Rigid Body Dynamics Library

Implements a rigid kinematic loop (or bodytobody) constraints as described in Ch. 8 of Featherstone's Rigid Body Dynamics Algorithms book. More...
#include <Constraint_Loop.h>
Public Member Functions  
LoopConstraint ()  
LoopConstraint (const unsigned int bodyIdPredecessor, const unsigned int bodyIdSuccessor, const Math::SpatialTransform &XPredecessor, const Math::SpatialTransform &XSuccessor, const Math::SpatialVector &constraintAxisInPredessor, bool enableBaumgarteStabilization=false, double stabilizationTimeConstant=0.1, const char *loopConstraintName=NULL, unsigned int userDefinedId=std::numeric_limits< unsigned int >::max(), bool positionLevelConstraint=true, bool velocityLevelConstraint=true)  
void  bind (const Model &model) override 
Any local memory that has a dimension of N, where N is the length of QDot, is resized in this function. More...  
void  calcConstraintJacobian (Model &model, const double time, const Math::VectorNd &Q, const Math::VectorNd &QDot, Math::MatrixNd &GSysUpd, ConstraintCache &cache, bool updateKinematics=false) override 
In this function the matrix of this contraint is inserted into the system constraint Jacobian (GSysOutput). The submatrix begins at rowInSystem, has sizeOfConstraint number of rows, and fills the full number of columns in G. More...  
void  calcGamma (Model &model, const double time, const Math::VectorNd &Q, const Math::VectorNd &QDot, const Math::MatrixNd &GSys, Math::VectorNd &gammaSysUpd, ConstraintCache &cache, bool updateKinematics=false) override 
In this function the vector of this constraint is inserted into the righthandside vector of the system. The vector begins at rowInSystem, and has sizeOfConstraint rows. More...  
void  calcPositionError (Model &model, const double time, const Math::VectorNd &Q, Math::VectorNd &errSysUpd, ConstraintCache &cache, bool updateKinematics=false) override 
In this function the sub vector of this constraint is inserted into the position error vector of the system. If the constraint is velocitylevel constraint or higher (noted in the boolean member variable positionConstraint) this should be set to zero. The vector begins at rowInSystem, and has sizeOfConstraint rows. More...  
void  calcVelocityError (Model &model, const double time, const Math::VectorNd &Q, const Math::VectorNd &QDot, const Math::MatrixNd &GSys, Math::VectorNd &derrSysUpd, ConstraintCache &cache, bool updateKinematics=false) override 
In this function the sub vector of this constraint is inserted into the position error vector of the system. If the constraint is an accelerationlevel constraint (noted in the boolean member variable velocityConstraint) this sub vector should be zero. The vector begins at rowInSystem, and has sizeOfConstraint rows. More...  
void  calcConstraintForces (Model &model, const double time, const Math::VectorNd &Q, const Math::VectorNd &QDot, const Math::MatrixNd &GSys, const Math::VectorNd &lagrangeMultipliersSys, std::vector< unsigned int > &constraintBodiesUpd, std::vector< Math::SpatialTransform > &constraintBodyFramesUpd, std::vector< Math::SpatialVector > &constraintForcesUpd, ConstraintCache &cache, bool resolveAllInRootFrame=false, bool updateKinematics=false) override 
This function resolves the generalized forces this constraint applies to the system into the wrenches that are applied to the bodies that are involved in the constraint. More...  
const std::vector< Math::SpatialVector > &  getConstraintAxes () 
void  appendConstraintAxis (const Math::SpatialVector &constraintAxis, bool positionLevelConstraint=true, bool velocityLevelConstraint=true) 
Public Member Functions inherited from Constraint  
virtual void  bind (const Model &model)=0 
Any local memory that has a dimension of N, where N is the length of QDot, is resized in this function. More...  
virtual void  calcConstraintJacobian (Model &model, const double time, const Math::VectorNd &Q, const Math::VectorNd &QDot, Math::MatrixNd &GSysOutput, ConstraintCache &cache, bool updateKinematics=false)=0 
In this function the matrix of this contraint is inserted into the system constraint Jacobian (GSysOutput). The submatrix begins at rowInSystem, has sizeOfConstraint number of rows, and fills the full number of columns in G. More...  
virtual void  calcGamma (Model &model, const double time, const Math::VectorNd &Q, const Math::VectorNd &QDot, const Math::MatrixNd &GSys, Math::VectorNd &gammaSysOutput, ConstraintCache &cache, bool updateKinematics=false)=0 
In this function the vector of this constraint is inserted into the righthandside vector of the system. The vector begins at rowInSystem, and has sizeOfConstraint rows. More...  
virtual void  calcPositionError (Model &model, const double time, const Math::VectorNd &Q, Math::VectorNd &errSysOutput, ConstraintCache &cache, bool updateKinematics=false)=0 
In this function the sub vector of this constraint is inserted into the position error vector of the system. If the constraint is velocitylevel constraint or higher (noted in the boolean member variable positionConstraint) this should be set to zero. The vector begins at rowInSystem, and has sizeOfConstraint rows. More...  
virtual void  calcVelocityError (Model &model, const double time, const Math::VectorNd &Q, const Math::VectorNd &QDot, const Math::MatrixNd &GSys, Math::VectorNd &derrSysOutput, ConstraintCache &cache, bool updateKinematics=false)=0 
In this function the sub vector of this constraint is inserted into the position error vector of the system. If the constraint is an accelerationlevel constraint (noted in the boolean member variable velocityConstraint) this sub vector should be zero. The vector begins at rowInSystem, and has sizeOfConstraint rows. More...  
virtual void  calcConstraintForces (Model &model, const double time, const Math::VectorNd &Q, const Math::VectorNd &QDot, const Math::MatrixNd &GSys, const Math::VectorNd &LagrangeMultipliersSys, std::vector< unsigned int > &constraintBodiesOutput, std::vector< Math::SpatialTransform > &constraintBodyFramesOutput, std::vector< Math::SpatialVector > &constraintForcesOutput, ConstraintCache &cache, bool resolveAllInRootFrame=false, bool updateKinematics=false)=0 
This function resolves the generalized forces this constraint applies to the system into the wrenches that are applied to the bodies that are involved in the constraint. More...  
virtual  ~Constraint () 
Constraint ()  
Constraint (const char *nameOfConstraint, unsigned int typeOfConstraint, unsigned int sizeOfConstraint, unsigned int userDefinedIdNumber)  
void  addToConstraintSet (const unsigned int rowIndex) 
This function is called by the functions in ConstraintSet that add a Constraint to the system. DO NOT TOUCH THIS. More...  
unsigned int  getUserDefinedId () 
void  setUserDefinedId (unsigned int userDefinedId) 
void  getConstraintJacobian (const Math::MatrixNd &GSys, Math::MatrixNd &GConstraint) 
void  getGamma (const Math::VectorNd &gammaSys, Math::VectorNd &gammaConstraint) 
void  getPositionError (const Math::VectorNd &errSys, Math::VectorNd &errConstraint) 
void  getVelocityError (const Math::VectorNd &derrSys, Math::VectorNd &derrConstraint) 
void  getBaumgarteStabilizationParameters (Math::Vector2d &bgParamsUpd) 
void  getBaumgarteStabilizationForces (const Math::VectorNd &errPos, const Math::VectorNd &errVel, Math::VectorNd &baumgarteForces) 
void  addInBaumgarteStabilizationForces (const Math::VectorNd &errPosSys, const Math::VectorNd &errVelSys, Math::VectorNd &gammaSysOutput) 
unsigned int  getConstraintType () 
unsigned int  getConstraintSize () 
unsigned int  getConstraintIndex () 
void  setBaumgarteTimeConstant (double tStab) 
Calculates and sets the Baumgarte stabilization coefficients as a function of tStab, the approximate timeconstant of stabilization. More...  
void  setEnableBaumgarteStabilization (bool flagEnableBaumgarteStabilization) 
bool  isBaumgarteStabilizationEnabled () 
void  enableConstraintErrorFromPositionLevel (unsigned int constraintSubIndex) 
: Will set the vectors positionConstraint and velocityConstraint to be consistent with a constraint that is described from the positionlevel up. More...  
void  enableConstraintErrorFromVelocityLevel (unsigned int constraintSubIndex) 
: Will set the vectors positionConstraint and velocityConstraint to be consistent with a constraint that is described from the velocitylevel up: position errors will be set to zero while velocity errors will be computed. More...  
void  enableConstraintErrorFromAccelerationLevel (unsigned int constraintSubIndex) 
: Will set the vectors positionConstraint and velocityConstraint to be consistent with a constraint that is described from the accelerationlevel: both position and velocity errors will be set to zero. More...  
void  enableConstraintErrorFromPositionLevel () 
: Will set the all elements in positionConstraint and velocityConstraint to be consistent with a constraint that is described from the positionlevel up. More...  
void  enableConstraintErrorFromVelocityLevel () 
: Will set the all elements in positionConstraint and velocityConstraint to be consistent with a constraint that is described from the velocitylevel up. More...  
void  enableConstraintErrorFromAccelerationLevel () 
: Will set the all elements in positionConstraint and velocityConstraint to be consistent with a constraint that is described from the accelerationlevel up. More...  
bool  getPositionLevelError (unsigned int constraintSubIndex) 
Returns the boolean value that determines whether or not positionlevel errors are computed for this subindex into this constraint. More...  
bool  getVelocityLevelError (unsigned int constraintSubIndex) 
Returns the boolean value that determines whether or not velocitylevel errors are computed for this subindex into this constraint. More...  
const char *  getName () 
const std::vector< unsigned int > &  getBodyIds () 
const std::vector< Math::SpatialTransform > &  getBodyFrames () 
Private Attributes  
std::vector< Math::SpatialVector >  T 
Vector of constraint axis resolved in the predecessor frame. More...  
double  dblA 
A local working double. More...  
Additional Inherited Members  
Protected Attributes inherited from Constraint  
std::string  name 
A user defined name which is unique to this constraint set. More...  
unsigned int  id 
A user defined id which is unique to this constraint set. More...  
unsigned int  typeOfConstraint 
The type of this constraint. More...  
unsigned int  sizeOfConstraint 
The number of rows that this constraint adds to G. More...  
unsigned int  rowInSystem 
The first row in G that corresponds to this constraint. More...  
std::vector< unsigned int >  bodyIds 
The index of the predecessor body in the vector of bodies in Model. More...  
std::vector< Math::SpatialTransform >  bodyFrames 
Transform from the frame of the predecessor body to the constraint frame. More...  
Math::Vector2d  baumgarteParameters 
bool  baumgarteEnabled 
A flag which enables or disables Baumgarte stabilization. More...  
std::vector< bool >  positionConstraint 
std::vector< bool >  velocityConstraint 
Implements a rigid kinematic loop (or bodytobody) constraints as described in Ch. 8 of Featherstone's Rigid Body Dynamics Algorithms book.
For details on this constraint please do read this documentation. However note that a typical user of RBDL should not need to use any of the functions described in this class but instead should use the functions that are defined in ConstraintSet (AddContactConstraint, calcForces, calcPositionError, calcVelocityError, calcBaumgarteStabilizationForces, etc) when working with this constraint. For those interested in all of the details of this constraint and how it works please refer to the source code for this class, and its base class.
A LoopConstraint will zero the acceleration between bodyfixed points and in the spatial directions . The user specifies and by passing in the spatial transform from the origin of the predecessor body to the predecessor frame ( , ) and likewise for the successor body to the successor frame ( , ). The spatial directions that the constraint is applied are specified in the vector which is resolved in the coordinates of the predecessor frame.
As with any other constraint this positionlevel constraint is index reduced and applied at the acceleration level. This constraint will only be satisfied at the positionlevel and velocitylevel if, prior to enabling the constraint, the constraint equations are satisified at the position and velocity levels. When assembling the constraint the functions CalcAssemblyQ and CalcAssemblyQDot can be used to satisfy this constraint at the position and velocity levels.
During the process of integration numerical error may accumulate. To prevent this error from growing Baumgarte stabilization can be enabled using the function setEnableBaumgarteStabilization provided in the base class. Numerical drift is usually small with this constraint because is body fixed. When this constraint is used in an optimal control problem Baumgarte stabilization may also be used to guide the solver to physically valid model configurations. Without stabilization the solver may introduce large constraint errors which will otherwise not be reduced. By default Baumgarte stabilization is not enabled.
By default this constraint does have its positionlevel and velocitylevel errors defined. This has the consequence that CalcAssemblyQ will update the position of the model to satisfy these constraints, as will
CalcAssemblyQDot at the velocity level. In addition, Baumgarte stabilization will apply forces to the model in response to constraint errors at both the position and velocity level.
Definition at line 72 of file Constraint_Loop.h.
LoopConstraint  (  ) 
Definition at line 26 of file Constraint_Loop.cc.
LoopConstraint  (  const unsigned int  bodyIdPredecessor, 
const unsigned int  bodyIdSuccessor,  
const Math::SpatialTransform &  XPredecessor,  
const Math::SpatialTransform &  XSuccessor,  
const Math::SpatialVector &  constraintAxisInPredessor,  
bool  enableBaumgarteStabilization = false , 

double  stabilizationTimeConstant = 0.1 , 

const char *  loopConstraintName = NULL , 

unsigned int  userDefinedId = std::numeric_limits<unsigned int>::max() , 

bool  positionLevelConstraint = true , 

bool  velocityLevelConstraint = true 

) 
bodyIdPredecessor  the identifier of the predecessor body 
bodyIdSuccessor  the identifier of the successor body 
XPredecessor  a spatial transform localizing the constrained frames on the predecessor body, expressed with respect to the predecessor body frame. Note the position vector should be the r_BPB (from the body's origin, to the predessor frame, in the coordinates of the body's frame) and E_BP (the rotation matrix that will rotate vectors from the coordinates of the P frame to the coordinates of the body's frame). 
XSuccessor  a spatial transform localizing the constrained frames on the successor body, expressed with respect to the successor body frame. Note the position vector should be the r_BSB (from the body's origin, to the successor frame, in the coordinates of the body's frame) and E_BS (the rotation matrix that will rotate vectors from the coordinates of the S frame to the coordinates of the body's frame). 
constraintAxisInPredessor  a spatial vector, resolved in the frame of the predecessor frame, indicating the axis along which the constraint acts. 
enableBaumgarteStabilization  (optional, default false) setting this flag to true will modify the right hand side of the acceleration equation with a penaltiy term that is proportional to the constraint error scaled by a constant. 
stabilizationTimeConstant  (optional, defaults to 0.1 sec) this value scales the strength of Baumgarte stabilization so that the settling time of the error is proportional the value given here. 
name  a human readable name (optional, default: NULL). Set this field to a unique name (within this ConstraintSet) so that the function GetConstraintIndex can find it. 
userDefinedId  a user defined id (optional, defaults to max()). Set this field to a unique number (within this ConstraintSet) so that the function GetConstraintIndex can find it. 
positionLevelConstraint  (optional, defaults to true to be consistent with the original implementation): When set to true, position errors will be computed for this constraint. This has the consequence that the function CalcAssemblyQ will assemble this constraint at the position level. In addition if Baumgarte stabilization is enabled, stabilization forces will be applied as a function of the position error. 
velocityLevelConstraint  (optional, defaults to true to be consistent with the original implementation) : This flag controls whether or not velocity errors are computed for this constraint. When velocity errors are computed they are used by CalcAssemblyQDot (to assemble this constraint at the velocity level) and by Baumgarte stabilization (if it is enabled) to modify the right hand side of the acceleration equation with a penalty term proportional to error. 
Definition at line 31 of file Constraint_Loop.cc.
References Constraint::bodyFrames, Constraint::bodyIds, LoopConstraint::dblA, std::fabs(), Constraint::positionConstraint, Constraint::setBaumgarteTimeConstant(), Constraint::setEnableBaumgarteStabilization(), LoopConstraint::T, and Constraint::velocityConstraint.
void appendConstraintAxis  (  const Math::SpatialVector &  constraintAxis, 
bool  positionLevelConstraint = true , 

bool  velocityLevelConstraint = true 

) 
constraintAxis  to append. This constraintAxis must have a norm of 1 and be normal to the existing constraintAxis 
positionLevelConstraint  if true position errors will be evaluated for this constraint entry. 
velocityLevelConstraint  if true velocity errors will be evalulated for this constraint entry. 
Definition at line 351 of file Constraint_Loop.cc.
References LoopConstraint::dblA, std::fabs(), Constraint::positionConstraint, Constraint::sizeOfConstraint, LoopConstraint::T, and Constraint::velocityConstraint.

overridevirtual 
Any local memory that has a dimension of N, where N is the length of QDot, is resized in this function.
model  a reference to the multibody model. Use the model's fields of qdot_size to size local memory (if any) that depends on the model. 
Implements Constraint.
Definition at line 73 of file Constraint_Loop.cc.

overridevirtual 
This function resolves the generalized forces this constraint applies to the system into the wrenches that are applied to the bodies that are involved in the constraint.
model  a reference to the multibody model. 
time  the time which is included so that rheonomic constraints might be included (in the future). 
Q  the vector of generalized positions. 
QDot  the vector of generalized velocities. 
GSys  a reference to the constraint Jacobian for the entire system. If is needed in this function do not reevaluate it but instead extract it from the system : this constraint's submatrix begins at rowInSystem, has sizeOfConstraint rows, and the full number of columns of GSys. 
LagrangeMultipliersSys  the vector of Lagrange multipliers for the entire system. The Lagrange multipliers for this constraint begin at rowInSystem and has sizeOfConstraint elements. 
constraintBodiesOutput  contains the indices of the bodies that contain the local frames listed in constraintBodyFramesOutput. If resolveAllInRootFrame is true, all of these indicies should be set to 0: in this case all of the wrenches are resolved in the root frame. 
constraintBodyFramesOutput  contains the local transformation from the origin of each body frame listed in constraintBodiesOutput to the frame in which the constraint wrench is applied. Note the frame is located on the body. If resolveAllInRootFrame is true, all of these frames have their origins resolved in the global frame and their orientation set to match that tof the global frame. 
constraintForcesOutput  contains the wrenches that the constraint applies to the local frames listed in constraintBodyFramesOutput. Note the force is resolved in the frame.If resolveAllInRootFrame is true, this wrench should be rotated into the coordinates of the root frame. 
cache  a ConstraintCache object which contains ample preallocated memory that can be used to reduce the memory footprint of each Constraint implementation. 
resolveAllInRootFrame  When this parameter is  false: the wrenches are resolved into their local frames.  true: the wrenches are resolved into coordinates of the global frame 
updateKinematics  setting this flag to true will cause all calls to kinematic dependent functions to be updated using the generalized coordinates passed into this function. 
Implements Constraint.
Definition at line 269 of file Constraint_Loop.cc.
References SpatialTransform::apply(), Constraint::bodyFrames, Constraint::bodyIds, RigidBodyDynamics::CalcBodyToBaseCoordinates(), RigidBodyDynamics::CalcBodyWorldOrientation(), SpatialTransform::E, SpatialTransform::r, MX_Xd_dynamic::resize(), Constraint::rowInSystem, Constraint::sizeOfConstraint, ConstraintCache::stA, ConstraintCache::stB, ConstraintCache::svecA, ConstraintCache::svecB, and LoopConstraint::T.

overridevirtual 
In this function the matrix of this contraint is inserted into the system constraint Jacobian (GSysOutput). The submatrix begins at rowInSystem, has sizeOfConstraint number of rows, and fills the full number of columns in G.
model  a reference to the multibody model. 
time  the time which is included so that rheonomic constraints might be included (in the future). 
Q  the vector of generalized positions. 
QDot  the vector of generalized velocities. 
GSysOutput  a reference to the constraint Jacobian for the entire system. Insert the G submatrix for this constraint beginning and rowInSystem, with a length sizeOfConstraint rows, and a width of the full number of columns in GSysOutput. 
cache  a ConstraintCache object which contains ample preallocated memory that can be used to reduce the memory footprint of each Constraint implementation. 
updateKinematics  setting this flag to true will cause all calls to kinematic dependent functions to be updated using the generalized coordinates passed into this function. 
Implements Constraint.
Definition at line 83 of file Constraint_Loop.cc.
References SpatialTransform::apply(), MX_Xd_dynamic::block(), Constraint::bodyFrames, Constraint::bodyIds, RigidBodyDynamics::CalcBodyToBaseCoordinates(), RigidBodyDynamics::CalcBodyWorldOrientation(), RigidBodyDynamics::CalcPointJacobian6D(), MX_Xd_dynamic::cols(), SpatialTransform::E, ConstraintCache::mat6NA, ConstraintCache::mat6NB, SpatialTransform::r, Constraint::rowInSystem, MX_Xd_dynamic::setZero(), Constraint::sizeOfConstraint, ConstraintCache::stA, ConstraintCache::svecA, and LoopConstraint::T.

overridevirtual 
In this function the vector of this constraint is inserted into the righthandside vector of the system. The vector begins at rowInSystem, and has sizeOfConstraint rows.
model  a reference to the multibody model. 
time  the time which is included so that rheonomic constraints might be included (in the future). 
Q  the vector of generalized positions. 
QDot  the vector of generalized velocities. 
GSys  a reference to the constraint Jacobian for the entire system. If is needed in this function do not reevaluate it but instead extract it from the system . 
gammaSysOutput  the system's gamma vector. Insert the gamma subvector for this constraint beginning and rowInSystem and with a length of sizeOfConstraint rows. 
cache  a ConstraintCache object which contains ample preallocated memory that can be used to reduce the memory footprint of each Constraint implementation. 
updateKinematics  setting this flag to true will cause all calls to kinematic dependent functions to be updated using the generalized coordinates passed into this function. 
Implements Constraint.
Definition at line 122 of file Constraint_Loop.cc.
References SpatialTransform::apply(), Constraint::bodyFrames, Constraint::bodyIds, RigidBodyDynamics::CalcBodyToBaseCoordinates(), RigidBodyDynamics::CalcBodyWorldOrientation(), RigidBodyDynamics::CalcPointAcceleration6D(), RigidBodyDynamics::CalcPointVelocity6D(), RigidBodyDynamics::Math::crossm(), SpatialTransform::E, SpatialTransform::r, Constraint::rowInSystem, Constraint::sizeOfConstraint, ConstraintCache::stA, ConstraintCache::svecA, ConstraintCache::svecB, ConstraintCache::svecC, ConstraintCache::svecD, ConstraintCache::svecE, ConstraintCache::svecF, LoopConstraint::T, and ConstraintCache::vecNZeros.

overridevirtual 
In this function the sub vector of this constraint is inserted into the position error vector of the system. If the constraint is velocitylevel constraint or higher (noted in the boolean member variable positionConstraint) this should be set to zero. The vector begins at rowInSystem, and has sizeOfConstraint rows.
model  a reference to the multibody model 
time  the time which is included so that rheonomic constraints might be included (in the future). 
Q  the vector of generalized positions. 
errSysOutput  the system's constraint position error vector. Insert the position error subvector for this constraint beginning and rowInSystem and with a length of sizeOfConstraint rows. 
cache  a ConstraintCache object which contains ample preallocated memory that can be used to reduce the memory footprint of each Constraint implementation. 
updateKinematics  setting this flag to true will cause all calls to kinematic dependent functions to be updated using the generalized coordinates passed into this function. 
Implements Constraint.
Definition at line 176 of file Constraint_Loop.cc.
References Constraint::bodyFrames, Constraint::bodyIds, RigidBodyDynamics::CalcBodyToBaseCoordinates(), RigidBodyDynamics::CalcBodyWorldOrientation(), SpatialTransform::E, ConstraintCache::mat3A, Constraint::positionConstraint, SpatialTransform::r, Constraint::rowInSystem, Constraint::sizeOfConstraint, ConstraintCache::stA, ConstraintCache::stB, ConstraintCache::svecA, and LoopConstraint::T.

overridevirtual 
In this function the sub vector of this constraint is inserted into the position error vector of the system. If the constraint is an accelerationlevel constraint (noted in the boolean member variable velocityConstraint) this sub vector should be zero. The vector begins at rowInSystem, and has sizeOfConstraint rows.
model  a reference to the multibody model. 
time  the time which is included so that rheonomic constraints might be included (in the future). 
Q  the vector of generalized positions. 
QDot  the vector of generalized velocities. 
GSys  a reference to the constraint Jacobian for the entire system. If is needed in this function do not reevaluate it but instead extract it from the system : this constraint's submatrix begins at rowInSystem, has sizeOfConstraint rows, and the full number of columns of GSys. 
derrSysOutput  the system's constraint velocity error vector. Insert the velocity error subvector for this constraint beginning and rowInSystem and with a length of sizeOfConstraint rows. 
cache  a ConstraintCache object which contains ample preallocated memory that can be used to reduce the memory footprint of each Constraint implementation. 
updateKinematics  setting this flag to true will cause all calls to kinematic dependent functions to be updated using the generalized coordinates passed into this function. 
Implements Constraint.
Definition at line 238 of file Constraint_Loop.cc.
References MX_Xd_dynamic::cols(), Constraint::rowInSystem, Constraint::sizeOfConstraint, and Constraint::velocityConstraint.

inline 
Definition at line 215 of file Constraint_Loop.h.

private 
A local working double.
Definition at line 236 of file Constraint_Loop.h.

private 
Vector of constraint axis resolved in the predecessor frame.
Definition at line 234 of file Constraint_Loop.h.