Can I include an ode45 in a for loop

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Mohamed Amine BELYAMANI 2020-7-17

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https://ww2.mathworks.cn/matlabcentral/answers/566817-can-i-include-an-ode45-in-a-for-loop

编辑： Mohamed Belyamani 2020-7-27

I'm working on an LQR controller for an autonomous drone and I'm having problems with the ode45 solver. My code goes like this:

T = 20;
dt = 0.1;
X0 = zeros(12,1);
for i=0:dt:T
   timeRange = i:dt:i+dt;
   P = TrajectoryRef(X0);
   U = Command_lqr(X0,P);
   X = EquationSolver(U,X0,timeRange);
   %since ode45 has an independent timestep i register the last value and sign it as the next input
 X0 = X(size(X,1),:);
end

But i keep getting wrong values in the result.

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Walter Roberson 2020-7-20

Please describe your current strategy, since we as outside observerse do not know what TrajectoryRef or Command_lqr do. At the moment it kind of looks to me as if you have steps in the wrong order. What is it that the output of the EquationSolver tells you?

I have not done any drone control work... I would kind of expect the outline to go like

taking into account current position and velocities, pick a general target. This should probably involve path planning to avoid obstacles
taking into account current position and velocities, pick a short-term target that you would hope to get to in one time-step. If your sensors and algorithms were really good this could include obstacle avoidance, but you need a lot more experience if you hope to be able to just barely miss a corner knowing that the wind pattern might be different on the other part. The first stage general target would generally try to stay out of "mistakes were made" range of obstacles.
using the current position and velocities as some of the initial conditions, run an inverse kinematics or Boundary Value Problem to figure out what power to apply to which motors to achieve the short term destination
apply the predicted needed powers
get information back about where you ended up after the time step, including updated positions and velocities
loop back

You seem to be doing a forward ODE rather than a BVP, and it is not clear to me why you are doing that.

Also, I think the ODE should always be run in time 0 to dt, not from elapsed time until now. You are doing corrections as you go, so at any timestep it was never the case that you ran a consistent set of original inputs that would have led you from the origin to where you are now if you had just run the ODE that long. You are now where you are now, and you want to make predictions about times relative to now.

It is possible that my general outline is not practical in the form stated, due to the time required to solve the ode, during which you have to keep flying. Ideally after giving the command you would keep computing unstead of just waiting doing nothing until the device reported back.

Because of the potential cost of running a BVP, I could imagine that it might be necessary in practice to use an approximation ODE that is easier / faster to solve but which perhaps does not take into account all terms, relying on the fact that the reports back about where you really got to imply you have to make corrections anyhow. The implication might be that in still air your simplified ODE might not reflect the most efficient way to fly, but that in changing wind conditions the model errors might be less than the errors imposed by outside force.

Walter Roberson 2020-7-20

Hmmm... I do not know enough about how that class of drones are controlled. I presume that some of the controls have to do with angles of surfaces, and that other controls have to do with velocities of motors. But I do not know, for example, anything about slew rates, about how quickly controls can be changed, about whether it is necessary to keep track of current acceleration of a control because potentially the rate of change of acceleration might be limited. And I do not know anything about issues such as difficulty in getting a motor started again... I know that in some cases (at least for much larger devices) there are cases when starting a motor is hard enough that it can make sense to have a forward motor and a reverse motor both, with one running at idling speed and not enough to overcome the full power of the other motor, so that neither motor ever needs to stop... https://www.motioncontrolonline.org/content-detail.cfm/Motion-Control-News/Understanding-Backlash-and-Stiction/content_id/310

I have never worked with drones, so I do not know which of these things need to be taken into consideration in practice.

Mohamed Belyamani 2020-7-27

编辑：Mohamed Belyamani 2020-7-27

I'm looking into it as well, for now the ode solver is capable of achieving the takeoff of the drone without any problems, but the real issue lies in controlling the pitch and roll, so i'm looking into implementing BVP or InverseKinematic to see if there is any change.

About the path planning, since i'm working with ultrasonic sensors for now, is it possible to simulate or implement the sensors in a way that would detect obstacles along the way. I've started working with Simscape since I modeled my drone in SolidWorks and I saw fit to actually have the command as PWM. I know that the best solution is working with Gazebo using ROS but I couldn't get to install the software since it is kinda difficult (for me) to install it on Windows.

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