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?
  • $\begingroup$ I too would like to know the solution to this problem $\endgroup$ Commented Oct 25, 2018 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. $\endgroup$ Commented Oct 25, 2018 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
    Commented Oct 26, 2018 at 23:03
  • $\begingroup$ I found this paper with i think could be be adapted to do this linklink $\endgroup$ Commented Nov 18, 2018 at 21:01


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