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An optimal path planning problem for heterogeneous multi-vehicle systems

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Klaučo M., Blažek S., Kvasnica M.
International Journal of Applied Mathematics and Computer Science
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2016
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tom 26
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nr 2
297-308
EN
A path planning problem for a heterogeneous vehicle is considered. Such a vehicle consists of two parts which have the ability to move individually, but one of them has a shorter range and is therefore required to keep in a close distance to the main vehicle. The objective is to devise an optimal path of minimal length under the condition that at least one part of the heterogeneous system visits all desired waypoints exactly once. Two versions of the problem are considered. One assumes that the order in which the waypoints are visited is known a priori. In such a case we show that the optimal path can be found by solving a mixed-integer second-order cone problem. The second version assumes that the order in which the waypoints are visited is not known a priori, but can be optimized so as to shorten the length of the path. Two approaches to solve this problem are presented and evaluated with respect to computational complexity.
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Reliable robust path planning with application to mobile robots

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Pepy R., Kieffer M., Walter E.
International Journal of Applied Mathematics and Computer Science
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2009
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tom 19
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nr 3
413-424
EN
This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic path planning in robotics.
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Optimization-based approach to path planning for closed chain robot systems

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Szynkiewicz W., Błaszczyk J.
International Journal of Applied Mathematics and Computer Science
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2011
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tom 21
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nr 4
659-670
EN
An application of advanced optimization techniques to solve the path planning problem for closed chain robot systems is proposed. The approach to path planning is formulated as a “quasi-dynamic” NonLinear Programming (NLP) problem with equality and inequality constraints in terms of the joint variables. The essence of the method is to find joint paths which satisfy the given constraints and minimize the proposed performance index. For numerical solution of the NLP problem, the IPOPT solver is used, which implements a nonlinear primal-dual interior-point method, one of the leading techniques for large-scale nonlinear optimization.
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