Robot Dynamics

By dynamics, I mean things like, how fast can you make it go. How much acceleration is enough and how fast can you negotiate bends.

Tempting though it might be to think that speed is of the essence, there is no point tearing up the coutryside if you don’t know where you are going, or you get lost or you end up in a ditch. As you cannot win without getting to the maze centre, solve all those problems first then work on doing it quickly. Having said that, it might be as well to ensure that your design is capable of adequate performance when (if) you have solve the more critical task of just getting there.

There are many factors to consider in relation to the dynamic performance of your micromouse.

Friction, particularly between wheel and maze, is pretty critical to your ability to accelerate, brake and turn reliably. the maze surface will probably be something like plywood or particle board, painted black. In spite of the existence or rules, you cannot depend upon the surface to be smooth, clean or particularly grippy for your tyres. You can’t even depend on it to be the same everywhere. Apart from the inevitable accumulation of dust, the UK maze used at Technogames has been ‘refinished’ in one corner and has quite a different surface.

The coefficient of friction, µ, is a number, usually between 0 and 1, which describes how much resistance there is between two surfaces. Static friction is the force that stops stuff from sliding. Kinetic friction is the force that opposes sliding once it has started. Kinetic friction is always less than static friction. Thus, when you push a box along the floor, it is harder to get it moving than it is to keep it moving. For this reason, once an object starts to slide, it will tend to continue sliding. Sadly, most peoples understanding of this comes exclusively from accidents: rugs slipping on floors, cups sliding on trays and cars sliding on roads. School textbooks generally state that µ is limited to a maximum value of 1. This is clearly not so and much depends upon the surfaces in question. A typical figure for rubber on wood might be about 0.7.

Another important concept is that of inertia or momentum. Bodies tend to resist change. Even in space, with no friction, it takes effort to get things moving and effort to stop them when they are moving. This applies not only to linear motion, it takes effort to start and stop things spinning.

So, the whole of physics is conspiring against you. Your mouse doesn’t want to move, when it gets moving you have to keep at it or it will stop and yet when you want it to stop, it tries to keep going. Imperfections in everything means that the conditions change constantly and nothing seems to go where you pointed it. Turning corners is at least as bad as trying to go in a straight line.

What you need is control, and an understanding of some of the things that are acting to frustrate your will and prevent the mouse from reaching its goal in a timely and elegant fashion.

10 thoughts on “Robot Dynamics

  1. Raj

    I want to calculate the motor torque for the drive wheels. It’s a 4wd robot.  so how can I go about it?

  2. peteh

    Do you mean that you need to calculate how much torque will be needed from the motors?
    Or how much torque the exsting motors have?

  3. Raj

    Hello again.
    My question is why you’ve considered acceleration, a=ug while calculation of torque needed at the wheels? Also shouldn’t the co-efficient of friction should be rolling instead of static ?

  4. Peter Harrison Post author

    It is not clear what coefficient of friction should be used. The point here is simply to give a guide. Assume there is enough friction for whatever acceleration you consider reasonable and calculate the torque based upon that.

  5. Thanh

    Helo, I’m Thanh in vietnamme! How I know locate of micromouse in Maze when it move forward 2 spaces or more? mean is different between 2 spaces on straight-line! I must control pwm motor add count interup for know locate? thanks you very much? Plesea forward email to:

  6. Peter Harrison Post author

    That is exactly right. You must count pulses from the wheel encoders. use the sum of the left and right encoder counts for distance and the difference for angle.

  7. Thanh

    I understood, I have a litle questions need help during make a micromouse, I’am looking forward to help from you. Thanks you so much!

  8. Thanh

    Hi peter, I see micromouse have 4 sensor, 2 front and 2 sensor angle 45 degrees for left and right, I don’t know why disposition 2 sensor angle 45 degrees without disposition sensor left righ on a straight -line?
    (compare picture: with )
    – How I decide micromouse turn left,turn right or move forward, when Micromouse go on Crossroads, I don’t know principles move of micromouse in MAZE, (I used PIC 18F4550), Can you Instructions Me algorithm micromouse?
    Thanks you!

  9. Peter Harrison Post author

    There are many ways to decide which way to go. The simplest it to just turn towards the cell that is closest to the goal.

    For the sensors, you will need at least a pair at an angle (45 degrees is fine) and at least one pointing forwards. More will make some things easier. For now concentrate on the simple things and worry about better performance only when you can get the mouse to the goal.

Leave a Reply