Is there any "instrument take-off system"?
While there is not a specific physical system dedicated to instrument departures per se, there are procedures that rely upon instrument flight rules (IFR) navigation equipment that ensure obstacle clearance when departing from an airport in instrument meteorological conditions (IMC).

From the Aeronautical Information Manual 5-2-8.


  Instrument departure procedures are preplanned instrument
  flight rule (IFR) procedures which provide
  obstruction clearance from the terminal area to the
  appropriate en route structure. There are two types of
  DPs, Obstacle Departure Procedures (ODPs), printed
  either textually or graphically, and Standard Instrument
  Departures (SIDs), always printed graphically.
  All DPs, either textual or graphic may be designed using
  either conventional or RNAV criteria. RNAV
  procedures will have RNAV printed in the title,
  e.g., SHEAD TWO DEPARTURE (RNAV). ODPs
  provide obstruction clearance via the least onerous
  route from the terminal area to the appropriate en
  route structure. ODPs are recommended for obstruction
  clearance and may be flown without ATC
  clearance unless an alternate departure procedure
  (SID or radar vector) has been specifically assigned
  by ATC. Graphic ODPs will have (OBSTACLE)
  printed in the procedure title, e.g., GEYSR THREE DEPARTURE (OBSTACLE), or, CROWN ONE
  DEPARTURE (RNAV) (OBSTACLE). Standard Instrument
  Departures are air traffic control (ATC)
  procedures printed for pilot/controller use in graphic
  form to provide obstruction clearance and a transition
  from the terminal area to the appropriate en route
  structure. SIDs are primarily designed for system enhancement
  and to reduce pilot/controller workload.
  ATC clearance must be received prior to flying a SID.
  All DPs provide the pilot with a way to depart the airport
  and transition to the en route structure safely.
  Pilots operating under 14 CFR Part 91 are strongly
  encouraged to file and fly a DP at night, during marginal
  Visual Meteorological Conditions (VMC) and
  Instrument Meteorological Conditions (IMC), when
  one is available. The following paragraphs will provide
  an overview of the DP program, why DPs are
  developed, what criteria are used, where to find them,
  how they are to be flown, and finally pilot and ATC
  responsibilities.


There are many details involved in actually using these procedures to make safe departures in IMC. The Instrument Procedures Handbook Chapter 1 is an excellent resource for pilots who want to review these procedures, what they provide and how to use them correctly.

Here is an example of an ODP from my home airport, KCRG. There are some very tall towers less than 10 nautical miles from the airport. They are enormous and easy to avoid under visual conditions, but when IMC prevails these procedures are absolutely life-saving with such large obstructions nearby. They are taken from this takeoff minimums document.



Here is an example of a SID. These are always graphically depicted and will usually be found at larger airports. Here are pages 1 and 2 of the full SID.