A Mechanical Model of a Human Arm Making a Shot on Goal in Air Hockey: Error Sensitivity and Goal Equivalence

Open Access
- Author:
- Morgen, Zachary
- Area of Honors:
- Engineering Science
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Joseph Paul Cusumano, Thesis Supervisor
Christian Peco, Thesis Honors Advisor - Keywords:
- mathematical model
goal equivalence
motor variability
brain lateralization - Abstract:
- A big question in the field of neuroscience concerns brain lateralization and the motion controls that each hemisphere of the brain implements. The dynamic dominance model states the left hemisphere (in right handers) is proficient at predictive control, while the right hemisphere is proficient at impedance control [1]. Predictive control schemes output precisely timed and synchronized muscle forces to needed to accomplish a goal-directed task, whereas impedance control schemes adjust the effective stiffness and damping properties of the limbs to reject unexpected disturbances. To investigate this claim, a mechanical model of a human arm taking a shot in air hockey was constructed. The two-link model is impedance-based in that its joint torques are generated by effective stiffness and damping properties modeled using torsional springs and dampers. The equations of motion for the arm mechanism and for the puck after it is struck. The game of air hockey provides an example of a goal-directed task. Simulations of our model were used to study how its accuracy depends on system parameters. This is done by first finding the goal function for the task, which is then used in to determine a goal equivalent manifold (GEM) for the arm as it executes a single shot on goal. The GEM maps system parameters (e.g., stiffnesses and damping coefficients) to error at the goal. The GEM provides a fundamental way to quantify and visualize the sensitivity of the task performance (i.e., error at the target) to changes in system parameters. This geometric characterization of sensitivity allows us to simulate the relation between fluctuations in body-level variability and goal variability at the target position of the air hockey game. This was done by examining fluctuations in impedance elements, and how further deviations in those values result in a larger goal-level error at the target. Specifically, deviations in system parameters that are normal to the tangent plane of the GEM.