Constraint.cpp

/*********************************************************************
* Software License Agreement (BSD License)
*
*  Copyright (c) 2014, Rice University
*  All rights reserved.
*
*  Redistribution and use in source and binary forms, with or without
*  modification, are permitted provided that the following conditions
*  are met:
*
*   * Redistributions of source code must retain the above copyright
*     notice, this list of conditions and the following disclaimer.
*   * Redistributions in binary form must reproduce the above
*     copyright notice, this list of conditions and the following
*     disclaimer in the documentation and/or other materials provided
*     with the distribution.
*   * Neither the name of the Rice University nor the names of its
*     contributors may be used to endorse or promote products derived
*     from this software without specific prior written permission.
*
*  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
*  "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
*  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
*  FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
*  COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
*  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
*  BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
*  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
*  CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
*  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
*  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
*  POSSIBILITY OF SUCH DAMAGE.
*********************************************************************/
 
/* Author: Zachary Kingston */
 
#include "ompl/base/Constraint.h"
#include "ompl/base/spaces/constraint/ConstrainedStateSpace.h"
 
void ompl::base::Constraint::function(const State *state, Eigen::Ref<Eigen::VectorXd> out) const
{
    function(*state->as<ConstrainedStateSpace::StateType>(), out);
}
 
void ompl::base::Constraint::jacobian(const State *state, Eigen::Ref<Eigen::MatrixXd> out) const
{
    jacobian(*state->as<ConstrainedStateSpace::StateType>(), out);
}
 
void ompl::base::Constraint::jacobian(const Eigen::Ref<const Eigen::VectorXd> &x, Eigen::Ref<Eigen::MatrixXd> out) const
{
    Eigen::VectorXd y1 = x;
    Eigen::VectorXd y2 = x;
    Eigen::VectorXd t1(getCoDimension());
    Eigen::VectorXd t2(getCoDimension());
 
    // Use a 7-point central difference stencil on each column.
    for (std::size_t j = 0; j < n_; j++)
    {
        const double ax = std::fabs(x[j]);
        // Make step size as small as possible while still giving usable accuracy.
        const double h = std::sqrt(std::numeric_limits<double>::epsilon()) * (ax >= 1 ? ax : 1);
 
        // Can't assume y1[j]-y2[j] == 2*h because of precision errors.
        y1[j] += h;
        y2[j] -= h;
        function(y1, t1);
        function(y2, t2);
        const Eigen::VectorXd m1 = (t1 - t2) / (y1[j] - y2[j]);
        y1[j] += h;
        y2[j] -= h;
        function(y1, t1);
        function(y2, t2);
        const Eigen::VectorXd m2 = (t1 - t2) / (y1[j] - y2[j]);
        y1[j] += h;
        y2[j] -= h;
        function(y1, t1);
        function(y2, t2);
        const Eigen::VectorXd m3 = (t1 - t2) / (y1[j] - y2[j]);
 
        out.col(j) = 1.5 * m1 - 0.6 * m2 + 0.1 * m3;
 
        // Reset for next iteration.
        y1[j] = y2[j] = x[j];
    }
}
 
bool ompl::base::Constraint::project(State *state) const
{
    return project(*state->as<ConstrainedStateSpace::StateType>());
}
 
bool ompl::base::Constraint::project(Eigen::Ref<Eigen::VectorXd> x) const
{
    // Newton's method
    unsigned int iter = 0;
    double norm = 0;
    Eigen::VectorXd f(getCoDimension());
    Eigen::MatrixXd j(getCoDimension(), n_);
 
    const double squaredTolerance = tolerance_ * tolerance_;
 
    function(x, f);
    while ((norm = f.squaredNorm()) > squaredTolerance && iter++ < maxIterations_)
    {
        jacobian(x, j);
        x -= j.jacobiSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(f);
        function(x, f);
    }
 
    return norm < squaredTolerance;
}
 
double ompl::base::Constraint::distance(const State *state) const
{
    return distance(*state->as<ConstrainedStateSpace::StateType>());
}
 
double ompl::base::Constraint::distance(const Eigen::Ref<const Eigen::VectorXd> &x) const
{
    Eigen::VectorXd f(getCoDimension());
    function(x, f);
    return f.norm();
}
 
bool ompl::base::Constraint::isSatisfied(const State *state) const
{
    return isSatisfied(*state->as<ConstrainedStateSpace::StateType>());
}
 
bool ompl::base::Constraint::isSatisfied(const Eigen::Ref<const Eigen::VectorXd> &x) const
{
    Eigen::VectorXd f(getCoDimension());
    function(x, f);
    return f.allFinite() && f.squaredNorm() <= tolerance_ * tolerance_;
}