tailieunhanh - Robot Motion Planning and Control - J.P. Laumond Part 8

Tham khảo tài liệu 'robot motion planning and control - . laumond part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Optimal Trajectories for Nonholonomic Mobile Robots 167 On the other hand by showing that the synthesis constructed for the Reeds and Shepp problem verifies the required regularity conditions we have found another proof to confirm this result a posteriori by applying Boltianskii s sufficient optimality conditions. Though this theorem allows to prove very strong results in a very simple way we have shown the narrowness of its application area by considering the neighbouring example of Dubins for which the regularity conditions no longer apply because of the discontinuity of path length. The last two examples illustrate the difficulty very often encountered in studying of optimal control problems. First the adjoint equations are seldom integrable making only possible the local characterization of optimal paths. The search for switching times is then a very difficult problem. Furthermore as we have seen in studying the problem of Dubins with inertial control it is possible to face Fuller-like phenomenon though the solution could seem to be a priori intuitively simple. 168 p. Souères and . Boissonnat References 1. Berkovitz Optimal Control Theory Springer- Verlag New York 1974. 2. . Boissonnat A. Cerezo and J. Leblond Shortest paths of bounded curvature in the plane in IEEE Int. Conf on Robotics and Automation Nice France 1992. 3. . Boissonnat A. Cerezo and J. Leblond A Note on Shortest Paths in the Plane Subject to a Constraint on the Derivative of the Curvature INRIA Report No 2160 January 1994 4. . Boltyanskii Sufficient conditions for optimality and the justification of the dynamic programming method J. Siam Control vol 4 No 2 1966. 5. Brockett Control Theory and Singular Riemannian Geometry New Direction in Applied mathematics . Hilton and . Young eds Springer pp 11-27 Berlin 1981. 6. LN. Bronhstein and . Semendyayev A guide-book to Mathematics for technologists and engineers Pergamon Press 1964. 7. p. Brunovsky Every normal linear .

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