Brian Corteil is a two-times winner at Pi Wars. At the Cambridge Raspberry Jam on 17th September 2016, he gave an excellent talk about building a Pi Wars-winning robot. You can see a recording of that talk below:
At the Pi Wars Conference in October 2019, he followed this talk by another called “How NOT to Build a Pi Wars Robot”
The Raspberry Pi Guy’s robotics series
Here is Matthew Timmons-Brown’s series on getting started with robotics and tackling some of the fundamental challenges you will face in competitions such as Pi Wars. They’re a little old, now, and he bases his series around the defunct 4Tronix Pi2Go Lite, but the techniques are still valid!