This genial animated sci-fi comedy about astronaut chimps is an unpretentious summer pleasure, an entertaining mix of adventure and comedy that even manages to find some heart.

Ham III (voice of “Saturday Night Live’s” Andy Samberg) is a chimpanzee circus performer whose most popular trick is being shot from a cannon. As he rises higher in the sky before crashing down to earth again, he reaches wistfully toward the moon, thinking of his grandfather Ham, who was sent up in a space capsule by NASA back in 1961. Ham’s only family now is his grandfather’s friend Houston (voice of Carlos Alazraqui), who has been looking out for Ham as long as he can remember.

But Ham III does not like rules, authority, or thinking of himself as a hero, so when NASA wants him to go on a space mission, he declines. However, it turns out it was not a request but an order, so he soon finds himself in training with some serious and highly qualified space chimps, Titan (voice of Patrick Warburton), Luna (voice of Cheryl Hines of “Curb Your Enthusiasm”), and Comet (voice of Zach Shada).

The chimps are needed because an American space probe has been sucked into a wormhole and ended up on an alien planet. It is too dangerous to send humans after it, but the Senator in charge (Stanley Tucci) is willing to send the chimps. And so Titan and Luna, whose entire space experience is being part of a historical exhibit about what happened with the first Ham in 1961 are sent up with Ham III, who is added to provide some public relations sizzle. Comet and Houston stay home to provide support. And yes, Houston, we have some problems.

On the alien planet, a bully named Zartog (voice of Jeff Daniels and more silly than scary) is using the space probe to control the sweet-natured, jelly-bean-colored inhabitants and force them to give him a really extreme home makeover. Will the chimps complete their mission and return home with their ship or will they help solve the problem that earth’s technology has created?

Everyone has some lessons to learn as the chimps have to navigate hostile terrain (including the Valley of the Very Bad Things and a monster with a lot of big, sharp teeth), confront Zartog, and do some DYI construction to find their way home. They will prove that they can do more than the humans thought and even more than they knew was possible themselves.

Samberg is an appealing hero and the brisk pacing and lively visuals keep things moving. These astro-chimps have the right stuff.