go to Kashhyyk. I mean, he really didn't do anything there. he just stood there and watched the battle. He could have just sent his troops alone there or else Luminara Unduli, who I understand was on Kashhyyk, could have been the Jedi to go there. Yoda didn't help anyways and then he'd have been on Courscant and he and Mace would have beat the shit outta Palpatine.
Also, what've happened if Grievous would have been killed on the Invisible Hand? Palpatine'd have to excuse to keep his power + Obi-Wan would stay on Courscant. Without his powers Palpatine's plans would be ruined. I doubt he'd stop Obi-Wan and Anakin from killing Grievous, so would it be game over for Sidious then?
I'll bet my buttons Yoda did more than what we see. Either that or it was an excuse to get him off Coruscant.
And if Grievous had died on the Invisible Hand?
Sidious take HUGE risks and gambles. If Grievous died, than I wouldn't put it past Palpatine to conjure up another threat which required the seperation between OB and Anakin. He most likely KNEW that the Council would dismiss Anakin's suggestion that he go take on Grievous, and he probably KNEW that OB would take his place.
Remember, there was always the fact that the Seperatist leaders had to be found, he could use their hiding to prolong the war and figure out another scheme.
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From the novel, Yoda leaves as part of the lame ass Jedi plan to bait out the second Sith.
"It may not be enough," Mace Windu said. "Let us take this one step farther - we should appear shorthanded, and weak, giving Sidious an opening to make a move he thinks will go unobserved. I'm thinking that perhaps we should let the Chancellor's office know that Yoda and I have been forced to take the field-"
[skip a bit]
Yoda: "The Seperatist attack on Kashyyyk, a compelling excuse will make. And good relations with the Wookies I have; destroy the droid armies I can, and still be available to Coruscant, should Sidious take the bait"
None of those choices is why he went there. He went there because thats what Jedi did in the clone wars. They were generals of the clone armies. And that battle needed a general, and Yoda felt he was the best candidate. So he went. There's not much else to it.