system
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human
[Star Wars ROTS] So Palpatine's plan was to get himself captured, hope they sent Anakin to rescue him, get his loyal servant killed, try not to get killed himself either by Grievous or on a out of control ship crashing in to a planet and...... wait what?

As plans go this doesn't sound like one of the best. Risk everything for absolutely nothing, what!!??!!
gpt
I believe that the plan does make sense when you take a few things into account. 

Palpatine can sense the future using the Force, so he is most likely aware of what course his plans will take. 

Palpatine has multiple good outcomes to this course of action. You have to remember that Palpatine is playing both sides of this war, even when the Republic is losing or suffering he is winning. Gaining more emergency power in the Senate, increasing the military capabilities of both the droid army and the Clone Army all come about the more turbulent the war is. 

However by the start of Episode III the war is drawing to a close, the Clones are winning which means that there are already whispers of dissent, talk of Palpatine giving up his emergency power. Palpatine needs to show that the closing hours of the war are the most desperate in order to maintain the momentum he's built up. And what better way to show this than a desperate attack on the Capatil of The Republic and an attempt at his own wellbeing. And the attack is desperate, it results in the loss of nearly an entire Droid fleet including a flagship for an incredibly risky gain. What's more their was luckily a Republic fleet close enough to engage them. This of course puts the Republic in an even better position to win the war than before. Coincidence? No. Timing. Palpatine knows the exact locations of all of the fleets and troops, since he plays both sides of the war. He knows that the attack is doomed when he tells Grievous to do it, and this is also how he forces a confrontation between Dooku and Anakin, he knows that Anakin and Obi will be the closest Jedi when he picks the date for the attack. 
 
Ok, but what if something goes wrong? Well it's still good for Palpatine. 

What if the kidnapping is successful? Well now the Republic goes into an even bigger panic mode and he can still manipulate events. Awesome. 

What if Count Dooku wins the duel? Well Palpatine is in the room, he can use the force to ensure Anakin doesn't die/gets the upper hand. It also means that he can manipulate Anakin more. Awesome. 

TLDR: Palpatine has thought this through, he controls nearly every aspect of the kidnapping and he comes out ahead politically no matter the outcome.