def _import(self, value, check=True): if isinstance(value, np.ndarray) and self.isvalid(value, check=check): if value.shape == (3, 3): # it's an se(3) return base.vexa(value) elif value.shape == (3, ): # it's a twist vector return value raise TypeError('bad type passed')
def _import(self, value, check=True): if isinstance(value, np.ndarray) and self.isvalid(value, check=check): if value.shape == (4, 4): # it's an se(3) return base.vexa(value) elif value.shape == (6, ): # it's a twist vector return value elif base.ishom(value, check=check): return base.trlog(value, twist=True, check=False) raise TypeError('bad type passed')
def trexp2(S, theta=None, check=True): """ Exponential of so(2) or se(2) matrix :param S: se(2), so(2) matrix or equivalent velctor :type T: ndarray(3,3) or ndarray(2,2) :param theta: motion :type theta: float :return: matrix exponential in SE(2) or SO(2) :rtype: ndarray(3,3) or ndarray(2,2) :raises ValueError: bad argument An efficient closed-form solution of the matrix exponential for arguments that are se(2) or so(2). For se(2) the results is an SE(2) homogeneous transformation matrix: - ``trexp2(Σ)`` is the matrix exponential of the se(2) element ``Σ`` which is a 3x3 augmented skew-symmetric matrix. - ``trexp2(Σ, θ)`` as above but for an se(3) motion of Σθ, where ``Σ`` must represent a unit-twist, ie. the rotational component is a unit-norm skew-symmetric matrix. - ``trexp2(S)`` is the matrix exponential of the se(3) element ``S`` represented as a 3-vector which can be considered a screw motion. - ``trexp2(S, θ)`` as above but for an se(2) motion of Sθ, where ``S`` must represent a unit-twist, ie. the rotational component is a unit-norm skew-symmetric matrix. .. runblock:: pycon >>> from spatialmath.base import * >>> trexp2(skew(1)) >>> trexp2(skew(1), 2) # revolute unit twist >>> trexp2(1) >>> trexp2(1, 2) # revolute unit twist For so(2) the results is an SO(2) rotation matrix: - ``trexp2(Ω)`` is the matrix exponential of the so(3) element ``Ω`` which is a 2x2 skew-symmetric matrix. - ``trexp2(Ω, θ)`` as above but for an so(3) motion of Ωθ, where ``Ω`` is unit-norm skew-symmetric matrix representing a rotation axis and a rotation magnitude given by ``θ``. - ``trexp2(ω)`` is the matrix exponential of the so(2) element ``ω`` expressed as a 1-vector. - ``trexp2(ω, θ)`` as above but for an so(3) motion of ωθ where ``ω`` is a unit-norm vector representing a rotation axis and a rotation magnitude given by ``θ``. ``ω`` is expressed as a 1-vector. .. runblock:: pycon >>> from spatialmath.base import * >>> trexp2(skewa([1, 2, 3])) >>> trexp2(skewa([1, 0, 0]), 2) # prismatic unit twist >>> trexp2([1, 2, 3]) >>> trexp2([1, 0, 0], 2) :seealso: trlog, trexp2 """ if base.ismatrix(S, (3, 3)) or base.isvector(S, 3): # se(2) case if base.ismatrix(S, (3, 3)): # augmentented skew matrix if check and not base.isskewa(S): raise ValueError("argument must be a valid se(2) element") tw = base.vexa(S) else: # 3 vector tw = base.getvector(S) if base.iszerovec(tw): return np.eye(3) if theta is None: (tw, theta) = base.unittwist2_norm(tw) elif not base.isunittwist2(tw): raise ValueError("If theta is specified S must be a unit twist") t = tw[0:2] w = tw[2] R = base.rodrigues(w, theta) skw = base.skew(w) V = np.eye(2) * theta + (1.0 - math.cos(theta)) * skw + ( theta - math.sin(theta)) * skw @ skw return base.rt2tr(R, V @ t) elif base.ismatrix(S, (2, 2)) or base.isvector(S, 1): # so(2) case if base.ismatrix(S, (2, 2)): # skew symmetric matrix if check and not base.isskew(S): raise ValueError("argument must be a valid so(2) element") w = base.vex(S) else: # 1 vector w = base.getvector(S) if theta is not None and not base.isunitvec(w): raise ValueError("If theta is specified S must be a unit twist") # do Rodrigues' formula for rotation return base.rodrigues(w, theta) else: raise ValueError( " First argument must be SO(2), 1-vector, SE(2) or 3-vector")
def trlog2(T, check=True, twist=False): """ Logarithm of SO(2) or SE(2) matrix :param T: SE(2) or SO(2) matrix :type T: ndarray(3,3) or ndarray(2,2) :param check: check that matrix is valid :type check: bool :param twist: return a twist vector instead of matrix [default] :type twist: bool :return: logarithm :rtype: ndarray(3,3) or ndarray(3); or ndarray(2,2) or ndarray(1) :raises ValueError: bad argument An efficient closed-form solution of the matrix logarithm for arguments that are SO(2) or SE(2). - ``trlog2(R)`` is the logarithm of the passed rotation matrix ``R`` which will be 2x2 skew-symmetric matrix. The equivalent vector from ``vex()`` is parallel to rotation axis and its norm is the amount of rotation about that axis. - ``trlog(T)`` is the logarithm of the passed homogeneous transformation matrix ``T`` which will be 3x3 augumented skew-symmetric matrix. The equivalent vector from ``vexa()`` is the twist vector (6x1) comprising [v w]. .. runblock:: pycon >>> from spatialmath.base import * >>> trlog2(trot2(0.3)) >>> trlog2(trot2(0.3), twist=True) >>> trlog2(rot2(0.3)) >>> trlog2(rot2(0.3), twist=True) :seealso: :func:`~trexp`, :func:`~spatialmath.base.transformsNd.vex`, :func:`~spatialmath.base.transformsNd.vexa` """ if ishom2(T, check=check): # SE(2) matrix if base.iseye(T): # is identity matrix if twist: return np.zeros((3, )) else: return np.zeros((3, 3)) else: if twist: return base.vexa(scipy.linalg.logm(T)) else: return scipy.linalg.logm(T) elif isrot2(T, check=check): # SO(2) rotation matrix if twist: return base.vex(scipy.linalg.logm(T)) else: return scipy.linalg.logm(T) else: raise ValueError("Expect SO(2) or SE(2) matrix")