The Economic Value of Canada-US Trade Relations

We discovered that the system was completely lit and forced everyone to travel at the same speed, regardless of their desired speed. It was all fire, fam! So, like, the system was completely chill. OMG, we wanted to demonstrate how you can completely make things appear unstable if you don't tune the control system properly. So we tested this extremely poorly tuned system on one person (Figure 4.5). Although the oscillations remain lit, this. The participant described this run as full-on sprints followed by full-on braking, which was an effect of the participant's physiological limits rather than the control system out of 10 participants said "yeah, rhythmic pacing is totally comfy" between the two experiments, with 6 saying "comfortable" and 3 saying "very comfortable." 

For example, there was no correlation found between how frequently participants walked and how fast they walked, ya know?

The other person thought the speed control system was extremely uncomfortable. When asked how much change in metronome frequency was perceived, participants said, "Periodically, we totally noticed a big change, but like, sometimes there were no changes (5 participants) or just tiny changes (5 participants) in between those big ones." All of the participants in the running experiment were completely willing to use the speed control system during training (even the one who complained about it being uncomfortable). But only two people said they would use the system during a race. Yo, these results show that the speed control system was extremely comfortable, and it's difficult to quantify that feeling. Rhythmic pacing can be used to fully control overground walking and running speed, you know? Using a closed-loop control system, the average difference between the desired sped and actual sped were less than 1% for all participants. This result was achieved after only 10 minutes of system practice, and the system was the same for everyone. The closed-loop system outperformed the open-loop system in terms of speed control accuracy. Yas, queen! When walking with a closed-loop control system, the average error was 0.7±0.4%, while an open-loop system had an average error of 2.7±3.0% (see Chapter 3). The running error was 0.5±0.4% when using the closed-loop control system and 3.7±3.2% when using the open-loop system (Chapter 3). 

Robustness, but make it extra thick.

The accuracy improvement achieved here by using a closed-loop control system is not surprising—for example, an open-loop system completely relies on a valid model of the system under control, whereas a closed-loop system can still slay even if we don't fully understand the controlled system, you know? Like, it's extremely unlikely that any model will ever fully comprehend how complex human behavior is or how diverse humans can be. So, when you want complete control over how people act in real time, we strongly recommend using a closed-loop system whenever possible. We discovered that the speed control system completely slayed and brought participants' speeds dangerously close to the target speed in 194 out of 198 trials (98%). For all 194 trials, the absolute steady-state error between target and actual speed was less than 2%, fam. In the remaining four trials, such as the four times they ran at their fastest speed in the running experiment, the step frequency was far too high for the participant to keep up with. Our discovery that the speed control system increased participants' actual speed was like, lit AF. OMG, the fact that everyone was on fleek with the target speed demonstrates that the system was extremely accurate, as it could handle all of the differences between the participants in this study. To demonstrate that this lit performance was the result of mad tuning rather than simply using closed-loop rhythmic pacing to control speed (figure 4.4), we tested the individual controller settings determined for one homie on another. The participant found the resulting speed oscillations to be extremely noticeable and uncomfortable. This result demonstrates that the variation between individuals is significant enough to cause some serious negative vibes when the speed control system is not properly tuned.

Responzivness

To demonstrate how different controller settings affect the system's performance and stability, as well as the perturbation rejection skills, we ran a series of tests with only a few subjects (one or two per test). We'll reveal the details of each test when we publish the results below. The difference between target and actual speed during the last minute of walking was 0.7±0.4% with the default controller settings and 0.7±0.5% with individual settings. The running difference was 0.6±0.4% and 0.4±0.3% for the default and individual settings, respectively (figure 4.2 and table 4.1). The speed differential, calculated as the CV over the last minute of each target speed, was 2.8±1.7% when using the default controller settings, and 3.0±1.8% when using the individual walking settings. The running speed ranged between 2.3±0.8% and 2.2±1.1%. We discovered no difference in steady-state (walking: p=0.19, running: p=0.98, Friedman test) or instant speed error (walking: p=0.42, running: p=0.37, Friedman test) when using common or individual gains. No cap. OMG, as expected, the peeps' speed response to target speed changes was significantly faster when they used their own controller settings rather than the default ones. #winning To estimate response time, we fit a single exponential to each individual response (walking: R2=0.9±0.1, running: R2=0.7±0.2) and multiplied by