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<div class="title">Use of Projections in OMPL </div> </div>
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<div class="textblock"><p>Most planning algorithms use a data structure (in addition to the tree/graph of motions) for guiding the exploration of the space. In many cases, this data structure is in the form of a discretization of the state space. For practical purposes, discretizing the state space itself is not feasible, due to its high dimensionality. An approach taken by many algorithms is to use projections from the state space to a low dimensional Euclidean space (R<sup>k</sup>, k usually around 2 or 3), and discretize that Euclidean space instead. This includes algorithms such as <a class="el" href="classompl_1_1geometric_1_1EST.html" title="Expansive Space Trees.">ompl::geometric::EST</a>, <a class="el" href="classompl_1_1geometric_1_1SBL.html" title="Single-Query Bi-Directional Probabilistic Roadmap Planner with Lazy Collision Checking.">ompl::geometric::SBL</a>, <a class="el" href="classompl_1_1geometric_1_1KPIECE1.html" title="Kinematic Planning by Interior-Exterior Cell Exploration.">ompl::geometric::KPIECE1</a>. This projection can also be thought of as a hash function that maps states to cells in a low dimensional Euclidean space.</p>
<p>To support this notion of projections, OMPL includes <a class="el" href="classompl_1_1base_1_1ProjectionEvaluator.html" title="Abstract definition for a class computing projections to Rn. Implicit integer grids are imposed on th...">ompl::base::ProjectionEvaluator</a>. This is an abstract class whose main operation is <a class="el" href="classompl_1_1base_1_1ProjectionEvaluator.html#a748a31a8f4e5737e93fcd74a430b0baf" title="Compute the projection as an array of double values.">ompl::base::ProjectionEvaluator::project()</a>, which takes a <a class="el" href="classompl_1_1base_1_1State.html" title="Definition of an abstract state.">ompl::base::State</a>* and produces a <a class="el" href="namespaceompl_1_1base.html#aa83f2e90d56884b236b1e400d116b10b" title="The datatype for state projections. This class contains a real vector.">ompl::base::EuclideanProjection</a> (this is a representation of an array of real numbers).</p>
<p><a class="el" href="classompl_1_1base_1_1ProjectionEvaluator.html" title="Abstract definition for a class computing projections to Rn. Implicit integer grids are imposed on th...">ompl::base::ProjectionEvaluator</a> also includes utilities for discretizing the projected space (the low dimensional, Euclidean one). In particular, grids can be implicitly imposed on the projection space by setting cell sizes (a real value for each dimension of the Euclidean space), using ompl::base::ProjectionEvaluator::setCellDimensions(). The coordinates in the grid that correspond to a specific projection can be computed using <a class="el" href="classompl_1_1base_1_1ProjectionEvaluator.html#ad8ce42480db15d62a8996f569921aae9" title="Compute integer coordinates for a projection.">ompl::base::ProjectionEvaluator::computeCoordinates()</a>. If the sizes of cells for the grid have not been set, <a class="el" href="classompl_1_1base_1_1ProjectionEvaluator.html#a53a89a6b5980089e884f83ae78453a71" title="Perform configuration steps, if needed.">ompl::base::ProjectionEvaluator::setup()</a> uses sampling to identify sizes such that each dimension of the projection space is split into roughly 20 parts. This is merely a default and the user is encouraged to set desired cell sizes.</p>
<p>Projections are specific to state spaces. This means that each <a class="el" href="classompl_1_1base_1_1StateSpace.html" title="Representation of a space in which planning can be performed. Topology specific sampling, interpolation and distance are defined.">ompl::base::StateSpace</a> has its corresponding set of <a class="el" href="classompl_1_1base_1_1ProjectionEvaluator.html" title="Abstract definition for a class computing projections to Rn. Implicit integer grids are imposed on th...">ompl::base::ProjectionEvaluator</a>. In the implementation of state spaces, it is recommended that projections are set in the <a class="el" href="classompl_1_1base_1_1StateSpace.html#a18363a441aa3ec273b5a32bb9f9f21f3" title="Register the projections for this state space. Usually, this is at least the default projection...">ompl::base::StateSpace::registerProjections()</a> function. Although not required, it is good practice to register all projections to their corresponding state space, as this ensures calling <a class="el" href="classompl_1_1base_1_1ProjectionEvaluator.html#a53a89a6b5980089e884f83ae78453a71" title="Perform configuration steps, if needed.">ompl::base::ProjectionEvaluator::setup()</a> when needed. Most state spaces have at least a default projection set by <a class="el" href="classompl_1_1base_1_1StateSpace.html#a18363a441aa3ec273b5a32bb9f9f21f3" title="Register the projections for this state space. Usually, this is at least the default projection...">ompl::base::StateSpace::registerProjections()</a>. The user is encouraged to define appropriate projections, if available.</p>
<p>Example code for adding a projection for an R<sup>n</sup> state space: </p>
<div class="fragment"><pre class="fragment"> <span class="keyword">using namespace </span>ompl;
<span class="keyword">class </span>MyProjection : <span class="keyword">public</span> base::ProjectionEvaluator
{
<span class="keyword">public</span>:
MyProjection(<span class="keyword">const</span> <a class="code" href="classompl_1_1base_1_1StateSpacePtr.html" title="A boost shared pointer wrapper for ompl::base::StateSpace.">base::StateSpacePtr</a> &space) : base::ProjectionEvaluator(space)
{
}
<span class="keyword">virtual</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> getDimension(<span class="keywordtype">void</span>)<span class="keyword"> const</span>
<span class="keyword"> </span>{
<span class="keywordflow">return</span> 2;
}
<span class="keyword">virtual</span> <span class="keywordtype">void</span> defaultCellDimensions(<span class="keywordtype">void</span>)
{
cellDimensions_.resize(2);
cellDimensions_[0] = 0.1;
cellDimensions_[1] = 0.25;
}
<span class="keyword">virtual</span> <span class="keywordtype">void</span> project(<span class="keyword">const</span> <a class="code" href="classompl_1_1base_1_1State.html" title="Definition of an abstract state.">base::State</a> *state, <a class="code" href="namespaceompl_1_1base.html#aa83f2e90d56884b236b1e400d116b10b" title="The datatype for state projections. This class contains a real vector.">base::EuclideanProjection</a> &projection)<span class="keyword"> const</span>
<span class="keyword"> </span>{
<span class="keyword">const</span> <span class="keywordtype">double</span> *values = state-><a class="code" href="classompl_1_1base_1_1State.html#ae4ed5c095a6b2d4a5c946b91bc65e9cb" title="Cast this instance to a desired type.">as</a><<a class="code" href="classompl_1_1base_1_1RealVectorStateSpace_1_1StateType.html" title="The definition of a state in Rn">base::RealVectorStateSpace::StateType</a>>()->values;
projection.<a class="code" href="classompl_1_1base_1_1RealVectorStateSpace_1_1StateType.html#a916575eb76687da3b47a2d9699128498" title="The value of the actual vector in Rn">values</a>[0] = (values[0] + values[1]) / 2.0;
projection.values[1] = (values[2] + values[3]) / 2.0;
}
};
...
<a class="code" href="classompl_1_1base_1_1StateSpacePtr.html" title="A boost shared pointer wrapper for ompl::base::StateSpace.">base::StateSpacePtr</a> space;
<a class="code" href="classompl_1_1base_1_1PlannerPtr.html" title="A boost shared pointer wrapper for ompl::base::Planner.">base::PlannerPtr</a> planner;
space->registerProjection(<span class="stringliteral">"myProjection"</span>, <a class="code" href="classompl_1_1base_1_1ProjectionEvaluatorPtr.html" title="A boost shared pointer wrapper for ompl::base::ProjectionEvaluator.">base::ProjectionEvaluatorPtr</a>(<span class="keyword">new</span> MyProjection(space)));
...
planner->as<<a class="code" href="classompl_1_1geometric_1_1KPIECE1.html" title="Kinematic Planning by Interior-Exterior Cell Exploration.">geometric::KPIECE1</a>>()->setProjectionEvaluator(<span class="stringliteral">"myProjection"</span>);
</pre></div><p>For more reading on this topic, please see: <br/>
Șucan, Ioan A., Kavraki Lydia E., On the Performance of Random Linear Projections for Sampling-Based Motion Planning, in <em>IEEE/RSJ International Conference on Intelligent Robots and Systems</em>, pp. 2434-2439, Oct 2009. DOI: <a href="http://dx.doi.org/10.1109/IROS.2009.5354403">http://dx.doi.org/10.1109/IROS.2009.5354403</a>. </p>
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