Associate Professor Cleveland State University, United States
Introduction: As engineering problems increasingly address human-technology interaction, models of human behavior become increasingly valuable. While high fidelity models are more likely to accurately mimic human behaviors, models that are quick and easy to implement are also beneficial.
Proportional-integral-derivative (PID) controllers are widely used for their simplicity and robustness. In mechanical systems where position is used as an error signal, the proportional (P) term acts like a spring and the derivative (D) term acts like a damper. Similarly, biomechanics researchers often approximate human muscle behavior as combinations of springs and dampers. It stands to reason that biomimetic forces can be generated with a controller of a similar nature.
Similar previous work has been performed; researchers modeled the internal PID controllers of human balance during swaying motions[1]. Other researchers determined PD gains for muscles in an electrically stimulated planar arm[2]. Neuroscience researchers have shown that humans’ adaptive control of a pointer with a joystick in a wayfinding task resembles PID control[3]. However, a biologically based PID model of human arm force-generating behavior remains to be seen.
The goal of this work is to find gains for P, PI, PD, and PID controllers which simulate the internal controllers of humans holding a mass static as force perturbations are applied. We also test which controller type can be used to best mimic the measured forces generated while humans held a robotic end-effector instrumented with a force/torque sensor. These gains can be used to simulate realistic human static-hold behavior in future work.
Materials and
Methods: A total of 9 able-bodied participants were recruited. Their ages ranged from 20 to 28. Informed written consent was obtained for each caregiver according to the protocols approved by the Institutional Review Board at Cleveland State University (IRB-FY2016-331).
We asked the participants to hold a robotic end-effector static as force perturbations were randomly applied. The end-effector moved to the target locations before the force perturbations were applied, and the target location was also marked with hanging plastic balls as shown in Figure 1. Each trial lasted for 2 seconds, with a constant perturbation force applied for the duration of the trial. We collected the force applied during the trial as well as the coordinates of the end-effector. Each individual participant completed a total of 42 trials.
After collecting the force and position data, we used simulated annealing[4] to solve the optimization described in Figure 2 to best fit an individual's P, PI, PD, or PID gains for a biomimetic controller. We then compared the force outputs of the biomimetic controller to each of the individual’s force measurements by determining the error. We performed a 2 way ANOVA to test the effect of controller type on the accuracy of the subject-specific biomimetic controller and determine if there were significant differences in biomimetic controller fit between subjects.
Results, Conclusions, and Discussions: We present representative results of a biomimetic PD controller’s force output compared to the force applied by the human to hold the robotic end effector steady in Figure 3. The biomimetic controller’s force generally matches the force applied by the human participant. We also present a biomimetic PID controller compared to forces from the same trial in Figure 4. The PID controller force quickly deviates, applying much more force than is required.
When comparing the ability of the controllers to mimic human behavior, the P controller had the lowest error, and PI controller had the highest error, shown in Figure 5. The controller type had a significant impact on biomimetic performance (p < < 0.001) but performance did not differ significantly between participant’s data (p = 0.1038). This means that P and PD controllers more accurately modeled the 9 participants’ behavior across the participants. These results are also supported by a study[5] which found that stiffness had the largest contribution in a human arm impedance model. Both results provide evidence that when tasked with holding an object static, humans control arm muscles in a manner that mimics stiff springs as in a P controller.
In[3], researchers determined that a PI model of control best fit how humans interacted with a cursor to find unknown points on a screen. Coupled with the results of this study, as well as those in[5], it can be inferred that different levels of human behavior are best approximated by different controllers. In order to hold things still, we make our arms into strong springs, but to find unknown locations, we incorporate the knowledge of the total error of our past guesses.
This study provides gains to create a simple controller which simulates a human holding a mass static. It also provides a method for generating and testing participant-specific gains, so a unique person can be quickly simulated using a simple controller.
Acknowledgements (Optional): This work was supported by NSF Grant 1751821.
References: [1] - K. HIDENORI and Y. Jiang, "A PID model of human balance keeping," in IEEE Control Systems Magazine, vol. 26, no. 6, pp. 18-23, Dec. 2006. [2] - K.M. Jagodnik, A.J. van den Bogert, "Optimization and evaluation of a proportional derivative controller for planar arm movement," Journal of Biomechanics, Volume 43, Issue 6, 2010. [3] - H. Ritz, M.R. Nassar, M.J. Frank, A. Shenhav. "A Control Theoretic Model of Adaptive Learning in Dynamic Environments." J. Cogn Neurosci. 2018. [4] - W.L. Goffe, G.D. Ferrier, J. Rogers, "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Volume 60, Issues 1–2, 1994. [5] - P. K. Artemiadis, P. T. Katsiaris, M. V. Liarokapis and K. J. Kyriakopoulos, "Human arm impedance: Characterization and modeling in 3D space," 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, 2010.
