MOTION PLANNING FOR THREE-DIMENSIONAL ARM MANIPULATORS in Visual Studio .NET

Draw PDF 417 in Visual Studio .NET MOTION PLANNING FOR THREE-DIMENSIONAL ARM MANIPULATORS
MOTION PLANNING FOR THREE-DIMENSIONAL ARM MANIPULATORS
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decision-making mechanism of Ap into 3D space by complementing the set of local directions by elements upward and downward. We now turn to the study of ve fundamental motions in 3D, which will be later incorporated into the 3D algorithm.
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Motion I Along the M-Line. Starting at point S, the C-point moves along the M-line, as in Figure 6.7, segment SH; this corresponds to Pc (C-point) moving along the Pc (M-line) (segment S H , Figure 6.7). Unless algorithm Ap calls for terminating the procedure, one of these two events can take place:
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1. A wall is met; this corresponds to Pc (C-point) encountering an obstacle. Algorithm Ap now has to decide whether Pc (C-point) will move along Pc (M-line), or turn left or right to go around the obstacle. Accordingly, the C-point will choose to reverse its local direction along the M-line, or to turn left or right to go around the wall. In the latter case we choose a path along the intersection curve between the wall and the M-plane, which combines two advantages: (i) While not true in the worst case, due to obstacle monotonicity the M-plane typically contains one of the shortest paths around the obstacle; and (ii) after passing around the obstacle, the C-point will meet the M-line exactly at the point of its intersection with the obstacle (point L, Figure 6.7), and so the path will be simpler. In general, all three joints participate in this motion. 2. A Type III+ or III obstacle is met. The C-point cannot proceed along the M-line any longer. The local objective of the arm here is to maneuver around the obstacle so as to meet the M-line again at a point that is closer to T than the encounter point. Among various ways to pass around the obstacle, we choose here motion in the V-plane. The intersection curve between the Type III obstacle and the V-plane is a simple planar curve. It follows from the monotonicity property of Type III obstacles that when the front (rear) part of link l3 hits an obstacle, then any motion upward (accordingly, downward) along the obstacle will necessarily bring the C-point to the ceiling ( oor) of the C-space. Therefore, a local contact information is suf cient here for a global planning inference that the local direction downward (upward ) along the intersection curve between the V-plane and the obstacle is a promising direction. In the example in Figure 6.9a, the resulting motion produces the curve abc.
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Motion II Along the Intersection Curve Between the M-Plane and a Wall. In Cp , this motion corresponds to Pc (C-point) moving around the obstacle boundary curve in the chosen direction (see Figure 6.12, segments H1 aL1 and H1 a L1 ). One of these two events can take place:
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1. The M-line is encountered, as at point L1 , Figure 6.12; in Cp this means Pc (M-line) is encountered. At this point, algorithm Ap will decide whether
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THE CASE OF THE PPP (CARTESIAN) ARM
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Figure 6.12 The path in C-space in the presence of obstacles O1 , O2 and O3 of Figure 6.2. Trajectory SH1 aL1 bH2 cdL2 eT is the actual path of the arm endpoint; S H1 a b H2 c d L2 e T is its projection onto the plane (l1 , l2 ).
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Pc (C-point) should start moving along the Pc (M-line) or continue moving along the intersection curve between the M-plane and the obstacle boundary. Accordingly, the C-point will either resume its motion along the M-line, as in Motion I, or will keep moving along the M-plane/obstacle intersection curve. 2. A Type III+ or III obstacle is met. In Cp , the Pc (C-point) keeps moving in the same local direction along the obstacle boundary (path segments bcL and b L , Figure 6.11). As for C-point, there are two possible directions for it to follow the intersection curve between the Type III obstacle
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