I have defined a quadcopter that I control with a PID controller. The dynamics that define it are such.

$$T=mg+m\ddot{z}$$

$$\theta=\frac{\ddot{x}}{-9.82}$$

$$\phi=\frac{\ddot{y}}{9.82}$$

As you can see I always need acceleration to actuate so I have defined a trajectory that allows via points that I took from a robot manipulator book and applied it to the quadcopter. The trajectories give me a position for PID and an acceleration for dynamics actuating. However, those trajectories (cubic polynomials) do not look good in the 3d world as you can see on the figure. So what trajectory should I use on a quadcopter?

On the figure, I tried to make a reference trajectory to look like a circle but the blends "ruins" it. There are 10 via points here.

• The attached figure is the reference trajectory or the trajectory the quadcopter makers trying to follow the reference using your PID controllers? Dec 4, 2021 at 11:06
• This figure is the reference trajectory and not the PID real-world drone. Sorry for not clarifying. Dec 4, 2021 at 11:12
• Could you also clarify with what you mean by cubic polynomial? Do you mean a cubic spline? Dec 4, 2021 at 11:22
• They are not important as they do not work anyway. But they are the "Cubic polynomials for a path with via points. An example is here: philadelphia.edu.jo/academics/inaimi/uploads/… from slides 11 to 12. I am not trying to fix this one. I am trying to find a better one. Dec 4, 2021 at 11:40