added python script for terrain flow derivation (optical flow for terrain

height estimation)

Signed-off-by: Roman <bapstroman@gmail.com>

EKF/python/terrain_flow_derivation/derive_terrain_flow.py

@@ -0,0 +1,98 @@
+"""
+
+This script calculates the observation scalars (H matrix) for fusing optical flow
+measurements for terrain estimation.
+
+@author: roman
+"""
+
+from sympy import *
+
+# q: quaternion describing rotation from frame 1 to frame 2
+# returns a rotation matrix derived form q which describes the same
+# rotation
+def quat2Rot(q):
+    q0 = q[0]
+    q1 = q[1]
+    q2 = q[2]
+    q3 = q[3]
+
+    Rot = Matrix([[q0**2 + q1**2 - q2**2 - q3**2, 2*(q1*q2 - q0*q3), 2*(q1*q3 + q0*q2)],
+                  [2*(q1*q2 + q0*q3), q0**2 - q1**2 + q2**2 - q3**2, 2*(q2*q3 - q0*q1)],
+                   [2*(q1*q3-q0*q2), 2*(q2*q3 + q0*q1), q0**2 - q1**2 - q2**2 + q3**2]])
+
+    return Rot
+
+# take an expression calculated by the cse() method and write the expression
+# into a text file in C format
+def write_simplified(P_touple, filename, out_name):
+    subs = P_touple[0]
+    P = Matrix(P_touple[1])
+    fd = open(filename, 'a')
+
+    is_vector = P.shape[0] == 1 or P.shape[1] == 1
+
+    # write sub expressions
+    for index, item in enumerate(subs):
+        fd.write('float ' + str(item[0]) + ' = ' + str(item[1]) + ';\n')
+
+    # write actual matrix values
+    fd.write('\n')
+
+    if not is_vector:
+        iterator = range(0,sqrt(len(P)), 1)
+        for row in iterator:
+            for column in iterator:
+                fd.write(out_name + '(' + str(row) + ',' + str(column) + ') = ' + str(P[row, column]) + ';\n')
+    else:
+        iterator = range(0, len(P), 1)
+
+        for item in iterator:
+            fd.write(out_name + '(' + str(item) + ') = ' + str(P[item]) + ';\n')
+
+    fd.write('\n\n')
+    fd.close()
+
+########## Symbolic variable definition #######################################
+
+
+# vehicle velocity
+v_x = Symbol("v_x", real=True)  # vehicle body x velocity
+v_y = Symbol("v_y", real=True)  # vehicle body y velocity
+
+# unit quaternion describing vehicle attitude, qw is real part
+qw = Symbol("q0", real=True)
+qx = Symbol("q1", real=True)
+qy = Symbol("q2", real=True)
+qz = Symbol("q3", real=True)
+q_att = Matrix([qw, qx, qy, qz])
+
+# terrain vertial position in local NED frame
+_terrain_vpos = Symbol("_terrain_vpos", real=True)
+
+_terrain_var = Symbol("_terrain_var", real=True)
+
+# vehicle vertical position in local NED frame
+pos_z = Symbol("z", real=True)
+
+R_body_to_earth = quat2Rot(q_att)
+
+# Optical flow around x axis
+flow_x = -v_y / (_terrain_vpos - pos_z) * R_body_to_earth[2,2]
+
+# Calculate observation scalar
+H_x = Matrix([flow_x]).jacobian(Matrix([_terrain_vpos]))
+
+H_x_simple = cse(H_x, symbols('t0:30'))
+
+# Optical flow around y axis
+flow_y = v_x / (_terrain_vpos - pos_z) * R_body_to_earth[2,2]
+
+# Calculate observation scalar
+H_y = Matrix([flow_y]).jacobian(Matrix([_terrain_vpos]))
+
+H_y_simple = cse(H_y, symbols('t0:30'))
+
+write_simplified(H_x_simple, "flow_x_observation.txt", "Hx")
+write_simplified(H_y_simple, "flow_y_observation.txt", "Hy")
+