This is the Roborally variant - which may prove less complicated in the end.
Bots don't just move about randomly, they require programs to get them moving unless they are equipped with a remote control - or if the Mad Scientist is seated on the Bot, or in the same hex as the Bot. Each bot requires programming cards. Each turn is divided into 7 phases. A Bot may have one card programmed for each phase in which it moves. All Bots will shoot at any enemy Bot or Mad Scientist that is an applicable target in a phase. No Bot may fire a weapon more than once per turn.
At the start of each turn, each player lays out up to 7 cards. One for each movement point that the Bot has. Once all players have their cards laid out face down, the turn begins and cards are turned over phase by phase. The player's Mad Scientist character moves each phase according to their speed as well - but they aren't programmed.
No Bot may have more cards than their movement points (which are directly related to how many Movement Speed components are in their chassis).
Bots may have less cards than their movement points - especially if crossing more difficult terrain that requires the expenditure of more than one movement point.
Interpreting how programming cards affect a Bot is up to the players involved - but you should always err on the side of intelligence. If Bots have a choice of movement between ways that may injure them, or destroy property the player doesn't want to destroy - the Bot can choose to go another way.
In cases of conflict in movement - lighter Bots always move before heavier Bots.