Helllo

Single layer of 64 neurons with 8 input and outputs and learning rate set to 0.1. 

Training cases created for vertical take off. The Universal Approximate was constructed for smooth function:

CONTROL: Vn+1 --> Vn 

V is {motor1, motor2, motor3, motor4, Roll, Pitch, Yaw, zcoor}

Desired from simulator: 

{motor1, motor2, motor3, motor4, Roll, Pitch, Yaw, zcoor}

{0.701, 0.7, 0.7, 0.7, 0.500005, 0.491911, 0.500174, 0.051289}

NN calculated thru adaptive learning from a set of 105,000 test cases, offline, zcoor was normalized by a factor maxZ = 30:

Obtained from NN learning:

{motor1, motor2, motor3, motor4, Roll, Pitch, Yaw, zcoor}

{0.751359, 0.69765, 0.743422, 0.710697, 0.572931, 0.580407, 0.620613, 0.107281}  

First four numbers are the motors's RPM, normalized between 0 and 1.

Complexity:

128 multiplications and additions required + 10 multiplications and 4 additions for taylor series expansion of Sigmoid function around 0. 128 word or long word for the learning matrices. 

The motors' accuracy is around the second digit, which for a plane should be ok, but for quad copter is not enough!

I will recheck the calculations , but I am afraid the motor number needs to be broken into two sums in order to attain the accuracy.

Observations:

1. I changed the 64 neurons to 128 and it did not change. The matrices should be randomized between -0.5 and +0.5 or lesser accuracy is obtained. 

2. 105,000 test cases for the learning took several minutes (less than 5) on an IMAC. Original test cases where 7000 but then entirety was repeated 15 times again i.e. 105,000 = 15 * 7000. 

TODO:

1. Look at larger arithmetic accuracy.

2. Experiment with 2 layers of neurons 

3. Obtain theoretical accuracy for upper and lower bounds 

4. Break the motors numbers into a sum of two e.g. 0.701 will become (0.7, 0.1), then shit 0.1 to the right once to get the sum. 

D