J1 = np.append(J_la,J_ra, axis = 0) edot1 = -0.01*e1 Jplus1 = np.linalg.pinv(J1) P1 = eye(robot.nq - 1) - Jplus1*J1 qdot1 = Jplus1 * edot1 Mrh = robot.Mrh(q) e2 = Mrh.translation[0:3,0] - pos_rw_des J2 = Mrh.rotation * robot.Jrh(q)[:3,:] Jplus2 = npl.pinv(J2) e2 = e2 edot2 = -0.01*e2 J2 = J2 Jplus2 = np.linalg.pinv(J2) qdot2 = qdot1 + npl.pinv(J2*P1) * (edot2 - J2*qdot1) qdot = qdot2 robot.increment(q,qdot) robot.display(q) # Debug : x_la = robot.Mrh(q).translation[0,0] y_la = robot.Mrh(q).translation[1,0] x_ra = robot.Mrh(q).translation[0,0] y_ra = robot.Mrh(q).translation[1,0] x_com_des = (x_la + x_ra) /2 y_com_des = (y_la + y_ra) /2 Mcom = robot.com(q) e_x_com = Mcom.item(0) - x_com_des e_y_com = Mcom.item(1) - y_com_des #print "( x/y com : ",Mcom[0,0],Mcom[1,0],")" #print "( x/y com desired : ",x_com_des,y_com_des,")" #print "( Ground contact condition z left/right : ", z_la_des,z_ra_des,")" #print "( contact feet with ground z left/right : ",robot.Mrh(q).translation[2,0],robot.Mrh (q).translation[2,0],")"
# Tutorial 4
from pinocchio.romeo_wrapper import RomeoWrapper
robot = RomeoWrapper('/local/bchattop/devel/src/pinocchio/models/romeo.urdf')
import pinocchio as se3
from pinocchio.utils import *
import numpy as np
execfile("Script1.py")
q = robot.q0
v = rand(robot.nv)
xdes = np.matrix([3.0,1.0,2.0]).T
for i in range(1000):
Mrh = robot.Mrh(q)
e = Mrh.translation[0:3,0] - xdes
J = Mrh.rotation * robot.Jrh(q)[:3,:]
qdot = -npl.pinv(J)*e
robot.increment(q,qdot*1e-2)
robot.display(q)
updateJointConfiguration(M,'l_wrist')
qp.init(H, g, A, lb, ub, lbA, ubA, np.array([100]))
else:
qp.hotstart(H, g, A, lb, ub, lbA, ubA, np.array([100]))
sol = np.zeros(robot.nv)
qp.getPrimalSolution(sol)
a = np.matrix(sol).T
se3.rnea(robot.model,robot.data,q,v,a)
tau_joints = robot.data.tau[6:]
## configuration integration
v += np.matrix(a*dt)
robot.increment(q,v*dt)
## Display new configuration
robot.display(q)
display_com_projection(robot,q)
time.sleep(0.005)
'''### manual resolution
## posture task
err_post_pos = Kp_post*(q[7:]-q0[7:])
err_post_vel = Kd_post*(v[6:]-v0[6:])
err_post = eps_post*(err_post_pos + err_post_vel)
J_post = np.hstack([np.zeros([robot.nv-6,6]), np.eye(robot.nv-6) ])
class PinocchioControllerAcceleration(object):
def __init__(self, dt):
self.dt = dt
self.robot = RomeoWrapper("/local/tflayols/softwares/pinocchio/models/romeo.urdf")
self.robot.initDisplay()
self.robot.loadDisplayModel("world/pinocchio", "pinocchio")
self.robot.display(self.robot.q0)
self.robot.viewer.gui.refresh()
self.q = np.copy(self.robot.q0)
self.v = np.copy(self.robot.v0)
self.a = np.copy(self.robot.v0)
self.dq = np.matrix(np.zeros([self.robot.nv, 1]))
def controlLfRfCom(
self,
Lf=[0.0, 0.0, 0.0],
dLf=[0.0, 0.0, 0.0],
Rf=[0.0, 0.0, 0.0],
dRf=[0.0, 0.0, 0.0],
Com=[0, 0, 0.63],
dCom=[0.0, 0.0, 0.0],
):
def robotint(q, dq):
M = se3.SE3(se3.Quaternion(q[6, 0], q[3, 0], q[4, 0], q[5, 0]).matrix(), q[:3])
dM = se3.exp(dq[:6])
M = M * dM
q[:3] = M.translation
q[3:7] = se3.Quaternion(M.rotation).coeffs()
q[7:] += dq[6:]
def robotdoubleint(q, dq, ddq, dt):
dq += dt * ddq
robotint(q, dq)
def errorInSE3(M, Mdes):
"""
Compute a 6-dim error vector (6x1 np.maptrix) caracterizing the difference
between M and Mdes, both element of SE3.
"""
error = se3.log(Mdes.inverse() * M)
return error.vector()
def errorInSE3dyn(M, Mdes, v_frame, v_des):
gMl = se3.SE3.Identity()
gMl.rotation = M.rotation
# Compute error
error = errorInSE3(M, Mdes)
v_error = v_frame - gMl.actInv(v_des)
# ~ a_corriolis = self.robot.acceleration(q,v,0*v,self._link_id, update_geometry)
# ~ a_corriolis.linear += np.cross(v_frame.angular.T, v_frame.linear.T).T
# ~ a_tot = a_ref - gMl.actInv(a_corriolis)
return error, v_error.vector()
def errorLinkInSE3dyn(linkId, Mdes, v_des, q, v):
# Get the current configuration of the link
M = self.robot.position(q, linkId)
gMl = se3.SE3.Identity()
gMl.rotation = M.rotation
v_frame = self.robot.velocity(q, v, linkId)
# Compute error
error = errorInSE3(M, Mdes)
v_error = v_frame - gMl.actInv(v_des)
a_corriolis = self.robot.acceleration(q, v, 0 * v, linkId)
# ~ a_corriolis.linear += np.cross(v_frame.angular.T, v_frame.linear.T).T
# ~ a_tot = gMl.actInv(a_corriolis) #a_ref - gMl.actInv(a_corriolis)
a_tot = a_corriolis
# ~ dJdq = a_tot.vector() *self.dt
dJdq = a_corriolis.vector()
return error, v_error.vector(), dJdq
def null(A, eps=1e-6): # -12
"""Compute a base of the null space of A."""
u, s, vh = np.linalg.svd(A)
padding = max(0, np.shape(A)[1] - np.shape(s)[0])
null_mask = np.concatenate(((s <= eps), np.ones((padding,), dtype=bool)), axis=0)
null_space = scipy.compress(null_mask, vh, axis=0)
return scipy.transpose(null_space)
XYZ_LF = np.array(Lf) + np.array([0.0, 0.0, 0.07])
RPY_LF = np.matrix([[0.0], [0.0], [0.0]])
SE3_LF = se3.SE3(se3.utils.rpyToMatrix(RPY_LF), XYZ_LF)
XYZ_RF = np.array(Rf) + np.array([0.0, 0.0, 0.07])
RPY_RF = np.matrix([[0.0], [0.0], [0.0]])
SE3_RF = se3.SE3(se3.utils.rpyToMatrix(RPY_RF), XYZ_RF)
# _RF________________________________________________________________
Jrf = self.robot.Jrf(self.q).copy()
Jrf[:3] = self.robot.Mrf(self.q).rotation * Jrf[:3, :] # Orient in the world base
v_ref = se3.se3.Motion(np.matrix([dRf[0], dRf[1], dRf[2], 0.0, 0.0, 0.0]).T)
errRf, v_errRf, dJdqRf = errorLinkInSE3dyn(self.robot.rf, SE3_RF, v_ref, self.q, self.v)
# _LF________________________________________________________________
Jlf = self.robot.Jlf(self.q).copy()
Jlf[:3] = self.robot.Mlf(self.q).rotation * Jlf[:3, :] # Orient in the world base
v_ref = se3.se3.Motion(np.matrix([dLf[0], dLf[1], dLf[2], 0.0, 0.0, 0.0]).T)
errLf, v_errLf, dJdqLf = errorLinkInSE3dyn(self.robot.lf, SE3_LF, v_ref, self.q, self.v)
# _COM_______________________________________________________________
Jcom = self.robot.Jcom(self.q)
p_com, v_com, a_com = self.robot.com(self.q, self.v, self.v * 0.0)
errCOM = self.robot.com(self.q) - (np.matrix(Com).T)
# ~ v_com = Jcom*self.v
v_errCOM = v_com - (np.matrix(dCom).T)
dJdqCOM = a_com
# _Trunk_____________________________________________________________
idx_Trunk = self.robot.index("root")
MTrunk0 = self.robot.position(self.robot.q0, idx_Trunk)
MTrunk = self.robot.position(self.q, idx_Trunk)
# errTrunk=errorInSE3(MTrunk0,MTrunk)[3:6]
JTrunk = self.robot.jacobian(self.q, idx_Trunk)[3:6]
# v_frame = self.robot.velocity(self.q,self.v,idx_Trunk)
# v_ref= se3.se3.Motion(np.matrix([.0,.0,.0,.0,.0,.0]).T)
# errTrunk,v_errTrunk = errorInSE3dyn(MTrunk,MTrunk0,v_frame,v_ref)
errTrunk, v_errTrunk, dJdqTrunk = errorLinkInSE3dyn(idx_Trunk, MTrunk0, v_ref, self.q, self.v)
errTrunk = errTrunk[3:6]
v_errTrunk = v_errTrunk[3:6]
dJdqTrunk = dJdqTrunk[3:6]
# _TASK1 STACK_______________________________________________________
K = 100.0
Kp_foot = K
Kp_com = K
Kp_Trunk = K
Kp_post = K
Kd_foot = 2 * np.sqrt(Kp_foot)
Kd_com = 2 * np.sqrt(Kp_com)
Kd_Trunk = 2 * np.sqrt(Kp_Trunk)
Kd_post = 2 * np.sqrt(Kp_post)
err1 = np.vstack([Kp_foot * errLf, Kp_foot * errRf, Kp_com * errCOM, Kp_Trunk * errTrunk])
v_err1 = np.vstack([Kd_foot * v_errLf, Kd_foot * v_errRf, Kd_com * v_errCOM, Kd_Trunk * v_errTrunk])
dJdq1 = np.vstack([dJdqLf, dJdqRf, dJdqCOM, dJdqTrunk])
J1 = np.vstack([Jlf, Jrf, Jcom, JTrunk])
# _TASK2 STACK_______________________________________________________
# _Posture___________________________________________________________
Jpost = np.hstack([zero([self.robot.nv - 6, 6]), eye(self.robot.nv - 6)])
errPost = Kp_post * (self.q - self.robot.q0)[7:]
v_errPost = Kd_post * (self.v - self.robot.v0)[6:]
errpost = -1 * (self.q - self.robot.q0)[7:]
err2 = errPost
v_err2 = v_errPost
J2 = Jpost
# Hierarchical solve_________________________________________________
qddot = npl.pinv(J1) * (-1.0 * err1 - 1.0 * v_err1 - 1.0 * dJdq1)
Z = null(J1)
qddot += Z * npl.pinv(J2 * Z) * (-(1.0 * err2 + 1.0 * v_err2) - J2 * qddot)
self.a = qddot
self.v += np.matrix(self.a * self.dt)
self.robot.increment(self.q, np.matrix(self.v * self.dt))
# ~ robotdoubleint(self.q,self.dq,qddot,self.dt)
# ~ self.v=self.dq/self.dt
self.robot.display(self.q)
self.robot.viewer.gui.refresh()
return self.robot.com(self.q), Jcom * self.v, errCOM, v_errCOM
