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TrajoptPlant.py
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import numpy as np
import random
from GRiD.RBDReference import RBDReference
from GRiD.URDFParser import URDFParser
from overloading import matrix_
class TrajoptPlant:
def __init__(self, integrator_type: int = 0, options = {}, need_path: bool = False):
self.validate_integrator_type(integrator_type)
self.integrator_type = integrator_type
self.set_default_options(options, need_path)
self.options = options
self.saved_Minv=[]
self.saved_c=[]
# self.saved_df_du=[]
self.saved_dc_du=[]
self.saved_qdd=[]
self.saved_dqdd=[]
def validate_integrator_type(self, integrator_type: int):
if not (integrator_type in [0, 1, 2, 3, 4, -1]):
print("Invalid integrator options are [0 : euler, 1 : semi-implicit euler, 2 : midpoint, 3 : rk3, 4 : rk4, -1 : hard-coded as dynamics")
exit()
def set_default_options(self, options: dict, need_path: bool = False):
options.setdefault('path_to_urdf', None)
options.setdefault('gravity', -9.81)
if need_path and (not options.get('path_to_urdf')):
print("You must include the 'path_to_urdf' in the options.")
exit()
##############################
# Child class must implement #
##############################
def forward_dynamics(self):
raise NotImplementedError
def forward_dynamics_gradient(self):
raise NotImplementedError
def get_num_pos(self):
raise NotImplementedError
def get_num_vel(self):
raise NotImplementedError
def get_num_cntrl(self):
raise NotImplementedError
##############################
# Child class must implement #
##############################
# [ v ;
# qdd ]
def qdd_to_xdot(self, xk: np.ndarray, qdd: np.ndarray):
nq = self.get_num_pos()
nv = self.get_num_vel()
nu = self.get_num_cntrl()
if(self.options['overloading']):
return matrix_.vstack(xk[nq:], qdd).flatten()
else:
return np.vstack((xk[nq:], qdd)).flatten()
# [ 0 ; eye ; 0
# dqdd/dq ; dqdd/dv ; dqdd/du ]
def dqdd_to_dxdot(self, dqdd: np.ndarray):
nq = self.get_num_pos()
nv = self.get_num_vel()
m = self.get_num_cntrl()
if(self.options['overloading']):
top = matrix_.hstack(np.zeros((nq,nq)), np.eye(nv), np.zeros((nq,m)))
return matrix_.vstack(top, dqdd)
else:
top = np.hstack((np.zeros((nq,nq)), np.eye(nv), np.zeros((nq,m))))
return np.vstack((top, dqdd))
def integrator(self, xk: np.ndarray, uk: np.ndarray, dt: float, return_gradient: bool = False, iter_1=0, iter_2=0, iter_3=0):
n = len(xk)
if self.integrator_type == -1: # hard coded into model
if not return_gradient:
return self.integrator(xk,uk)
else:
return self.integrator_gradient(xk,uk)
if self.integrator_type == 0: # euler
# xkp1 = xk + dt * [vk,qddk]
# dxkp1 = [Ix | 0u ] + dt*[ 0q, Iv, 0u; dqdd]
qdd = self.forward_dynamics(xk,uk, iter_1, iter_2, iter_3)
xdot = self.qdd_to_xdot(xk, qdd)
xkp1 = xk+dt*xdot
if not return_gradient:
return xkp1 #np.reshape(xkp1, (xkp1.shape[0],1))[:,0]
else:
dqdd = self.forward_dynamics_gradient(xk,uk,iter_1, iter_2, iter_3)
dxdot = self.dqdd_to_dxdot(dqdd)
if(self.options['overloading']):
A = matrix_(np.eye(n))+dt*dxdot[:,0:n]
else:
A = np.eye(n) + dt*dxdot[:,0:n]
B = dt*dxdot[:,n:]
return A, B
elif self.integrator_type == 1: # semi-implicit euler
# vkp1 = vk + dt*qddk
# qkp1 = qk + dt*vkp1
# xkp1 = [qkp1; vkp1]
# dxkp1 = [Ix | 0u ] + dt*[[0q, Iv, 0u] + dt*dqdd; dqdd]
nq = self.get_num_pos()
nv = self.get_num_vel()
nu = self.get_num_cntrl()
qdd = self.forward_dynamics(xk,uk,iter_1, iter_2, iter_3)
vkp1 = xk[nq:]+dt*qdd
qkp1 = xk[0:nq]+dt*vkp1
if(self.options['overloading']):
if not return_gradient:
return matrix_.hstack(qkp1,vkp1).transpose()
else:
dqdd = self.forward_dynamics_gradient(xk,uk,)
zIz = matrix_.hstack(np.zeros((nq,nq)),np.eye(nq),np.zeros((nq,nu)))
Iz = matrix_.hstack(np.eye(nq+nv),np.zeros((nq+nv,nu)))
AB = Iz+dt*matrix_.vstack(zIz+dt*dqdd, dqdd)
return AB[:,0:nq+nv], AB[:,nq+nv:]
else:
if not return_gradient:
return np.hstack((qkp1,vkp1)).transpose()
else:
dqdd = self.forward_dynamics_gradient(xk,uk)
zIz = np.hstack((np.zeros((nq,nq)),np.eye(nq),np.zeros((nq,nu))))
Iz = np.hstack((np.eye(nq+nv),np.zeros((nq+nv,nu))))
AB = Iz + dt*np.vstack((zIz + dt*dqdd, dqdd))
return AB[:,0:nq+nv], AB[:,nq+nv:]
elif self.integrator_type == 2: # midpoint
xdot1 = self.qdd_to_xdot(xk, self.forward_dynamics(xk,uk, iter_1, iter_2, iter_3))
midpoint = xk+0.5*dt*xdot1
xdot2 = self.qdd_to_xdot(xk, self.forward_dynamics(midpoint,uk, iter_1, iter_2, iter_3))
xkp1 = xk+dt*xdot2
if not return_gradient:
return xkp1
else:
if(self.options['overloading']):
dxdot1 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(xk,uk, iter_1, iter_2, iter_3))
A1 = matrix_(np.eye(n))+0.5*dt*dxdot1[:,0:n]
B1 = 0.5*dt*dxdot1[:,n:]
dxdot2 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(midpoint,uk, iter_1, iter_2, iter_3))
A2 = matrix_(np.eye(n))+0.5*dt*dxdot2[:,0:n]
B2 = 0.5*dt*dxdot2[:,n:]
A = A2@A1
B = A2@B1+B2
else:
dxdot1 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(xk,uk, iter_1, iter_2, iter_3))
A1 = np.eye(n) + 0.5*dt*dxdot1[:,0:n]
B1 = 0.5*dt*dxdot1[:,n:]
dxdot2 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(midpoint,uk, iter_1, iter_2, iter_3))
A2 = np.eye(n) + 0.5*dt*dxdot2[:,0:n]
B2 = 0.5*dt*dxdot2[:,n:]
A = np.matmul(A2,A1)
B = np.matmul(A2,B1) + B2
return A, B
elif self.integrator_type == 3: # rk3
xdot1 = self.qdd_to_xdot(xk, self.forward_dynamics(xk,uk, iter_1, iter_2, iter_3))
point1 = xk+0.5*dt*xdot1
xdot2 = self.qdd_to_xdot(xk, self.forward_dynamics(point1,uk, iter_1, iter_2, iter_3))
point2 = xk+0.75*dt*xdot2
xdot3 = self.qdd_to_xdot(xk, self.forward_dynamics(point2,uk, iter_1, iter_2, iter_3))
xkp1 = xk+(dt/9)*(2*xdot1+3*xdot2+4*xdot3)
if not return_gradient:
return xkp1
else:
if(self.options['overloading']):
dxdot1 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(xk,uk, iter_1, iter_2, iter_3))
A1 = matrix_(np.eye(n))+2/9*dt*dxdot1[:,0:n]
B1 = 2/9*dt*dxdot1[:,n:]
dxdot2 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(point1,uk, iter_1, iter_2, iter_3))
A2 = matrix_(np.eye(n))+1/3*dt*dxdot2[:,0:n]
B2 = 1/3*dt*dxdot1[:,n:]
dxdot3 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(point2,uk, iter_1, iter_2, iter_3))
A3 = matrix_(np.eye(n))+4/9*dt*dxdot3[:,0:n]
B3 = 4/9*dt*dxdot1[:,n:]
A = A3@(A2@A1)
B = A3@(A2@B1)+A3@B2+B3
return A,B
else:
dxdot1 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(xk,uk, iter_1, iter_2, iter_3))
A1 = np.eye(n) + 2/9*dt*dxdot1[:,0:n]
B1 = 2/9*dt*dxdot1[:,n:]
dxdot2 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(point1,uk, iter_1, iter_2, iter_3))
A2 = np.eye(n) + 1/3*dt*dxdot2[:,0:n]
B2 = 1/3*dt*dxdot1[:,n:]
dxdot3 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(point2,uk, iter_1, iter_2, iter_3))
A3 = np.eye(n) + 4/9*dt*dxdot3[:,0:n]
B3 = 4/9*dt*dxdot1[:,n:]
A = np.matmul(A3,np.matmul(A2,A1))
B = np.matmul(A3,np.matmul(A2,B1)) + np.matmul(A3,B2) + B3
return A,B
elif self.integrator_type == 4: # rk4
xdot1 = self.qdd_to_xdot(xk, self.forward_dynamics(xk,uk,iter_1, iter_2, iter_3))
point1 = xk+0.5*dt*xdot1
xdot2 = self.qdd_to_xdot(xk, self.forward_dynamics(point1,uk, iter_1, iter_2, iter_3))
point2 = xk+0.5*dt*xdot2
xdot3 = self.qdd_to_xdot(xk, self.forward_dynamics(point2,uk,iter_1, iter_2, iter_3))
point3 = xk+dt*xdot3
xdot4 = self.qdd_to_xdot(xk, self.forward_dynamics(point3,uk, iter_1, iter_2, iter_3))
xkp1 = xk+(dt/6)*(xdot1+2*xdot2+2*xdot3+xdot4)
if not return_gradient:
return xkp1
else:
if(self.options['overloading']):
dxdot1 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(xk,uk,iter_1, iter_2, iter_3))
A1 = matrix_(np.eye(n))+1/6*dt*dxdot1[:,0:n]
B1 = 1/6*dt*dxdot1[:,n:]
dxdot2 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(point1,uk, iter_1, iter_2, iter_3))
A2 = matrix_(np.eye(n))+1/3*dt*dxdot2[:,0:n]
B2 = 1/3*dt*dxdot1[:,n:]
dxdot3 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(point2,uk,iter_1, iter_2, iter_3))
A3 = matrix_(np.eye(n))+1/3*dt*dxdot3[:,0:n]
B3 = 1/3*dt*dxdot1[:,n:]
dxdot4 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(point3,uk,iter_1, iter_2, iter_3))
A4 = matrix_(np.eye(n))+1/6*dt*dxdot4[:,0:n]
B4 = 1/6*dt*dxdot1[:,n:]
A = (A4@(A3@(A2@A1)))
B = A4@(A3@(A2@B1))+A4@(A3@B2)+A4@B3+B4
return A,B
else:
dxdot1 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(xk,uk, iter_1, iter_2, iter_3))
A1 = np.eye(n) + 1/6*dt*dxdot1[:,0:n]
B1 = 1/6*dt*dxdot1[:,n:]
dxdot2 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(point1,uk, xk, iter_1, iter_2, iter_3))
A2 = np.eye(n) + 1/3*dt*dxdot2[:,0:n]
B2 = 1/3*dt*dxdot1[:,n:]
dxdot3 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(point2,uk, xk,iter_1, iter_2, iter_3))
A3 = np.eye(n) + 1/3*dt*dxdot3[:,0:n]
B3 = 1/3*dt*dxdot1[:,n:]
dxdot4 = self.dqdd_to_dxdot(self.forward_dynamics_gradient(point3,uk, xk,iter_1, iter_2, iter_3))
A4 = np.eye(n) + 1/6*dt*dxdot4[:,0:n]
B4 = 1/6*dt*dxdot1[:,n:]
A = np.matmul(A4,np.matmul(A3,np.matmul(A2,A1)))
B = np.matmul(A4,np.matmul(A3,np.matmul(A2,B1))) + np.matmul(A4,np.matmul(A3,B2)) + np.matmul(A4,B3) + B4
return A,B
class URDFPlant(TrajoptPlant):
def __init__(self, integrator_type = 0, options = {}):
super().__init__(integrator_type, options, True)
parser = URDFParser()
self.robot = parser.parse(options['path_to_urdf'])
if(self.robot is None):
raise ValueError("Failed to parse URDF file at the given path.")
self.rbdReference = RBDReference(self.robot)
def forward_dynamics(self, x: np.ndarray, u: np.ndarray, iter_1=0, iter_2=0, iter_3=0):
nq = self.get_num_pos()
q = x[0:nq]
qd = x[nq:]
(c, _, _, _) = self.rbdReference.rnea(q, qd, None, self.options['gravity'])
Minv = self.rbdReference.minv(q)
if(self.options['overloading']):
qdd = Minv@(u-c)
else:
qdd = np.matmul(Minv,(u-c))
self.saved_c.append({'value':c,' iteration': iter_1,'outer_iteration':iter_2, 'line_search_iteration': iter_3})
self.saved_Minv.append({'value':Minv,'iteration':iter_1,'outer_iteration':iter_2, 'line_search_iteration': iter_3})
self.saved_qdd.append({'value':qdd,'iteration':iter_1,'outer_iteration':iter_2, 'line_search_iteration': iter_3})
return qdd
def forward_dynamics_gradient(self, x: np.ndarray, u: np.ndarray, iter_1=0, iter_2=0, iter_3=0):
nq = self.get_num_pos()
q = x[0:nq]
qd = x[nq:]
(c, _, _, _) = self.rbdReference.rnea(q, qd, None, self.options['gravity'])
Minv = self.rbdReference.minv(q)
if(self.options['overloading']):
qdd = Minv@(u-c)
dc_du = self.rbdReference.rnea_grad(q, qd, qdd, self.options['gravity'])
df_du = (-Minv)@dc_du
dqdd= matrix_.hstack(df_du,Minv)
else:
qdd = np.matmul(Minv,(u-c))
dc_du = self.rbdReference.rnea_grad(q, qd, qdd, self.options['gravity'])
df_du = np.matmul(-Minv,dc_du)
dqdd= np.hstack((df_du,Minv))
self.saved_Minv.append({'value':Minv,'iteration':iter_1,'outer_iteration':iter_2, 'line_search_iteration': iter_3})
self.saved_c.append({'value':c,'iteration':iter_1,'outer_iteration':iter_2, 'line_search_iteration': iter_3})
self.saved_qdd.append({'value':qdd,'iteration':iter_1,'outer_iteration':iter_2 ,'line_search_iteration': iter_3})
self.saved_dc_du.append({'value':dc_du,'iteration':iter_1,'outer_iteration':iter_2, 'line_search_iteration': iter_3})
self.saved_dqdd.append({'value':dqdd, 'iteration':iter_1,'outer_iteration':iter_2, 'line_search_iteration': iter_3})
return dqdd
def get_num_pos(self):
return self.robot.get_num_pos()
def get_num_vel(self):
return self.robot.get_num_vel()
def get_num_cntrl(self):
return self.robot.get_num_cntrl()