An optimal path planning problem for heterogeneous multi-vehicle systems

Abstract

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.

An advance in infinite graph models for the analysis of transportation networks

“…In fact, there are several papers where the interest focuses on placing a specific service for drivers inside an edge (see, e.g., Peng et al, 2013;Kudělka et al, 2015). Some others deal with the problem of designing a network to improve the global efficiency (see the works of Milková (2009) or Klaučo et al (2016) for typical examples).…”

Path planning for an autonomous underwater vehicle in a cluttered underwater environment based on the heat method

“…In the quasi-static current field or the time-varying dynamic current field, optimizing the energy cost of traveling in ocean environments is also an important goal in AUV mission planning. Many of the developed planning algorithms integrated the current map with an evolutionary path planner (Klaučo et al, 2016;Chen et al, 2018;Makdah et al, 2019), providing an energy efficient path with the limitation of monotonicity in one coordinate of the path. Particle swarm optimization (Witt and Dunbabin, 2008;Mahmoud Zadeh et al, 2017;Wu, 2019) was studied for energy conservation by taking advantage of the time-varying ocean currents, which does not incorporate survival of the fittest and has no conventional evolutionary operators.…”

Multiquery Motion Planning in Uncertain Spaces: Incremental Adaptive Randomized Roadmaps

“…Such an ability is provided using a motion planning procedure. Motion planning can be defined as moving a mobile robot between a pair of start and goal configurations in an environment filled with obstacles, while avoiding any collision with obstacles and the environments boundaries (Kingston et al, 2018;Klaučo et al, 2016). It has been proven that the motion planning problem in its simplest form is NP-complete (Canny, 1988;González et al, 2016), meaning that the running time of the algorithm is exponential in the degree of freedom which makes the motion planning problem a challenging research area.…”