Establishing metrics and control laws for the learning process: ball and beam balancing

Abstract

Understanding how dexterity improves with practice is a fundamental challenge of motor control and neurorehabilitation. Here we investigate a ball and beam implementation of a dexterity puzzle in which subjects stabilize a ball at the mid-point of a beam by manipulating the angular position of the beam. Stabilizability analysis of different biomechanical models for the ball and beam task with time-delayed proportional-derivative feedback identified the angular position of the beam as the manipulated variable. Consequently, we monitored the changes in the dynamics with learning by measuring changes in the control parameters. Two types of stable motion are possible: node type (nonoscillatory) and spiral type (oscillatory). Both types of motion are observed experimentally and correspond to well-defined regions in the parameter space of the control gains. With practice the control gains for each subject move close to or on the portion of the boundary which separates the node-type and spiral-type solutions and which is associated with the rightmost characteristic exponent of smallest real part. These observations suggest that with learning the control gains for ball and beam balancing change in such a way that minimizes overshoot and the settling time. This study provides an example of how mathematical analysis together with careful experimental observations can shed light onto the early stages of skill acquisition. Since the difficulty of this task depends on the length of the beam, ball and beam balancing tasks may be useful for the rehabilitation of children with dyspraxia and those recovering from a stroke. Keywords Human balancing • Reaction time • Visual feedback • Motor control • Learning Communicated by Benjamin Lindner.

Response to Perturbation During Quiet Standing Matches Delayed State Feedback With Precisely Tuned Control Gains

“…No significant changes were observed on the parameters over the trials implying that the identified feedback mechanism has been already learned and practiced before during the activities of daily living. The effect of learning process is more pronounced when a new and unknown task is to be performed, e.g, ball-and-beam balancing 45 , balancing on balance board 54 , beam walking 55 or combined quiet standing and stick balancing 28 . A question arises whether practice or other techniques can be developed to further improve the performance against sudden perturbations.…”

“…Lighter shaded region to the right of the dashed line is associated with Im(λ 1 ) > 0 and the corresponding solution component reads B 1 e λ 1 t +B 1 eλ 1 t , which is oscillatory with angular frequency Im(λ 1 ) (hereλ 1 andB 1 are the complex conjugate of λ 1 and B 1 , respectively). The black-green dashed line is called node-spiral separation line since it separates node type and spiral type solutions 45 . Note that the point (p * , d * ) corresponding to the fastest response lies on the node-spiral separation line.…”

“…We pose three hypotheses related to the location of the fitted control gains. We base our hypotheses on three observations: 1) PD controllers with gains located in the lower left quadrant of the stability diagram are most robust to the effects of random perturbations 43 ; 2) expert pole balancers increase maneuverability while minimizing energetic costs for balance control by adapting gains in the lower left quadrant of the stability diagram 44 ; and 3) the control gains for subjects who do ball-and-beam balancing are progressively tuned towards the node-spiral separation line as their skill improves 45 . Statistical analysis show that H1 and H3 are accepted and H2 is rejected.…”

Rolling balance board of adjustable geometry as a tool to assess balancing skill and to estimate reaction time delay

“…Since the model of the human body and the operation of the CNS involve many uncertain parameters, it is advantageous to consider tasks associated with low-degree-of-freedom mechanical models with well-defined physical properties. For instance, stick balancing [4,6,11,16], ankle strategy during quiet standing [5,9,15,17,18] and ball and beam balancing [19] are often modelled as a single inverted pendulum system, while ankle-hip strategy during quiet standing [20,21] and standing on a balance board [22][23][24] are modelled as a generalized double inverted pendulum.…”

Parametric Study of Changes in Human Balancing Skill by Repeated Balancing Trials on Rolling Balance Board

“…The behavior of the CNS can be analyzed by performing simple balancing tasks that can be described by lowdegree-of-freedom mechanical models. For example, stick balancing [9][10][11], ankle strategy during quiet standing [12][13][14][15] and ball and beam [16] balancing are often modelled as a single-segment single-joint inverted pendulum, while hip strategy during quiet standing [17][18][19] and standing on a balance board [20][21][22] are modelled as a system of double inverted pendulum.…”