how to make the relationship between velocity and time be linear by python

edit

You have two ways of doing this :

• By calculations :

You have to define the acceleration you want (well in your case this is a deceleration). Taking your example, you want to go from 0.2 m/s to 0.05 m/s in 20 seconds meaning you have dv = -0.15 and dt = 20. (dv = vfinal - vinitial that's why it's negative). Since a = dv/dt you know you want a constant acceleration of -0.0075 m/s² (or a deceleration of 0.0075 m/s²).

Now if you integrate the equation of the acceleration and assume the acceleration is constant you get v = a * t + K (K is another constant from the integration). You know v(t=0)=0.2 so you have v = a * 0 + K = 0.2 => K = 0.2. You also know that a = -0.0075 so that's it you have the linear relationship between velocity and time :

v = -0.0075 * t + 0.2

• Another option is to use a velocity smoother which basically do all those calculations for you. You can set limits for the acceleration and velocity. There is a package compatible with the turtlebot (with the mobile base kobuki to be accurate) : yocs_velocity_smoother. You will need to use a launch file with a nodelet manager and define a yaml file to set your parameters and then call the nodelet. I can give you a launch file example if you want.

Edit :

I tried to solve by the first way, my issue is in how to find (t,t0) in python with rospy because of lacking my experience in ROS

You will need to save the starting time when you start decelerating and then just substract the current time to get the value for t. It can be done like that :

#global variable outside your callback
starting_time = rospy.get_rostime().to_sec()
save_time = True 
...
if(save_time == True):
    save_time = False  #Condition only the first time
    starting_time = rospy.get_rostime().to_sec() #save the current time
now = rospy.get_rostime().to_sec()
t = now - starting_time           
self.twist.linear.x = -0.0075 * t + 0.2
self.cmd_vel_pub.publish(self.twist)

For the second method you can go to the wiki I've linked and select the indigo version, I just saw that there is no documentation for the melodic distribution. Moreover you can see an example by looking at standalone.launch and check the standalone.yaml file too. This package allows you to set speed limits and acceleration limits so with your example you don't have to change your code, just to use the velocity_smoother_nodelet and set the parameter accel_lim_v to 0.0075.

Edit 2:

I need to recount from zero when lost my face

You just need to reset your flag save_time when you don't see the face anymore with an else condition for example :

if(type(faces) == tuple):
    if(save_time == True):
        save_time = False  #Condition only the first time
        starting_time = rospy.get_rostime().to_sec() #save the current time
    now = rospy.get_rostime().to_sec()
    t = now - starting_time           
    self.twist.linear.x ...