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Passive vs. Active Control of Rhythmic Ball Bouncing:The Role of Visual Information
Isabelle A. SieglerUniv Paris-Sud
Benot G. BardyUniversity of Montpellier I
William H. WarrenBrown University
The simple task of bouncing a ball on a racket offers a model system for studying how human actors exploitthe physics and information of the environment to control their behavior. Previous work shows that peopletake advantage of a passively stable solution for ball bouncing but can also use perceptual information toactively stabilize bouncing. In this article, we investigate (a) active and passive contributions to the control ofbouncing, (b) the visual information in the balls trajectory, and (c) how it modulates the parameters of racketoscillation. We used a virtual ball bouncing apparatus to manipulate the coefficient of restitution andgravitational acceleration g during steady-state bouncing (Experiment 1) and sudden transitions (Experiment2) to dissociate informational variables. The results support a form of mixed control, based on the half-periodof the balls trajectory, in which racket oscillation is actively regulated on every cycle in order to keep thesystem in or near the passively stable region. The mixed control mode may be a general strategy for integratingpassive stability with active stabilization in perceptionaction systems.
Keywords: perception and action, visual control, rhythmic movement, dynamical systems
Adaptive behavior, by definition, requires the spatiotemporalcoordination of ones actions with the surrounding environment.Accounting for the organization of adaptive behavior thus dependson understanding the dynamics of the interaction between agentand environment (Warren, 2006). A critical issue is the degree towhich human actors exploit environmental constraints, includingphysical properties and informational variables, in order to achievestable patterns of behavior in a given task. To the extent that theydo so, responsibility for the organization in behavior cannot simplybe attributed to internal neural structure, but must be distributedacross an embodied agent and its environment (Gibson, 1979).
The task of bouncing a ball on a racket offers a deceptivelysimple model system with which to investigate these behavioraldynamics. Rhythmically hitting a ball to a constant height impli-cates the entire cycle of perception and action: when the racketapplies a force to the ball at impact, this alters the state ofthe environment and generates multisensory information about theballs trajectory, which can reciprocally be used to regulate theracket cycle. The central question is precisely how the actor
exploits the physical and informational constraints of the ballracket system to stabilize rhythmic bouncing.
Schaal, Atkeson, and Sternad (1996) originally showed that ifthe ball is hit at a particular point in a rackets harmonic cycle,bouncing is passively stable, that is, will continue to a constantheight indefinitely despite small perturbations, without active per-ceptual control. The evidence indicates that participants indeedprefer the passively stable regime (Sternad, Duarte, Katsumata, &Schaal, 2001), and thus appear to exploit this physical stabilityproperty. However, recent results also show that participants ac-tively stabilize bouncing under some conditions (de Rugy, Wei,Muller, & Sternad, 2003; Morice, Siegler, Bardy, & Warren,2007), implying that they also take advantage of perceptual infor-mation to control the racket oscillation. In the present study we usea virtual bouncing apparatus to investigate three issues: first, thecontributions of active and passive control to the stabilization ofbouncing; second, the visual information that is used for thiscontrol; and third, the parameters of racket oscillation that aremodulated by such information.
Dynamics of Ball Bouncing
The dynamics of bouncing a ball on a racket in one (vertical)dimension was analyzed by Schaal et al. (1996) and Dijkstra,Katsumata, de Rugy, and Sternad (2004). Assuming that racketmotion is harmonic (sinusoidal), the bouncing ball map predictsthe state variables of racket phase r at impact and ball launchvelocity vb after impact, for given parameter values of the gravi-tational constant g, coefficient of restitution , racket period Tr,and racket amplitude Ar. The coefficient of restitution representsthe elasticity of the ball-racket system (i.e. the bounciness of the
Isabelle A. Siegler, Univ Paris-Sud; Benot G. Bardy, University ofMontpellier I; and William H. Warren, Brown University.
This research was supported by the National Science Foundation GrantBCS-0450218 and by the ENACTIVE European Commission network ofexcellence IST #002114. The authors would like to thank Bruno Manteland Antoine Morice for their assistance with the research, and DagmarSternad for helpful discussions.
Correspondence regarding this article should be addressed to IsabelleSiegler, Univ Paris-Sud, Laboratoire Controle Moteur et Perception,UPRES EA 4042, Orsay, F- 91405 Cedex. E-mail: email@example.com
Journal of Experimental Psychology: 2010 American Psychological AssociationHuman Perception and Performance2010, Vol. 36, No. 3, 729750
0096-1523/10/$12.00 DOI: 10.1037/a0016462
ball with a constant racket). Analysis of the bouncing ball mapdemonstrated the existence of a passive stability regime: If impactoccurs during the last quarter of the racket cycle, when the racketsupward motion has a positive velocity but is decelerating, thenfollowing small perturbations of the ball or racket the system willrelax back to a stable period-1 attractor, with constant values of vbr, and bounce height. The bouncing ball system is thus self-stabilizing, such that small errors will die away without activeerror correction.
Specifically, the ball-racket system is passively stable if racketacceleration at impact (ar) remains in the negative range
1 2 ar 0. (1)
For example, with 0.5 and g 9.8 m/s2, racket accelerationmust be between 10.9 and 0 m/s2 for passive stability, andanalysis revealed a narrower region of maximal stability between5 and 2 m/s2. Intuitively, self-stabilization occurs because anupward perturbation of the ball will delay impact with the decel-erating racket, so the racket will have a lower impact velocity andhit the ball to a lower height, yielding an earlier impact in the nextcycle. Over multiple cycles, this compensates for the upwardperturbation; and vice versa for a downward perturbation. Thus,exploiting passive stability obviates the need for active errorcorrection of small perturbations.
Passive or Active Stabilization?
However, the existence of a passively stable regime does notrule out a contribution of active perceptual control. Perceptualinformation may be used to identify the passive regime duringlearning, to initialize the system in the passive region at the onsetof bouncing, or to maintain ongoing bouncing. The first aim of thepresent study was to determine the mode of control used tomaintain bouncing, specifically how it combines active and pas-sive stabilization.
At one extreme is (a) the pure passive control hypothesis, whichargues that bouncing is maintained through passive stabilizationalone in an open-loop fashion, without relying on perceptualinformation. At the other extreme is (b) the pure active controlhypothesis, that perceptual information is used to actively stabilizebouncing on every cycle in a closed-loop fashion, without regardto passive stability. One example is the mirror algorithm inwhich racket velocity symmetrically mirrors ball velocity, yieldingbouncing outside the passively stable range, with positive impactaccelerations (Buhler, Koditschek, & Kindlmann, 1994). An inter-mediate hypothesis is what we will call (c) hybrid control, inwhich small perturbations are passively stabilized while largeperturbations outside the passive range are actively stabilized. Thisimplies a threshold at the stability boundary where perceptualcontrol is initiated, based on the magnitude of the perturbation.Finally, (d) the mixed control hypothesis proposes that activestabilization exploits the passive physics of the task. On this view,bouncing is perceptually controlled on each cycle in order to keepthe system in or near the passively stable region, thereby reducingthe magnitude of racket adjustment and increasing stability.
Initial reports confirmed that experienced participants tend tobounce in the passively stable region, with negative impact accel-
erations clustered in the maximally stable range (Schaal et al.,1996; Sternad et al., 2001). In addition, the variability of impactacceleration and ball amplitude were lowest in the maximallystable range, as expected. With practice, impact accelerationsbecame progressively negative over trials and converged to themaximally stable region (Sternad et al., 2001). This evidenceindicates that actors exploit passive stability, consistent with thepassive control hypothesis.
However, subsequent reports found that bouncing could also besustained in the unstable region, with positive impact accelera-tions, implicating a form of active control (Siegler, Mantel,Warren, & Bardy, 2003; Morice et al., 2007). To probe thispossibility, de Rugy et al. (2003) perturbed the coefficient ofrestitution at single impacts during ongoing bouncing (equiva-lent to perturbing the launch velocity), destabilizing the system ona majority of trials. They observed that participants rapidly com-pensated for large perturbations by adjusting the period of racketoscillation, so that impact acceleration and phase returned to thepassively stable range within two to three cycles. These results aresuggestive of hybrid control, in which perturbations beyond thepassively stable range are actively correcte