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iros_casadi_3.py
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iros_casadi_3.py
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# %%
import numpy as np
import math
from scipy.special import erf
from casadi import *
import json
# %%
class Quadcopter():
def __init__(self, x_init):
self.A = np.array([[0,0,1,0],[0,0,0,1],[0,0,0,0],[0,0,0,0]])
self.B = np.array([[0,0],[0,0],[1,0],[0,1]])
self.W = np.zeros([sysParam['nx'], sysParam['nx']]) # noise covariance for velocity
self.W[0,0] = sysParam['scalor_noise']
self.W[1,1] = sysParam['scalor_noise']
self.xdot = np.zeros((sysParam['nx'],1))
# Definite intial conditions
if any(x_init) == None:
self.x = np.zeros((sysParam['nx'],1))
else:
self.x = x_init
def model(self, u):
noise = np.random.multivariate_normal([0,0,0,0], self.W).reshape(-1,1)
self.xdot = [email protected](-1,1) + [email protected](-1,1) + noise
for i in range(10):
self.x += np.squeeze((sysParam['deltaT']/10.)*self.xdot)
# if __name__ == '__main__':
# x_init = np.zeros((sysParam['nx'],1))
# quad = Quadcopter(x_init=x_init)
# u = np.array([1,1])
# quad.model(u)
# %%
class Controller():
def __init__(self):
pass
def comp_vectors (self, p_i, p_j):
""" compute the two tangent vectors and norm vectors """
W_v = sysParam['scalor_noise']*np.identity(int(sysParam['nx']/2)) # noise covariance
delta_1, delta_2 = sysParam['threshold'], sysParam['threshold']
radius = sysParam['radius'] + sysParam['radius']
p_ij = p_j - p_i
norm_p_ij = norm_2(p_ij)
sin_alpha = radius / norm_p_ij
cos_alpha = np.sqrt(norm_p_ij**2 - radius**2) / norm_p_ij
tangent_trans_1 = np.array([[cos_alpha, sin_alpha], [-sin_alpha, cos_alpha]])
T_ij_1 = tangent_trans_1@p_ij
N_ij_1 = np.array([[0,1],[-1,0]])@(T_ij_1)
kappa_1 = np.sqrt(2*N_ij_1.T@W_v@N_ij_1)*erf(1-2*delta_1)
tangent_trans_2 = np.array([[cos_alpha, -sin_alpha], [sin_alpha, cos_alpha]])
T_ij_2 = tangent_trans_2@(p_ij)
N_ij_2 = np.array([[0,-1],[1,0]])@(T_ij_2)
kappa_2 = np.sqrt(2*N_ij_2.T@W_v@N_ij_2)*erf(1-2*delta_2)
return N_ij_1, kappa_1, N_ij_2, kappa_2
def control(self, p_i, p_others, v_others, idx_host, xr):
deltaT = sysParam['deltaT']
N = sysParam['N_pred']
nx = sysParam['nx']
nu = sysParam['nu']
num_robot = sysParam['num_robot']
Q = np.zeros([nx,nx])
Q[0,0] = 1000
Q[1,1] = 1000
Q[2,2] = 100
Q[3,3] = 100
R = np.zeros([nu,nu])
R[0,0] = 0
R[1,1] = 0
ndim = sysParam['ndim'] # dimension = 2
states = SX.sym('ss', nx, 1)
controls = SX.sym('u', nu, 1)
W = np.zeros([sysParam['nx'], sysParam['nx']]) # noise covariance for velocity
W[0,0] = sysParam['scalor_noise']
W[1,1] = sysParam['scalor_noise']
f = Function('f', [states, controls], [globals().get('quad_'+str(idx_host)).A @states + \
globals().get('quad_'+str(idx_host)).B@controls + np.random.multivariate_normal([0,0,0,0], W).reshape(-1,1)])
X = SX.sym('X', nx, (N+1))
U = SX.sym('U', nu, N)
P = SX.sym('P', (nx+N*(nx+nu)))
""" define obj and constr for MPC """
obj = 0
constr = []
st = X[:,0]
constr = vertcat(constr, st-P[0:nx])
for k in range(N):
st = X[:,k]
con = U[:,k]
P_st_ref = P[((nx+nu)*(k+1)-nu) : ((nx+nu)*(k+1)+nx-nu)]
# P_u_ref = P[((nx+nu)*(k+1)+nx-nu):((nx+nu)*(k+1)+nx)]
# obj += (st-P_st_ref).T @ Q @ (st-P_st_ref) + (con-P_u_ref).T @ R @ (con-P_u_ref)
obj += (st-P_st_ref).T @ Q @ (st-P_st_ref) + (con).T @ R @ (con)
st_next = X[:,k+1]
f_value = f(st, con)
st_next_value = st + deltaT*f_value
constr = vertcat(constr, st_next-st_next_value)
if sysParam['isAvoid'] == True:
p_i = st[0:ndim]
for j in range(num_robot-1):
p_j = p_others[:,j]
v_j = v_others[:,j]
if norm_2(globals().get('quad_'+ str(idx_host)).x[0:2] - p_j) < sysParam['detect_range']:
N_ij_1, kappa_1, N_ij_2, kappa_2 = self.comp_vectors(p_i, p_j)
v_i = st[ndim:nx]
# ========= NO chance constraints =========
# constr = vertcat(constr, -(dot(N_ij_1,v_i) - dot(N_ij_1,v_j))*(dot(N_ij_2,v_i) - dot(N_ij_2,v_j)) )
# ========= YES chance constraints ========
constr = vertcat(constr, kappa_1 + dot(N_ij_1,v_j) - dot(N_ij_1,v_i) )
constr = vertcat(constr, kappa_2 + dot(N_ij_2,v_j) - dot(N_ij_2,v_i) )
else:
pass
""" formulate NLP problem and solver """
OPT_variables = vertcat( X.reshape((nx*(N+1),1)), U.reshape((nu*N,1)) ) # (412,1)
nlp_prob = dict(f=obj, x=OPT_variables, g=constr, p=P)
opts = {'ipopt.max_iter':1000, 'ipopt.print_level':0, 'print_time':0, 'ipopt.acceptable_tol':1e-8, \
'ipopt.acceptable_obj_change_tol':1e-6, 'show_eval_warnings':False}
solver = nlpsol('solver', 'ipopt', nlp_prob, opts)
""" set arguments, i.e. constraints (inequality Bounds and enquality constraints) """
args = {}
if sysParam['isAvoid'] == True:
g_lim_low = np.zeros((1,nx))
for k in range(N):
g_lim_low = np.append(g_lim_low, np.zeros([1,nx]))
for j in range(num_robot-1):
if norm_2(globals().get('quad_'+ str(idx_host)).x[0:2] - p_others[:,j]) < sysParam['detect_range']:
# ========== NO chance constraints =========
# g_lim_low = np.append(g_lim_low, -inf)
# ========== YES chance constraints =========
g_lim_low = np.append(g_lim_low, [-inf, -inf])
g_lim_upp = np.zeros_like(g_lim_low)
args['lbg'] = g_lim_low
args['ubg'] = g_lim_upp
else:
g_lim_low = np.zeros((1,nx*(N+1)))
g_lim_upp = np.zeros((1,nx*(N+1)))
args['lbg'] = g_lim_low
args['ubg'] = g_lim_upp
x_lim_low = DM((nx*(N+1)+nu*N),1)
# begin to set bounds for states
x_lim_low[0:(nx*(N+1)):nx,0] = -inf
x_lim_low[1:(nx*(N+1)):nx,0] = -inf
x_lim_low[2:(nx*(N+1)):nx,0] = -10
x_lim_low[3:(nx*(N+1)):nx,0] = -10
# begin to set bounds for control inputs
x_lim_low[(nx*(N+1)) :, 0] = -100
x_lim_upp = DM((nx*(N+1)+nu*N),1)
# begin to set bounds for states
x_lim_upp[0:(nx*(N+1)):nx,0] = inf
x_lim_upp[1:(nx*(N+1)):nx,0] = inf
x_lim_upp[2:(nx*(N+1)):nx,0] = 10
x_lim_upp[3:(nx*(N+1)):nx,0] = 10
# begin to set bounds for control inputs
x_lim_upp[(nx*(N+1)) :, 0] = 100
args['lbx'] = x_lim_low
args['ubx'] = x_lim_upp
""" begin to compute (mpc problem) """
x0 = globals().get('quad_'+ str(idx_host)).x # initial condition (nx, )
xs = xr[:,0] # reference position (4, ) xr:(4,26)
u0 = np.zeros((N,nu)) # (25, 4)
X0 = repmat(x0, 1, (N+1)).T # initialize the states decision variables (26,4)
args['p'] = DM(nx+N*(nx+nu),1) # (154, 1)
args['p'][0:nx] = x0
for k in range(N):
args['p'][((nx+nu)*(k+1)-nu) : ((nx+nu)*(k+1)+nx-nu)] = xr[:,k]
# initialize optimization decision variables
args['x0'] = vertcat(X0.reshape(((nx*(N+1)), 1)), u0.reshape(((nu*N), 1))) #(154, 1)
sol = solver(x0=args['x0'], lbx=args['lbx'], ubx=args['ubx'], lbg=args['lbg'], ubg=args['ubg'], p=args['p'])
solx = sol['x']
solx_u = np.array(solx)[(nx*(N+1)):(solx.shape[0]+1)]
u = solx_u.reshape((N,nu))
control_input = u[0,:]
X0 = solx[0:nx*(N+1)].reshape(((N+1), nx))
# shift trajectory to initialize the next step
X0 = vertcat(X0[1:,:], X0[-1,:])
state_pred = np.array(X0)
return control_input, state_pred
# %%
""" Compute reference states """
def reference(X_init_all, X_end_all, idx_host):
locals()['_xr_x_'+str(idx_host)] = np.linspace(X_init_all[0,idx_host], \
X_end_all[0,idx_host], int(sysParam['runtime']/sysParam['deltaT']))
locals()['_xr_y_'+str(idx_host)] = np.linspace(X_init_all[1,idx_host], \
X_end_all[1,idx_host], int(sysParam['runtime']/sysParam['deltaT']))
locals()['_xr_vx_'+str(idx_host)] = ((X_end_all[0,idx_host] - X_init_all[0,idx_host])/sysParam['runtime'])*np.ones(int(sysParam['runtime']/sysParam['deltaT']))
locals()['_xr_vy_'+str(idx_host)] = ((X_end_all[1,idx_host] - X_init_all[1,idx_host])/sysParam['runtime'])*np.ones(int(sysParam['runtime']/sysParam['deltaT']))
locals()['xr_'+str(idx_host)] = np.vstack([locals().get('_xr_x_'+str(idx_host)), locals().get('_xr_y_'+str(idx_host)), locals().get('_xr_vx_'+str(idx_host)), locals().get('_xr_vy_'+str(idx_host))])
return locals()['xr_'+str(idx_host)]
# %%
""" Main """
global sysParam
sysParam = {"case": 4, "deltaT":0.05, "N_pred": 25, "runtime":10, "radius": 0.1, \
"nx": 4, "nu": 2, "ndim":2, "mass": 1, "scalor_noise": 0.01, "isAvoid": True, \
"threshold":0.1, 'detect_range':1}
if sysParam['case'] == 1 or sysParam['case'] == 2:
sysParam['num_robot'] = 6
elif sysParam['case'] == 3 or sysParam['case'] == 4:
sysParam['num_robot'] = 12
if __name__ == '__main__':
X_init_all = np.zeros((sysParam['nx'],sysParam['num_robot']))
X_end_all = np.zeros((sysParam['nx'],sysParam['num_robot']))
if sysParam['case'] == 1:
# case 1
X_init_all[0,:] = [-4, -2, 2, 4, -2, 2]
X_init_all[1,:] = [ 0, 2, 2, 0, -2, -2]
X_end_all[0,:] = [ 4, -2, 2, -4, -2, 2]
X_end_all[1,:] = [ 0, -2, -2, 0, 2, 2]
elif sysParam['case'] == 2:
# case 2
X_init_all[0,:] = [-4, -2, 2, 4, -2, 2]
X_init_all[1,:] = [ 0, 2, 2, 0, -2, -2]
X_end_all[0,:] = [ 4, 2, -2, -4, 2, -2]
X_end_all[1,:] = [ 0, -2, -2, 0, 2, 2]
elif sysParam['case'] == 3:
# case 3
X_init_all[0,:] = [-6, -4, -2, 0, 2, 4, 6, -4, -2, 0, 2, 4]
X_init_all[1,:] = [ 0, 2, 4, 6, 4, 2, 0, -2, -4, -6, -4, -2]
X_end_all[0,:] = [ 6, -4, -2, 0, 2, 4, -6, -4, -2, 0, 2, 4]
X_end_all[1,:] = [ 0, -2, -4, -6, -4, -2, 0, 2, 4, 6, 4, 2]
elif sysParam['case'] == 4:
# case 4
X_init_all[0,:] = [-6, -4, -2, 0, 2, 4, 6, -4, -2, 0, 2, 4]
X_init_all[1,:] = [ 0, 2, 4, 6, 4, 2, 0, -2, -4, -6, -4, -2]
X_end_all[0,:] = [ 6, 4, 2, 0, -2, -4, -6, 4, 2, 0, -2, -4]
X_end_all[1,:] = [ 0, -2, -4, -6, -4, -2, 0, 2, 4, 6, 4, 2]
# Initiallize
for idx_host in range(sysParam['num_robot']):
globals()['xr_'+str(idx_host)] = reference(X_init_all, X_end_all, idx_host)
locals()['x_init_'+str(idx_host)] = X_init_all[:,idx_host]
globals()['quad_'+str(idx_host)] = Quadcopter(locals()['x_init_'+str(idx_host)])
globals()['controller_'+str(idx_host)] = Controller()
locals()['u_result_'+str(idx_host)] = []
locals()['x_result_'+str(idx_host)] = [ globals()['quad_'+str(idx_host)].x.tolist() ]
for iter in range(int(sysParam['runtime']/sysParam['deltaT']-sysParam['N_pred'])):
for idx_host in range(sysParam['num_robot']):
p_i = globals()['quad_'+str(idx_host)].x[0:sysParam['ndim']]
j = 0
p_others = np.zeros([sysParam['ndim'], (sysParam['num_robot']-1)])
v_others = np.zeros([sysParam['ndim'], (sysParam['num_robot']-1)])
for idx_j in [m for m in range(sysParam['num_robot']) if m != idx_host]:
p_others[:,j] = globals().get('quad_'+str(idx_j)).x[0:sysParam['ndim']]
v_others[:,j] = globals().get('quad_'+str(idx_j)).x[sysParam['ndim']:sysParam['nx']]
j += 1
u, state_pred = globals().get('controller_'+str(idx_host)).control(p_i, \
p_others, v_others, idx_host, locals().get('xr_'+str(idx_host))[:,iter:int(iter+(sysParam['N_pred']+1))] )
globals()['quad_'+str(idx_host)].model(u)
print ('-------------------')
print ("iteration #", iter)
print ("time: ", iter*sysParam['deltaT'])
print ('number of robot: ', idx_host)
print ('control input: ', u)
print ('states: ', globals().get('quad_'+str(idx_host)).x.reshape(-1,1))
print ("reference loc: ", locals().get('xr_'+str(idx_host))[:,iter])
locals()['u_result_'+str(idx_host)].append(u.tolist())
locals()['x_result_'+str(idx_host)].append(globals().get('quad_'+str(idx_host)).x.tolist())
""" save data """
results = {}
for idx_host in range(sysParam['num_robot']):
results['x_results_'+str(idx_host)] = locals().get('x_result_'+str(idx_host))
results['u_results_'+str(idx_host)] = locals().get('u_result_'+str(idx_host))
results['x_reference_'+str(idx_host)] = globals().get('xr_'+str(idx_host)).tolist()
if sysParam['isAvoid'] == False:
with open('results_No_avoid_data.json', 'w') as json_file:
json.dump(results, json_file)
else:
with open('case'+str(sysParam['case'])+'.json', 'w') as json_file:
json.dump(results, json_file)
# %%