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Because of the unique choice of the local direction, there is no need to investigate the whole curve of the virtual boundary If, while passing around the obstacle in the chosen local direction, the arm reaches one of the limits of l2 , it can safely conclude that it is dealing with a Type II obstacle, so the arm should start looking for the second curve of the virtual boundary using the complementary M-line The procedure is further simpli ed through the use of the following statement similar to the one in Section 522: Lemma 551 For the two-link revolute prismatic (RP) arm, if position T is reachable from the starting position S, then there exists a path from S to T such that it corresponds to a monotonic change of the joint value 1 .

<= 0; <= 0;

In the motion planning procedure, a ag is used to indicate processing of each of the two curves of a Type II virtual boundary When the complementary M-line is introduced, the numbering of hit and leave points starts over; Lo = S The distance used is a Euclidean distance in W -space Assume the M1 -line is the shorter of the two complementary M-lines The procedure RP-Arm Algorithm includes the following steps 1 Establish an M1 -line as the M-line Set the ag down Set j = 1 Go to Step 2 2 From point Lj 1 , the arm moves along the M-line until one of the following occurs: (a) Target T is reached The procedure stops (b) An obstacle is encountered and a hit point, Hj , is de ned.

In case of a front contact, choose the local direction such that it corresponds to decreasing values of l2 In the case of a rear contact, choose the local direction such that it corresponds to increasing values of l2 Go to Step 3 3 The arm follows the virtual boundary until one of the following occurs: (a) The target is reached The procedure stops S T (b) Current joint value 1 is outside the interval ( 1 , 1 ) The target cannot be reached The procedure stops (c) The M-line is met at a distance d from T such that d < d(Hj , T ) Point Lj is de ned Increment j Go to Step 2 (d) The value l2 approaches one of its limits, and the ag is down (ie, the rst curve of the virtual boundary of a Type II obstacle has been processed).

done, load C*U[1] begin <= U1; <= iCLow; <= 1; <= State3;

Rule Number One: Don t Become Cocky John laughed. I ve got one of those, too. And he s right. I ve made some bad mistakes in my trading by being too cocky. Yeah, right, I thought. Whatever. If I was making $100,000 per month, I d have my shoes shined at my desk and my wife would have a hundred iPods. I d work for a month and take the rest of the year off. I wondered if John had met Craig s secret mentor. From the way that John was looking at me, I got the feeling that he was wondering if Craig had mentioned this same friend. I wanted to talk about it with John, but we 45

Set the ag up Set j = 1 Establish an M2 -line as the M-line Move the arm back to S Go to Step 2 (e) The value l2 approaches one of its limits, and the ag is up (ie, the second curve of the virtual boundary of a Type II obstacle has been processed) The target cannot be reached The procedure stops..

<= 0; <= 0;

73 H Choset, I Konukseven, and J Burdick Mobile robot navigation: issues in implementating the generalized voronoi graph in the plane In Proceedings of the IEEE/SICE/RSJ International Conference on Multisensor Fusion and Integration for Intelligent Systems, 1996 74 H Choset, I Konukseven, and J Burdick Sensor based planning for a planar rod robot In Proceedings of the 1996 International Conference on Robotics and Automation, Minneapolis, MN, 1996 75 N Rao, S Iyenger, C Jorgensen, and C Weisbin On terrain acquisition by a nite-sized mobile robot in plane In Proceedings of the 1987 IEEE International Conference on Robotics and Automation, Raleigh, NC, May 1987 76 I Kamon, E Rimon, and E Rivlin Range-sensor based navigation in three dimensions In Proceedings of the IEEE International Conference on Robotics and Automation, Detroit, MI, 1999 77 V Lumelsky and K R Harinarayan Decentralized motion planning for multiple mobile robots: The cocktail party model.

had the FOMC report in just a little while, and I decided that I needed to get my trading account up and ready So are you trading still I asked, hoping to get a bit more information about John s plans Yes I m having some trouble pulling the trigger on my trades Some of the best ones in fact But it will pass I am down for the year still, but I am confident that will change And you I only have a small account But it s positive right now How much I don t know, I answered And then I calculated the percentage gain in my head Seventy percent so far He nearly choked Seventy percent Your account is up 70 percent for the year What was the big deal At the rate I was going, it would be up 100 percent by today.