wrapper.py 28.2 KB
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import pinocchio as se3
import numpy as np
import time
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import os
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from models import osim_parser
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from pinocchio.utils import XYZQUATToViewerConfiguration, zero, se3ToXYZQUAT
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from bmtools.algebra import quaternion_from_matrix, euler_matrix
from bmtools.filters import *
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class Wrapper():
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    def __init__(self, model_path=None, mesh_path=None, name='Robot',OsimModel=True):
        self.name = name
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        if model_path is None:
            model_path = '/local/gmaldona/devel/biomechatronics/models/GX.osim'
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        r = osim_parser.Osim2PinocchioModel()
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        self.mesh_path = mesh_path
        self.model_path = model_path
        r.parseModel(self.model_path,self.mesh_path)
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        self.upperPositionLimitOsim = r.upperPositionLimit
        self.upperPositionLimitOsim = r.upperPositionLimit
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        self.model = r.model 
        self.visuals = r.visuals
        self.data = r.data
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        self.v0 = zero(self.model.nv)
        self.q0 = zero(self.model.nq)
        self.q = self.q0
        self.oMp = se3.utils.rotate('z',np.pi/2) * se3.utils.rotate('x',np.pi/2)
        self.markersFreq = np.float(400.)
        self.dt = np.float(1/400.)
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        self.v = zero(self.model.nv)
        self.a = zero(self.model.nv)
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        self.fext = self.data.hg.vector.copy()
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    @property
    def nq(self):
        return self.model.nq

    @property
    def nv(self):
        return self.model.nv

    def addLandmark(self, nodeName, size):
        self.viewer.gui.addLandmark(nodeName, size)
    
    def displayJointLandmarks(self):
        #create nodes
        for i in range(1,self.model.nbodies):
            #idx = self.model.getJointId(self.visuals[i][1]) 
            pose =  self.data.oMi[i]
            #self.viewer.gui.addXYZaxis('world/'+self.model.names[i], [0., 1., 0., .5], 0.02, 0.1)
            #self.viewer.gui.addLandmark('world/'+self.model.names[i], 0.3)
            self.placeObject('world/'+self.model.names[i], pose, True)

    def getNodeList(self):
        return self.viewer.gui.getNodeList()

    def getSubTree(self, idx):
        subtree = []
        idx_p = self.model.parents[idx]
        #dof = human.model.joints[idx_p].idx_q
        #subtree.append([idx_p, dof])
        subtree.append(idx_p)
        while True:
            idx_p = self.model.parents[idx_p]
            #dof = human.model.joints[idx_p].idx_q
            #subtree.append([idx_p, dof])
            subtree.append(idx_p)
            if idx_p == 0:
                break
        return subtree

    def update(self,q):
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        se3.computeAllTerms(self.model, self.data, self.q, self.v)
        #se3.forwardKinematics(self.model, self.data, q, self.v, self.a)
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        #- se3::forwardKinematics 
        #- se3::crba
        #- se3::nonLinearEffects
        #- se3::computeJacobians 
        #- se3::centerOfMass                                                                                  
        #- se3::jacobianCenterOfMass
        #- se3::kineticEnergy   
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        #- se3::potentialEnergy   
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        se3.framesKinematics(self.model, self.data, q)
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        se3.computeJacobians(self.model, self.data, q)
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        se3.rnea(self.model, self.data, q, self.v, self.a)
        self.biais(self.q, self.v)
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        self.q = q.copy()        
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    def parseTrial(self, data):
        q=[]
        for i in range(0, len(data)):
            q.append( self.dof2pinocchio(data[i][:]) )
        return q
        
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    def parseTrialVel(self, data):
        dq=[]
        for i in range(0, len(data)):
            dq.append( self.vel2pinocchio(data[i][:]) )
        return dq

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    def readOsim(self, filename):
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        extension = os.path.splitext(filename)[1]
        if extension == '.mot':
            print 'parsing motion data'
            trial = osim_parser.readOsim(filename)
            trial['osim_data'] = trial['data']
            trial['pinocchio_data'] = np.asmatrix(self.parseTrial(trial['data'][:]))
            trial['pinocchio_kine'] = np.asmatrix(self.parseTrialVel(trial['data'][:]))
            trial['time'] = np.asmatrix(trial['time'][:])
            return trial
        elif extension == '.sto':
            print 'parsing force data'
            trial = np.asmatrix(osim_parser.readOsim(filename))
            return trial
        else:
            print 'could not parse, do not know the extension:'
            print extension
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    def inverseDynamics(self, q, v, a, f_ext=None):
        '''ID(q, v, a, f_ext)
         f_ext: Vector of external forces expressed in the local frame of each joint 
         do it recursively
        '''
        if f_ext is None:
            for i in range(0, len(q)):
                Tau.append(se3.rnea(self.model, self.data, q, v, a))
        else:
            for i in range(0, len(q)):
                Tau.append(se3.rnea(self.model, self.data, q, v, a, f_ext))
        return Tau

    def forwardDynamics(self):
        pass

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#    def position(self, q, index, update_geometry=True):
#        if update_geometry:
#            se3.forwardKinematics(self.model, self.data, q)
#        return self.data.oMi[index] 
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    def differentiate(self, q1, q2):
        return se3.differentiate(self.model, np.asmatrix(q1), np.asmatrix(q2))
        
    def generalizedVelocity(self, Q, dt):
        return np.asmatrix( np.gradient(Q, dt) )
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    def biais(self, q, v):
        ''' the coriolis, centrifugal and gravitational effects '''
        return se3.nle(self.model, self.data, q, v)

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    def bias(self, q, v, update_kinematics=True):
        if(update_kinematics):
            return se3.nle(self.model, self.data, q, v)
        return self.data.nle

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    def generalizedAcceleration(self, V, dt):
        return np.asmatrix(np.gradient(V, dt))

    def velocity(self, q, v, index, update_kinematics=True):
        if update_kinematics:
            se3.forwardKinematics(self.model, self.data, q, v)
        return self.data.v[index]

    def acceleration(self, q, v, a, index, update_acceleration=True):
        if update_acceleration:
            se3.forwardKinematics(self.model, self.data, q, v, a)
        return self.data.a[index]

    def forwardKinematics(self, q, v=None, a=None):
        if v is not None:
            if a is not None:
                se3.forwardKinematics(self.model, self.data, q, v, a)
            else:
                se3.forwardKinematics(self.model, self.data, q, v)
        else:
            se3.forwardKinematics(self.model, self.data, q)

    def computeAllKinematics(self, Q):
        self.Q = Q
        self.V = self.generalizedVelocity(self.Q, self.dt)
        self.A = self.generalizedAcceleration(self.V, self.dt)
        #se3.forwardKinematics(self.model, self.data, self.Q, self.V, self.A)
        
    def playForwardKinematics(self, Q, sleep=0.0025, step=10, record=False):
        ''' playForwardKinematics(q, sleep, step, record)
        '''
        # TODO at verical line to plot as in opensim during playing
        rec = {'q':[],'com':[], 'Jcom':[]}
        for i in range(0, len(Q),step):
            self.q = Q[i]
            self.display(self.q, osimref=True, com=True, updateKinematics=False)
            time.sleep(sleep)
            if record is True:
                #rec =  self.record()
                rec['q'].append(self.q)
                rec['com'].append(self.com(self.q).getA()[:,0])
                rec['Jcom'].append(self.Jcom(se3.jacobianCenterOfMass(self.model, self.data, self.q)))
        if record is True:
            return rec


    def record(self, motion, variable, idx=None):
        Jtask = []
        task = []
        if variable is 'joint':
            for i in range(0, len(motion)):
                se3.forwardKinematics(self.model, self.data, motion[i])
                #task['rotation'].append(se3.utils.matrixToRpy(self.data.oMi[idx].rotation))
                #task['translation'].append(self.data.oMi[idx].translation)
                #task.append([self.data.oMi[idx].translation, 
                #             se3.utils.matrixToRpy(self.data.oMi[idx].rotation)])
                #task.append(np.row_stack((self.data.oMi[idx].translation, 
                #                          se3.utils.matrixToRpy(self.data.oMi[idx].rotation))))
                task.append(np.row_stack((self.data.oMi[idx].translation, 
                                          np.matrix(euler_from_matrix(
                                              self.data.oMi[idx].rotation,'syxz')).T)))
                #M = (self.data.oMi[idx-1].rotation).T*self.data.oMi[idx].rotation
                #task.append(np.row_stack((self.data.oMi[idx].translation,
                #                          np.matrix(euler_from_matrix(M,'sxyz')).T)))
                #M = self.oMp*self.data.oMi[idx].rotation
                Jtask.append(se3.jacobian(self.model, self.data, motion[i], idx, True, True))

        elif variable is 'com':
            for i in range(0, len(motion)):
                se3.forwardKinematics(self.model, self.data, motion[i])
                task.append(self.com(motion[i]).getA()[:,idx])
                Jtask.append(self.Jcom(motion[i]))
        

        return task, Jtask
            
    def kine(self, motion):
        q = []
        vel = []
        #hg = []
        for i in range(0, len(motion)):
            se3.forwardKinematics(self.model, self.data, motion[i])
            q.append(motion[i])
            if i is 0:
                vel.append(self.v0)
            else:
                vel.append(self.differentiate(q[i-1], q[i])/self.dt)
        #filter
        v=self.reshape(vel)
        v_hat=self.filterM(v, cutoff=35, fs=400, order=4)
        v_hat2 =self.reshape(v_hat)
        #    se3.ccrba(self.model, self.data, q[i], vel[i])
        #hg.append(self.data.hg)
        return q, v_hat2
    
    def reshape(self, X):
        r,c = np.shape(X)[0:2]
        X_hat = np.zeros((r,c))
        for i in xrange(r):
            xi = np.array(X[i])
            for j in xrange(c):
                X_hat[i,j] = xi[j]
        return X_hat
        
    def filter(self, X, cutoff=10, fs=400, order=4):
        X_hat = filtfilt_butter(X, cutoff, fs, order)
        return X_hat


    def filterM(self, M, cutoff=10, fs=400, order=4):
        t, dof = np.shape(M)[0:2]
        M_hat = np.zeros((t,dof))
        for i in xrange(dof):
            M_hat[:,i] = filtfilt_butter(M[:,i], cutoff, fs, order)
        return M_hat

    def cam(self, q, vel):
        hg = []
        for i in range(0, len(q)):
            se3.ccrba(self.model, self.data, q[i], vel[i])
            hg.append(self.data.hg.copy())
        return hg

    def com(self, q, v=None, a=None, update_kinematics=True):
        if v is not None:
            if a is None:
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                se3.centerOfMass(self.model, self.data, q, v)#, update_kinematics)
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                return self.data.com[0], self.data.vcom[0]
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            se3.centerOfMass(self.model, self.data, q, v, a)#, update_kinematics)
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            return self.data.com[0], self.data.vcom[0], self.data.acom[0]
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        return se3.centerOfMass(self.model, self.data, q)#, update_kinematics)
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    def Jcom(self, q): #, update_kinematics=True):
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        return se3.jacobianCenterOfMass(self.model, self.data, q)
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        #if(update_kinematics):
        #    return se3.jacobianCenterOfMass(self.model, self.data, q)
        #return self.data.Jcom
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    def mass(self, q, update_kinematics=True):
        if(update_kinematics):
            return se3.crba(self.model, self.data, q)
        return self.data.M

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    def getDoF(self, jointName):
        idx = self.model.getJointId(jointName)
        if idx < len (self.model.joints):
            idx = self.model.joints[idx].idx_q
            return idx
        else:
            raise Exception('The body segment name is not recognized in skeletor model')
    
    def increment(self, q, dq):
        q_next = se3.integrate(self.model,q,dq)
        q[:] = q_next[:]

    def jacobian(self, q, index, update_geometry=True, local_frame=True):
        return se3.jacobian(self.model, self.data, q, index, local_frame, update_geometry)
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    def computeJacobians(self, q):
        return se3.computeJacobians(self.model, self.data, q)
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    ''' Compute the placements of all the operational frames and put the results in data.
        To be called after forwardKinematics.
    '''
    def framesKinematics(self, q):
        se3.framesKinematics(self.model, self.data, q)

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    def framePosition(self, index, q=None):
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        f = self.model.frames[index]
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        if q is not None:
            se3.forwardKinematics(self.model, self.data, q)
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        return self.data.oMi[f.parent].act(f.placement)

    def frameVelocity(self, index):
        f = self.model.frames[index]
        return f.placement.actInv(self.data.v[f.parent])
        
    ''' Return the spatial acceleration of the specified frame. '''
    def frameAcceleration(self, index):
        f = self.model.frames[index]
        return f.placement.actInv(self.data.a[f.parent])
        
    def frameClassicAcceleration(self, index):
        f = self.model.frames[index]
        a = f.placement.actInv(self.data.a[f.parent])
        v = f.placement.actInv(self.data.v[f.parent])
        a.linear += np.cross(v.angular.T, v.linear.T).T
        return a;
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        ''' Call computeJacobians if update_geometry is true. 
        If not, user should call computeJacobians first. 
        Then call getJacobian and return the resulted jacobian matrix. 
        Attention: if update_geometry is true,the function computes 
        all the jacobians of the model. It is therefore outrageously 
        costly wrt a dedicated call. Use only with update_geometry for prototyping.
    '''
    def frameJacobian(self, q, index, update_geometry=True, local_frame=True):
        return se3.frameJacobian(self.model, self.data, q, index, local_frame, update_geometry)
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    def dof2pinocchio(self, dof):
        ''' qPinocchio = dof2pinocchio(dof = GX generalize coordinates)
        
        - Convert OpenSim generalized coordinates vector into equivalent Pinocchio generalized coordinates
        - This function is designed to work with the GX model
        

        - GX OpenSim generalized coordinates:
        dof = [pelvis,  0..5
        rhip, rknee, rankle, rsubtalar, rmtp,  6..8, 9, 10, 11, 12
        lhip, lknee, lankle, lsubtalar, lmtp, 13..15, 16, 17, 18, 19
        back, neck, 20..22, 23..25
        rshoulder, relbow, rpro_sup, rwrist flexion, rwrist deviation, rfingers flexion 26..28, 29, 30, 31, 32, 33
        lshoulder, lelbow, lpro_sup, lwrist flexion, lwrist deviation, lfingers flexion 34..36, 37, 38, 39, 40, 41
        
        - Pinocchio correspondance:
        q = [pelvis,  0..6
        rhip, rknee, rankle, rsubtalar, rmtp,  7..10, 11, 12, 13, 14
        lhip, lknee, lankle, lsubtalar, lmtp, 15..18, 19, 20, 21, 22
        back, neck, 23..26, 27..30
        rshoulder, relbow, rpro_sup, rwrist flexion, rwrist deviation, rfingers flexion 31..34, 35, 36, 37, 38, 39
        lshoulder, lelbow, lpro_sup, lwrist flexion, lwrist deviation, lfingers flexion 40..43, 44, 45, 46, 47, 48
        '''
        #Change OpenSim values to correpond to Pinocchio model
        pt = np.squeeze(np.array( self.oMp * np.matrix(dof[3:6]).T )) #tx,ty,tz
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        #pt = np.squeeze(np.array(  np.matrix(dof[3:6]).T )) #tx,ty,tz
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        pelvis = quaternion_from_matrix(euler_matrix((dof[2]),dof[0],dof[1],'szxy'))
        #dof[39]=-dof[39]#wrist flexion l
        #dof[40]=-dof[40]#wrist deviation l
        rshoulder = quaternion_from_matrix(euler_matrix(dof[28],dof[26],dof[27],'rzxy'))
        lshoulder = quaternion_from_matrix(euler_matrix(-dof[36],dof[34],-dof[35],'rzxy'))
        rhip = quaternion_from_matrix(euler_matrix(dof[8],dof[6],dof[7],'szxy'))
        lhip = quaternion_from_matrix(euler_matrix(-dof[15],dof[13],-dof[14],'szxy'))
        back = quaternion_from_matrix(euler_matrix(dof[22],dof[20],dof[21],'szxy'))
        neck = quaternion_from_matrix(euler_matrix(dof[25],dof[23],dof[24],'szxy'))

        q = np.array([ tuple(pt[0:3])+tuple([pelvis[1],pelvis[2],pelvis[3],pelvis[0]])
                        +tuple([rhip[1],rhip[2],rhip[3],rhip[0]])+tuple(dof[9:13])
                        +tuple([lhip[1],lhip[2],lhip[3],lhip[0]])+tuple(dof[16:20])
                        +tuple([back[1],back[2],back[3],back[0]])
                        +tuple([neck[1],neck[2],neck[3],neck[0]])
                        +tuple([rshoulder[1],rshoulder[2],rshoulder[3],rshoulder[0]])+tuple(dof[29:34])
                        +tuple([lshoulder[1],lshoulder[2],lshoulder[3],lshoulder[0]])+tuple(dof[37:42])
                        ])[0]
        return q
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    def vel2pinocchio(self, dof):
        #Change OpenSim values to correpond to Pinocchio model
        pt = np.squeeze(np.array( self.oMp * np.matrix(dof[0:3]).T )) #tx,ty,tz
        dq = np.array([ tuple(pt[0:3])+tuple(dof[0:3])+tuple(dof[6:42]) ])[0]
        return dq
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    #test individual joints
    def move(self, name, dof):
        if name == 'pelvis_tilt':
            quat = rpytoQUAT(dof,se3.utils.npToTuple(self.q[1])[0],se3.utils.npToTuple(self.q[2])[0])
            self.q[3] = quat[0]
            self.q[4] = quat[1]
            self.q[5] = quat[2]
            self.q[6] = quat[3]
            self.display(self.q)
        if name == 'pelvis_list':
            quat = rpytoQUAT(se3.utils.npToTuple(self.q[0])[0],dof,se3.utils.npToTuple(self.q[2])[0])
            self.q[3] = quat[0]
            self.q[4] = quat[1]
            self.q[5] = quat[2]
            self.q[6] = quat[3]
            self.display(self.q)
        if name == 'pelvis_rotation':
            quat = rpytoQUAT(se3.utils.npToTuple(self.q[0])[0],se3.utils.npToTuple(self.q[1])[0],dof)
            self.q[3] = quat[0]
            self.q[4] = quat[1]
            self.q[5] = quat[2]
            self.q[6] = quat[3]
            self.display(self.q)
        if name == 'pelvis_tx':
            self.q[0] = dof
            self.display(self.q)
        if name == 'pelvis_ty':
            self.q[1] = dof
            self.display(self.q)
        if name == 'pelvis_tz':
            self.q[2] = dof
            self.display(self.q)
    #POSES
    def zero_poseDisplay(self):
        v = zero(self.model.nv)
        q = zero(self.model.nq)
        q[6] = 1
        self.q = q
        return q

    def half_sitting(self):
        q = self.q0
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        q[2] = 0.92#0.81
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        v = self.v0
        idx = self.model.getJointId('hip_r')
        idx = self.model.joints[idx].idx_q
        M = se3.SE3.Identity()
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        M.rotation = rotate('x', 0.2) * rotate('y', -0.05)
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        Mquat = se3ToXYZQUAT(M)
        q[idx] = Mquat[3]
        q[idx+1] = Mquat[4]
        q[idx+2] = Mquat[5]
        q[idx+3] = Mquat[6]
        idx = self.model.getJointId('hip_l')
        idx = self.model.joints[idx].idx_q
        M = se3.SE3.Identity()
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        M.rotation = rotate('x', 0.2) * rotate('y', 0.05)
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        Mquat = se3ToXYZQUAT(M)
        q[idx] = Mquat[3]
        q[idx+1] = Mquat[4]
        q[idx+2] = Mquat[5]
        q[idx+3] = Mquat[6]
        idx = self.model.getJointId('knee_r')
        idx = self.model.joints[idx].idx_q
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        q[idx] = -0.4#1.22
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        idx = self.model.getJointId('knee_l')
        idx = self.model.joints[idx].idx_q
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        q[idx] = -0.4
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        idx = self.model.getJointId('ankle_r')
        idx = self.model.joints[idx].idx_q
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        q[idx] = 0.25#0.61
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        idx = self.model.getJointId('ankle_l')
        idx = self.model.joints[idx].idx_q
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        q[idx] = 0.25
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        idx = self.model.getJointId('mtp_r')
        idx = self.model.joints[idx].idx_q
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        q[idx] = -0.05
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        idx = self.model.getJointId('mtp_l')
        idx = self.model.joints[idx].idx_q
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        q[idx] = -0.05
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        # Torso and head
        idx = self.model.getJointId('back')
        idx = self.model.joints[idx].idx_q
        M = se3.SE3.Identity()
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        M.rotation = rotate('x', -0.2)
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        Mquat = se3ToXYZQUAT(M)
        q[idx] = Mquat[3]
        q[idx+1] = Mquat[4]
        q[idx+2] = Mquat[5]
        q[idx+3] = Mquat[6]
        idx = self.model.getJointId('neck')
        idx = self.model.joints[idx].idx_q
        M = se3.SE3.Identity()
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        M.rotation = rotate('x', 0.2)
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        Mquat = se3ToXYZQUAT(M)
        q[idx] = Mquat[3]
        q[idx+1] = Mquat[4]
        q[idx+2] = Mquat[5]
        q[idx+3] = Mquat[6]
        # upper body
        idx = self.model.getJointId('acromial_r')
        idx = self.model.joints[idx].idx_q
        M = se3.SE3.Identity()
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        M.rotation = rotate('x', -0.2)*rotate('y',-0.18)
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        Mquat = se3ToXYZQUAT(M)
        q[idx] = Mquat[3]
        q[idx+1] = Mquat[4]
        q[idx+2] = Mquat[5]
        q[idx+3] = Mquat[6]
        idx = self.model.getJointId('acromial_l')
        idx = self.model.joints[idx].idx_q
        M = se3.SE3.Identity()
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        M.rotation = rotate('x', -0.2)*rotate('y',0.18)
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        Mquat = se3ToXYZQUAT(M)
        q[idx] = Mquat[3]
        q[idx+1] = Mquat[4]
        q[idx+2] = Mquat[5]
        q[idx+3] = Mquat[6]
        idx = self.model.getJointId('elbow_r')
        idx = self.model.joints[idx].idx_q
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        q[idx] = 0.7
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        idx = self.model.getJointId('elbow_l')
        idx = self.model.joints[idx].idx_q
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        q[idx] = 0.7
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        idx = self.model.getJointId('lunate_hand_r')
        idx = self.model.joints[idx].idx_q
        q[idx] = 0.15
        idx = self.model.getJointId('lunate_hand_l')
        idx = self.model.joints[idx].idx_q
        q[idx] = 0.15
        idx = self.model.getJointId('radioulnar_r')
        idx = self.model.joints[idx].idx_q
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        q[idx] = 1.
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        idx = self.model.getJointId('radioulnar_l')
        idx = self.model.joints[idx].idx_q
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        q[idx] = 1.#0.22
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        idx = self.model.getJointId('radius_lunate_r')
        idx = self.model.joints[idx].idx_q
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        q[idx] = -0.02
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        idx = self.model.getJointId('radius_lunate_l')
        idx = self.model.joints[idx].idx_q
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        q[idx] = 0.02
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        self.q = q
        return q

    # utils
    def SphericalToRPY(joint):
        # i.e. SphericalToRPY('hip_r')
        i = pinocchioRobot.getDoFIdx(joint)  
        quat = np.matrix([ pinocchioRobot.q[i,0], pinocchioRobot.q[i+1,0],                            
                           pinocchioRobot.q[i+2,0], pinocchioRobot.q[i+3,0] ], np.float)  
        quat = np.squeeze(np.asarray(quat))                
        rpy = se3.utils.matrixToRpy(se3.Quaternion(quat[3], quat[0], quat[1], quat[2]).matrix())    
        return rpy 










    
    def showCoM(self, q, segment=None):
        if segment is None:
            pose = self.com(q)
            CoM = se3.SE3.Identity()
            CoM.translation = pose
            self.display.viewer.gui.addXYZaxis('world/sphere', [0., 1., 0., .5], 0.03, 0.3)
            self.display.place("world/sphere", CoM, True)
        elif segment is 'All':
            self.com(q)
            for i in range(0,len(self.data.com)):
                if i == 0:
                    pose = self.data.com[i]
                    CoM = se3.SE3.Identity()
                    CoM.translation = pose
                    #CoM = self.data.oMi[i]*CoM
                    self.display.viewer.gui.addXYZaxis('world/CoM', [0., 0., 1., .8], 0.03, 0.2)
                    self.display.place('world/CoM', CoM, True)
                else:
                    visualName = self.visuals[i][0] 
                    pose = self.model.inertias[i].lever
                    CoM = se3.SE3.Identity()
                    CoM.translation = pose                     
                    CoM = self.data.oMi[i]*CoM
                    self.display.viewer.gui.addXYZaxis('world/'+visualName+'CoM', [0., 1., 0., .5], 0.02, 0.1)
                    self.display.place('world/'+visualName+'CoM', CoM, True)
                
        else:
            print 'each segment'


    def t_poseDisplay(self):
        q = zero(self.model.nq)
        q[6] = 1
        v = zero(self.model.nv)
        # Right Arm
        # This is used to obtain the index of the joint that will be rotated
        idx = self.model.getJointId('shoulder_r')
        idx = self.model.joints[idx].idx_q
        # The shoulder is a spherical joint expressed as quaterion to avoid the singularities of Euler angles
        # We first rotate the DoF in se3
        M = se3.SE3.Identity()
        M.rotation = rotate('y', -np.pi/2)
        # Now we convert it in a quaternion
        Mquat = se3ToXYZQUAT(M)
        q[idx] = Mquat[3]
        q[idx+1] = Mquat[4]
        q[idx+2] = Mquat[5]
        q[idx+3] = Mquat[6]
        
        
        # Rotate left arm
        idx = self.model.getJointId('shoulder_l')
        idx = self.model.joints[idx].idx_q
        M = se3.SE3.Identity()
        M.rotation = rotate('y', np.pi/2)
        Mquat = se3ToXYZQUAT(M)
        q[idx] = Mquat[3]
        q[idx+1] = Mquat[4]
        q[idx+2] = Mquat[5]
        q[idx+3] = Mquat[6]

        # Now the forward dynamics is computed to obtain the T pose
        self.display(q,v)
        self.q = q

        
    #def printSegments(self):
    #    for i in range(0, len(self.model.names)):
    #        print(self.model.names[i])

    def printJoints(self):
        for i in range(0, len(self.model.names)):
            print(self.model.names[i])

    def rotate(self, q, body_name, axis, angle):
        idx = self.getDoFIdx(body_name)
        '''
            Pelvis is a freeflyer joint [0,...,6]
        '''
        if body_name == ('Pelvis_body'):
            self.rotateFFJ(q, axis, angle, idx)
            return
        '''
            The thorax is a spherical joint [7,...,11]
        '''
        if body_name == ('Thorax_body'):
            self.rotateSPHJ(q, axis, angle, idx)
            return
            
        if body_name == 'Head_Neck_body':
            self.rotateSPHJ(q, axis, angle, idx)
            return
        
        if body_name == 'RArm_body':
            self.rotateSPHJ(q, axis, angle, idx)
            return

        if body_name == 'LArm_body':
            self.rotateSPHJ(q, axis, angle, idx)
            return

        # check axis
        if body_name == 'RForearm_body':
            self.rotateREVJ(q, 'x', angle, idx)
            return

        if body_name == 'LForearm_body':
            self.rotateREVJ(q, 'x', angle, idx)
            return

        if body_name == 'RHand_body':
            self.rotateREVJ(q, 'x', angle, idx)
            return

        if body_name == 'LHand_body':
            self.rotateREVJ(q, 'x', angle, idx)    
            return
        
        if body_name == 'RThigh_body':
            self.rotateSPHJ(q, axis, angle, idx)
            return

        if body_name == 'LThigh_body':
            self.rotateSPHJ(q, axis, angle, idx)
            return

        if body_name == 'RShank_body':
            self.rotateREVJ(q, 'x', angle, idx)
            return

        if body_name == 'LShank_body':
            self.rotateREVJ(q, 'x', angle, idx)
            return
        
        if body_name == 'RFoot_body':
            self.rotateREVJ(q, 'x', angle, idx)
            return

        if body_name == 'LFoot_body':
            self.rotateREVJ(q, 'x', angle, idx)
            return

        if body_name == 'HRFingers_body':
            self.rotateREVJ(q, 'x', angle, idx)
            return

        if body_name == 'HLFingers_body':
            self.rotateREVJ(q, 'x', angle, idx)
            return
        
        if body_name == 'FRFingers_body':
            self.rotateREVJ(q, 'x', angle, idx)
            return

        if body_name == 'FLFingers_body':
            self.rotateREVJ(q, 'x', angle, idx)
            return

    def play(self, q,v):            
        se3.forwardKinematics(self.model, self.data, q, v)
        displayModel(self.data, self.visuals)
        self.q = q            
        self.showCoM(q,'All')
        
    def rotateFFJ(self, q, axis, angle, idx):
        v = zero(self.model.nv)
        M = se3.SE3.Identity()
        #M.rotation = self.data.oMi[idx].rotation * rotate(axis, angle)
        M.rotation = rotate(axis, angle)
        Mquat = se3ToXYZQUAT(M)
        for dof in range (idx, idx+7):
            q[dof] = Mquat[dof-idx]
        self.play(q,v)
        
    def rotateSPHJ(self, q, axis, angle, idx):
        v = zero(self.model.nv)
        M = se3.SE3.Identity()
        #M.rotation = self.data.oMi[idx].rotation * rotate(axis, angle)
        M.rotation = rotate(axis, angle)
        Mquat = se3ToXYZQUAT(M)
        for dof in range (idx, idx+4):
            q[dof] = Mquat[3+dof-idx]
        self.play(q,v)

    def rotateREVJ(self, q, axis, angle, idx):
            #M = se3.SE3.Identity()
            #M.rotation = self.data.oMi[idx].rotation * rotate(axis, angle)
            #Mquat = se3ToXYZQUAT(M)
        v = zero(self.model.nv)
        q[idx]=angle
        self.play(q,v)