43,588 research outputs found
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
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
RRT* Combined with GVO for Real-time Nonholonomic Robot Navigation in Dynamic Environment
Challenges persist in nonholonomic robot navigation in dynamic environments.
This paper presents a framework for such navigation based on the model of
generalized velocity obstacles (GVO). The idea of velocity obstacles has been
well studied and developed for obstacle avoidance since being proposed in 1998.
Though it has been proved to be successful, most studies have assumed equations
of motion to be linear, which limits their application to holonomic robots. In
addition, more attention has been paid to the immediate reaction of robots,
while advance planning has been neglected. By applying the GVO model to
differential drive robots and by combining it with RRT*, we reduce the
uncertainty of the robot trajectory, thus further reducing the range of
concern, and save both computation time and running time. By introducing
uncertainty for the dynamic obstacles with a Kalman filter, we dilute the risk
of considering the obstacles as uniformly moving along a straight line and
guarantee the safety. Special concern is given to path generation, including
curvature check, making the generated path feasible for nonholonomic robots. We
experimentally demonstrate the feasibility of the framework.Comment: 6 pages, 9 figures, accepted by RCAR 201
Computing Shortest Paths among Curved Obstacles in the Plane
A fundamental problem in computational geometry is to compute an
obstacle-avoiding Euclidean shortest path between two points in the plane. The
case of this problem on polygonal obstacles is well studied. In this paper, we
consider the problem version on curved obstacles, commonly modeled as
splinegons. A splinegon can be viewed as replacing each edge of a polygon by a
convex curved edge (polygons are special splinegons). Each curved edge is
assumed to be of O(1) complexity. Given in the plane two points s and t and a
set of pairwise disjoint splinegons with a total of vertices, we
compute a shortest s-to-t path avoiding the splinegons, in
time, where k is a parameter sensitive to the
structures of the input splinegons and is upper-bounded by . In
particular, when all splinegons are convex, is proportional to the number
of common tangents in the free space (called "free common tangents") among the
splinegons. We develop techniques for solving the problem on the general
(non-convex) splinegon domain, which also improve several previous results. In
particular, our techniques produce an optimal output-sensitive algorithm for a
basic visibility problem of computing all free common tangents among
pairwise disjoint convex splinegons with a total of vertices. Our algorithm
runs in time and space, where is the number of all
free common tangents. Even for the special case where all splinegons are convex
polygons, the previously best algorithm for this visibility problem takes
time.Comment: 45 pages, 21 figures; to appear in TALG; an extended-abstract
appeared in SoCG 201
Payoff-based Inhomogeneous Partially Irrational Play for Potential Game Theoretic Cooperative Control of Multi-agent Systems
This paper handles a kind of strategic game called potential games and
develops a novel learning algorithm Payoff-based Inhomogeneous Partially
Irrational Play (PIPIP). The present algorithm is based on Distributed
Inhomogeneous Synchronous Learning (DISL) presented in an existing work but,
unlike DISL,PIPIP allows agents to make irrational decisions with a specified
probability, i.e. agents can choose an action with a low utility from the past
actions stored in the memory. Due to the irrational decisions, we can prove
convergence in probability of collective actions to potential function
maximizers. Finally, we demonstrate the effectiveness of the present algorithm
through experiments on a sensor coverage problem. It is revealed through the
demonstration that the present learning algorithm successfully leads agents to
around potential function maximizers even in the presence of undesirable Nash
equilibria. We also see through the experiment with a moving density function
that PIPIP has adaptability to environmental changes.Comment: 28 pages, 11 figures, submitted to IEEE TA
Lifelong Multi-Agent Path Finding for Online Pickup and Delivery Tasks
The multi-agent path-finding (MAPF) problem has recently received a lot of
attention. However, it does not capture important characteristics of many
real-world domains, such as automated warehouses, where agents are constantly
engaged with new tasks. In this paper, we therefore study a lifelong version of
the MAPF problem, called the multi-agent pickup and delivery (MAPD) problem. In
the MAPD problem, agents have to attend to a stream of delivery tasks in an
online setting. One agent has to be assigned to each delivery task. This agent
has to first move to a given pickup location and then to a given delivery
location while avoiding collisions with other agents. We present two decoupled
MAPD algorithms, Token Passing (TP) and Token Passing with Task Swaps (TPTS).
Theoretically, we show that they solve all well-formed MAPD instances, a
realistic subclass of MAPD instances. Experimentally, we compare them against a
centralized strawman MAPD algorithm without this guarantee in a simulated
warehouse system. TP can easily be extended to a fully distributed MAPD
algorithm and is the best choice when real-time computation is of primary
concern since it remains efficient for MAPD instances with hundreds of agents
and tasks. TPTS requires limited communication among agents and balances well
between TP and the centralized MAPD algorithm.Comment: In AAMAS 201
Hybrid DDP in Clutter (CHDDP): Trajectory Optimization for Hybrid Dynamical System in Cluttered Environments
We present an algorithm for obtaining an optimal control policy for hybrid
dynamical systems in cluttered environments. To the best of our knowledge, this
is the first attempt to have a locally optimal solution for this specific
problem setting. Our approach extends an optimal control algorithm for hybrid
dynamical systems in the obstacle-free case to environments with obstacles. Our
method does not require any preset mode sequence or heuristics to prune the
exponential search of mode sequences. By first solving the relaxed problem of
getting an obstacle-free, dynamically feasible trajectory and then solving for
both obstacle-avoidance and optimality, we can generate smooth, locally optimal
control policies. We demonstrate the performance of our algorithm on a
box-pushing example in a number of environments against the baseline of
randomly sampling modes and actions with a Kinodynamic RRT
Online exploration outside a convex obstacle
A watchman route is a path such that a direct line of sight exists between
each point in some region and some point along the path. Here, we study
watchman routes outside a convex polygon, i.e., in R^2\O, where O is a convex
polygon. We study the problem of a watchman route in an online setting, i.e.,
in a setting where the watchman is only aware of the vertices of the polygon to
which it had a direct line of sight along its route. We present an algorithm
guaranteeing a ~89.83 competitive ratio relative to the optimal offline path
length
Path Planning in Dynamic Environments with Adaptive Dimensionality
Path planning in the presence of dynamic obstacles is a challenging problem
due to the added time dimension in search space. In approaches that ignore the
time dimension and treat dynamic obstacles as static, frequent re-planning is
unavoidable as the obstacles move, and their solutions are generally
sub-optimal and can be incomplete. To achieve both optimality and completeness,
it is necessary to consider the time dimension during planning. The notion of
adaptive dimensionality has been successfully used in high-dimensional motion
planning such as manipulation of robot arms, but has not been used in the
context of path planning in dynamic environments. In this paper, we apply the
idea of adaptive dimensionality to speed up path planning in dynamic
environments for a robot with no assumptions on its dynamic model.
Specifically, our approach considers the time dimension only in those regions
of the environment where a potential collision may occur, and plans in a
low-dimensional state-space elsewhere. We show that our approach is complete
and is guaranteed to find a solution, if one exists, within a cost
sub-optimality bound. We experimentally validate our method on the problem of
3D vehicle navigation (x, y, heading) in dynamic environments. Our results show
that the presented approach achieves substantial speedups in planning time over
4D heuristic-based A*, especially when the resulting plan deviates
significantly from the one suggested by the heuristic.Comment: Accepted in SoCS 201
Dynamic Path Planning and Movement Control in Pedestrian Simulation
Modeling and simulation of pedestrian behavior is used in applications such
as planning large buildings, disaster management, or urban planning.
Realistically simulating pedestrian behavior is challenging, due to the
complexity of individual behavior as well as the complexity of interactions of
pedestrians with each other and with the environment. This work-in-progress
paper addresses the tactical (path planning) and the operational level
(movement control) of pedestrian simulation from the perspective of
multiagent-based modeling. We propose (1) an novel extension of the JPS routing
algorithm for tactical planning, and (2) an architecture how path planning can
be integrated with a social-force based movement control. The architecture is
inspired by layered architectures for robot planning and control. We validate
correctness and efficiency of our approach through simulation runs.Comment: This paper was accepted for the preproceedings of The 2nd
International Workshop on Agent-based modelling of urban systems (ABMUS
2017), http://www.modelling-urban-systems.com
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