screws.txi

《机器人数学导论》中的matlab程序

@node DrawScrew,ForwardKinematics,DrawFrame,Reference
@findex DrawScrew
@bullet{} @code{DrawScrew}

@quotation
@code{DrawScrew[q, w, h]} generates a graphical description of a screw.
@end quotation

@c -------- ForwardKinematics
@node ForwardKinematics,HomogeneousToTwist,DrawScrew,Reference
@findex ForwardKinematics
@bullet{} @code{ForwardKinematics}

@quotation
@code{ForwardKinematics[@{xi1,th1@},...,@{xiN,thN@},g0]} computes the
forward kinematics via the product of exponentials formula.
@end quotation

@c -------- HomogeneousToTwist
@node HomogeneousToTwist,InertiaToCoriolis,ForwardKinematics,Reference
@findex HomogeneousToTwist
@bullet{} @code{HomogeneousToTwist}

@quotation
@code{HomogeneousToTwist[xi]} converts xi from a 4x4 matrix to a 6 vector.

@end quotation

@c -------- InertiaToCoriolis
@node InertiaToCoriolis,PointToHomogeneous,HomogeneousToTwist,Reference
@findex InertiaToCoriolis
@bullet{} @code{InertiaToCoriolis}

@quotation
@code{InertiaToCoriolis[M, theta]} computes the Coriolis matrix given the 
inertia matrix, M, and a list of the joint variables, theta.

This function is part of the @code{RobotLinks.m} package.
@end quotation

@c -------- PointToHomogeneous
@node PointToHomogeneous,PrismaticTwist,InertiaToCoriolis,Reference
@findex PointToHomogeneous
@bullet{} @code{PointToHomogeneous}

@quotation
@code{PointToHomogeneous[q]} gives the homogeneous representation of a point.

@code{PointToHomogeneous} converts a point in Euclidean space
to its homogeneous representation by appending a `1' to the vector.
@refill

@end quotation

@c -------- PrismaticTwist
@node PrismaticTwist,RevoluteTwist,PointToHomogeneous,Reference
@findex PrismaticTwist
@bullet{} @code{PrismaticTwist}

@quotation
@code{PrismaticTwist[q,w]} gives the 6-vector corresponding to point q 
on the axis and a screw with axis w for a prismatic joint.

This function is part of the @code{RobotLinks.m} package.
@end quotation

@c -------- RevoluteTwist
@node RevoluteTwist,RPToHomogeneous,PrismaticTwist,Reference
@findex RevoluteTwist
@bullet{} @code{RevoluteTwist}

@quotation
@code{RevoluteTwist[q,w]} gives the 6-vector corresponding to point q on 
the axis and a screw with axis w for a revolute joint.

This function is part of the @code{RobotLinks.m} package.
@end quotation

@c -------- RPToHomogeneous
@node RPToHomogeneous,RigidAdjoint,RevoluteTwist,Reference
@findex RPToHomogeneous
@bullet{} @code{RPToHomogeneous}

@quotation
@code{RPToHomogeneous[R,p]} forms homogeneous matrix from rotation
matrix R and position vector p.

@code{RPToHomogeneous} converts an element (R, p) in SE(3) into a 4x4 matrix.
@refill

@end quotation

@c -------- RigidAdjoint
@node RigidAdjoint,RigidInverse,RPToHomogeneous,Reference
@findex RigidAdjoint
@bullet{} @code{RigidAdjoint}

@quotation
@code{RigidAdjoint[g]} gives the adjoint matrix corresponding to g.

@code{RigidAdjoint} constructs a 6x6 matrix which represents the adjoint
of the rigid transformation @code{g}.  The rigid transformation @code{g}
should be a 4x4 homogeneous matrix representing and element of SE(3).
@xref{RPToHomogeneous}
@refill

@end quotation

@c -------- RigidInverse
@node RigidInverse,RigidOrientation,RigidAdjoint,Reference
@findex RigidInverse
@bullet{} @code{RigidInverse}

@quotation
@code{RigidInverse[g]} gives the inverse transformation of g.
@end quotation

@c -------- RigidOrientation
@node RigidOrientation,RigidPosition,RigidInverse,Reference
@findex RigidOrientation
@bullet{} @code{RigidOrientation}

@quotation
@code{RigidOrientation[g]} extracts the rotation matrix @code{R} from @code{g}.

@code{RigidOrientation} extracts the rotation component of a rigid
motion from the 4x4 homogeneous matrix @code{g}.
@xref{RigidPosition}.
@refill

@end quotation

@c -------- RigidPosition
@node RigidPosition,RigidTwist,RigidOrientation,Reference
@findex RigidPosition
@bullet{} @code{RigidPosition}

@quotation
@code{RigidPosition[g]} extracts the position vector @code{p} from @code{g}.

@code{RigidPosition} extracts the translational component of a rigid
motion from the 4x4 homogeneous matrix @code{g}.
@xref{RigidOrientation}.
@refill

@end quotation

@c -------- RigidTwist
@node RigidTwist,RotationAxis,RigidPosition,Reference
@findex RigidTwist
@bullet{} @code{RigidTwist}

@quotation
@code{RigidTwist[g]} returns an equivalent twist given a rigid motion @code{g}.

@code{RigidTwist} calculates a twist which generates the rigid motion
@code{g}.  This twist is not unique.
@refill

@end quotation

@c -------- RotationAxis
@node RotationAxis,RotationQ,RigidTwist,Reference
@findex RotationAxis
@bullet{} @code{RotationAxis}

@quotation
@code{RotationAxis[R]} finds the rotation axis for a rotation matrix.

@code{RotationAxis} finds an equivalent axis for a given rotation
matrix.
@refill

@end quotation

@c -------- RotationQ
@node RotationQ,ScrewSize,RotationAxis,Reference
@findex RotationQ
@bullet{} @code{RotationQ}

@quotation
@code{RotationQ[M]} tests wether a matrix @code{M} is a rotation matrix.

@code{RotationQ} checks to see if @code{M} is a 3x3 matrix which satisfies
@code{Transpose[M] . M == IdentityMatrix[3]} and @code{Det[M] == 1}.
@code{RotationQ} may return @code{False} for non-numeric matrices.
@refill

@end quotation

@c -------- ScrewSize
@node ScrewSize,ScrewToTwist,RotationQ,Reference
@findex ScrewSize
@bullet{} @code{ScrewSize}

@quotation
@code{ScrewSize} is an option for @code{DrawScrew} which sets the length
of a screw.
@end quotation

@c -------- ScrewToTwist
@node ScrewToTwist,SkewExp,ScrewSize,Reference
@findex ScrewToTwist
@bullet{} @code{ScrewToTwist}

@quotation
@code{ScrewToTwist[h, q, w]} returns the twist coordinates of a screw.
@end quotation

@c -------- SkewExp
@node SkewExp,SkewToAxis,ScrewToTwist,Reference
@findex SkewExp
@bullet{} @code{SkewExp}

@quotation
@code{SkewExp[w, theta]} gives the matrix exponential of an axis
@code{w}.  Default value of @code{theta} is 1.

@code{SkewExp} uses Rodriguez's formula to calculate the matrix
exponential of a skew-symmetric matrix.  @code{w} can either be a
3-vector or a skew-symmetrix matrix.
@refill

@end quotation

@c -------- SkewToAxis
@node SkewToAxis,SpatialJacobian,SkewExp,Reference
@findex SkewToAxis
@bullet{} @code{SkewToAxis}

@quotation
@code{SkewToAxis[S]} extracts a vector from a skew-symmetric matrix S.

@code{SkewToAxis} extracts a 3-vector from a 3x3 skew-symmetric matrix.
@refill

@end quotation

@c -------- SpatialJacobian
@node SpatialJacobian,StackCols,SkewToAxis,Reference
@findex SpatialJacobian
@bullet{} @code{SpatialJacobian}

@quotation
@code{SpatialJacobian[@{xi1,th1@},@{xi2,th2@},...,g0]} computes the spatial 
manipulator Jacobian of a robot defined by the given twists.

This function is part of the @code{RobotLinks.m} package.
@end quotation

@c -------- StackCols
@node StackCols,StackRows,SpatialJacobian,Reference
@findex StackCols
@bullet{} @code{StackCols}

@quotation
@code{StackCols[mat1, mat2, ...]} stacks matrix columns together
@end quotation

@c -------- StackRows
@node StackRows,TwistAxis,StackCols,Reference
@findex StackRows
@bullet{} @code{StackRows}

@quotation
@code{StackRows[mat1, mat2, ...]} stacks matrix rows together
@refill

@end quotation

@c -------- TwistAxis
@node TwistAxis,TwistExp,StackRows,Reference
@findex TwistAxis
@bullet{} @code{TwistAxis}

@quotation
@code{TwistAxis[xi]} gives axis of a screw corresponding to a twist.
@end quotation

@c -------- TwistExp
@node TwistExp,TwistMagnitude,TwistAxis,Reference
@findex TwistExp
@bullet{} @code{TwistExp}

@quotation
@code{TwistExp[xi, theta]} gives the matrix exponential of a twist
@code{xi}.  Default value of @code{theta} is 1.

@code{TwistExp} computes the matrix exponential of a twist.  The twist
may be specified as either a 6-vector (which will be converted to a 4x4
matrix with @code{TwistToHomogeneous}) or a 4x4 twist matrix.
@refill

@end quotation

@c -------- TwistMagnitude
@node TwistMagnitude,TwistPitch,TwistExp,Reference
@findex TwistMagnitude
@bullet{} @code{TwistMagnitude}

@quotation
@code{TwistMagnitude[xi]} returns the magnitude of a twist.
@end quotation

@c -------- TwistPitch
@node TwistPitch,TwistToHomogeneous,TwistMagnitude,Reference
@findex TwistPitch
@bullet{} @code{TwistPitch}

@quotation
@code{TwistPitch[xi]} returns the pitch of a twist.

@code{TwistPitch} returns the pitch of a twist vector or matrix.  An
inifinite pitch twist returns @code{Inifinity}.
@refill

@end quotation

@c -------- TwistToHomogeneous
@node TwistToHomogeneous,VectorToHomogeneous,TwistPitch,Reference
@findex TwistToHomogeneous
@bullet{} @code{TwistToHomogeneous}

@quotation
@code{TwistToHomogeneous[xi]} converts @code{xi} from a 6 vector to a
4X4 matrix.

@code{TwistToHomogeneous} converts a twist to its 4x4 homogeneous
representation.
@refill

@end quotation

@c -------- VectorToHomogeneous
@node VectorToHomogeneous,,TwistToHomogeneous,Reference
@findex VectorToHomogeneous
@bullet{} @code{VectorToHomogeneous}

@quotation
@code{VectorToHomogeneous[q]} gives the homogeneous representation of a point.

@code{VectorToHomogeneous} converts a point in Euclidean space
to its homogeneous representation by appending a `1' to the vector.
@refill

@end quotation

@c 
@c Index
@c
@iftex
@unnumbered Index
@printindex cp
@end iftex

@bye