Trajectory Direction Resulting_Direction
STRAIGHT   NORTH     NORTH
STRAIGHT   NaN       NORTH
LEFT       NaN       WEST
LEFT       NaN       WEST
LEFT       NaN       WEST
STRAIGHT   NaN       WEST
STRAIGHT   NaN       WEST
RIGHT      NaN       NORTH
RIGHT      NaN       NORTH
RIGHT      NaN       NORTH

df.loc[:,'direction'] = np.NaN
df.loc[df.index == 0, "direction"] = "WEST"
# mask is for finding when a signal hasnt changed in three seconds, but now has
mask = (df.trajectory != df.trajectory.shift(1)) & (df.trajectory == df.trajectory.shift(-1)) & (df.trajectory == df.trajectory.shift(-2))
df.loc[(mask) & (df['trajectory'] == 'LEFT') & (df['direction'].dropna().shift() == "WEST"),'direction'] = 'SOUTH'
df.loc[(mask) & (df['trajectory'] == 'LEFT') & (df['direction'].dropna().shift() == "SOUTH"),'direction'] = 'EAST'
df.loc[(mask) & (df['trajectory'] == 'LEFT') & (df['direction'].dropna().shift() == "EAST"),'direction'] = 'NORTH'
df.loc[(mask) & (df['trajectory'] == 'LEFT') & (df['direction'].dropna().shift() == "NORTH"),'direction'] = 'WEST'
df.loc[(mask) & (df['trajectory'] == 'RIGHT') & (df['direction'].dropna().shift() == "WEST"),'direction'] = 'NORTH'
df.loc[(mask) & (df['trajectory'] == 'RIGHT') & (df['direction'].dropna().shift() == "SOUTH"),'direction'] = 'WEST'
df.loc[(mask) & (df['trajectory'] == 'RIGHT') & (df['direction'].dropna().shift() == "EAST"),'direction'] = 'SOUTH'
df.loc[(mask) & (df['trajectory'] == 'RIGHT') & (df['direction'].dropna().shift() == "NORTH"),'direction'] = 'EAST'
df.loc[:,'direction'] = df.direction.fillna(method="ffill")
print(df[['trajectory','direction']])

thresh = 3
# mark the consecutive direction commands
blocks = df.Trajectory.ne(df.Trajectory.shift()).cumsum()


# group by blocks
groups = df.groupby(blocks)

# enumerate each block
df['mask'] = groups.cumcount()

# shift up to mark the beginning
# mod thresh to divide each block into small block of thresh
df['mask'] = groups['mask'].shift(1-thresh) % thresh

# for conversion of direction to letters:
changes = {'LEFT': -1,'RIGHT':1}
directions = {0:'NORTH', 1:'EAST', 2:'SOUTH', 3:'WEST'}

# update direction changes
direction_changes = (df.Trajectory
                     .where(df['mask'].eq(2))   # where the changes happends
                     .map(changes)              # replace the changes with number
                     .fillna(0)                 # where no direction change is 0
                    )
# mod 4 for the 4 direction
# and map
df['Resulting_Direction'] = (direction_changes.cumsum() % 4).map(directions)

Trajectory Direction Resulting_Direction  mask
0   STRAIGHT     NORTH               NORTH   NaN
1   STRAIGHT       NaN               NORTH   NaN
2       LEFT       NaN                WEST   2.0
3       LEFT       NaN                WEST   NaN
4       LEFT       NaN                WEST   NaN
5   STRAIGHT       NaN                WEST   NaN
6   STRAIGHT       NaN                WEST   NaN
7      RIGHT       NaN               NORTH   2.0
8      RIGHT       NaN               NORTH   NaN
9      RIGHT       NaN               NORTH   NaN