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.
The paper proposes to reduce complexity of explicit MPC feedback laws by representing regions over which the law is defined as (possibly non-convex) polygons. Each polygon is then represented only by its boundaries, which reduces the memory footprint of the feedback law. Even though significant amount of memory can be saved this way, the price to be paid is increased computational load associated by performing point location tasks in non-convex objects. Therefore we propose to devise inner and outer convex approximations of non-convex polygons to reduce the computational requirements. Such approximations allow to perform point location more effectively, leading to a reduction of the required on-line computational effort. Several ways to design suitable approximations are presented and efficacy of the proposed procedure is evaluated. IEEE Conference on Decision and Control (CDC)This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Laboratories, Inc., 2013 201 Broadway, Cambridge, Massachusetts 02139 Copyright c Mitsubishi Electric Research Polygonic Representation of Explicit Model Predictive ControlJuraj Oravec, Slavomír Blažek, Michal Kvasnica, and Stefano Di Cairano Abstract-The paper proposes to reduce complexity of explicit MPC feedback laws by representing regions over which the law is defined as (possibly non-convex) polygons. Each polygon is then represented only by its boundaries, which reduces the memory footprint of the feedback law. Even though significant amount of memory can be saved this way, the price to be paid is increased computational load associated by performing point location tasks in non-convex objects. Therefore we propose to devise inner and outer convex approximations of non-convex polygons to reduce the computational requirements. Such approximations allow to perform point location more effectively, leading to a reduction of the required on-line computational effort. Several ways to design suitable approximations are presented and efficacy of the proposed procedure is evaluated.
The paper proposes to reduce complexity of explicit MPC feedback laws by representing regions over which the law is defined as (possibly non-convex) polygons. Each polygon is then represented only by its boundaries, which reduces the memory footprint of the feedback law. Even though significant amount of memory can be saved this way, the price to be paid is increased computational load associated by performing point location tasks on non-convex objects. To reduce the computational requirements, we therefore propose to devise inner and outer convex approximations of non-convex polygons. Such approximations then allow to perform point location more effectively, leading to reduction of the required on-line computational effort. Several ways to design suitable approximations are presented and efficacy of the proposed procedure is evaluated.
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