60,522 research outputs found
Efficient motion planning for problems lacking optimal substructure
We consider the motion-planning problem of planning a collision-free path of
a robot in the presence of risk zones. The robot is allowed to travel in these
zones but is penalized in a super-linear fashion for consecutive accumulative
time spent there. We suggest a natural cost function that balances path length
and risk-exposure time. Specifically, we consider the discrete setting where we
are given a graph, or a roadmap, and we wish to compute the minimal-cost path
under this cost function. Interestingly, paths defined using our cost function
do not have an optimal substructure. Namely, subpaths of an optimal path are
not necessarily optimal. Thus, the Bellman condition is not satisfied and
standard graph-search algorithms such as Dijkstra cannot be used. We present a
path-finding algorithm, which can be seen as a natural generalization of
Dijkstra's algorithm. Our algorithm runs in time, where~ and are the number of vertices and
edges of the graph, respectively, and is the number of intersections
between edges and the boundary of the risk zone. We present simulations on
robotic platforms demonstrating both the natural paths produced by our cost
function and the computational efficiency of our algorithm
An Efficient Algorithm for Computing High-Quality Paths amid Polygonal Obstacles
We study a path-planning problem amid a set of obstacles in
, in which we wish to compute a short path between two points
while also maintaining a high clearance from ; the clearance of a
point is its distance from a nearest obstacle in . Specifically,
the problem asks for a path minimizing the reciprocal of the clearance
integrated over the length of the path. We present the first polynomial-time
approximation scheme for this problem. Let be the total number of obstacle
vertices and let . Our algorithm computes in time
a path of total cost
at most times the cost of the optimal path.Comment: A preliminary version of this work appear in the Proceedings of the
27th Annual ACM-SIAM Symposium on Discrete Algorithm
Static and Dynamic Path Planning Using Incremental Heuristic Search
Path planning is an important component in any highly automated vehicle
system. In this report, the general problem of path planning is considered
first in partially known static environments where only static obstacles are
present but the layout of the environment is changing as the agent acquires new
information. Attention is then given to the problem of path planning in dynamic
environments where there are moving obstacles in addition to the static ones.
Specifically, a 2D car-like agent traversing in a 2D environment was
considered. It was found that the traditional configuration-time space approach
is unsuitable for producing trajectories consistent with the dynamic
constraints of a car. A novel scheme is then suggested where the state space is
4D consisting of position, speed and time but the search is done in the 3D
space composed by position and speed. Simulation tests shows that the new
scheme is capable of efficiently producing trajectories respecting the dynamic
constraint of a car-like agent with a bound on their optimality.Comment: Internship Repor
Neural Networks in Mobile Robot Motion
This paper deals with a path planning and intelligent control of an
autonomous robot which should move safely in partially structured environment.
This environment may involve any number of obstacles of arbitrary shape and
size; some of them are allowed to move. We describe our approach to solving the
motion-planning problem in mobile robot control using neural networks-based
technique. Our method of the construction of a collision-free path for moving
robot among obstacles is based on two neural networks. The first neural network
is used to determine the "free" space using ultrasound range finder data. The
second neural network "finds" a safe direction for the next robot section of
the path in the workspace while avoiding the nearest obstacles. Simulation
examples of generated path with proposed techniques will be presented.Comment: 9 Page
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