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kinematics.py
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kinematics.py
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#***************************************************************************
#* *
#* Copyright (c) 2012 Gael Ecorchard <galou_breizh@yahoo.fr> *
#* *
#* This program is free software; you can redistribute it and/or modify *
#* it under the terms of the GNU Lesser General Public License (LGPL) *
#* as published by the Free Software Foundation; either version 2 of *
#* the License, or (at your option) any later version. *
#* for detail see the LICENCE text file. *
#* *
#* This program is distributed in the hope that it will be useful, *
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
#* GNU Library General Public License for more details. *
#* *
#* You should have received a copy of the GNU Library General Public *
#* License along with this program; if not, write to the Free Software *
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
#* USA *
#* *
#***************************************************************************
__title__ = "FreeCAD Symoro+ Workbench - Kinematics"
__author__ = "Gael Ecorchard <galou_breizh@yahoo.fr>"
__url__ = ["http://free-cad.sourceforge.net"]
from joint import Joint
from chain import Chain
def table_ok(table):
# Comparator function to order according to the antecedant index,
# which is the first element in a joint description of the table
# notation.
cmp_antc = lambda j1, j2: cmp(j1[0], j2[0])
sorted_table = sorted(table, cmp=cmp_antc) #I: returns sorted table according to its antecedant
return (sorted_table == list(table)) #I: Checks if current table is sorted
def Ttomatrix(T):
# TODO: remove FreeCAD dependency from this module
from FreeCAD import Base
l = T.flatten().tolist() #I: flatten converts a matrix into an array and then it is converted into a list
return Base.Matrix(*l)
def get_joints_from_table(table):
joints = []
if not(table_ok):
raise ValueError('Antecedants should be sorted in the table')
for j, row in enumerate(table):
if (row[0] == 0):
antc = None
else:
antc = joints[row[0] - 1]
# TODO: redefine sameas by starting with index 0 (-1 <=> None)
if (row[1] == 0):
sameas = None
else:
sameas = joints[row[1] - 1]
jnt = Joint(
j=j + 1,
antc=antc,
sameas=sameas,
mu=row[2],
sigma=row[3],
gamma=row[4],
b=row[5],
alpha=row[6],
d=row[7],
theta=row[8],
r=row[9],
)
joints.append(jnt)
# TODO: add recursion detection for antecedants
return joints
def get_looproot(joints, joint):
"""Return the loop root for loop ending at joint
Argument 2, joint, must be the end joint with non-None sameas attribute.
The loop root is the last common joints of the two subchains ending at,
respectively joint and joint.sameas.
"""
chain = Chain(joints)
subchain1 = chain.get_subchain_to(joint)
subchain2 = chain.get_subchain_to(joint.sameas)
#I: returns the first common antecedant for both loops
for jnt in subchain2[::-1]:
if (jnt in subchain1):
return jnt
return None
def get_loops(joints):
"""I: Returns a list of tuples with roots and ends (cut joints) of loops"""
ends = []
roots = []
for jnt in joints:
# If jnt's sameas attribute is another joint and that this latter is
# not already in the list of end joints, add jnt.
end = jnt.sameas
if (not(end is None) and
not(end in ends)):
ends.append(end)
roots.append(get_looproot(joints, jnt))
return zip(roots, ends)
class Kinematics():
def __init__(self, table, base_t=None, tool_t=None):
self.table = table
if base_t is None:
self.base_t = [
[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]
else:
self.base_t = base_t
if tool_t is None:
self.tool_t = [
[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]
else:
self.tool_t = tool_t
self.joints = get_joints_from_table(self.table)
# List of actuated joints
self.ajoints = self.get_ajoints()
# List of passive joints
self.pjoints = self.get_pjoints()
# Actuated joints' variables
self.q = self.get_q()
# Passive joints' variables
self.qp = self.get_qp()
# Chains
self.chain = Chain(self.joints)
# Tuples (root, end) for each loop
self.loops = get_loops(self.joints)
# List of loop solvers
from loop_solver import LoopSolver
self.loopsolvers = [LoopSolver(self.joints, *l) for l in self.loops]
# TODO: ajoints as property
def get_ajoints(self):
"""Return the list of active joints, always in the same order"""
ajoints = []
for jnt in self.joints:
if (jnt.isactuated()):
ajoints.append(jnt)
return ajoints
# TODO: pjoints as property
def get_pjoints(self):
"""Return the list of passive joints, always in the same order"""
pjoints = []
for jnt in self.joints:
if (jnt.ispassive()):
pjoints.append(jnt)
return pjoints
# TODO: cjoints as property
def get_cjoints(self):
"""Return the list of cut joints, always in the same order"""
cjoints = []
for jnt in self.joints:
if not(jnt.sameas is None):
cjoints.append(jnt)
# TODO: define q as property
def get_q(self, index=None):
"""Returns the list of joint variables of active joints"""
if (index is None):
return [jnt.q for jnt in self.ajoints]
else:
return self.ajoints[index].q
# TODO: define qp as property
def get_qp(self, index=None):
"""Returns the list of joint variables of passive joints"""
if (index is None):
return [jnt.q for jnt in self.pjoints]
else:
return self.pjoints[index].q
def set_q(self, q, index=None):
if (index is None):
index = range(len(self.ajoints))
try:
self.ajoints[index].q = q
except (AttributeError, TypeError):
for i in index:
self.ajoints[i].q = q[i]
def set_qp(self, q, index=None):
if (index is None):
index = range(len(self.pjoints))
try:
self.pjoints[index].q = q
except (AttributeError, TypeError):
for i in index:
self.pjoints[i].q = q[i]
def get_joint_transform(self, joint):
"""Return the transform from base to joint
Return a tuple (m, Pjminus1), where m is the transformation
matrix from base (not base joint) to the joint, and Pjminus1 is the
position of previous joint.
"""
# Get the list of joints from base to joint
# The transform from the base to the base joint is given by
# self.base_t.
l = self.base_t[0] + self.base_t[1] + self.base_t[2] + self.base_t[3]
from FreeCAD import Base
m = Base.Matrix(*l)
Pj = Base.Vector(0, 0, 0)
for jnt in self.chain.get_subchain_to(joint):
# Pjminus1 is Pj from the step before
Pjminus1 = Pj
m *= Ttomatrix(jnt.T)
Pj = Base.Vector(m.A14, m.A24, m.A34)
return m, Pjminus1
def solve_loops(self):
for ls in self.loopsolvers:
ls.solve()