14,956 research outputs found
Path planning using harmonic functions and probabilistic cell decomposition
Potential-field approach based on harmonic functions have good path planning properties, although the explicit knowledge of the robot’s Configuration Space is required. To overcome this drawback, a combination with a random sampling scheme is proposed. Harmonic functions are computed over computed over a 2d –tree decomposition of a d-dimensional Configuration Space that is obtained with a probabilistic cell decomposition (sampling and classification). Cell sampling is biased towards the more promising regions by using the harmonic function values. Cell classification is performed by evaluating a set of configurations of the cell obtained with a deterministic sampling sequence that provides a good uniform and incremental coverage of the cell. The proposed planning framework open the use of harmonic functions to higher dimensional C-spaces
SDK: A proposal of a general and efficient deterministic sampling sequence
Previous works have already demonstrated that deterministic sampling can be competitive with respect to probabilistic sampling in sampling-based path planners. Nevertheless, the definition of a general sampling sequence for any d-dimensional Configuration Space satisfying the requirements needed for path planning is not a trivial issue, over a multi-grid cell decomposition, of the ordering of the 2d descendant cells of any parent cell. This ordering is generated by the digital construction method using a d x d matrix Td. A general expression of this matrix (i.e. for any d) is introduced and its performance analyzed in terms of the mutual distance. The paper ends with a performance evaluation of the use of the proposed deterministic sampling sequence in different well know path planner
Admissible Velocity Propagation : Beyond Quasi-Static Path Planning for High-Dimensional Robots
Path-velocity decomposition is an intuitive yet powerful approach to address
the complexity of kinodynamic motion planning. The difficult trajectory
planning problem is solved in two separate, simpler, steps: first, find a path
in the configuration space that satisfies the geometric constraints (path
planning), and second, find a time-parameterization of that path satisfying the
kinodynamic constraints. A fundamental requirement is that the path found in
the first step should be time-parameterizable. Most existing works fulfill this
requirement by enforcing quasi-static constraints in the path planning step,
resulting in an important loss in completeness. We propose a method that
enables path-velocity decomposition to discover truly dynamic motions, i.e.
motions that are not quasi-statically executable. At the heart of the proposed
method is a new algorithm -- Admissible Velocity Propagation -- which, given a
path and an interval of reachable velocities at the beginning of that path,
computes exactly and efficiently the interval of all the velocities the system
can reach after traversing the path while respecting the system kinodynamic
constraints. Combining this algorithm with usual sampling-based planners then
gives rise to a family of new trajectory planners that can appropriately handle
kinodynamic constraints while retaining the advantages associated with
path-velocity decomposition. We demonstrate the efficiency of the proposed
method on some difficult kinodynamic planning problems, where, in particular,
quasi-static methods are guaranteed to fail.Comment: 43 pages, 14 figure
Sensor Synthesis for POMDPs with Reachability Objectives
Partially observable Markov decision processes (POMDPs) are widely used in
probabilistic planning problems in which an agent interacts with an environment
using noisy and imprecise sensors. We study a setting in which the sensors are
only partially defined and the goal is to synthesize "weakest" additional
sensors, such that in the resulting POMDP, there is a small-memory policy for
the agent that almost-surely (with probability~1) satisfies a reachability
objective. We show that the problem is NP-complete, and present a symbolic
algorithm by encoding the problem into SAT instances. We illustrate trade-offs
between the amount of memory of the policy and the number of additional sensors
on a simple example. We have implemented our approach and consider three
classical POMDP examples from the literature, and show that in all the examples
the number of sensors can be significantly decreased (as compared to the
existing solutions in the literature) without increasing the complexity of the
policies.Comment: arXiv admin note: text overlap with arXiv:1511.0845
Obstacle Avoidance and Proscriptive Bayesian Programming
Unexpected events and not modeled properties of the robot environment are some of
the challenges presented by situated robotics research field. Collision avoidance is a basic security
requirement and this paper proposes a probabilistic approach called Bayesian Programming, which
aims to deal with the uncertainty, imprecision and incompleteness of the information handled to
solve the obstacle avoidance problem. Some examples illustrate the process of embodying the
programmer preliminary knowledge into a Bayesian program and experimental results of these
examples implementation in an electrical vehicle are described and commented. A video illustration
of the developed experiments can be found at http://www.inrialpes.fr/sharp/pub/laplac
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