How do I go about building a charger circuit?
Use 3 Li-Ion cells connected in series - like in the notebooks.
Create the charger, based on one of the specialized charger ICs - for example this, but there are thousands of them, so search the best for yourself.


2.1 If this design is too complex for you, buy some cheap Li-Ion battery charger and use its electronics - for example this one.


Design the charger as a dock station with some very-easy-to-plug-connector and put some fast blinking IR LED on it.
Using the IR LED light as a navigation signal, program your robot to go to the charger by itself, when the battery is critically discharged and to touch the connector.


Charging time for the Li-Ion batteries can be as small as 1h, but if it is too big for you, you can use another trick - instead of waiting for battery to charge, use two replaceable batteries mounted externally to the robot and design the charger to have two connect places. Then learn your robot to leave the discharged battery in the charger and to get the charged one from the second docking place.