Placement of IMU

In order to proceed with our work it was needed to find the hidden problems in this system, and for that the easiest approach is to simplify the structure.

After some experimentation we found that because we are using the kalman estimator from the IMU we were getting “false data”.  The kalman estimator has a slow stabilization, and only when it is stable the data it send is reliable.

Because we were applying fast transitions in order to identify the robot we were getting data that was not reliable. By simply changing the location of the IMU we can get the reliable data expected. You can see the comparison between results here.

Another solution is looking at raw data, like gyro data, instead of estimated data.

 

Controller Performance

The controller for the suspended pendulum is finally showing good results.

In the video bellow you can see two robots, they are exactly the same, but the one in front is actuated with a LQR controller, while the one behind does not have any kind of control action.

As you can see the one with a controller stabilizes faster than the one without it. We are still optimizing this controller to be faster, because when the robot is inverted it is needed that the control action is faster than what  currently is, otherwise the robot will fall.

Dead-zone of servos

Linear controllers do not deal well with non linearities like dead-zones of servos, and LQR is not an exception.

Currently we are working in a way to go arround it in order to obtain better results, and avoiding having problems when the controller for keeping it standing is designed.

An explanation of the “tricks” used and the graphical results can be viewed here.

More interesting than theory is actually seeing the effects of the “tricks” in the real robot, therefore we provide you a video with the experiments where the data from the pdf file was taken.

MIMO model assembly

In the previous post, it was shown the results of identification of the SISO models of the suspended robot.

In this post it is shown how to assemble SISO models into MIMO model, and the results obtained for our project.

The results are still for the suspended robot. It is still needed to invert this model in term of dynamics for us to be able to create a controler to make it stand.

You can find a simple and quick explanation of the process here. This works not only for our case but for all assemblies of SISO models into MIMO models. A precaution to have is to ensure that your project can be described by a set of SISO models.

To finish this post i provide a low quality sample of what you can find in the document.

Jacobian SISO Models

In order to make the robot to stand it is needed that we know the dynamics from the knee servos to the IMU and from the hip servos to the IMU. These dynamics are being identified based on transfer functions. Even though looking at the behaviour of the structure it is possible to see that what we want is a small order transfer function, the truth is we are dealing with a real signal. This signal has noise and it even measures vibration caused by the high flexibility of the legs of the robot.

Because of these facts the aproach mentioned in previous posts that suggests identifying with greater order models and then simplifying them is used. In the zip file SISO.zip there are pictures of the models identified (original and simplified), and a .txt file saying the orders of the best models (original ones only).

Just a reminder, identification of the transfer functions is done using ArX where the three parameters na, nb and nk represent the order of the denominator, numerator and number of delays, repectively.

Now we procede in assembling these SISO models into a MIMO model that represents the full robot, and from that MIMO model the controler will be synthesized.

I leave you with an example of what you will find in the zip file.

Frequency Identification

Hello and welcome to the Actuatedcharacter’s blog.

If you have been following us, you know that we are in the process of identifying Jacobian. For that we were using ArX models but the results we were obtaining weren’t that great. It was then suggested for us to try identification in frequency instead of identification in time. The following video shows an experiment to obtain data for frequency identification.

What happens here is that we actuate the knee servos with a sinusoidal signal wich increases the frequency over time, more precisely 0.2 Hz every 10 seconds.

Something unexpected ocurred as we were increasing the frequency. We reached a lateral vibration mode that can clearly be seen on the video.

Meanwhile ArX models are finally showing some decent results and so we went back to them, but it is still an interesting video for those of you who study structural behaviour.

Stay tuned for more updates on the project.