I have a case of a differential drive robot and a control system in a two-dimensional environment:

Now the problem: we would like to make our particle move from point A to point B, and from there to point C (a spline-based path), in the most optimal time and constrain our acceleration, deacceleration, velocity, and angular speed.

How would one do this assuming that our control system allows us to control either velocity or acceleration?

The most important things here are names of mathematical methods behind this task and explanation of how to apply them.

  • $\begingroup$ Are you assuming that you already have a valid path from A to B to C? Are you strictly asking about the controller? $\endgroup$
    – koverman47
    Jul 9 '18 at 16:34
  • $\begingroup$ @koverman47 assuming I have continuous polynomial functions describing the path from A to B and from B to C. $\endgroup$ Jul 9 '18 at 18:57

Keywords here are path-paramerization, time-parameterization, etc. Given a geometric path, these path-parameterization algorithms can give you the time-optimal velocity profile such that the robot moves along the path the fastest possible while respecting constraints.

The original paper on this topic is by Bobrow, Dubowsky, and Gibson. This one is, in my opinion, really well written. It explains well the general idea how path-parameterization works.

Nowadays, there are quite a few approaches to solving a time-parameterization problem (convex optimization, numerical integration, reachability analysis, etc.). You may refer to the paper and also references therein for more details on the methods and their corresponding implementation.


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