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dynamics.py
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import torch
import numpy as np
import pybullet as p
import articulate as art
from articulate.utils.bullet import *
from articulate.utils.rbdl import *
from utils import *
from qpsolvers import solve_qp
class PhysicsOptimizer:
physics_model_file = 'models/physics.urdf' # physics body model path
plane_file = 'models/plane.urdf' # (for debug) path to plane.urdf Please put plane.obj next to it.
physics_parameter_file = 'physics_parameters.json' # physics hyperparameters
test_contact_joints = ['LHIP', 'RHIP', 'SPINE1', 'LKNEE', 'RKNEE', 'SPINE2',
'SPINE3', 'LSHOULDER', 'RSHOULDER', 'HEAD',
'LELBOW', 'RELBOW', 'LHAND', 'RHAND', 'LFOOT', 'RFOOT'
] # 'LANKLE', 'RANKLE', 'NECK', 'LWRIST', 'RWRIST', 'LCLAVICLE', 'RCLAVICLE'
def __init__(self, debug=False, quiet=False):
mu = 0.6
supp_poly_size = 0.2
self.debug = debug
self.quiet = quiet
self.model = RBDLModel(self.physics_model_file, update_kinematics_by_hand=True)
self.params = read_debug_param_values_from_json(self.physics_parameter_file)
self.friction_constraint_matrix = np.array([[np.sqrt(2), -mu, 0],
[-np.sqrt(2), -mu, 0],
[0, -mu, np.sqrt(2)],
[0, -mu, -np.sqrt(2)]])
self.support_polygon = np.array([[-supp_poly_size / 2, 0, -supp_poly_size / 2],
[ supp_poly_size / 2, 0, -supp_poly_size / 2],
[-supp_poly_size / 2, 0, supp_poly_size / 2],
[ supp_poly_size / 2, 0, supp_poly_size / 2]])
if debug:
p.connect(p.GUI)
p.configureDebugVisualizer(flag=p.COV_ENABLE_Y_AXIS_UP, enable=1)
self.id_robot = p.loadURDF(self.physics_model_file, [0, 0, 0], useFixedBase=False, flags=p.URDF_MERGE_FIXED_LINKS)
change_color(self.id_robot, [198 / 255, 238 / 255, 0, 1.0])
p.loadURDF(self.plane_file, [0, -0.881, 0.0], [-0.7071068, 0, 0, 0.7071068])
load_debug_params_into_bullet_from_json(self.physics_parameter_file)
# states
self.last_x = []
self.q = None
self.qdot = np.zeros(self.model.qdot_size)
self.reset_states()
def reset_states(self):
self.last_x = []
self.q = None
self.qdot = np.zeros(self.model.qdot_size)
def optimize_frame(self, pose, jvel, contact, acc, return_grf=False):
q_ref = smpl_to_rbdl(pose, torch.zeros(3))[0]
v_ref = jvel.numpy()
c_ref = contact.sigmoid().numpy()
a_ref = acc.numpy()
q = self.q
qdot = self.qdot
if q is None:
self.q = q_ref
if return_grf:
return pose, torch.zeros(3), [], None
else:
return pose, torch.zeros(3)
# determine the contact joints and points
self.model.update_kinematics(q, qdot, np.zeros(self.model.qdot_size))
Js = [np.empty((0, self.model.qdot_size))]
collision_points, collision_joints = [], []
for joint_name in self.test_contact_joints:
joint_id = vars(Body)[joint_name]
pos = self.model.calc_body_position(q, joint_id)
if joint_id == Body.LFOOT and c_ref[0] > 0.5 and pos[1] <= self.params['floor_y'] + 0.03 or \
joint_id == Body.RFOOT and c_ref[1] > 0.5 and pos[1] <= self.params['floor_y'] + 0.03 or \
pos[1] <= self.params['floor_y']:
collision_joints.append(joint_name)
for ps in self.support_polygon + pos:
collision_points.append(ps)
pb = self.model.calc_base_to_body_coordinates(q, joint_id, ps)
Js.append(self.model.calc_point_Jacobian(q, joint_id, pb))
Js = np.vstack(Js)
nc = len(collision_points)
# minimize ||A1 * qddot - b1||^2 for A1, b1 in zip(As1, bs1)
# + ||A2 * lambda - b2||^2 for A2, b2 in zip(As2, bs2)
# + ||A3 * tau - b3||^2 for A3, b3 in zip(As3, bs3)
# s.t. G1 * qddot <= h1 for G1, h1 in zip(Gs1, hs1)
# G2 * lambda <= h2 for G2, h2 in zip(Gs2, hs2)
# G3 * tau <= h3 for G3, h3 in zip(Gs3, hs3)
# A_ * x = b_
As1, bs1, As2, bs2, As3, bs3 = [np.zeros((0, self.model.qdot_size))], [np.empty(0)], [np.empty((0, nc * 3))], \
[np.empty(0)], [np.zeros((0, self.model.qdot_size))], [np.empty(0)]
Gs1, hs1, Gs2, hs2, Gs3, hs3 = [np.zeros((0, self.model.qdot_size))], [np.empty(0)], [np.empty((0, nc * 3))], \
[np.empty(0)], [np.zeros((0, self.model.qdot_size))], [np.empty(0)]
A_, b_ = None, None
# joint angle PD controller
if True:
A = np.hstack((np.zeros((self.model.qdot_size - 3, 3)), np.eye((self.model.qdot_size - 3))))
b = self.params['kp_angular'] * art.math.angle_difference(q_ref[3:], q[3:]) - self.params['kd_angular'] * qdot[3:]
As1.append(A) # 72 * 75
bs1.append(b) # 72
# joint position PD controller (using root velocity + ref pose to determine target joint position)
if False:
for joint_name in ['ROOT', 'LHIP', 'RHIP', 'SPINE1', 'LKNEE', 'RKNEE', 'SPINE2', 'LANKLE', 'RANKLE',
'SPINE3', 'LFOOT', 'RFOOT', 'NECK', 'LCLAVICLE', 'RCLAVICLE', 'HEAD', 'LSHOULDER',
'RSHOULDER', 'LELBOW', 'RELBOW', 'LWRIST', 'RWRIST', 'LHAND', 'RHAND']:
joint_id = vars(Body)[joint_name]
cur_vel = self.model.calc_point_velocity(q, qdot, joint_id)
cur_pos = self.model.calc_body_position(q, joint_id)
tar_pos = self.model.calc_body_position(q_ref, joint_id) - q_ref[:3] + q[:3] + v_ref[0] * self.params['delta_t']
a_des = 3600 * (tar_pos - cur_pos) - 60 * cur_vel
A = self.model.calc_point_Jacobian(q, joint_id)
b = -self.model.calc_point_acceleration(q, qdot, np.zeros(75), joint_id) + a_des
As1.append(A * 2)
bs1.append(b * 2)
# joint position PD controller (using joint velocity to determine target joint position)
if True:
for joint_name, v in zip(['ROOT', 'LHIP', 'RHIP', 'SPINE1', 'LKNEE', 'RKNEE', 'SPINE2', 'LANKLE', 'RANKLE',
'SPINE3', 'LFOOT', 'RFOOT', 'NECK', 'LCLAVICLE', 'RCLAVICLE', 'HEAD', 'LSHOULDER',
'RSHOULDER', 'LELBOW', 'RELBOW', 'LWRIST', 'RWRIST'], v_ref[:22]):
joint_id = vars(Body)[joint_name]
if joint_id == Body.LFOOT or joint_id == Body.RFOOT: continue
cur_vel = self.model.calc_point_velocity(q, qdot, joint_id)
a_des = self.params['kp_linear'] * v * self.params['delta_t'] - self.params['kd_linear'] * cur_vel
A = self.model.calc_point_Jacobian(q, joint_id)
b = -self.model.calc_point_acceleration(q, qdot, np.zeros(75), joint_id) + a_des
As1.append(A * self.params['coeff_jvel'])
bs1.append(b * self.params['coeff_jvel'])
# joint velocity (without Jdot * qdot term)
if False:
for joint_name, v in zip(
['ROOT', 'LHIP', 'RHIP', 'SPINE1', 'LKNEE', 'RKNEE', 'SPINE2', 'LANKLE', 'RANKLE',
'SPINE3', 'LFOOT', 'RFOOT', 'NECK', 'LCLAVICLE', 'RCLAVICLE', 'HEAD', 'LSHOULDER',
'RSHOULDER', 'LELBOW', 'RELBOW', 'LWRIST', 'RWRIST', 'LHAND', 'RHAND'], v_ref):
joint_id = vars(Body)[joint_name]
A = self.model.calc_point_Jacobian(q, joint_id)
b = (-self.model.calc_point_velocity(q, qdot, joint_id) + v) / self.params['delta_t']
As1.append(A * 2)
bs1.append(b * 2)
# IMU acceleration
if False:
for joint_name, a in zip(['LWRIST', 'RWRIST', 'LKNEE', 'RKNEE', 'HEAD', 'ROOT'], a_ref):
joint_id = vars(Body)[joint_name]
offset = np.zeros(3)
A = self.model.calc_point_Jacobian(q, joint_id, offset)
b = -self.model.calc_point_acceleration(q, qdot, np.zeros(self.model.qdot_size), joint_id, offset) + a
bs1.append(b * self.params['coeff_acc'])
As1.append(A * self.params['coeff_acc'])
# lambda size
if False:
As2.append(np.eye(nc * 3) * self.params['coeff_lambda_old'])
bs2.append(np.zeros(nc * 3))
# Signorini’s conditions of lambda
if True:
if nc != 0:
A = [np.eye(3) * max(cp[1] - self.params['floor_y'], 0.005) for cp in collision_points]
A = art.math.block_diagonal_matrix_np(A)
As2.append(A * self.params['coeff_lambda'])
bs2.append(np.zeros(nc * 3))
# tau size
if True:
As3.append(art.math.block_diagonal_matrix_np([
np.eye(6) * self.params['coeff_virtual'],
np.eye(self.model.qdot_size - 6) * self.params['coeff_tau']
]))
bs3.append(np.zeros(self.model.qdot_size))
# contacting body joint velocity
if True:
for joint_name in self.test_contact_joints[:-2]:
joint_id = vars(Body)[joint_name]
pos = self.model.calc_body_position(q, joint_id)
if pos[1] <= self.params['floor_y']:
J = self.model.calc_point_Jacobian(q, joint_id)
v = self.model.calc_point_velocity(q, qdot, joint_id)
Gs1.append(-self.params['delta_t'] * J)
hs1.append(v - [-1e-1, 0, -1e-1])
Gs1.append(self.params['delta_t'] * J)
hs1.append(-v + [1e-1, 1e2, 1e-1])
# contacting foot velocity
if True:
for joint_name, stable in zip(['LFOOT', 'RFOOT'], c_ref):
joint_id = vars(Body)[joint_name]
pos = self.model.calc_body_position(q, joint_id)
J = self.model.calc_point_Jacobian(q, joint_id)
v = self.model.calc_point_velocity(q, qdot, joint_id)
th = -np.log(min(stable, 0.84999) / 0.85)
th_y = (self.params['floor_y'] - pos[1]) / self.params['delta_t']
Gs1.append(-self.params['delta_t'] * J)
hs1.append(v - [-th, th_y, -th])
Gs1.append(self.params['delta_t'] * J)
hs1.append(-v + [th, max(th, th_y) + 1e-6, th])
# GRF friction cone constraint
if True:
if nc > 0:
Gs2.append(art.math.block_diagonal_matrix_np([self.friction_constraint_matrix] * nc))
hs2.append(np.zeros(nc * 4))
# equation of motion (equality constraint)
if True:
M = self.model.calc_M(q)
h = self.model.calc_h(q, qdot)
A_ = np.hstack((-M, Js.T, np.eye(self.model.qdot_size)))
b_ = h
As1, bs1, As2, bs2, As3, bs3 = np.vstack(As1), np.concatenate(bs1), np.vstack(As2), np.concatenate(bs2), np.vstack(As3), np.concatenate(bs3)
Gs1, hs1, Gs2, hs2, Gs3, hs3 = np.vstack(Gs1), np.concatenate(hs1), np.vstack(Gs2), np.concatenate(hs2), np.vstack(Gs3), np.concatenate(hs3)
G_ = art.math.block_diagonal_matrix_np([Gs1, Gs2, Gs3])
h_ = np.concatenate((hs1, hs2, hs3))
P_ = art.math.block_diagonal_matrix_np([np.dot(As1.T, As1), np.dot(As2.T, As2), np.dot(As3.T, As3)])
q_ = np.concatenate((-np.dot(As1.T, bs1), -np.dot(As2.T, bs2), -np.dot(As3.T, bs3)))
# fast solvers are less accurate/robust, and may fail
init = self.last_x if False and len(self.last_x) == len(q_) else None
x = solve_qp(P_, q_, G_, h_, A_, b_, solver='quadprog', initvals=init)
# if x is None or np.linalg.norm(x) > 100000:
# x = solve_qp(P_, q_, G_, h_, A_, b_, solver='cvxopt', initvals=init)
if x is None or np.linalg.norm(x) > 100000:
if not self.quiet: print('Warning: QP infeasible. Ignoring Gx <= h constraints')
x = solve_qp(P_, q_, None, None, A_, b_, solver='quadprog', initvals=init)
qddot = x[:self.model.qdot_size]
GRF = x[self.model.qdot_size:-self.model.qdot_size]
tau = x[-self.model.qdot_size:]
qdot = qdot + qddot * self.params['delta_t']
q = q + qdot * self.params['delta_t']
self.q = q
self.qdot = qdot
self.last_x = x
if self.debug:
# self.clock.tick(60) # please install pygame
set_pose(self.id_robot, q)
self.params = read_debug_param_values_from_bullet()
if False: # visualize GRF (no smoothing)
p.removeAllUserDebugItems()
for point, force in zip(collision_points, GRF.reshape(-1, 3)):
p.addUserDebugLine(point, point + force * 1e-2, [1, 0, 0])
pose_opt, tran_opt = rbdl_to_smpl(q)
pose_opt = torch.from_numpy(pose_opt).float()[0]
tran_opt = torch.from_numpy(tran_opt).float()[0]
if not return_grf:
return pose_opt, tran_opt
else:
cj = [vars(art.SMPLJoint)[_].value for _ in collision_joints]
grf = torch.from_numpy(GRF).float().view(-1, 4, 3).sum(dim=1) if len(cj) > 0 else None
return pose_opt, tran_opt, cj, grf