Is it possible for Imams to exercise control over planets or natural forces through Allah's will without requiring His permission in every instance?
Anything that occurs depends on the permission of Allah.
As for whether the Imams can exert control over the natural world, through the permission of Allah, within Shi'ism, there are varying views. Some scholars hold that they have the capability to affect the natural world in any way. Others say they have this ability in special cases where a supranatural act (karamat) is called for. Still others reject this idea as heterodox (ghuluww).
I personally hold the first view.