I think I don't have enough English vocabulary to express this nuance. So please let me try to explain this visually.
「~てきた」
First of all, 「~てきた」 expresses something in the past.
If the speaker at present says 「~てきた」, s/he is talking about something which started sometime in the past and continued until now. Like the sentence,
「([今]{いま}まで)[私]{わたし}はまっすぐな[人生]{じんせい}を[歩]{あゆ}んできた」
I said "until now", however, actually, it can be "until sometime in the past".
For example, the sentence can be modified like this.
「[高校]{こうこう}を[卒業]{そつぎょう}するまで、[私]{わたし}はまっすぐな[人生]{じんせい}を[歩]{あゆ}んできた」
The speaker's point of view can be positioned anywhere in the timeline.
If the point of view is sometime in the future, the present tense of 「~てきた」, which is 「~てくる」, is appropriate to use.
For example,
「うちの[家系]{かけい}は、[母方]{ははかた}の[祖父]{そふ}も、[父方]{ちちかた}の[祖父]{そふ}も、[ハゲ]{はげ}ている。もちろん[父]{ちち}もだ。[早]{はや}ければ[数年]{すうねん}[以内]{いない}に、[私]{わたし}もハゲてくると[思]{おも}う」
「~ていった」
「~ていく」 means something which starts now or after now and will have been going for a period of time.
「~ていく」 is about the future. 「~ていった」 is the past tense of 「~ていく」. So, 「~ていった」 is also about a kind of future, but, the start point is sometime in the past.
Please don't forget that the speaker is still at present. But the point of view in her/his mind is in the distant past, and s/he talks about the future from the point of view.
Here is an example of 「~ていった」 then 「~てきた」 and 「~ていく」.
「[高校]{こうこう}[卒業]{そつぎょう}[後]{ご}も、[私]{わたし}は[サッカー]{さっかー}[一筋]{ひとすじ}のまっすぐな[人生]{じんせい}を[歩]{あゆ}んでいった。だが、あの[事故]{じこ}により、すべてが[一変]{いっぺん}してしまう。[動]{うご}かなくなった[右脚]{みぎあし}を[前]{まえ}に、私は[絶望]{ぜつぼう}に[飲]{の}まれ、[死]{し}ぬことばかり[考]{かんが}えるようになった。そんなとき、[彼]{かれ}と[出会]{であ}った。いつの[間]{ま}にか私は、死ぬことなど考えなくなった。彼と[一緒]{いっしょ}に[歩]{あゆ}んできた[人生]{じんせい}、そして、これから彼と一緒に歩んでいく人生こそ、[今]{いま}の私には[何]{なに}よりもかけがえのない[宝物]{たからもの}だから。」(written Japanese)
「~ていった」 can be used with 私は or 僕は if the speaker make it clear when it happened or when it started.
If the speaker doesn't mention when, the listener thinks that the speaker is talking about now thing, or before-now thing, or after-now thing. In other words, the listener thinks that the speaker's point of view is "now".
So, if you just say 「私はまっすぐな人生を歩んでいった」, people might think "your actual point of view is now because you don't specify when, but your sentence's point of view is sometime in the past, so the sentence you made must be wrong."
The solution for this kind of misunderstanding is to give listeners more information about when your point of view is. Here are examples.
「[彼]{かれ}と[別]{わか}れた[私]{わたし}はそれから、[夢]{ゆめ}に[向]{む}かって、まっすぐな[人生]{じんせい}を[歩]{あゆ}んでいった」
「[入院]{にゅういん}[中]{ちゅう}に[届]{とど}いた[沢山]{たくさん}のお[手紙]{てがみ}に、[私]{わたし}は[退院]{たいいん}[後]{ご}、ひとつひとつお[返事]{へんじ}を[書]{か}いていった」
「その[日]{ひ}その[映画]{えいが}を[観]{み}ながら、私の[気持]{きも}ちは[次第]{しだい}に[晴]{は}れていった」
There are situations in which, instead of 「〜ていった」, other words might be better to use. In some cases, people tend to use other words which have a clearer meaning, sophisticated impression, or more matching use with context. These are other words examples.
「[高校]{こうこう}[卒業]{そつぎょう}[後]{ご}も、[私]{わたし}は[サッカー]{さっかー}[一筋]{ひとすじ}のまっすぐな[人生]{じんせい}を[歩]{あゆ}み[続]{つづ}けた」
「高校卒業後、私は[新]{あたら}しい人生を歩み[始]{はじ}めた」
Please note that what I'm explaining here is 「~てきた」 and 「~ていった」 which mean time transition (from a time to another). When people use 「~てきた」 or 「~ていった」 to describe transfer from one place to another, the usage and function of these words might be a little different.
「~てきた」+
Just one more thing. I said that 「~てきた」 is about the past. However, if 「~てきた」 is used with a verb which means condition or state of something (like weather condition, health, etc), the nuance becomes a little different.
「[雨]{あめ}が[降]{ふ}ってきた」
「お[腹]{なか}が[痛]{いた}くなってきた」
are like this.
The rain started sometime in the recent past, and now the speaker noticed it and says 「雨が降ってきた」. 「~てきた」 is used to express changing condition.
「[雨]{あめ}がやんできた」
「[腹痛]{ふくつう}が[治]{おさ}まってきた」
In this case, the speaker also notices and says that the condition is changing now. The rain or pain is likely to stop in the near future. This type 「~てきた」 doesn't mean the completion of something. So "now", it's still raining a little, or the speaker still has a little pain.
By the way, this↓ kind of thing happens sometimes.
It's okay. Nobody knows the future actually. The speaker doesn't have to be sure about the future when using 「~てきた」. The point is what the speaker finds right now or found before now.
人生を歩んできた
22110,人生を歩んで来た
1689,人生を歩んでいった
160,人生を歩んで行った
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