Robot Motion Planning and Control - J P Laumond Part 3 pps

... pp. 38 5-4 00, 1984. 32 . J. Hopcroft, J. T. Schwartz and M. Sharir, "On the complexity of motion plan- ning for multiple independent objects: PSPACE-hardness of the warehouseman's problem," ... "Non-uniform discretization approximations for kinody- namic motion planning and its applications," Algorithms for Robotic Motion and Manipulation, WAFR...

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... Bellaiche and J J. Risler Ed., Progress in Mathe- matics, Birkh~user, 1996. 3. A. Beltaiche, J P. Laumond and J. Jacobs, "Controllability of car-like robots and complexity of the motion planning ... planning problem," in International Symposium on Intelligent Robotics, 32 2 -3 37 , Bangalore, India, 1991. 4. A. Bella~che, J P. Laumond and J J. Ris...

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... Mobile Robots 133 4.IJ ( ~-, ~ :.q J ). 44 - ~ r~,, + 1_ I ,-, '~. (~,',, ,-, ~ r'7.,, t " ;-~ .,.;,~ ~,) 0=0 + ,'< ;J: ~l:l/iz, t,~,-I . -~ "" Z-d 'T~L ... varies in [-Tr, ~] the partition of planes P0 induces a partition of R 2 x [-r, ~r]. Identifying the planes P_ ~ and P, we obtain a partition of the configuration s...

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... - o. (37 ) Optimal Trajectories for Nonholonomic Mobile Robots 161 However, Propositions 2 and 3 already indicate that the optimal control associated to problem (30 ), (31 ), (32 ) has a complex ... been possible to determine a dis- tance function providing a topological analysis of the path planning problem. In particular, for the Reeds and Shepp problem, we have proven tha...

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... Sys. 8 (1) pp. 3 9-5 4 (1991). 40. T. Lozano -P6 rez, "Spatial planning: a configuration space approach" in IEEE Trans. Comput. 32 (2) pp. 10 8-1 20 (Feb., 19 83) . 41. T. Lozano -P6 rez, "A ... Lozano -P6 rez, "A simple motion- planning algorithm for general robot manip- ulators" in IEEE J. Robotics Automat. 3 (3) pp. 22 4-2 38 (June, 1987)....

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... pp 8 1-1 00, 1978. 8. P. Brunovsky, "Existence of regular synthesis for general problems," J. Diff. Equa- tions 38 pp 31 7 -3 43, 1980. 9. X-N. Bui, P. Sou~res, J- D. Boissonnat and J- P ... Nonholonomic Car-Like Robot 177 1 .3 Open-loop vs. closed-loop control Some comments are now appropriate concerning the relationships between the planning and contr...

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... 0 and Xda(t) = Xd3(to). Define the feedback term fi as the following linear time-varying law ~1 ~ klXl (28) ~2 = -k222 k3 X3 k4 - ud-7 - 1124' (29) with kl positive, and k2, k3, ... mobile robots the point stabiliza- tion problem is considerably more difficult than trajectory tracking and path Feedback Control of a Nonholonomic Car-Like Robot 201 which is inpu...

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... 2 '/2(Z2, t) = E aj sin(/~jt) z2 +j j= O n-2 ~ /3( Z2, t) = ~ aj exp(bjz2 +j) - 1 sin(f/it), j= o exp(bjz2 +j) -+ 1 (71) (72) ( 73) Feedback Control of a Nonholonomic Car-Like Robot ... X1 z2 = X2 (61) Z3 = X3 zj +3 = kjzj+l + Lh~zj+2, j = 1, , n - 3, where k s (j = 1, ,n - 3) is a real positive number and Lh~zj = -~ hl(X) is the Lie de...

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