Your mouse is going to need sensors to tell it about itself and its environment.
Odometry is about how far and how fast your mouse has travelled. Open loop control is used with stepper motors. DC motors can take advantage of more sophisticated closed-loop control systems.
Wall sensors are used to detect the presence or absence of walls and to verify your position in the maze. They will also be important in ensuring that the mouse maintains an appropriate path without hitting any walls. For wall sensors, it may be more important to have good repeatability that absolute accuracy. The key is to avoid hitting anything. Thus it does not matter as much if you run with a small error as long it does not grow.
It is important to make sure that you place wall sensors well in front of the driving walls, or at least, the centre of rotation of your mouse. The greater this distance, the better your ability to maintain a straight course down the centre of the maze cells.
You will want to sample the sensors constantly while the pose is moving for good positional control. There are some key places/time for sampling. Detecting the existence of walls for mapping might be best done in the middle of a cell while positional sensing may be best done at the end or edge of a cell as there will not be a wall in every cell.
Sensors that look down over the walls may be designed to look for walls in adjacent cells as you pass a post. Done reliably, this could seriously reduce the need to run aound map building.
While you want to sample the sensors frequently, it may not be apropriate to leave them active all the time. Apart from any interference reducing benefit, you may have power contstraints that mean you can only turn on sensors in short bursts.
Forward looking sensors are essential to allow you to detect walls before you run into them. You will need to wirk out forward position sensing and speed so that, while exploring, you dont go so fast that you are unable to stop when a wall is detected. Forward sensors also give you a positive positional reference for calibrating sensors. As you approach a wall, you can creep up to it until a known position is reached. This should represent a multiple of 180mm from the last starting point regardless of what your wheel sensors say.
There may be some advantage to having two sets of forward sensors as they not only provide some redundancy but can be used to detect offset errors.
If you want to be able to run down diagonals you will have to be sure that your sensors are up to it. Side-looking sensors will be less effective when looking at posts at an angle. Top-down sensors need to be able to detect over a much greater range of distances.
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