Animation theory (natural animations)

I want, for example: to animate how a bird is flying through the sky, i am not talking about the animation of the wings, but how to animate an object random over a canvas.

I use to animate those kind of objects with a lot of randomisation, for example: move [object] from a to b (random distance, random speed, random x, random y, etc.).

But is that really the best way to do it? or is there any algorithm theory available on how to achieve the most natural behaviour.

The animation can be a bird, but it could also be dust, or flying sand)

(I hope my question is clear enough)