Researchers from the Seoul National University Biorobotics Laboratory have developed a lightweight and low-profile crawling phone case robot. The legs retract flat when not in use, keeping the form factor as small as possible. According to IEEE Spectrum:
To move the robot forward, a linkage (attached to a motor through a gearbox) pushes the leg back against the ground, as the knee joint keeps the leg straight. On the return stroke, the joint allows the leg to fold, making it compliant so that it doesn't exert force on the ground. The transmission that sends power from the gearbox to the legs is just 1.5-millimeter thick, but this incredibly thin and lightweight mechanical structure is quite powerful. A non-phone case version of the robot, weighing about 23 g, is able to crawl at 21 centimeters per second while carrying a payload of just over 300 g. That's more than 13 times its body weight.
Okay, so it can't technically choose where to crawl, it can sort of just vibrate itself in a relative forward motion. However, it's not hard to imagine this thing with enough sensors to actually make it functional enough to crawl to a charging pad or, better yet, into your hand. Sure, right now it looks like a disgusting vibrating phone monster, but imagine if that disgusting vibrating phone monster could also think. No matter where you go, you look over your shoulder and there's your phone. Sitting. Waiting. Plotting.
Keep going for video of the case in action.