def find_nvecs_old(self):
N = self.N
track = self.cline
nvecs = []
# new_track.append(track[0, :])
nvec = lib.theta_to_xy(np.pi/2 + lib.get_bearing(track[0, :], track[1, :]))
nvecs.append(nvec)
for i in range(1, len(track)-1):
pt1 = track[i-1]
pt2 = track[min((i, N)), :]
pt3 = track[min((i+1, N-1)), :]
th1 = lib.get_bearing(pt1, pt2)
th2 = lib.get_bearing(pt2, pt3)
if th1 == th2:
th = th1
else:
dth = lib.sub_angles_complex(th1, th2) / 2
th = lib.add_angles_complex(th2, dth)
new_th = th + np.pi/2
nvec = lib.theta_to_xy(new_th)
nvecs.append(nvec)
nvec = lib.theta_to_xy(np.pi/2 + lib.get_bearing(track[-2, :], track[-1, :]))
nvecs.append(nvec)
self.nvecs = np.array(nvecs)
def convert_pts_s_th(pts):
N = len(pts)
s_i = np.zeros(N-1)
th_i = np.zeros(N-1)
for i in range(N-1):
s_i[i] = lib.get_distance(pts[i], pts[i+1])
th_i[i] = lib.get_bearing(pts[i], pts[i+1])
return s_i, th_i
def cth_reward(self, s_p):
pt_i, pt_ii, d_i, d_ii = find_closest_pt(s_p[0:2], self.wpts)
d = lib.get_distance(pt_i, pt_ii)
d_c = get_tiangle_h(d_i, d_ii, d) / self.dis_scale
th_ref = lib.get_bearing(pt_i, pt_ii)
th = s_p[2]
d_th = abs(lib.sub_angles_complex(th_ref, th))
v_scale = s_p[3] / self.max_v
r = self.mh * np.cos(d_th) * v_scale - self.md * d_c
return r
def transform_obs(self, obs):
cur_v = [obs[3] / self.max_v]
cur_d = [obs[4] / self.max_d]
th_target = lib.get_bearing(obs[0:2], self.env_map.end)
alpha = lib.sub_angles_complex(th_target, obs[2])
th_scale = [(alpha) * 2 / np.pi]
scan = self.scan_sim.get_scan(obs[0], obs[1], obs[2])
nn_obs = np.concatenate([cur_v, cur_d, th_scale, scan])
return nn_obs
def find_centerline(self, show=True):
dt = self.dt
d_search = 0.8
n_search = 11
dth = (np.pi * 4/5) / (n_search-1)
# makes a list of search locations
search_list = []
for i in range(n_search):
th = -np.pi/2 + dth * i
x = -np.sin(th) * d_search
y = np.cos(th) * d_search
loc = [x, y]
search_list.append(loc)
pt = start = np.array([self.conf.sx, self.conf.sy])
self.cline = [pt]
th = self.stheta
while (lib.get_distance(pt, start) > d_search/2 or len(self.cline) < 10) and len(self.cline) < 500:
vals = []
self.search_space = []
for i in range(n_search):
d_loc = lib.transform_coords(search_list[i], -th)
search_loc = lib.add_locations(pt, d_loc)
self.search_space.append(search_loc)
x, y = self.xy_to_row_column(search_loc)
val = dt[y, x]
vals.append(val)
ind = np.argmax(vals)
d_loc = lib.transform_coords(search_list[ind], -th)
pt = lib.add_locations(pt, d_loc)
self.cline.append(pt)
if show:
self.plot_raceline_finding()
th = lib.get_bearing(self.cline[-2], pt)
print(f"Adding pt: {pt}")
self.cline = np.array(self.cline)
self.N = len(self.cline)
print(f"Raceline found --> n: {len(self.cline)}")
if show:
self.plot_raceline_finding(True)
self.plot_raceline_finding(False)
def get_curvature(pos_history):
n = len(pos_history)
ths = [
lib.get_bearing(pos_history[i], pos_history[i + 1])
for i in range(n - 1)
]
dth = [
abs(lib.sub_angles_complex(ths[i], ths[i + 1])) for i in range(n - 2)
]
total_curve = np.sum(dth)
avg_curve = np.mean(dth)
print(f"Total Curvatue: {total_curve}, Avg: {avg_curve}")
return total_curve
def __call__(self, s, a, s_p, r, dev):
if r == -1:
return r
else:
pt_i, pt_ii, d_i, d_ii = find_closest_pt(s_p[0:2], self.wpts)
d = lib.get_distance(pt_i, pt_ii)
d_c = get_tiangle_h(d_i, d_ii, d) / self.dis_scale
th_ref = lib.get_bearing(pt_i, pt_ii)
th = s_p[2]
d_th = abs(lib.sub_angles_complex(th_ref, th))
v_scale = s_p[3] / self.max_v
new_r = self.mh * np.cos(d_th) * v_scale - self.md * d_c
return new_r + r
def MinCurvatureTrajectory(pts, nvecs, ws):
"""
This function uses optimisation to minimise the curvature of the path
"""
w_min = - ws[:, 0] * 0.9
w_max = ws[:, 1] * 0.9
th_ns = [lib.get_bearing([0, 0], nvecs[i, 0:2]) for i in range(len(nvecs))]
N = len(pts)
n_f_a = ca.MX.sym('n_f', N)
n_f = ca.MX.sym('n_f', N-1)
th_f = ca.MX.sym('n_f', N-1)
x0_f = ca.MX.sym('x0_f', N-1)
x1_f = ca.MX.sym('x1_f', N-1)
y0_f = ca.MX.sym('y0_f', N-1)
y1_f = ca.MX.sym('y1_f', N-1)
th1_f = ca.MX.sym('y1_f', N-1)
th2_f = ca.MX.sym('y1_f', N-1)
th1_f1 = ca.MX.sym('y1_f', N-2)
th2_f1 = ca.MX.sym('y1_f', N-2)
o_x_s = ca.Function('o_x', [n_f], [pts[:-1, 0] + nvecs[:-1, 0] * n_f])
o_y_s = ca.Function('o_y', [n_f], [pts[:-1, 1] + nvecs[:-1, 1] * n_f])
o_x_e = ca.Function('o_x', [n_f], [pts[1:, 0] + nvecs[1:, 0] * n_f])
o_y_e = ca.Function('o_y', [n_f], [pts[1:, 1] + nvecs[1:, 1] * n_f])
dis = ca.Function('dis', [x0_f, x1_f, y0_f, y1_f], [ca.sqrt((x1_f-x0_f)**2 + (y1_f-y0_f)**2)])
track_length = ca.Function('length', [n_f_a], [dis(o_x_s(n_f_a[:-1]), o_x_e(n_f_a[1:]),
o_y_s(n_f_a[:-1]), o_y_e(n_f_a[1:]))])
real = ca.Function('real', [th1_f, th2_f], [ca.cos(th1_f)*ca.cos(th2_f) + ca.sin(th1_f)*ca.sin(th2_f)])
im = ca.Function('im', [th1_f, th2_f], [-ca.cos(th1_f)*ca.sin(th2_f) + ca.sin(th1_f)*ca.cos(th2_f)])
sub_cmplx = ca.Function('a_cpx', [th1_f, th2_f], [ca.atan2(im(th1_f, th2_f),real(th1_f, th2_f))])
get_th_n = ca.Function('gth', [th_f], [sub_cmplx(ca.pi*np.ones(N-1), sub_cmplx(th_f, th_ns[:-1]))])
d_n = ca.Function('d_n', [n_f_a, th_f], [track_length(n_f_a)/ca.tan(get_th_n(th_f))])
# objective
real1 = ca.Function('real1', [th1_f1, th2_f1], [ca.cos(th1_f1)*ca.cos(th2_f1) + ca.sin(th1_f1)*ca.sin(th2_f1)])
im1 = ca.Function('im1', [th1_f1, th2_f1], [-ca.cos(th1_f1)*ca.sin(th2_f1) + ca.sin(th1_f1)*ca.cos(th2_f1)])
sub_cmplx1 = ca.Function('a_cpx1', [th1_f1, th2_f1], [ca.atan2(im1(th1_f1, th2_f1),real1(th1_f1, th2_f1))])
# define symbols
n = ca.MX.sym('n', N)
th = ca.MX.sym('th', N-1)
nlp = {\
'x': ca.vertcat(n, th),
'f': ca.sumsqr(sub_cmplx1(th[1:], th[:-1])),
# 'f': ca.sumsqr(track_length(n)),
'g': ca.vertcat(
# dynamic constraints
n[1:] - (n[:-1] + d_n(n, th)),
# boundary constraints
n[0], #th[0],
n[-1], #th[-1],
) \
}
# S = ca.nlpsol('S', 'ipopt', nlp, {'ipopt':{'print_level':5}})
S = ca.nlpsol('S', 'ipopt', nlp, {'ipopt':{'print_level':0}})
ones = np.ones(N)
n0 = ones*0
th0 = []
for i in range(N-1):
th_00 = lib.get_bearing(pts[i, 0:2], pts[i+1, 0:2])
th0.append(th_00)
th0 = np.array(th0)
x0 = ca.vertcat(n0, th0)
lbx = list(w_min) + [-np.pi]*(N-1)
ubx = list(w_max) + [np.pi]*(N-1)
r = S(x0=x0, lbg=0, ubg=0, lbx=lbx, ubx=ubx)
x_opt = r['x']
n_set = np.array(x_opt[:N])
# thetas = np.array(x_opt[1*N:2*(N-1)])
return n_set
