# Create path with minimum curvature for Ackerman drive

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?
• I too would like to know the solution to this problem Oct 25, 2018 at 21:39
• 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. Oct 25, 2018 at 22:02
• 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) Oct 26, 2018 at 23:03
• I found this paper with i think could be be adapted to do this linklink Nov 18, 2018 at 21:01