Files

This lab description is available as a PDF file here. The code distribution may be downloaded (in zip format) here, or by running athrun 6.01 getFiles from an Athena machine or a 6.01 lab laptop.

1) Getting Started

Discuss your block diagram and your plots from last week's labs with your partner. If there are any differences, discuss them and decide which of the two models you plan to use for this week's lab¹.

2) Modular Simulation Framework

In last week's labs, you wrote a simulator for arbitrary LTI systems, and you used it to simulate the behavior of our first model of the "wall finder" system.

While this simulation was useful, the process was tedious: it involved solving for the system's difference equation by hand, and even when that was done, it required thinking about the end-to-end history in order to set the internal state of the system.

Today, we will introduce a new framework, which will take care of most of this tedium for us! You will use this framework today's lab to simulate your updated wall finder model, and you will implement it as part of this week's homework exercises.

2.1) Testing Your Model

Fill in the definition of the make_wall_finder_model in swLab03.py so that it constructs and returns a representation of your updated wall finder model using this framework.

Check Yourself 1:

Test your updated model by generating a plot of how it predicts the robot will respond when the robot starts out unmoving at 0.8 meters from the wall, its desired distance is 0.5 meters from the wall, and the length of a discrete timestep is 0.1 seconds.

3) Poles

In this section, we will try to predict a good value of the gain k using our model.

Note that the model that results from calling make_wall_finder_model contains a method called poles, which takes no arguments and returns a list of the poles of the system. Use this method (rather than simulation) to predict a good value of k.

Check Yourself 2:

Based on the poles, what value of k would you predict would cause robot to converge most quickly without overshooting? What properties of the poles indicate that the system will behave in this way?

4) Comparison

Finally, we would like to see how well our updated model compares against the behavior of the real robot. We will do this by running the real robot under different conditions, and seeing how our model compares when it is simulated under the same conditions.

Use soar to run wallFinderBrain.py on the real robot. This brain will run the wall finder behavior from design lab 1. When stop is pressed, it will generate a plot.

Start the robot roughly .8 meters away from a bubble-wrapped foam-core board. Run the brain six times with these same inital conditions, and with gain set to -0.5, -1, -2, -5, -10, and the optimum gain you found in the previous section, respectively. Each time, make sure that the trailing wheel of the robot is oriented such that it will not pivot when the robot starts moving forward. Save the plots generated by soar, as they may be useful when preparing for exams.

Checkoff 1:
Discuss the results of your experiments with a staff member. How did this updated model compare against your old model? How does it compare against the real robot? Does your answer depend on the value of k? If there are differences between your robot's behavior and that of the real robot, what accounts for them?

5) System Classes

5.1) Gain

5.2) R (Delay)

5.3) Cascade

5.4) FeedforwardAdd

5.5) FeedbackAdd

¹There is no real "right" model, but you should try to choose one that closely matches the behavior of the robot. (click to return to text)