DESIGN OF A GENERIC PATH PATH PLANNING SYSTEM AILAB Path Planning Workgroup.

DESIGN OF A GENERIC PATH PATH PLANNING SYSTEM

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OUTLINE

• Path Planning Basics

• Current Implementations

• System Design

• Conclusion

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PATH PLANNING BASICS

• Path

• Configuration

• Work Space

• Configuration Space (Cspace)– Cell Decomposition– Roadmap (Skeletonization)

• Free, Obstacle, Unknown Space

• Dimension and Degrees of Freedom

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Cell Decomposition

• Regular Grids

• Multiresolution Cells

• Trapezoidal Cells

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Roadmap (Skeletonization)

• Meadow Maps

• Generalized Voronoi Diagrams

• Visibility Graphs

• Probabilistic Roadmaps

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Properties of Path Planners

• Dynamic vs. static

• Global vs. local

• Optimal vs. suboptimal

• Complete vs. heuristic

• Metric vs. topological

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Classification of Obstacles

Category of Obstacles from Arai et. al. [Arai89, 28]

OBSTACLES

STATIC MOBILE

NEGOTIABLENON-

NEGOTIABLE

SCHEDULED UNSCHEDULED

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Path Planning Techniques

• Reactive Methods– Artificial Potential Fields– Vector Field Histogram Method

• Graph Traversing Methods– A* Algorithm– Best First / Breadth First / Greedy Search

• Wavefront Method• Other Methods

– Wall following, Space filling curves, Splines,Topological maps, etc.

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Problems with MA-PP

• Possible problems of applying ordinary PP methods to MAS are,– Collisions,– Deadlock situations, etc.

• Problems with MA-PP are,– Computational overhead,– Information exchange,– Communication overhead, etc.

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Approaches

• Cenralised: All robots in one composite system.+ Find complete and optimum solution if exists.+ Use complete information- Exponential computational complexity w.r.t # of robots - Single point of failure

• Decoupled: First generate paths for robots (independently), then handle interactions.+ Proportional computation time w.r.t # of robots + Robust- Not complete- Deadlocks may occur

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Improvements for MA-PP

• Priority assignment • Aging • Rule-Based methods • Resource allocation • Robot Groups• Virtual dampers and virtual springs• Assigning dynamic information to edges and

vertices...

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Characteristics of MAS

According to Dudek et. al. [Dudek96,53],

• Team Size1, 2, limited, infinite

• Communication RangeNone, Near, Infinite

• Communication TopologyBroadcast, Addressed, Tree, Graph

• Communication BandwidthHigh, Motion related, Low, Zero

• Team CompositionHomogeneous, Heterogeneous

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Characteristics of Domain

• Initial InformationNone, Partial, Complete

• Number of Targets1, Many

• Target AvailableTrue (i.e. go to target), False (i.e. explore for target)

• Stationary TargetsTrue, False

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Complexity of Path Planning

• In 3D work space finding exact solution is NP-HARD. [Xavier92, 54]

• Path planning is PSPACE-HARD. [Reif79,55]

• The compexity increases exponentially with,– Number of DOF [Canny88, 9]– Number of agents

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Imperfect solutions

• Used in case of compex problems,– Approximation– Probabilistic – Heuristic– Special cases

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CURRENT IMPLEMENTATIONS

• Sampling Based Algorithms– Incomplete, but efficient and practical

• Types– Multiple Query– Single Query

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Multiple Query

• A map is generated for multiple queries

• Fill the space adequately

• Probabilistic Roadmap– Uniform sampling of C-free– Local planner attempts connections– Biased sampling

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Single Query

• Suited for high dimensions

• Find a path as quick as possible

• RRTs– Grow from an initial state

• RRT-Connect : Grow from both initial and goal

– Expand by performing incremental motions

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Demos

• Path Planning– Probabilistic Roadmap (PRM)

• Different sampling methods

– Rapidly-exploring Random Trees (RRTs)• RRT• RRT-Connect

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SYSTEM DESIGN

* Following slides are based on Lavelle’s Motion Strategy Library, implemented in C++

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Overview

MODULES:

• Model

• Geom

• Problem

• Solver

• Scene

• Render

• Gui

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Model

• Contain incremental simulators that model the kinematics and dynamics of a variety of mechanical systems. The methods allow planning algorithms to compute the future system state, given the current state, an interval of time, and a control input applied over that interval.

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Geom

• These define the geometric representations of all obstacles in the world, and of each part of the robot. The methods allow planning algorithms to determine whether any of the robot parts are in collision with each other or with obstacles in the world. (PQP - the Proximity Query Package )

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Problem

• This is an interface class to a planner, which abstracts the designer of a planning algorithm away from particular details such as collision detection, and dynamical simulations. Each instance of a problem includes both an instance of Model and of Geometry. An initial state and final state are also included, which leads to a problem to be solved by a solver (typically a planning algorithm).

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Planner

• The most important module.

• Base for all path planners...

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CONCLUSION

• Path planning is a challenging task with many different applications.

• Each application may device its own path planning strategy.

• A generic path planning library may provide solution or guidelines for other path planners.

• ...

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QUESTIONS?

Thank [email protected]@gmail.com