# Trajectory tolerance limits

I have a trajectory planner, which calculates the trajectory assuming that the robot is following the planned trajectory. From sensors I get the position of the robot, which has an offset from the planned trajectory. I would like to define some limits, and when the "error" is over these limits I would like to send a reset signal to the trajectory planner in order to replan from the actual position of the robot.

Measurements that I can use:

• Position (x, y)
• Orientation ( $$\theta$$)
• Velocity longitudinal (v)
• Acceleration longitudinal (a)

The robot is a car-like robot, so my thought goes like this:

1. Vertical distance $$\Delta y$$, has the highest priority, in order not to bump on obstacles.
2. Distance from the point on trajectory $$\sqrt{\delta x + \delta y}$$
3. $$\Delta \theta$$
4. Velocity and acceleration are not so important.

First of all I would like to know if I am in the correct way about this assumptions, and if there is some literature that I could read on this topic.

Second how can I determine the limits for this errors? I was thinking for y taking the half of the robots' width.