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derivative.py
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import numpy as np
import casadi as cs
import adam_model
import parser
import copy
import random
import pickle
import datetime
import os
import pinocchio as pin
import time
import meshcat
def gravity(state):
opti = cs.Opti()
x_init = opti.parameter(robot.nx)
cost = 0
# Define decision variables
X, U = [], []
X += [opti.variable(robot.nx)]
X += [opti.variable(robot.nx)]
opti.subject_to(opti.bounded(robot.x_min, X[-1], robot.x_max))
U += [opti.variable(robot.nu)]
opti.subject_to(X[0] == x_init)
opti.subject_to(X[1] == robot.f_fun(X[0], U[0]))
# Torque constraints
opti.subject_to(opti.bounded(robot.tau_min, robot.tau_fun(X[0], U[0]), robot.tau_max))
opti.subject_to(X[1][robot.nq:] == [0,0,0])
opti.minimize(cost)
opts = {
'ipopt.print_level': 0,
'print_time': 0,
'ipopt.tol': 1e-6,
'ipopt.constr_viol_tol': 1e-6,
'ipopt.compl_inf_tol': 1e-6,
#'ipopt.hessian_approximation': 'limited-memory',
# 'detect_simple_bounds': 'yes',
'ipopt.max_iter': 1000,
#'ipopt.linear_solver': 'ma57',
'ipopt.sb': 'no'
}
opti.solver('ipopt', opts)
opti.set_value(x_init, state)
sol = opti.solve()
u = robot.tau_fun(sol.value(X[0]),sol.value(U[0]))
return u
def load(filename):
with open(filename, 'rb') as file:
loaded_data = pickle.load(file)
return loaded_data
def saturate_tau(u):
# for torque in np.nditer(u):
# if np.abs(torque)>robot.tau_max
for i in range(robot.nu):
if np.abs(u[i])>robot.tau_max[i]:
u[i] = np.sign(u[i])*robot.tau_max[i]
return u
def spawn_obstacles():
box0 = meshcat.geometry.Box([2, 2, 1e-3])
viz.viewer['world/obstacle/floor0'].set_object(box0)
viz.viewer['world/obstacle/floor0'].set_property('color', [0, 0, 1, 0.5])
viz.viewer['world/obstacle/floor0'].set_property('visible', True)
T_floor = np.eye(4)
viz.viewer['world/obstacle/floor0'].set_transform(T_floor)
# box1 = meshcat.geometry.Box([2, 2, 1e-3])
# viz.viewer['world/obstacle/floor1'].set_object(box1)
# viz.viewer['world/obstacle/floor1'].set_property('color', [0, 0, 1, 0.5])
# viz.viewer['world/obstacle/floor1'].set_property('visible', True)
# T_floor = np.eye(4)
# T_floor[:3,3] = np.array([0,0,0.6])
# viz.viewer['world/obstacle/floor1'].set_transform(T_floor)
# box2 = meshcat.geometry.Box([1e-3, 2, 2])
# viz.viewer['world/obstacle/floor2'].set_object(box2)
# viz.viewer['world/obstacle/floor2'].set_property('color', [0, 0, 1, 0.5])
# viz.viewer['world/obstacle/floor2'].set_property('visible', True)
# T_floor = np.eye(4)
# T_floor[:3,3] = np.array([0.5,0,0])
# viz.viewer['world/obstacle/floor2'].set_transform(T_floor)
sphere = meshcat.geometry.Sphere(0.12)
viz.viewer['world/obstacle/sphere'].set_object(sphere)
viz.viewer['world/obstacle/sphere'].set_property('color',[1, 0, 0, 1])
viz.viewer['world/obstacle/sphere'].set_property('visible', True)
T_obs = np.eye(4)
T_obs[:3, 3] = np.array([0.6,0.,0.12])
viz.viewer['world/obstacle/sphere'].set_transform(T_obs)
def check_collision(obstacles,state):
check=True
if len(obstacles['walls'])>0:
for i in obstacles['walls']:
check = check and (i['lb'] <= robot.ee_fun(state)[i['axis']] <= i['ub'])
if len(obstacles['objects'])>0:
for i in obstacles['objects']:
check = check and (np.linalg.norm(robot.ee_fun(state) - np.array(i['position'])) >= i['radius'])
return check
if __name__ == '__main__':
robot_name = 'fr3'
dof = 6
params = parser.Parameters(robot_name)
robot = adam_model.AdamModel(params,n_dofs=dof)
if robot.params.urdf_name == 'fr3':
robot.tau_max = np.array([17,87,8.7,34.8,2.4,4.8])
robot.tau_min = -np.array([17,87,8.7,34.8,2.4,4.8])
nq = robot.nq
max_steps = 500
kd = 200
ee_radius = 0.075
walls = [
{'axis':2, 'lb':0+ee_radius, 'ub':1e6, 'pos':0+ee_radius },
# {'axis':2, 'lb':-1e6, 'ub':0.5, 'pos':0.5},
# {'axis':0, 'lb':-1e6, 'ub':0.5, 'pos':0.5},
# {'axis':0, 'lb':-0.5, 'ub':1e5, 'pos':-0.5}
]
#walls = None
# objects modeled as spheres
objects = [
{'position':[0.6,0.,0.12], 'radius':0.12+ee_radius}
#{'position':[0.3,-0.35,0.25], 'radius':0.1}
]
obstacles = {'walls':walls,'objects':objects}
data_folder = os.path.join(os.getcwd(),'N-steps results')
x0_s = load(os.path.join(data_folder,'x0_failed2025-01-13 09:00:07.809522.pkl'))
description_dir = params.ROBOTS_DIR + f'{robot_name}_description'
rmodel, collision, visual = pin.buildModelsFromUrdf(description_dir + f'/urdf/{robot_name}.urdf',
package_dirs=params.ROOT_DIR)
geom = [collision, visual]
lockIDs = []
if robot_name == 'z1':
lockNames = ['joint5', 'joint6', 'jointGripper']
if robot_name == 'fr3':
lockNames = ['fr3_joint5', 'fr3_joint6', 'fr3_joint7', 'fr3_finger_joint1','fr3_finger_joint2']
lockNames = lockNames[(dof-4):]
for name in lockNames:
lockIDs.append(rmodel.getJointId(name))
rmodel_red, geom_red = pin.buildReducedModel(rmodel, geom, lockIDs, np.zeros(9 if robot_name == 'fr3' else 'z1'))
viz = pin.visualize.MeshcatVisualizer(rmodel_red, geom_red[0], geom_red[1])
viz.initViewer(loadModel=True, open=True)
viz.display(x0_s[0][:nq])
spawn_obstacles()
X0 = cs.MX.sym('X0', robot.nx)
U = cs.MX.sym('U',robot.nu)
Q = 0
for j in range(4):
k1 = robot.f_fun_forw(X0, U)
k2 = robot.f_fun_forw(X0 + robot.params.dt/2 * k1, U)
k3 = robot.f_fun_forw(X0 + robot.params.dt/2 * k2, U)
k4 = robot.f_fun_forw(X0 + robot.params.dt * k3, U)
X_F=X0+robot.params.dt/6*(k1 +2*k2 +2*k3 +k4)
F_disc_tau = cs.Function('F', [X0, U], [X_F])
print(f'number of simulations = {len(x0_s)}')
for i in range(len(x0_s)):
x_simu = np.zeros((robot.nx,max_steps))
x_simu[:,0] = x0_s[i]
#x_simu[nq:,0] = np.array([0,0,0])
for k in range(1,max_steps):
u_der = 0*robot.gravity(np.eye(4),x_simu[:nq,k-1])[-nq:] + \
robot.mass(np.eye(4), x_simu[:nq,k-1])[6:, 6:] @ (-kd*x_simu[nq:,k-1]) + \
robot.bias(np.eye(4), x_simu[:nq,k-1], np.zeros(6), x_simu[nq:,k-1])[6:]
u_der_tau = saturate_tau(u_der)
#u_der2 = gravity(x_simu[:,k-1])
x_simu[:,k] = np.squeeze(F_disc_tau(x_simu[:,k-1],u_der_tau))
# _, D,_ = np.linalg.svd(robot.jac(np.eye(4),x0_s[i][:robot.nq])[:3,6:])
# print(f'singularity indicator {np.abs((D[0]/D[-1]))}')
print(f'{i} : {x0_s[i]}')
print(robot.ee_fun(x0_s[i]))
if (render:=True):
for j in range(x_simu.shape[1]):
if not(check_collision(obstacles,x_simu[:,j])):
print('Collision')
viz.display(x_simu[:nq,j])
time.sleep(5)
break
viz.display(x_simu[:nq,j])
time.sleep((1/5))
print(j)
if np.linalg.norm(x_simu[:,j]-x_simu[:,j-1]) < 1e-4:
break