Head direction flexibility about ratinabox HOT 1 CLOSED

To clarify for @mehulrastogi:

• Head direction should be a variable called Agent.head_direction.

• It should be saved to the history dictionary each timestep, just like Ag.pos and Ag.velocity

• Inside the Agent params dictionary there should be a new param called head_direction_smoothing_timescale : float (in the equation below this is $\tau$). This defaults to $0.0$.

• Update the doc string to clarify what this param does

• Within Agent.update() there should be a call to a function called self.update_head_direction(dt)

• The update rule should be as follows (where $\hat{v}$ is the normalised velocity vector):
  $$hd = (1 - \frac{dt}{\tau}) \cdot hd + \frac{dt}{\tau} \hat{v}$$
  then normalise it
  $$hd = \frac{hd}{|hd|}$$
  Note: you'll need a catch for if $\tau==0$ when the update should just be $hd = \hat{v}$ or else you'll get divide by zero error. Even better would be an additional warning if $\tau$ is non-zero but smaller than $dt$ as this is when the equation breaks down. This warning should strongly advise then to increase $\tau$ or decrease $dt$ to avoid numerical problems but otherwise probably let them go ahead.

• This change should then reflected in the following Neurons classes which use head direction:

• ObjectVectorCells
• BoundaryVectorCells
• HeadDirectionCells

• It would be nice to keep support for 1D too even though here head direction is trivial, just a 1D array either [1.0] (forward) or [-1.0] (backwards).

Thanks! Let me know if you run into any troubles

from ratinabox.