proposed the two-stage algorithm. overshoot,but the result is not desirable,and the The first stage of PIO is the map and compass part.X= altitude of a UAV drops to the standard height with [XX…X…X]T is the vector of the pigeons' continual oscillation.To improve the performance of the positions,i is the number of virtual pigeons,and in algorithm,better methods are required. this paper the UAVs fly in 3-dimensional space,X=2.2 Improved method with slow diving strategy [x ]V=[VI V.V]T is the vector of the The problem in the former algorithm occurs mainly pigeons'velocities,V=[]is its element, in the altitude part,the height of the UAV decreases i∈{l,2,…,9}.Both X and V are randomly too fast and it dives sharply.To slow the process,the initialized when the program starts.The update update formula should be changed,not only to consider formulas are: the best local position but also the slowest diving (e:(t+1)=:(t)·exp(-Rt)+rand·(xe-x:) velocity.In the first part of PIO,the formula is not x:(t+1)=x,(t)+,(t+1) changed,but the method of acquiring the best local if t Tlabed (7) position is modified.The criterion is a linear In the formula above,the best local position combination of the distance error between the desired is selected from the distance between the desired and and the real positions and the diving speed.An UAV present positions.In order to find the best local that dives very slowly is imitated by the others.This is the so-called "slow diving strategy".The update position,all the distance errors are calculated and formula is: ranked,and only the position with the smallest e:(t+1)=v:(t)·exp(-Rt)+ distance is defined as the best local position.For the minimum optimization question,the fitness function is: r·[p·(xhea-x:)+(1-p）·] fitness(x (t))=x(t)-xmmdm(t)(8) x:(t+1)=x,(t)+,(t+1) After calculating the distance between the desired if t Tubd (10) and the present positions of all the pigeons,only half where serves as a regulatory factor in the range of(0, of the pigeons with lower fitness are selected for the 1);if approaches 0,the slowest pigeon will iteration.This ensures that the positions of these influence the team;if o approaches 1,best local pigeons converge to the desired position as fast as position will have much more of an effect.r(0,1)is possible. a random number. In the second part,the landmark operator is The second part of PIO should be modified in the employed.Its update formula is: following way:all the UAVs converge to the center of wu+1)=水四 the flock,which is calculated by a combination of the 2 UAV positions and the slowest diving speed.The ∑，()·fx,() update equation can be described as: xc(t+1)= ∑fx,(t) +1)=0 2 x,(t+1)=x,(t)+rand·(xc(t+1)-x:(t)) ∑x,()fx,()+10·x·f代x) ift≥Tlabel (9) xc(t+1)= ∑fx,(t)+10·xa·fx) Apparently,xic is the weighted average of all the x,(t+1)=x,(t)+rand·(xc(t+1)-x:(t)) nearby pigeons in pigeon i's communication distance. (11) It is supposed that the map and compass operator has ift≥Tlabel where x is the position of the UAV with the slowest already converged pigeons to the desired trajectory to a diving speed,this part represents the slowing diving great extent.As a result,the landmark operator only strategy. needs to speed up this process.The PIO algorithm has Fitness function Eq.(10)remains.Each UAV already been proven to be robust and reliable for an aircraft path planning problems However,for the has its own fitness value. optimization of consensus,PIO can improve theｔｈｅｉｒ ｗａｙ ｈｏｍｅ ａｎｄ ｐｒｏｐｏｓｅｄ ｔｈｅ ｔｗｏ⁃ｓｔａｇｅ ａｌｇｏｒｉｔｈｍ． Ｔｈｅ ｆｉｒｓｔ ｓｔａｇｅ ｏｆ ＰＩＯ ｉｓ ｔｈｅ ｍａｐ ａｎｄ ｃｏｍｐａｓｓ ｐａｒｔ． Ｘ ＝ ［Ｘ Ｔ １ Ｘ Ｔ ２ … Ｘ Ｔ ｉ … Ｘ Ｔ ｎ ］ Ｔ ｉｓ ｔｈｅ ｖｅｃｔｏｒ ｏｆ ｔｈｅ ｐｉｇｅｏｎｓ’ ｐｏｓｉｔｉｏｎｓ， ｉ ｉｓ ｔｈｅ ｎｕｍｂｅｒ ｏｆ ｖｉｒｔｕａｌ ｐｉｇｅｏｎｓ， ａｎｄ ｉｎ ｔｈｉｓ ｐａｐｅｒ ｔｈｅ ＵＡＶｓ ｆｌｙ ｉｎ ３⁃ｄｉｍｅｎｓｉｏｎａｌ ｓｐａｃｅ， Ｘｉ ＝ ［ｘｉ ｙｉ ｚｉ］ Ｔ ． Ｖ ＝ ［Ｖ Ｔ １ Ｖ Ｔ ２ … Ｖ Ｔ ｎ ］ Ｔ ｉｓ ｔｈｅ ｖｅｃｔｏｒ ｏｆ ｔｈｅ ｐｉｇｅｏｎｓ’ ｖｅｌｏｃｉｔｉｅｓ， Ｖｉ ＝ ［ｖｘ ｖｙ ｖｚ］ Ｔ ｉｓ ｉｔｓ ｅｌｅｍｅｎｔ， ｉ ∈｛１，２，…，９｝ ． Ｂｏｔｈ Ｘ ａｎｄ Ｖ ａｒｅ ｒａｎｄｏｍｌｙ ｉｎｉｔｉａｌｉｚｅｄ ｗｈｅｎ ｔｈｅ ｐｒｏｇｒａｍ ｓｔａｒｔｓ． Ｔｈｅ ｕｐｄａｔｅ ｆｏｒｍｕｌａｓ ａｒｅ： ｖｉ（ｔ ＋ １） ＝ ｖｉ（ｔ）·ｅｘｐ（ － Ｒｔ） ＋ ｒａｎｄ·（ｘｌｂｅｓｔ － ｘｉ） ｘｉ（ｔ ＋ １） ＝ ｘｉ（ｔ） ＋ ｖｉ（ｔ ＋ １） { ｉｆ ｔ ＜ Ｔｌａｂｅｌ （７） Ｉｎ ｔｈｅ ｆｏｒｍｕｌａ ａｂｏｖｅ， ｔｈｅ ｂｅｓｔ ｌｏｃａｌ ｐｏｓｉｔｉｏｎ ｘｌｂｅｓｔ ｉｓ ｓｅｌｅｃｔｅｄ ｆｒｏｍ ｔｈｅ ｄｉｓｔａｎｃｅ ｂｅｔｗｅｅｎ ｔｈｅ ｄｅｓｉｒｅｄ ａｎｄ ｐｒｅｓｅｎｔ ｐｏｓｉｔｉｏｎｓ． Ｉｎ ｏｒｄｅｒ ｔｏ ｆｉｎｄ ｔｈｅ ｂｅｓｔ ｌｏｃａｌ ｐｏｓｉｔｉｏｎ， ａｌｌ ｔｈｅ ｄｉｓｔａｎｃｅ ｅｒｒｏｒｓ ａｒｅ ｃａｌｃｕｌａｔｅｄ ａｎｄ ｒａｎｋｅｄ， ａｎｄ ｏｎｌｙ ｔｈｅ ｐｏｓｉｔｉｏｎ ｗｉｔｈ ｔｈｅ ｓｍａｌｌｅｓｔ ｄｉｓｔａｎｃｅ ｉｓ ｄｅｆｉｎｅｄ ａｓ ｔｈｅ ｂｅｓｔ ｌｏｃａｌ ｐｏｓｉｔｉｏｎ． Ｆｏｒ ｔｈｅ ｍｉｎｉｍｕｍ ｏｐｔｉｍｉｚａｔｉｏｎ ｑｕｅｓｔｉｏｎ， ｔｈｅ ｆｉｔｎｅｓｓ ｆｕｎｃｔｉｏｎ ｉｓ： ｆｉｔｎｅｓｓ（ｘｉ（ｔ）） ＝ ｘｉ（ｔ） － ｘｉｓｔａｎｄａｒｄ（ｔ） （８） Ａｆｔｅｒ ｃａｌｃｕｌａｔｉｎｇ ｔｈｅ ｄｉｓｔａｎｃｅ ｂｅｔｗｅｅｎ ｔｈｅ ｄｅｓｉｒｅｄ ａｎｄ ｔｈｅ ｐｒｅｓｅｎｔ ｐｏｓｉｔｉｏｎｓ ｏｆ ａｌｌ ｔｈｅ ｐｉｇｅｏｎｓ， ｏｎｌｙ ｈａｌｆ ｏｆ ｔｈｅ ｐｉｇｅｏｎｓ ｗｉｔｈ ｌｏｗｅｒ ｆｉｔｎｅｓｓ ａｒｅ ｓｅｌｅｃｔｅｄ ｆｏｒ ｔｈｅ ｉｔｅｒａｔｉｏｎ． Ｔｈｉｓ ｅｎｓｕｒｅｓ ｔｈａｔ ｔｈｅ ｐｏｓｉｔｉｏｎｓ ｏｆ ｔｈｅｓｅ ｐｉｇｅｏｎｓ ｃｏｎｖｅｒｇｅ ｔｏ ｔｈｅ ｄｅｓｉｒｅｄ ｐｏｓｉｔｉｏｎ ａｓ ｆａｓｔ ａｓ ｐｏｓｓｉｂｌｅ． Ｉｎ ｔｈｅ ｓｅｃｏｎｄ ｐａｒｔ， ｔｈｅ ｌａｎｄｍａｒｋ ｏｐｅｒａｔｏｒ ｉｓ ｅｍｐｌｏｙｅｄ． Ｉｔｓ ｕｐｄａｔｅ ｆｏｒｍｕｌａ ｉｓ： Ｎｐ（ｔ ＋ １） ＝ Ｎｐ（ｔ） ２ ｘｉＣ（ｔ ＋ １） ＝ ∑ｘｉ（ｔ）·ｆ（ｘｉ（ｔ）） ∑ｆ（ｘｉ（ｔ）） ｘｉ（ｔ ＋ １） ＝ ｘｉ（ｔ） ＋ ｒａｎｄ·（ｘｉＣ（ｔ ＋ １） － ｘｉ（ｔ）） ì î í ï ï ïï ï ï ïï ｉｆ ｔ ≥ Ｔｌａｂｅｌ （９） Ａｐｐａｒｅｎｔｌｙ， ｘｉＣ ｉｓ ｔｈｅ ｗｅｉｇｈｔｅｄ ａｖｅｒａｇｅ ｏｆ ａｌｌ ｔｈｅ ｎｅａｒｂｙ ｐｉｇｅｏｎｓ ｉｎ ｐｉｇｅｏｎ ｉ’ ｓ ｃｏｍｍｕｎｉｃａｔｉｏｎ ｄｉｓｔａｎｃｅ． Ｉｔ ｉｓ ｓｕｐｐｏｓｅｄ ｔｈａｔ ｔｈｅ ｍａｐ ａｎｄ ｃｏｍｐａｓｓ ｏｐｅｒａｔｏｒ ｈａｓ ａｌｒｅａｄｙ ｃｏｎｖｅｒｇｅｄ ｐｉｇｅｏｎｓ ｔｏ ｔｈｅ ｄｅｓｉｒｅｄ ｔｒａｊｅｃｔｏｒｙ ｔｏ ａ ｇｒｅａｔ ｅｘｔｅｎｔ． Ａｓ ａ ｒｅｓｕｌｔ， ｔｈｅ ｌａｎｄｍａｒｋ ｏｐｅｒａｔｏｒ ｏｎｌｙ ｎｅｅｄｓ ｔｏ ｓｐｅｅｄ ｕｐ ｔｈｉｓ ｐｒｏｃｅｓｓ． Ｔｈｅ ＰＩＯ ａｌｇｏｒｉｔｈｍ ｈａｓ ａｌｒｅａｄｙ ｂｅｅｎ ｐｒｏｖｅｎ ｔｏ ｂｅ ｒｏｂｕｓｔ ａｎｄ ｒｅｌｉａｂｌｅ ｆｏｒ ａｎ ａｉｒｃｒａｆｔ ｐａｔｈ ｐｌａｎｎｉｎｇ ｐｒｏｂｌｅｍ ［１５］ ． Ｈｏｗｅｖｅｒ， ｆｏｒ ｔｈｅ ｏｐｔｉｍｉｚａｔｉｏｎ ｏｆ ｃｏｎｓｅｎｓｕｓ， ＰＩＯ ｃａｎ ｉｍｐｒｏｖｅ ｔｈｅ ｏｖｅｒｓｈｏｏｔ， ｂｕｔ ｔｈｅ ｒｅｓｕｌｔ ｉｓ ｎｏｔ ｄｅｓｉｒａｂｌｅ， ａｎｄ ｔｈｅ ａｌｔｉｔｕｄｅ ｏｆ ａ ＵＡＶ ｄｒｏｐｓ ｔｏ ｔｈｅ ｓｔａｎｄａｒｄ ｈｅｉｇｈｔ ｗｉｔｈ ｃｏｎｔｉｎｕａｌ ｏｓｃｉｌｌａｔｉｏｎ． Ｔｏ ｉｍｐｒｏｖｅ ｔｈｅ ｐｅｒｆｏｒｍａｎｃｅ ｏｆ ｔｈｅ ａｌｇｏｒｉｔｈｍ， ｂｅｔｔｅｒ ｍｅｔｈｏｄｓ ａｒｅ ｒｅｑｕｉｒｅｄ． ２．２ Ｉｍｐｒｏｖｅｄ ｍｅｔｈｏｄ ｗｉｔｈ ｓｌｏｗ ｄｉｖｉｎｇ ｓｔｒａｔｅｇｙ Ｔｈｅ ｐｒｏｂｌｅｍ ｉｎ ｔｈｅ ｆｏｒｍｅｒ ａｌｇｏｒｉｔｈｍ ｏｃｃｕｒｓ ｍａｉｎｌｙ ｉｎ ｔｈｅ ａｌｔｉｔｕｄｅ ｐａｒｔ， ｔｈｅ ｈｅｉｇｈｔ ｏｆ ｔｈｅ ＵＡＶ ｄｅｃｒｅａｓｅｓ ｔｏｏ ｆａｓｔ ａｎｄ ｉｔ ｄｉｖｅｓ ｓｈａｒｐｌｙ． Ｔｏ ｓｌｏｗ ｔｈｅ ｐｒｏｃｅｓｓ， ｔｈｅ ｕｐｄａｔｅ ｆｏｒｍｕｌａ ｓｈｏｕｌｄ ｂｅ ｃｈａｎｇｅｄ， ｎｏｔ ｏｎｌｙ ｔｏ ｃｏｎｓｉｄｅｒ ｔｈｅ ｂｅｓｔ ｌｏｃａｌ ｐｏｓｉｔｉｏｎ ｂｕｔ ａｌｓｏ ｔｈｅ ｓｌｏｗｅｓｔ ｄｉｖｉｎｇ ｖｅｌｏｃｉｔｙ． Ｉｎ ｔｈｅ ｆｉｒｓｔ ｐａｒｔ ｏｆ ＰＩＯ， ｔｈｅ ｆｏｒｍｕｌａ ｉｓ ｎｏｔ ｃｈａｎｇｅｄ， ｂｕｔ ｔｈｅ ｍｅｔｈｏｄ ｏｆ ａｃｑｕｉｒｉｎｇ ｔｈｅ ｂｅｓｔ ｌｏｃａｌ ｐｏｓｉｔｉｏｎ ｉｓ ｍｏｄｉｆｉｅｄ． Ｔｈｅ ｃｒｉｔｅｒｉｏｎ ｉｓ ａ ｌｉｎｅａｒ ｃｏｍｂｉｎａｔｉｏｎ ｏｆ ｔｈｅ ｄｉｓｔａｎｃｅ ｅｒｒｏｒ ｂｅｔｗｅｅｎ ｔｈｅ ｄｅｓｉｒｅｄ ａｎｄ ｔｈｅ ｒｅａｌ ｐｏｓｉｔｉｏｎｓ ａｎｄ ｔｈｅ ｄｉｖｉｎｇ ｓｐｅｅｄ． Ａｎ ＵＡＶ ｔｈａｔ ｄｉｖｅｓ ｖｅｒｙ ｓｌｏｗｌｙ ｉｓ ｉｍｉｔａｔｅｄ ｂｙ ｔｈｅ ｏｔｈｅｒｓ． Ｔｈｉｓ ｉｓ ｔｈｅ ｓｏ⁃ｃａｌｌｅｄ “ ｓｌｏｗ ｄｉｖｉｎｇ ｓｔｒａｔｅｇｙ ”． Ｔｈｅ ｕｐｄａｔｅ ｆｏｒｍｕｌａ ｉｓ： ｖｉ（ｔ ＋ １） ＝ ｖｉ（ｔ）·ｅｘｐ（ － Ｒｔ） ＋ ｒ·［φ·（ｘｌｂｅｓｔ － ｘｉ） ＋ （１ － φ）·ｖｓｌｏｗ ］ ｘｉ（ｔ ＋ １） ＝ ｘｉ（ｔ） ＋ ｖｉ（ｔ ＋ １） ì î í ï ï ïï ｉｆ ｔ ＜ Ｔｌａｂｅｌ （１０） ｗｈｅｒｅ φ ｓｅｒｖｅｓ ａｓ ａ ｒｅｇｕｌａｔｏｒｙ ｆａｃｔｏｒ ｉｎ ｔｈｅ ｒａｎｇｅ ｏｆ （０， １） ； ｉｆ φ ａｐｐｒｏａｃｈｅｓ ０， ｔｈｅ ｓｌｏｗｅｓｔ ｐｉｇｅｏｎ ｗｉｌｌ ｉｎｆｌｕｅｎｃｅ ｔｈｅ ｔｅａｍ； ｉｆ φ ａｐｐｒｏａｃｈｅｓ １， ｂｅｓｔ ｌｏｃａｌ ｐｏｓｉｔｉｏｎ ｗｉｌｌ ｈａｖｅ ｍｕｃｈ ｍｏｒｅ ｏｆ ａｎ ｅｆｆｅｃｔ． ｒ ∈ （０，１） ｉｓ ａ ｒａｎｄｏｍ ｎｕｍｂｅｒ． Ｔｈｅ ｓｅｃｏｎｄ ｐａｒｔ ｏｆ ＰＩＯ ｓｈｏｕｌｄ ｂｅ ｍｏｄｉｆｉｅｄ ｉｎ ｔｈｅ ｆｏｌｌｏｗｉｎｇ ｗａｙ： ａｌｌ ｔｈｅ ＵＡＶｓ ｃｏｎｖｅｒｇｅ ｔｏ ｔｈｅ ｃｅｎｔｅｒ ｏｆ ｔｈｅ ｆｌｏｃｋ， ｗｈｉｃｈ ｉｓ ｃａｌｃｕｌａｔｅｄ ｂｙ ａ ｃｏｍｂｉｎａｔｉｏｎ ｏｆ ｔｈｅ ＵＡＶ ｐｏｓｉｔｉｏｎｓ ａｎｄ ｔｈｅ ｓｌｏｗｅｓｔ ｄｉｖｉｎｇ ｓｐｅｅｄ． Ｔｈｅ ｕｐｄａｔｅ ｅｑｕａｔｉｏｎ ｃａｎ ｂｅ ｄｅｓｃｒｉｂｅｄ ａｓ： Ｎｐ（ｔ ＋ １） ＝ Ｎｐ（ｔ） ２ ｘｉＣ（ｔ ＋ １） ＝ ∑ｘｉ（ｔ）·ｆ（ｘｉ（ｔ）） ＋ １０·ｘｓｌｏｗ·ｆ（ｘｓｌｏｗｓ） ∑ｆ（ｘｉ（ｔ）） ＋ １０·ｘｓｌｏｗ·ｆ（ｘｓｌｏｗ） ｘｉ（ｔ ＋ １） ＝ ｘｉ（ｔ） ＋ ｒａｎｄ·（ｘｉＣ（ｔ ＋ １） － ｘｉ（ｔ）） ì î í ï ï ïï ï ï ïï ｉｆ ｔ ≥ Ｔｌａｂｅｌ （１１） ｗｈｅｒｅ ｘｓｌｏｗ ｉｓ ｔｈｅ ｐｏｓｉｔｉｏｎ ｏｆ ｔｈｅ ＵＡＶ ｗｉｔｈ ｔｈｅ ｓｌｏｗｅｓｔ ｄｉｖｉｎｇ ｓｐｅｅｄ， ｔｈｉｓ ｐａｒｔ ｒｅｐｒｅｓｅｎｔｓ ｔｈｅ ｓｌｏｗｉｎｇ ｄｉｖｉｎｇ ｓｔｒａｔｅｇｙ． Ｆｉｔｎｅｓｓ ｆｕｎｃｔｉｏｎ Ｅｑ． （ １０） ｒｅｍａｉｎｓ． Ｅａｃｈ ＵＡＶ ｈａｓ ｉｔｓ ｏｗｎ ｆｉｔｎｅｓｓ ｖａｌｕｅ． ·５７４· 智 能 系 统 学 报 第 １２ 卷