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force_joystick.py
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force_joystick.py
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# !/usr/bin/env python3
import casadi as cs
from horizon.transcriptions import integrators
import matplotlib.pyplot as plt
import numpy as np
class ForceJoystick:
def __init__(self, dt, n_step=10, sys_dim=2, opt=None):
self.__dim = sys_dim
if opt is None:
opt = dict()
if 'mass' not in opt:
opt['mass'] = np.ones(self.__dim)
if 'spring' not in opt:
opt['spring'] = np.zeros(self.__dim)
if 'damp' not in opt:
opt['damp'] = np.zeros(self.__dim)
self.__mass = opt['mass'] # virtual mass
self.__spring = opt['spring'] # damping coefficient
self.__damp = opt['damp'] # spring coefficient
self.__dt = dt
self.__n_step = n_step
self.__x_int = np.zeros([self.__dim * 2, self.__n_step])
self.__position_ref = np.zeros([self.__dim])
self.__init_integrator()
def __parameteric_RK4(self, x, u, xdot, p):
L = 0
f_RK = cs.Function('f_RK', [x, u, p], [xdot, L])
nx = x.size1()
nv = u.size1()
np = p.size1()
X0_RK = cs.SX.sym('X0_RK', nx)
U_RK = cs.SX.sym('U_RK', nv)
DT_RK = cs.SX.sym('DT_RK', 1)
P_RK = cs.SX.sym('P_RK', np)
X_RK = X0_RK
Q_RK = 0
k1, k1_q = f_RK(X_RK, U_RK, P_RK)
k2, k2_q = f_RK(X_RK + DT_RK / 2. * k1, U_RK, P_RK)
k3, k3_q = f_RK(X_RK + DT_RK / 2. * k2, U_RK, P_RK)
k4, k4_q = f_RK(X_RK + DT_RK * k3, U_RK, P_RK)
X_RK = X_RK + DT_RK / 6. * (k1 + 2. * k2 + 2. * k3 + k4)
Q_RK = Q_RK + DT_RK / 6. * (k1_q + 2. * k2_q + 2. * k3_q + k4_q)
f = cs.Function('F_RK', [X0_RK, U_RK, DT_RK, P_RK], [X_RK, Q_RK], ['x', 'u', 'dt', 'p'], ['f', 'qf'])
return f
def __init_integrator(self):
# system definition
p = cs.SX.sym('pos', self.__dim)
v = cs.SX.sym('vel', self.__dim)
F = cs.SX.sym('force', self.__dim)
# initial position
p0 = cs.SX.sym('pos_0', self.__dim)
# v0 = cs.SX.sym('vel_0', self.__dim)
v0 = np.zeros([self.__dim])
# v0.assign([0, 0, 0])
# mass-spring-damper
x = cs.vertcat(p, v)
xdot = cs.vertcat(v, (F - self.__damp * (v - v0) - self.__spring * (p - p0))/self.__mass)
self.integrator = self.__parameteric_RK4(x, F, xdot, p0)
def update(self, x_current, u_current):
# integrate for n step
for step_i in range(self.__n_step):
# assuming that the input is constant (Force is constant for the whole integration)
int_state = self.integrator(x_current, u_current, self.__dt, self.__position_ref)[0]
x_current = int_state.full()
self.__x_int[:, step_i] = x_current.flatten()
def getIntegratedState(self):
return self.__x_int
def getDimension(self):
return self.__dim
def setPositionReference(self, pos_ref):
self.__position_ref = pos_ref
if __name__ == '__main__':
sys_dim = 3
x0 = np.zeros([2 * sys_dim, 1]) #m
F0 = np.zeros(sys_dim) #N/m
x0[0] = 5
dt = 0.01
m_virtual = np.array([50, 50, 50])
k_virtual = np.array([10, 10, 0])
d_virtual = 2 * np.sqrt(k_virtual * m_virtual)
n_steps = 10
fj = ForceJoystick(dt,
n_step=n_steps,
sys_dim=sys_dim,
opt=dict(damp=d_virtual, spring=k_virtual))
x_traj = np.zeros(sys_dim)
v_traj = list()
t_traj = list()
t_curr = 0
plt.ion()
fig, ax = plt.subplots(1, 2)
x, y, z = [],[], []
future_sc_xy = list()
future_sc_xz = list()
alpha_vec = [1 - (i/n_steps) for i in range(n_steps)]
for step_i in range(n_steps):
future_sc_xy.append(ax[0].scatter(x, y, color='b', alpha = alpha_vec[step_i]))
for step_i in range(n_steps):
future_sc_xz.append(ax[1].scatter(x, z, color='b', alpha = alpha_vec[step_i]))
sc_xy = ax[0].scatter(x,y, color='r')
sc_xz = ax[1].scatter(x,z, color='r')
plt.draw()
lim = 10
ax[0].set_title('xy')
ax[0].set_xlim(-lim, lim)
ax[0].set_ylim(-lim, lim)
ax[1].set_title('xz')
ax[1].set_xlim(-lim, lim)
ax[1].set_ylim(-lim, lim)
ax[0].set_box_aspect(1)
ax[1].set_box_aspect(1)
fj.setPositionReference(x0[:3, 0])
x_curr = x0
for t in range(10000):
# if 80 < t < 100:
# F0 = np.array([50, 0, 50])
# else:
# F0 = np.array([0, 0, 0])
# if t > 80:
# fj.setPositionReference(np.array([0, 0, 0]))
print("F applied: ", F0)
fj.update(x_curr[:, 0], F0)
x_curr = fj.getIntegratedState()
t_curr = t_curr + dt
# xy plane
sc_xy.set_offsets(np.c_[x_curr[0, 0], x_curr[1, 0]])
for step_i in range(1, n_steps):
future_sc_xy[step_i].set_offsets(np.c_[x_curr[0, step_i],x_curr[1, step_i]])
# xz plane
sc_xz.set_offsets(np.c_[x_curr[1, 0], x_curr[2, 0]])
for step_i in range(1, n_steps):
future_sc_xz[step_i].set_offsets(np.c_[x_curr[1, step_i],x_curr[2, step_i]])
fig.canvas.draw_idle()
plt.pause(0.01)
plt.show()