jT Obstacle ov & Target Movement ni v & i ni T j njT nj v & Fig. 2 Judgment of obstacle In the case of nj nj ni ni v v T T cos cos & & d , i is unaffected because i can't catch up with j . Then, i is given max iv in the target direction. In the contrasting case of nj nj ni ni v v T T cos cos & & ! , it is thought that there is a possibility of getting jammed up because i approaches j in the direction from i to j . Then, time ij t' , in which i and j come into contact with the direction from i to j , is requested by Eq. (5): nj nj ni ni j i j i ij v v x x r r t T T cos cos & & & & ' (5) Next, from the relation of the position and the velocity at t , position j ix x c c & & , of i j , at ij t t ' are obtained respectively. It is judged from the j ix x c c & & , whether the center of jc exists in the affected area of ic . When jc doesn't exist it (Fig.3(a)), it is assumed not to receive the influence of deceleration vector ov & , because i is not intervened in particle j . Then, i is given max iv in the target direction. On the other hand, when existing (Fig.3(b)), deceleration vector ov & acts on i because j jams in i . ic jc i j ic jc i j (a) 0 ov & (b) 0z ov & Fig. 3 Judgment of affected area Deceleration ov & is requested from Eq. (6) by using the OV function of Eq. (2) (Fig. 4(a)). j i j i ij ni ni ij o x x x x t x v V x v c c ' ' ' , min cos T D & & (6) In addition, by using ov & , movement direction nic T of the direction from i to jc at time t t ' is given by Eq. (7), j j i ni t o ni t ni t v v v c c c c ' ¸ ¸ ¹ · ¨ ¨ © § T T T T sin sin cos cos max 1 & & (7) and the movement velocity is given by expression (8) (Fig. 4(b)), ° ° ¯ ° ° ® ¸ ¹ · ¨ © § ! ¸ ¹ · ¨ © § ¸ ¹ · ¨ © § d c c c c c c 6 6 cos 6 max max S T T S T T S T T j ni j ni i ni j ni i ni v v v v & & (8) 233
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