2
$\begingroup$

I'm trying to create a trajectory between two given poses for an Ackerman drive. The poses are defined as follows:

  • Current Pose

    • position $(x_0, y_0)$
    • rotation on z-axis $\theta_0$
  • Final Pose

    • position $(x_f, y_f)$
    • rotation on z-axis $\theta_f$

The trajectory has to be 2 times differentiable with minimum curvature and needs a smooth transition to it's predecessor trajectory (the steering change between two trajectories can't be instant).

I always stumble upon parts of the solution but am struggling to put everything together. Some people suggest using bezier curves or cubic polynomials but I couldn't find a concrete example (something like: given current pose $[(0,0),0]$ and final pose $[(1,1),\frac{\pi}{2}]$ you can calculate the trajectory like this ...).

So my questions are:

  1. Is that paper actually solving my problem?
  2. Are there any useful tutorials/implementations/examples out there that are a bit more explanatory?
$\endgroup$
  • $\begingroup$ I too would like to know the solution to this problem $\endgroup$ – Robert Sutton Oct 25 '18 at 21:39
  • $\begingroup$ The paper seems to set out a solution, but it is beyond my math skill set to implement it as code. It also points to some unsolved problems around singularities, that is where there are multiple solutions. $\endgroup$ – Robert Sutton Oct 25 '18 at 22:02
  • $\begingroup$ I found another approach to this problem. Matlab seems to have the exact functionality i asked for. (Still figuring out how to implement this on my own) $\endgroup$ – RobinW Oct 26 '18 at 23:03
  • $\begingroup$ I found this paper with i think could be be adapted to do this linklink $\endgroup$ – Robert Sutton Nov 18 '18 at 21:01

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.