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I' m looking for a trajectory generator (the algorithm doesn't matter, since I m going to write it using C++ ) that generates a trajectory (a parametric curve in space) defined point by point which is going lately to be feed into my quadrotor drivers.

I'm honest: I don't know where to start.

  1. Reading the following interesting answer. But the problem here is: the trajectory has a PD controller with it. My quadrotor should take just a parametric curve as input.
  2. OMPL: this library seems very powerful and interesting. It let the user to define a planner which many different algorithms. The problem is that it is not well documented, good examples and explanations are missing and till now I could'nt find anything related to quadrotors, which does use that library. There is an example for a quadrotor, which doesn't find my expectations and I cannot figure out, how to implement it in my package. I don't want just copy and paste code that I don't understand.
  3. B-Spline and Bezier Curve...and the whole family of parametric curves. I found very interesting libraries in internet that implement those algorithm directly C++. The problem here is: I can define some points in space, generate a spline that contains them and interpolate points for the PID controller in the quadrotor. The basic idea is like a dog chasing a rabbit. A point is generated from the start point of the spline and regularly sent to the quadrotor. The latter flies behind the point, trying to reach it until a goal point has been reached. What is the problem here?!? In this case I can only generate a curve based on geometric properties and not considering the dynamic and the kinematic of the quadrotor (which I would consider for a future project). The rabbit runs and has a tighter curve radius than the dog, which could result in a strange behavior of the quadrotor.

I'd like same good tips to point to the right direction.

Which kind of trajectory planner are usually developed fr such an application?

Thanks! Regards

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Wilhelm
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  • Shouldn't a good controller free you from dynamics concerns when specifying a trajectory? – Daniel Eberts Dec 25 '14 at 13:36
  • Could you be more specific Daniel? – Wilhelm Dec 25 '14 at 15:28
  • A controller needs anyway a sort of a path or trajectory to follow – Wilhelm Dec 25 '14 at 15:29
  • What I mean: If you already have an acceleration-based controller, you can pretty much go ahead with defining a trajectory with B-splines or whatever you like. Note, however, the difference between a trajectory and a path: the former defines positions and velocities, the latter just positions, without any velocity information. – Daniel Eberts Dec 25 '14 at 16:05
  • I still don't understand what do you mean specifically. I wrote a controller using a backstepping integrator technique link pp.39. I acts on position, velocity. Acceleration is feedforwarded (in my code I put it simply to zero). – Wilhelm Dec 25 '14 at 17:25
  • About the trajectory: I want to be able to generate (given some 3D control points) a spline which connect them. For every interpolation point (between the 3D control points) I need to define position, velocity, aceleration. I put wrongly path in my previous comment – Wilhelm Dec 25 '14 at 17:27
  • Ah, I see. I'm not very well versed in trajectory planning, but perhaps libraries like www.roboticslibrary.org/ or MRPT ( http://www.mrpt.org/ ) provide something helpful. – Daniel Eberts Dec 25 '14 at 17:42
  • @Dave, may I ask you how did you implement the position control in the paper you mentioned? In my code, arcsin() yields undefined number due to the fact that Ux*sin(psi) + Uy*cos(psi) is out of arcsin domain. – CroCo May 22 '15 at 19:44
  • @CroCo Yes: the problem is that in your case - somehow - the variables Ux and Uy are > than 1. Be sure that you use the right equations (3.39 and 3.40) (the multiplication with the term (m/U1) is for this reason very important). If everything is nice then you should check your parameter coefficients ($\alpha_{7}, \alpha_{8}$ and so on....AND the computatioon of U1 must be bone BEFORE any other calculations: Otherwise m/U1 gives...infinity as a result. Keep us informed – Wilhelm May 23 '15 at 07:54
  • @Dave, I have two questions, how did you tune parameter coefficients? Second, which ODE solver did you use? I'm using Euler method because it is a fixed size step. – CroCo May 23 '15 at 18:41
  • Ok: 1- with try&error. I started with some coefficients found in a paper and than I tried with small adjustments; 2- Since I ve programmed in C++, I was not constrained to use an integrator provided by matlab or simulink. In C++ you have to write yours. I personally used the Runge-Kutta 4th Order to integrate from acceleration to position. I suggest to read this link which explains the difference very well – Wilhelm May 23 '15 at 18:49
  • @Dave, thank you again for being patient and informative. Actually I'm using Runge-Kutta in boost library. In your code, is there any constrain on the generated angles? In my code, `DesiredPsi = atan2( Yd - x[2], Xd - x[0] );

    DesiredPhi = asin( Uxsin( DesiredPsi ) - Uycos( DesiredPsi ) );

    DesiredTheta = asin( (Uxcos(DesiredPsi) + Uysin(DesiredPsi)) / cos(DesiredPhi) );` with no constrains.

     – CroCo May 23 '15 at 20:24
  • Also, are there any constrains on the range of asin in your code? Or you simply chose the parameters in such a way that the value that is passed to asin in the proper range of asin. – CroCo May 23 '15 at 20:29
  • For attitude control, backstepping is working with me. – CroCo May 23 '15 at 21:49
  • Yes, I did a saturation function. The resulting angle may not be > than 89 deg. BUT the problem in your code is the way you are calculating Ux and Uy. – Wilhelm May 24 '15 at 05:00
  • Here a piece of my code with the backstepping integrator: link The terms $Kx_, Ky_$ are for aerodynamics effects so you can put them = 0 – Wilhelm May 24 '15 at 05:09
  • @Dave, thank you so much. It is now working. great. It seems the problem with parameters' values. This causes $U_{x}, U_{y}$ to be high. Can you share a saturation function how did you implemented? Thank you again for being informative and helpful. I really appreciate your kindness – CroCo May 24 '15 at 15:53

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