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// Copyright (c) 2015, LAAS-CNRS |
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// Authors: Florent Lamiraux |
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// |
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// Redistribution and use in source and binary forms, with or without |
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// modification, are permitted provided that the following conditions are |
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// met: |
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// |
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// 1. Redistributions of source code must retain the above copyright |
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// notice, this list of conditions and the following disclaimer. |
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// |
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// 2. Redistributions in binary form must reproduce the above copyright |
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// notice, this list of conditions and the following disclaimer in the |
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// documentation and/or other materials provided with the distribution. |
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// |
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
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// HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH |
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// DAMAGE. |
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#ifndef HPP_CONSTRAINTS_EXPLICIT_HH |
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#define HPP_CONSTRAINTS_EXPLICIT_HH |
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#include <hpp/constraints/implicit.hh> |
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namespace hpp { |
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namespace constraints { |
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/// \addtogroup constraints |
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/// \{ |
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/** Explicit numerical constraint |
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An explicit numerical constraint is a constraint such that some |
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configuration variables called \b output are function of the |
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others called \b input. |
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Let |
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\li \f$(ic_{1}, \cdots, ic_{n_{ic}})\f$ be the list of indices |
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corresponding to ordered input configuration variables, |
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\li \f$(oc_{1}, \cdots, oc_{n_{oc}})\f$ be the list of indices |
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corresponding to ordered output configuration variables, |
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\li \f$(iv_{1}, \cdots, iv_{n_{iv}})\f$ be the list of indices |
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corresponding to ordered input degrees of freedom, |
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\li \f$(ov_{1}, \cdots, ov_{n_{ov}})\f$ be the list of indices |
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corresponding to ordered output degrees of freedom. |
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Recall that degrees of freedom refer to velocity vectors. |
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Let us notice that \f$n_{ic} + n_{oc}\f$ is less than the robot |
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configuration size, and \f$n_{iv} + n_{ov}\f$ is less than the velocity |
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size. Some degrees of freedom may indeed be neither input nor output. |
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Then the differential function is of the form |
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\f{eqnarray*}{ |
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\mathbf{q}_{out} - g \left(\mathbf{q}_{in}\right) |
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\ \ &\mbox{with}& |
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\mathbf{q}_{out} = \left(q_{oc_{1}} \cdots q_{oc_{n_{oc}}}\right)^T, |
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\ \ \ \mathbf{q}_{in} = (q_{ic_{1}} \cdots q_{ic_{n_{ic}}})^T |
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\f} |
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It is straightforward that an equality constraint with this function can |
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solved explicitely: |
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\f{align*}{ |
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\mathbf{q}_{out} &- g \left(\mathbf{q}_{in}\right) = rhs \\ |
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& \mbox {if and only if}\\ |
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\mathbf{q}_{out} &= g \left(\mathbf{q}_{in}\right) + rhs \\ |
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\f} |
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If function \f$f\f$ takes values in a Lie group (SO(2), SO(3)), |
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the above "+" between a Lie group element and a tangent vector |
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has to be undestood as the integration of the constant velocity from |
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the Lie group element: |
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\f{equation*}{ |
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\mathbf{q} + \mathbf{v} = \mathbf{q}.\exp (\mathbf{v}) |
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\f} |
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where \f$\mathbf{q}\f$ is a Lie group element and \f$\mathbf{v}\f$ is a |
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tangent vector. |
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Considered as a Implicit instance, the expression of the Jacobian of |
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the DifferentiableFunction above depends on the output space of function |
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\f$f\f$. The rows corresponding to values in a vector space are |
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expressed as follows. |
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for any index \f$i\f$ between 0 and the size of velocity vectors, either |
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\li \f$\dot{q}_i\f$ is an input degree of freedom: |
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\f$\exists j\f$ integer, \f$1 \leq j \leq n_{iv}\f$ such that |
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\f$i=iv_{j}\f$, |
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\li \f$\dot{q}_i\f$ is an output degree of freedom: |
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\f$\exists j\f$ integer, \f$1\leq j \leq n_{ov}\f$ such that |
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\f$i=ov_{j}\f$, or |
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\li \f$\dot{q}_i\f$ neither input nor output. In this case, the |
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corresponding column is equal to 0. |
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\f{equation*}{ |
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J = \left(\begin{array}{cccccccccccc} |
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\cdots & ov_1 & \cdots & iv_{1} & \cdots & ov_2 & \cdots & iv_2 & \cdots & |
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ov_{n_{ov}} & \cdots \\ |
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& 1 & & & & 0 & & & & |
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& \\ |
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& 0 & & & & 1 & & & & |
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& \\ |
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& & & -\frac{\partial g}{q_1} & & & & -\frac{\partial |
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g}{q_2} \\ |
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&&&&&\\ |
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& 0 & & & & 0 & & & & 1 |
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\end{array}\right) |
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\f} |
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The rows corresponding to values in SO(3) have the following expression. |
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\f{equation*}{ |
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J = \left(\begin{array}{cccccccccccc} |
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ov_1 \ ov_2 \ ov_3 & iv_1 \cdots iv_{n_{iv}} \\ |
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J_{log}(R_{g}^T R_{out}) & -J_{log}(R_{g}^T R_{out})R_{out}^T R_{g} |
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\frac{\partial g}{\partial q_{in}} \end{array}\right) \f} where \li |
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\f$R_{out}\f$ is the rotation matrix corresponding to unit quaternion |
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\f$(q_{oc1},q_{oc2},q_{oc3},q_{oc4})\f$, \li \f$R_{g}\f$ is the rotation matrix |
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corresponding to the part of the output value of \f$f\f$ corresponding to SO(3), |
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\li \f$J_{log}\f$ is the Jacobian matrix of function that associates |
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to a rotation matrix \f$R\f$ the vector \f$\omega\f$ such that |
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\f{equation*}{ |
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R = \exp (\left[\omega\right]_{\times}) |
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\f} |
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**/ |
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class HPP_CONSTRAINTS_DLLAPI Explicit : public Implicit { |
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public: |
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/// Copy object and return shared pointer to copy |
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virtual ImplicitPtr_t copy() const; |
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/// Create instance and return shared pointer |
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/// |
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/// \param configSpace Configuration space on which the constraint is |
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/// defined, |
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/// \param function relation between input configuration variables and |
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/// output configuration variables, |
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/// \param inputConf set of integer intervals defining indices |
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/// \f$(ic_{1}, \cdots, ic_{n_{ic}})\f$, |
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/// \param outputConf set of integer intervals defining indices |
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/// \f$(oc_{1}, \cdots, oc_{n_{oc}})\f$, |
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/// \param inputVelocity set of integer defining indices |
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/// \f$(iv_{1}, \cdots, iv_{n_{iv}})\f$. |
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/// \param outputVelocity set of integer defining indices |
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/// \f$(ov_{1}, \cdots, ov_{n_{ov}})\f$. |
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/// \param mask mask defining which components of the error are |
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/// taken into account to determine whether the constraint |
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/// is satisfied (See parent class for details). |
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static ExplicitPtr_t create( |
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const LiegroupSpacePtr_t& configSpace, |
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const DifferentiableFunctionPtr_t& function, const segments_t& inputConf, |
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const segments_t& outputConf, const segments_t& inputVelocity, |
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const segments_t& outputVelocity, |
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const ComparisonTypes_t& comp = ComparisonTypes_t(), |
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std::vector<bool> mask = std::vector<bool>()); |
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/// Create a copy and return shared pointer |
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static ExplicitPtr_t createCopy(const ExplicitPtr_t& other); |
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/// Function that maps input to output |
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/// \return function \f$f\f$. |
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DifferentiableFunctionPtr_t explicitFunction() const { |
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return inputToOutput_; |
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} |
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/// Get output configuration variables |
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const segments_t& outputConf() const { return outputConf_; } |
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/// Get output degrees of freedom |
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const segments_t& outputVelocity() const { return outputVelocity_; } |
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/// Get input configuration variables |
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const segments_t& inputConf() const { return inputConf_; } |
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/// Get input degrees of freedom |
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const segments_t& inputVelocity() const { return inputVelocity_; } |
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/// Compute the value of the output configuration variables |
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/// \param qin input configuration variables, |
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/// \param rhs right hand side of constraint |
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/// |
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/// The default implementation computes |
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/// \f{equation} |
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/// g \left((q_{ic_{1}} \cdots q_{ic_{n_{ic}}})^T\right) + rhs |
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/// \f} |
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virtual void outputValue(LiegroupElementRef result, vectorIn_t qin, |
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LiegroupElementConstRef rhs) const; |
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/// Compute Jacobian of output value |
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/// |
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/// \f{eqnarray*} |
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/// J &=& \frac{\partial}{\partial\mathbf{q}_{in}}\left(g(\mathbf{q}_{in}) |
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/// + rhs\right). |
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/// \f} |
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/// \param qin vector of input variables, |
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/// \param g_value \f$f(\mathbf{q}_{in})\f$ provided to avoid |
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/// recomputation, |
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/// \param rhs right hand side (of implicit formulation). |
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virtual void jacobianOutputValue(vectorIn_t qin, |
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LiegroupElementConstRef g_value, |
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LiegroupElementConstRef rhs, |
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matrixOut_t jacobian) const; |
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protected: |
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/// Constructor |
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/// |
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/// \param configSpace Configuration space on which the constraint is |
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/// defined, |
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/// \param function relation between input configuration variables and |
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/// output configuration variables, |
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/// \param inputConf set of integer intervals defining indices |
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/// \f$(ic_{1}, \cdots, ic_{n_{ic}})\f$, |
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/// \param outputConf set of integer intervals defining indices |
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/// \f$(oc_{1}, \cdots, oc_{n_{oc}})\f$, |
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/// \param inputVelocity set of integer defining indices |
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/// \f$(iv_{1}, \cdots, iv_{n_{iv}})\f$. |
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/// \param outputVelocity set of integer defining indices |
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/// \f$(ov_{1}, \cdots, ov_{n_{ov}})\f$. |
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/// \param mask mask defining which components of the error are |
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/// taken into account to determine whether the constraint |
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/// is satisfied (See parent class for details). |
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Explicit(const LiegroupSpacePtr_t& configSpace, |
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const DifferentiableFunctionPtr_t& function, |
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const segments_t& inputConf, const segments_t& outputConf, |
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const segments_t& inputVelocity, const segments_t& outputVelocity, |
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const ComparisonTypes_t& comp, std::vector<bool> mask); |
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/// \copydoc Explicit (const LiegroupSpacePtr_t&, const |
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/// DifferentiableFunctionPtr_t&, const segments_t& inputConf, const |
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/// segments_t& outputConf, const segments_t& inputVelocity, const |
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/// segments_t&, const ComparisonTypes_t&); \param implicitFunction |
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/// differentiable function of the implicit |
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/// formulation if different from default expression |
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/// \f{equation}{ |
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/// \mathbf{q}_{out} - g \left(\mathbf{q}_{in}\right), |
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/// \f} |
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Explicit(const DifferentiableFunctionPtr_t& implicitFunction, |
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const DifferentiableFunctionPtr_t& function, |
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const segments_t& inputConf, const segments_t& outputConf, |
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const segments_t& inputVelocity, const segments_t& outputVelocity, |
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const ComparisonTypes_t& comp, std::vector<bool> mask); |
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/// Copy constructor |
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Explicit(const Explicit& other); |
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bool isEqual(const Implicit& other, bool swapAndTest) const; |
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// Store weak pointer to itself |
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void init(const ExplicitWkPtr_t& weak); |
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protected: |
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// Relation between input and output configuration variables |
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DifferentiableFunctionPtr_t inputToOutput_; |
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segments_t inputConf_; |
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segments_t outputConf_; |
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segments_t inputVelocity_; |
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segments_t outputVelocity_; |
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Explicit() {} |
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private: |
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ExplicitWkPtr_t weak_; |
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HPP_SERIALIZABLE(); |
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}; // class Explicit |
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/// \} |
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} // namespace constraints |
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} // namespace hpp |
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BOOST_CLASS_EXPORT_KEY(hpp::constraints::Explicit) |
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#endif // HPP_CONSTRAINTS_EXPLICIT_HH |
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