Path-finding using only neural network - tensorflow

Question

I'm trying to train a neural network for a path-finding problem on 10x10 grid map but it seems it doesn't work. Here is the details:
My input to the neural network is 10x10x2 matrix where first 10x10 represents obstacles on the map, second 10x10 represents only two points, initial and final points.
My output to the system is the shorthest path found by A* algorithm. I've written a code that produces desired number of cases, and the optimal route is found by A* just after producing the case. I want to teach finding this paths to neural network. As an example, the general structure for 4x4 case is like below.
obstacles matrix(input):
0 0 0 0
0 1 1 1
0 1 1 0
0 0 0 0
initial and final point matrix(input):
0 1 0 0
0 0 0 0
0 0 0 1
0 0 0 0
route(desired output):
1 1 0 0
1 0 0 0
1 0 0 1
1 1 1 1
Also, I'm adding the pictures of a case and the output of neural network.
obstacles
start and target points
desired route
combined image
Up to now, I've described the inputs and output of the neural network. I'm trying to train network using 3 fully connected layer but it seems it does not learn the pattern. Here is my network:
x = tf.placeholder(dtype=tf.float32, shape=[None,10,10,2])
y = tf.placeholder(dtype=tf.float32, shape=[None,10,10])
rate = tf.placeholder(dtype=tf.float32)
# flatten the input
x_flatten = tf.contrib.layers.flatten(x)
y_flatten = tf.contrib.layers.flatten(y)
# fully connected layer
fc = tf.layers.dense(inputs=x_flatten, units=1000, activation=tf.nn.tanh)
fc = tf.layers.dropout(fc, rate=rate, training=True) # rate = 0.3
fc = tf.layers.dense(inputs=fc, units=500, activation=tf.nn.tanh)
logits = tf.layers.dense(inputs=fc, units=100, activation=None)
cost = tf.reduce_mean(tf.abs(logits - y_flatten))
optimizer = tf.train.AdamOptimizer().minimize(cost)
Finally, I'm adding the outcome of the NN after training with 1000 cases and 20 epochs, and the ground truth together.
training outcome
test outcome
I have also tried CNN but it also did not work. Any suggestions will be welcomed, thanks in advance.