just my 50 cents contribute for that damn funny plan, how to Plan to Stay Fresh and cool when kids say your informatic toys get them hot and sticky, like in summer when it's just too hot and they are too bored to stay indoor following you, and they prefer other toys: Kids love robots!, so … why don't you go for a tiny robotic application ?
the wicked plan to teach them something should look like the following ideas:
idea1: OdometryPlaying Odometry is "cool game" (yes, you can do it with Arduino1), it's used by some robots, whether they be legged or wheeled, to estimate (not determine) their position relative to a starting location. It solves the question "where Am I (within the map)?". This method is sensitive to errors due to the integration of velocity measurements over time to give position estimates. Rapid and accurate data collection, equipment calibration, and processing are required in most cases for odometry to be used effectively. You just need a good pair of brushless motors and thier optical encoders (encourage efficiency), and you are ready to use all of these data from motion sensors to estimate change in position over time. The hardware is a bit more expensive than what you need for a fly-robot (500 euro at least for a quad rotors, 300 euro for a pair of good motors + encoders + H bridge + a robotic carrier), It comes with less complexity, and it's safer (if a fly robot crashes …. while Odometry-robots just don't fly)
idea1.1: Dead-reckoningIn terms of robotics, Odometry vs dead-reckoning might the the step next: Deduced reckoning is figuring out where you are after starting from a known position, by using your speed, direction and time, and It's effectively integration of velocity, at sea you would know your direction from a compass, speed by any one of various means, and important complications like the wind speed and direction would be estimated.
Dead-reckoning systems are based on estimating position relative to sensors. These sensors can be accelerometers, gyroscopes (say, you can use an IMU), whell encoders (recycling what you have already used for Odometry), infrared sensors, gps, etc. which have to placed on body of robot. So we can calculate displacement or coordinates. Odometry is a sub topic of dead-reckoning and based on wheel displacement calculations, literally it counts the "footsteps" as an estimate of your walking speed. A wheeled vehicle would instead count wheel revolutions, that's equivalent to counting footsteps, … and to tell you the Truth Odometry isn't very accurate on its own as wheel slippage, carpet "springiness" and uneven floors can affect accuracy, even if a separate heading sensor can help with accurate headings at least, though.
Dead-reckoning (requires Arduino2, at least) adds more complexity, more costs, but more accuracy and fun
idea2: Inverse kinematicsPlaying Inverse kinematics is an other cool game, even if the math is definitively more more complex (you need Arduino2, or a faster ARM board with a lot of ram), as it refers to the use of the kinematics equations of a robot to determine the joint parameters that provide a desired position of the end-effector, while the movement of a kinematic chain (robot body) is modeled by the kinematics equations of the chain, as rigid body with degree of freedom. These equations define the configuration of the chain in terms of its joint parameters. Forward kinematics uses the joint parameters to compute the configuration of the chain, and inverse kinematics reverses this calculation to determine the joint parameters that achieves a desired configuration.
It's funny because it involves two cool sub-gools:
path planning, and
motion planning, both of them combined as specification of the movement of a robot so that its end-effector achieves a desired task is known as motion planning. Inverse kinematics transforms the motion plan into joint actuator trajectories for the robot.
about kit, I was thinking about
this, which can add a few kit, which you can buy and use to immediately enjoy the fun, and then replace with your own made
just my 50 cents