Linux cannot normally run on a PSP because the Memory Management Unit (MMU) is not present in the hardware. The PSP has the power to run Linux, but not the hardware. That is why uCLinux (modified Linux) is used as an alternative.

Android is a modified form of Linux; therefore the answer is no, it cannot run on a PSP.

But… that does not mean it is not completely impossible. Using uCLinux to run Android runtime is possible, it just requires a large amount of modification.

You may ask yourself… What happened to the Utopia project?

Source: http://wololo.net/talk/viewtopic.php?f=20&t=9676

Android wrote: Why can’t we install Android on PSPs?

 
Linux kernel requires a specific piece of hardware called “memory manager”, which is not present on PSP. It does exist on MIPS processors (the one PSP uses) but Sony removed it on their custom MIPS (Allegrex) used on PSP. It has nothing to do with PSP’s power (which is way powerful enough). Linux can run on 486 PCs, which are way less powerful than PSP.

Android wrote: Why are the Utopia devs creating a new OS? can’t they just find a way to make an Android or mini Linux OS compatible with PSP’s hardware?

 
Because they want to. Anyway Utopia is an abandoned project. Anyway, there’s a heavily modified Linux that runs on PSP: uCLinux. But don’t expect to run a PC-like distro with this…

Android wrote: Why is Linux installable on PS3 but not PSP?

 
PS3 does have a MMU (Memory Manager Unit).