Functions for tank movement (differential steering)

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I'm programming a game, of sorts, where a tank is steered based on the thrust applied to each of its caterpillar-tracks.



I'm in need of two functions:



$R(T_l, T_r, d)$



which will return the angular velocity of the tank, in radians/s, and



$S(T_l, T_r, d)$



which will return the current speed which the tank should be travelling, in units/s, where $T_l$ = the thrust on the left wheel, $T_r$ = the thrust on the right wheel, and $d$ = the distance between the origin (middle) of the tank and any of the wheels.



As a diagram, it would look like this:
Tank
Notice that there are a few parts of the diagram which I haven't already mentioned ($[a,b]$, and $s$), which I will explain soon.



I have thought of a few pieces of a possible solution, however I'm not sure how effectively this will work:



  1. Let the vector $mathbf l mathrm = [-d, T_l]$, and $mathbf r mathrm = [d, T_r]$, so that they are the tips of the visual representations of the thrusts (in the diagram, the tips of the arrows $T_l$ and $T_r$).

  2. The angular velocity is the angle between the perpendicular of $overrightarrowlr$
    and the origin of the tank.

  3. The speed is the distance between the midpoint of $overrightarrowlr$ and the origin of the tank.

Is this correct? If so, how would I calculate the values? If not, what would be the correct way?




vectors simulation




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    up vote
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    down vote

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    I'm programming a game, of sorts, where a tank is steered based on the thrust applied to each of its caterpillar-tracks.



    I'm in need of two functions:



    $R(T_l, T_r, d)$



    which will return the angular velocity of the tank, in radians/s, and



    $S(T_l, T_r, d)$



    which will return the current speed which the tank should be travelling, in units/s, where $T_l$ = the thrust on the left wheel, $T_r$ = the thrust on the right wheel, and $d$ = the distance between the origin (middle) of the tank and any of the wheels.



    As a diagram, it would look like this:
    Tank
    Notice that there are a few parts of the diagram which I haven't already mentioned ($[a,b]$, and $s$), which I will explain soon.



    I have thought of a few pieces of a possible solution, however I'm not sure how effectively this will work:



    1. Let the vector $mathbf l mathrm = [-d, T_l]$, and $mathbf r mathrm = [d, T_r]$, so that they are the tips of the visual representations of the thrusts (in the diagram, the tips of the arrows $T_l$ and $T_r$).

    2. The angular velocity is the angle between the perpendicular of $overrightarrowlr$
      and the origin of the tank.

    3. The speed is the distance between the midpoint of $overrightarrowlr$ and the origin of the tank.

    Is this correct? If so, how would I calculate the values? If not, what would be the correct way?




    vectors simulation




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I'm programming a game, of sorts, where a tank is steered based on the thrust applied to each of its caterpillar-tracks.



      I'm in need of two functions:



      $R(T_l, T_r, d)$



      which will return the angular velocity of the tank, in radians/s, and



      $S(T_l, T_r, d)$



      which will return the current speed which the tank should be travelling, in units/s, where $T_l$ = the thrust on the left wheel, $T_r$ = the thrust on the right wheel, and $d$ = the distance between the origin (middle) of the tank and any of the wheels.



      As a diagram, it would look like this:
      Tank
      Notice that there are a few parts of the diagram which I haven't already mentioned ($[a,b]$, and $s$), which I will explain soon.



      I have thought of a few pieces of a possible solution, however I'm not sure how effectively this will work:



      1. Let the vector $mathbf l mathrm = [-d, T_l]$, and $mathbf r mathrm = [d, T_r]$, so that they are the tips of the visual representations of the thrusts (in the diagram, the tips of the arrows $T_l$ and $T_r$).

      2. The angular velocity is the angle between the perpendicular of $overrightarrowlr$
        and the origin of the tank.

      3. The speed is the distance between the midpoint of $overrightarrowlr$ and the origin of the tank.

      Is this correct? If so, how would I calculate the values? If not, what would be the correct way?




      vectors simulation




      share|cite|improve this question











      I'm programming a game, of sorts, where a tank is steered based on the thrust applied to each of its caterpillar-tracks.



      I'm in need of two functions:



      $R(T_l, T_r, d)$



      which will return the angular velocity of the tank, in radians/s, and



      $S(T_l, T_r, d)$



      which will return the current speed which the tank should be travelling, in units/s, where $T_l$ = the thrust on the left wheel, $T_r$ = the thrust on the right wheel, and $d$ = the distance between the origin (middle) of the tank and any of the wheels.



      As a diagram, it would look like this:
      Tank
      Notice that there are a few parts of the diagram which I haven't already mentioned ($[a,b]$, and $s$), which I will explain soon.



      I have thought of a few pieces of a possible solution, however I'm not sure how effectively this will work:



      1. Let the vector $mathbf l mathrm = [-d, T_l]$, and $mathbf r mathrm = [d, T_r]$, so that they are the tips of the visual representations of the thrusts (in the diagram, the tips of the arrows $T_l$ and $T_r$).

      2. The angular velocity is the angle between the perpendicular of $overrightarrowlr$
        and the origin of the tank.

      3. The speed is the distance between the midpoint of $overrightarrowlr$ and the origin of the tank.

      Is this correct? If so, how would I calculate the values? If not, what would be the correct way?





      vectors simulation





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      share|cite|improve this question




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      asked Jul 14 at 17:03









      Jacob Garby

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