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Sensing Intelligence Motion - How Robots & Humans Move - Vladimir J. Lumelsky Part 7

Tham khảo tài liệu 'sensing intelligence motion - how robots & humans move - vladimir j. lumelsky part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 156 ACCOUNTING FOR BODY DYNAMICS THE JOGGER S PROBLEM 0 Ci .G Ck Ci 1 .0 tỉ a T Figure 4.6 Because of its inertia immediately after its position Ci the robot temporarily loses the intermediate target Ti. a The robot keeps moving around the obstacle until it spots Ti and then it continues toward Ti. b When because of an obstacle the whole segment Ci Ti becomes invisible at point Ck 1 the robot stops returns back to Ci and then moves toward Ti along the line Ci Ti . Convergence. To prove convergence of the described procedure we need to show the following i At every step of the path the algorithm guarantees collision-free motion. ii The set of intermediate targets Ti is guaranteed to lie on the convergent path. iii The planning strategy guarantees that the current intermediate target will not be lost. Together ii and iii assure that a path to the target position T will be found if one exists. Condition i can be shown by induction condition ii is provided by the VisBug procedure see Section 3.6 which also includes the test for target reachability. Condition iii is satisfied by the procedure Find Lost Target of the Maximum Turn Strategy. The following two propositions hold Proposition 2. Under the Maximum Turn Strategy algorithm assuming zero velocity VS 0 at the start position S at each step of the path there exists at least one stopping path. By design the stopping path is a straight-line segment. Choosing the next step so as to guarantee existence of a stopping path implies two requirements There should be at least one safe direction of motion and the value of velocity that would allow stopping within the visible area. The latter is ensured by the choice of system parameters see Eq. 4.1 and the safety conditions Section 4.2.2 . As to the existence of safe directions proceed by induction We need to show that MAXIMUM TURN STRATEGY 157 if a safe direction exists at the start point and at an arbitrary step i then there is a safe direction at the step i 1 . Since at the