There are not a lot of arduino robot kits out there which are good for STEM. Here are a few that we like.
One of very few robot arm kits available, the LittleArm is a versatile and affordable robot kit to learn about the arduino. The arm has four microservos which articulate its various joints. The arm comes loaded with the software needed to control it and record actions through a desktop computer. Users may reprogram the arm with their own code created in the Arduino IDE or with programs such as Scratch.
A good kit for experimenting with outdoor robotics, this tank can be outfitted with Bluetooth and any number of sensors, though none are included in the basic kit. Additionally, the kit does not have a breadboard requiring solder to modify or add circuits and sensors. This is a kit that would be ideal for junior-high to high school level students.
Another good mobile Arduno robot kit. The Bombini includes several touch sensors and is simple enough to be quickly assembled by students. But, the Bombini does require the purchase of additional components such as breadboards to be easily modifiable and built upon.
Sainsmart Robot Arm
This kit is really for much more advanced users. While the arm has many degrees of freedom it is relatively under powered and cannot lift compared to its overall size. There is also no software support for the arm. The remote is a great opportunity to learn about interfacing with the Arduino but it can be difficult.
A classic robot kit the BOEBot has been an introductory kit for many roboticists. It is a simple kit and is easily modifiable. The kit includes everything needed to get started including multiple sensors and electronic components, as well as a breadboard to mount them.
Robot Smart Car
A good kit for more advanced students, this mobile robot is large enough to support all kinds of applications, such as carrying items. It is relatively affordable and has the power needed to traverse any kind of floored surface.
The MBOT is a newer arduino-based robot kit. It is a quick and simple kit to assemble and comes with sensors to get started. The one disadvantage is that the MBOT is purely a programmable kit. After assembly there is little to no modification that can be done on the mechanics or electronics. The control board of the robot is also custom so it is not easily hacked or modified, making it difficult to craft new lessons around the robot.