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updated orientation scripts with blog post rewrite
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| ''' | ||
| Copyright (C) 2018 Travis DeWolf | ||
| This program is free software: you can redistribute it and/or modify | ||
| it under the terms of the GNU General Public License as published by | ||
| the Free Software Foundation, either version 3 of the License, or | ||
| (at your option) any later version. | ||
| 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 General Public License for more details. | ||
| You should have received a copy of the GNU General Public License | ||
| along with this program. If not, see <http://www.gnu.org/licenses/>. | ||
| ''' | ||
| import numpy as np | ||
|
|
||
| from abr_control.arms import ur5 as arm | ||
| from abr_control.interfaces import VREP | ||
| from abr_control.utils import transformations | ||
|
|
||
|
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||
| # initialize our robot config | ||
| robot_config = arm.Config(use_cython=True) | ||
|
|
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| # create our interface | ||
| interface = VREP(robot_config, dt=.005) | ||
| interface.connect() | ||
|
|
||
| # specify which parameters [x, y, z, alpha, beta, gamma] to control | ||
| # NOTE: needs to be an array to properly select elements of J and u_task | ||
| ctrlr_dof = np.array([True, True, True, True, True, True]) | ||
|
|
||
| # control gains | ||
| kp = 300 | ||
| ko = 300 | ||
| kv = np.sqrt(kp+ko) * 1.5 | ||
|
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||
| orientations = [ | ||
| [0, 0, 0], | ||
| [np.pi/4, np.pi/4, np.pi/4], | ||
| [-np.pi/4, -np.pi/4, np.pi/2], | ||
| [0, 0, 0], | ||
| ] | ||
| positions =[ | ||
| [0.15, -0.1, 0.6], | ||
| [-.15, 0.0, .7], | ||
| [.2, .2, .6], | ||
| [0.15, -0.1, 0.6] | ||
| ] | ||
|
|
||
| try: | ||
| print('\nSimulation starting...\n') | ||
| count = 0 | ||
| index = 0 | ||
| while 1: | ||
| # get arm feedback | ||
| feedback = interface.get_feedback() | ||
| hand_xyz = robot_config.Tx('EE', feedback['q']) | ||
|
|
||
| if (count % 200) == 0: | ||
| # change target once every simulated second | ||
| if index >= len(orientations): | ||
| break | ||
| interface.set_orientation('target', orientations[index]) | ||
| interface.set_xyz('target', positions[index]) | ||
| index += 1 | ||
|
|
||
| target = np.hstack([ | ||
| interface.get_xyz('target'), | ||
| interface.get_orientation('target')]) | ||
|
|
||
| # set the block to be the same orientation as end-effector | ||
| R_e = robot_config.R('EE', feedback['q']) | ||
| EA_e = transformations.euler_from_matrix(R_e, axes='rxyz') | ||
| interface.set_orientation('object', EA_e) | ||
|
|
||
| # calculate the Jacobian for the end effectora | ||
| # and isolate relevate dimensions | ||
| J = robot_config.J('EE', q=feedback['q'])[ctrlr_dof] | ||
|
|
||
| # calculate the inertia matrix in task space | ||
| M = robot_config.M(q=feedback['q']) | ||
|
|
||
| # calculate the inertia matrix in task space | ||
| M_inv = np.linalg.inv(M) | ||
| Mx_inv = np.dot(J, np.dot(M_inv, J.T)) | ||
| if np.linalg.det(Mx_inv) != 0: | ||
| # do the linalg inverse if matrix is non-singular | ||
| # because it's faster and more accurate | ||
| Mx = np.linalg.inv(Mx_inv) | ||
| else: | ||
| # using the rcond to set singular values < thresh to 0 | ||
| # singular values < (rcond * max(singular_values)) set to 0 | ||
| Mx = np.linalg.pinv(Mx_inv, rcond=.005) | ||
|
|
||
| u_task = np.zeros(6) # [x, y, z, alpha, beta, gamma] | ||
|
|
||
| # calculate position error | ||
| u_task[:3] = -kp * (hand_xyz - target[:3]) | ||
|
|
||
| # Method 1 ------------------------------------------------------------ | ||
| # | ||
| # transform the orientation target into a quaternion | ||
| q_d = transformations.unit_vector( | ||
| transformations.quaternion_from_euler( | ||
| target[3], target[4], target[5], axes='rxyz')) | ||
|
|
||
| # get the quaternion for the end effector | ||
| q_e = transformations.unit_vector( | ||
| transformations.quaternion_from_matrix( | ||
| robot_config.R('EE', feedback['q']))) | ||
| # calculate the rotation from the end-effector to target orientation | ||
| q_r = transformations.quaternion_multiply( | ||
| q_d, transformations.quaternion_conjugate(q_e)) | ||
| u_task[3:] = q_r[1:] * np.sign(q_r[0]) | ||
|
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||
|
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| # Method 2 ------------------------------------------------------------ | ||
| # From (Caccavale et al, 1997) Section IV - Quaternion feedback ------- | ||
| # | ||
| # get rotation matrix for the end effector orientation | ||
| # R_EE = robot_config.R('EE', feedback['q']) | ||
| # # get rotation matrix for the target orientation | ||
| # R_d = transformations.euler_matrix( | ||
| # target[3], target[4], target[5], axes='rxyz')[:3, :3] | ||
| # R_ed = np.dot(R_EE.T, R_target) # eq 24 | ||
| # q_e = transformations.quaternion_from_matrix(R_ed) | ||
| # q_e = transformations.unit_vector(q_e) | ||
| # u_task[3:] = np.dot(R_EE, q_e[1:]) # eq 34 | ||
|
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||
|
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||
| # Method 3 ------------------------------------------------------------ | ||
| # From (Caccavale et al, 1997) Section V - Angle/axis feedback -------- | ||
| # | ||
| # R_EE = robot_config.R('EE', feedback['q']) | ||
| # # get rotation matrix for the target orientation | ||
| # R_d = transformations.euler_matrix( | ||
| # target[3], target[4], target[5], axes='rxyz')[:3, :3] | ||
| # R = np.dot(R_target, R_EE.T) # eq 44 | ||
| # q_e = transformations.quaternion_from_matrix(R) | ||
| # q_e = transformations.unit_vector(q_e) | ||
| # u_task[3:] = 2 * q_e[0] * q_e[1:] # eq 45 | ||
|
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||
|
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||
| # Method 4 ------------------------------------------------------------- | ||
| # From (Yuan, 1988) and (Nakanishi et al, 2008) ------------------------ | ||
| # NOTE: This implementation is not working properly -------------------- | ||
| # | ||
| # # transform the orientation target into a quaternion | ||
| # q_d = transformations.unit_vector( | ||
| # transformations.quaternion_from_euler( | ||
| # target[3], target[4], target[5], axes='rxyz')) | ||
| # # get the quaternion for the end effector | ||
| # q_e = transformations.unit_vector( | ||
| # transformations.quaternion_from_matrix( | ||
| # robot_config.R('EE', feedback['q']))) | ||
| # | ||
| # # given r = [r1, r2, r3] | ||
| # # r^x = [[0, -r3, r2], [r3, 0, -r1], [-r2, r1, 0]] | ||
| # S = np.array([ | ||
| # [0.0, -q_d[2], q_d[1]], | ||
| # [q_d[2], 0.0, -q_d[0]], | ||
| # [-q_d[1], q_d[0], 0.0]]) | ||
| # | ||
| # # calculate the difference between q_e and q_d | ||
| # # from (Nakanishi et al, 2008). NOTE: the sign of the last term | ||
| # # is different from (Yuan, 1998) to account for Euler angles in | ||
| # # world coordinates instead of local coordinates. | ||
| # # dq = (w_d * [x, y, z] - w * [x_d, y_d, z_d] - | ||
| # # [x_d, y_d, z_d]^x * [x, y, z]) | ||
| # # the sign of quaternion that moves between q_e and q_d | ||
| # u_task[3:] = -(q_d[0] * q_e[1:] - q_e[0] * q_d[1:] + | ||
| # np.dot(S, q_e[1:])) | ||
| # | ||
| # --------------------------------------------------------------------- | ||
|
|
||
| u_task[3:] *= ko # scale orientation signal by orientation gain | ||
| # remove uncontrolled dimensions from u_task | ||
| u_task = u_task[ctrlr_dof] | ||
|
|
||
| # transform from operational space to torques | ||
| # add in velocity and gravity compensation in joint space | ||
| u = (np.dot(J.T, np.dot(Mx, u_task)) - | ||
| kv * np.dot(M, feedback['dq']) - | ||
| robot_config.g(q=feedback['q'])) | ||
|
|
||
| # apply the control signal, step the sim forward | ||
| interface.send_forces(u) | ||
| count += 1 | ||
|
|
||
| finally: | ||
| interface.disconnect() |
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