Prototype for sending commands to an Arduino Uno
Fixing minor errors

There are 2 minor errors you should fix and they are related to the commands to type:

print ('=================================================================')
print ('rth_dir ---&gt; Return To Home by direct path')
print ('rth_log ---&gt; Return To Home by logged data')
print ('a ---&gt; imediatly returns to home medium speed: EMERGENCY ONLY')                 
print ('get log ---&gt; prints all travel log since home point')
print ('=================================================================')


Actually typing rth_dir and rth_log lead to errors. What you actually meant was rth dir and rth log respectively (removed the underscore).

Handling the keyboard interrupt exception

When the user aims to exit your application and presses Ctrl + C, this exception is thrown but not handled:

    ...
    trans_com_in = input('COMMAND COM: ')
KeyboardInterrupt


You can handle the KeyboardInterrupt exception by running a sys.exit() this way:

def trans_com(): 
    try:
        # The previous function body here
    except KeyboardInterrupt:
       sys.exit()


Better command line approach

You can make your code much cleaner and more efficient if you rely on a parser for command-line options such as the one that comes with Python itself and called argparse. With that in mind, your in addition to cleanness and efficiency of the code mentioned before, this module will help you to get rid of several other lines of code. I

What I mean is that you can substitute these lines:

elif trans_com_in == 'coms':
    print ('=================================================================')
    print ('rth_dir ---&gt; Return To Home by direct path')
    print ('rth_log ---&gt; Return To Home by logged data')
    print ('a ---&gt; imediatly returns to home medium speed: EMERGENCY ONLY!')
    print ('get log ---&gt; prints all travel log since home point')
    print ('=================================================================')
    print ('')
    return trans_com()

  else:
    print ('Unknown command, type "coms" for list of all commands')
    print ('')
    return trans_com()


by using argparse accordingly; for example:

import argparse
# ...
# ...
parser = argparse.ArgumentParser(description="Prototype for sending commands to an Arduino Uno.")
group = parser.add_mutually_exclusive_group(required=True)
group.add_argument("--rth dir", help="Return To Home by direct path.")
group.add_argument("--rth log", help="Return To Home by logged data.")
group.add_argument("--a", help="Imediatly returns to home medium speed: EMERGENCY ONLY!")
group.add_argument("-- get log", help="Prints all travel log since home point.")
args = parser.parse_args()


This approach will  automatically lead several other lines of your code , such as these  ones, to be useless:

else:
    print ('Unknown command, type "coms" for list of all commands')
    print ('')


and:

trans_com_in = input('COMMAND COM: ')


Because when the user tries to run your code this way: python3 solution.py, the Python interpreter will trigger this exception that is self expressing:
    python3 solution.py
    usage: solution.py [-h]
                       (--rth dir RTH DIR | --rth log RTH LOG | --a A | -- get log  GET LOG)
    solution.py: error: one of the arguments --rth dir --rth log --a -- get log is required

By typing the --help (or -h) option, the user can see the information you already wanted to display in your current code:

python3 solution.py -h
usage: solution.py [-h]
                   (--rth dir RTH DIR | --rth log RTH LOG | --a A | -- get log  GET LOG)

Prototype for sending commands to an Arduino Uno.

optional arguments:
  -h, --help           show this help message and exit
  --rth dir RTH DIR    Return To Home by direct path.
  --rth log RTH LOG    Return To Home by logged data.
  --a A                Imediatly returns to home medium speed: EMERGENCY ONLY!
  -- get log  GET LOG  Prints all travel log since home point.


Now with this approach, you need to change your code accordingly, and I think that will be easy for you to do by checking the content of args variable instead of that of trans_com_in.

Other notes


You can type: 

print ('PROTOTYPE COMMAND PROMPT FOR TRANS COM\n')


instead of:

print ('PROTOTYPE COMMAND PROMPT FOR TRANS COM')
print ('')

Choose better names: Functions' names like rth_dir(), trans_com() and log_dir() do not tell much about their purpose unless the maintainer of your code digs into their bodies. You should choose names that express right away the purpose of those functions. The same observation is valid when it comes to other variables (such as trans_com_in, r_time, l_time, left, right.
Leave only one blank line between the definitions of your functions. Please check PEP8 for more details.