# 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 – Robert Sutton Oct 25 '18 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. – Robert Sutton Oct 25 '18 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) – RobinW Oct 26 '18 at 23:03
• I found this paper with i think could be be adapted to do this linklink – Robert Sutton Nov 18 '18 at 21:01