Accuracy of cmd_vel message

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I have tried the following short program to control a Turtlebot 2 in both Gazebo and on a real Turtlebot 2.
The final position of the robot in both cases is far from that which I had expected. I apply a 1 rad/sec rotation for 3.14 seconds. I would expect very close to 1/2 a turn (pi radians) each cycle. But the result is about 20% farther. So in 5 cycles, I get about 3 full rotations. This is consistent with both the Gazebo simulation and with my physical Turtlebot.

So the question is: am I mis-understanding something? Or is this simply a case where relying on twist messages for a certain amount of time is just very inaccurate?

Regards, Madeleine.

int main(int argc, char** argv)
{
  ROS_INFO("Initializing");
  ros::init(argc, argv, "simple_nav");

  const double rotVelocity = 1.0;         //radians / sec
  const double finalRotation = PI;

  ros::NodeHandle node;
  ros::Publisher cmdVelPub = node.advertise<geometry_msgs::Twist>("/mobile_base/commands/velocity", 1);
  ros::Rate loopRate(0.1);

  //Set up the message
  geometry_msgs::Twist msg;
  msg.angular.z = rotVelocity;

  while(ros::ok())
  {
    double t0 = ros::Time::now().toSec();
    double t1 = ros::Time::now().toSec();
    double currentRot = 0.0;
    while((t1-t0) <= PI) {
      cmdVelPub.publish(msg);
      t1 = ros::Time::now().toSec();
      currentRot = rotVelocity * (t1-t0);
      std::cout << "Current rotation: " << currentRot << std::endl;
    }

    loopRate.sleep();
  }

  return 0;
}