single_transform.py

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import numpy
from numpy import matrix, vsplit, sin, cos, reshape, zeros, pi
import rospy

import PyKDL
import yaml, math

# This represents the transform for a single joint in the URDF
# parameters are x,y,z and rotation as angle-axis

param_names = ['x','y','z','a','b','c']

class SingleTransform:
    def __init__(self, config = [0, 0, 0, 0, 0, 0], name=""):
        self._name = name
        eval_config = [eval(str(x)) for x in config]
        self._config = reshape(matrix(eval_config, float), (-1,1))

        rospy.logdebug("Initializing single transform %s with params [%s]", name, ", ".join(["% 2.4f" % x for x in eval_config]))
        self.inflate(self._config)

    def calc_free(self, free_config):
        return [x == 1 for x in free_config]

    def params_to_config(self, param_vec):
        return param_vec.T.tolist()[0]

    # Convert column vector of params into config
    def inflate(self, p):
        self._config = p.copy()  # Once we can back compute p from T, we don't need _config

        # Init output matrix
        T = matrix( zeros((4,4,), float))
        T[3,3] = 1.0
        
        # Copy position into matrix
        T[0:3,3] = p[0:3,0]
        
        # Renormalize the rotation axis to be unit length
        U,S,Vt = numpy.linalg.svd(p[3:6,0])
        a = U[:,0]
        rot_angle = S[0]*Vt[0,0]
        
        # Build rotation matrix
        c = cos(rot_angle)
        s = sin(rot_angle)
        R = matrix( [ [   a[0,0]**2+(1-a[0,0]**2)*c, a[0,0]*a[1,0]*(1-c)-a[2,0]*s, a[0,0]*a[2,0]*(1-c)+a[1,0]*s],
                      [a[0,0]*a[1,0]*(1-c)+a[2,0]*s,    a[1,0]**2+(1-a[1,0]**2)*c, a[1,0]*a[2,0]*(1-c)-a[0,0]*s],
                      [a[0,0]*a[2,0]*(1-c)-a[1,0]*s, a[1,0]*a[2,0]*(1-c)+a[0,0]*s,    a[2,0]**2+(1-a[2,0]**2)*c] ] )

        T[0:3,0:3] = R
        self.transform = T

    # Take transform, and convert into 6 param vector
    def deflate(self):
        # todo: This currently a hacky stub. To be correct, this should infer the parameter vector from the 4x4 transform
        return self._config

    # Returns # of params needed for inflation & deflation
    def get_length(self):
        return len(param_names)


# Convert from rotation-axis-with-angle-as-magnitude representation to Euler RPY
def angle_axis_to_RPY(vec):
    angle = math.sqrt(sum([vec[i]**2 for i in range(3)]))
    hsa = math.sin(angle/2.)
    if epsEq(angle, 0):
        return (0.,0.,0.)
    quat = [vec[0]/angle*hsa, vec[1]/angle*hsa, vec[2]/angle*hsa, math.cos(angle/2.)]
    rpy = quat_to_rpy(quat)
    return rpy

# Convert from Euler RPY to rotation-axis-with-angle-as-magnitude
def RPY_to_angle_axis(vec):
    if epsEq(vec[0], 0) and epsEq(vec[1], 0) and epsEq(vec[2], 0):
        return [0.0, 0.0, 0.0]
    quat = rpy_to_quat(vec)
    angle = math.acos(quat[3])*2.0
    hsa = math.sin(angle/2.)
    axis = [quat[0]/hsa*angle, quat[1]/hsa*angle, quat[2]/hsa*angle]
    return axis
    
def rpy_to_quat(rpy):
    return PyKDL.Rotation.RPY(rpy[0], rpy[1], rpy[2]).GetQuaternion()

def quat_to_rpy(q):
    return PyKDL.Rotation.Quaternion(q[0], q[1], q[2], q[3]).GetRPY()

#return 1 if value1 and value2 are within eps of each other, 0 otherwise
def epsEq(value1, value2, eps = 1e-10):
    if math.fabs(value1-value2) <= eps:
        return 1
    return 0