[Gerben42]

I have noticed that almost all forcing pass systems make use of relay bidding. Do any of you know forcing pass systems that rely on the principle of natural bidding (possibly after artificial opening bids)?

[bluecalm]

Lambda in first version (from Lukasz Slawinski) was quite natural.
Openers were:
pass = 13+
1D = 0-7
All other bids are 8-12pc
1C = even hand or some 7carders (can't remember exactly)
1H = split suits (SD or HC)
1S = red or black suits
1N = majors or minors (all those bids are in principle 5-4 but could be 4-4 if suits are strong)
2C/D/H/S = natural, 5+ one suited

True there was a relay (always next bid) but replies to it were natural (you show your 5card suit or bid 2NT with 5-5 and clarify your distribution naturally after another relay, 2nd relay is game forcing).
All other bids which aren't relays are made by "guessing principle" you bid either your suit naturally or hoping to guess partner's suit. Partner is guessing what you mean (if you bid his long suit he assumes you bid to his suit, if you bid his short suit partner assumes your suit is natural).
After PASS you can still play lambda but now 13+hands are in 1C.
All you need to make it complete ready to go system is "dynamic 1NT" which you use after 1D opener. It could be any very strong hand. After that you need some follow ups.
If you don't bid 2nd relay but your suit naturally it's f1 and subsequent bidding is natural.

This description is basically enough to play whole system. It's not completely natural as it contains relays but replies to those are natural and system "feels" very natural and easy to play.

[nigel_k]

Typically after a 13+ pass you reach a position that is similar to bidding after a strong club opening, e.g.

Pass-1♣: Any 7-11
Pass-1♦: Any 0-6
Pass-1♥+: Positive response with 12+
Also Pass-1♣-1♦ is game forcing so the 7-11 hand now makes 'positive' responses

Whether the positive responses are relay, precision style, or something else, is up to you.

[Flameous]

It feels quite natural that FP systems use relays because one of the main reasons to use FP is to get that one more important step. Because relay bidding uses room more efficiently (For describing one hand) than natural, it seems sort of waste to use forcing pass and then just use space consuming natural bids. (You get very little compared to playing precision with natural continuations)
Of course if you count fert as a good thing in the system, there's reason to do it

[Free]

If you play 1♣ as 4+♥ and 1♦ as 4+♠, you can use step 1 as "start natural bidding" and step 2 as relay. That way (if your opps behave) opener can show a lot of his hand in 2 calls:
1♣-1♦-1♥ = 5+♥, continue like a normal 1♥ opening
1♣-1♦-1♠ = 4-4M
1♣-1♦-1NT = balanced with 4♥
1♣-1♦-2m = 4♥, 5+m
...

As a bonus, you keep the possibilities of relays intact. If you want to get rid of all relays, you can just play 1♣-1♥ as a weak hand that would pass a 1♥ opening.