Arduino /cmd_vel and /odom with Pololu motors w/ encoder

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Sorry, have to recommend rosserial. I recommend we focus on the problem you have with it. I use a variant of your motor in a 4wd wild thumper, so short answer: Yes it is possible.

I'm not yet sure where exactly your problem is, seems to me that there are multiple, we should identify these and solve each in its own question. You should start with sending cmd_vel to your arduino, send raw pwm values first instead of m/s, e.g.

rostopic pub -1 cmd_vel geometry_msgs/Twist '[255, 0, 0]' '[0, 0, 0.0]'

for max speed forward. Write this value in the OCR register of your arduino.

To give a short answer for reading the encoders: They use gray code, so use something like this code to decode it:

  static int8_t last;
  int8_t new, diff;
  unsigned char status = (PINA >> 4) & 0x3;

  new = 0;
  if(status & 0x1)
        new = 3;
  if(status & 0x2)
        new ^= 1;          // convert gray to binary
  diff = last - new;        // difference last - new
  if( diff & 1 ){        // bit 0 = value (1)
        last = new;          // store new as next last
        enc_delta += (diff & 2) - 1;    // bit 1 = direction (+/-)
  }