1 Comparing Internal Models of the Dynamics of the Visual Environment S. Carver, T. Kiemel, H. van der Kooij, J.J. Jeka Biol. Cybern. 92, 147–163 (2005) S. Carver, T. Kiemel, H. van der Kooij, J.J. Jeka Biol. Cybern. 92, 147–163 (2005)

2 Introduction The human postural control system responds to the motion of visual scene. The human postural control system responds to the motion of visual scene. The implicit assumptions it makes about the visual environment are unknown. The implicit assumptions it makes about the visual environment are unknown. Environmental changes require an updating of sensory weights to current conditions so that muscular commands are based on the most precise and reliable sensory information available. Environmental changes require an updating of sensory weights to current conditions so that muscular commands are based on the most precise and reliable sensory information available. One approach to do this task has involved the implementation of an internal model. One approach to do this task has involved the implementation of an internal model. The human postural control system responds to the motion of visual scene. The human postural control system responds to the motion of visual scene. The implicit assumptions it makes about the visual environment are unknown. The implicit assumptions it makes about the visual environment are unknown. Environmental changes require an updating of sensory weights to current conditions so that muscular commands are based on the most precise and reliable sensory information available. Environmental changes require an updating of sensory weights to current conditions so that muscular commands are based on the most precise and reliable sensory information available. One approach to do this task has involved the implementation of an internal model. One approach to do this task has involved the implementation of an internal model.

3 IntroductionIntroduction Van der Kooij (2001) was the first to propose an internal model of the environment as part of the postural control system (in response to translation / rotation of the support base). Van der Kooij (2001) was the first to propose an internal model of the environment as part of the postural control system (in response to translation / rotation of the support base). The internal model derives its prediction of the sensory signals not only by simulating the dynamics of the body and its sensors, but also by simulating the dynamics of the environment. The internal model derives its prediction of the sensory signals not only by simulating the dynamics of the body and its sensors, but also by simulating the dynamics of the environment. To implement a simulation of the environment, the nervous system must have a model of how it changes in order to estimate its next state (e.g., random walk process). To implement a simulation of the environment, the nervous system must have a model of how it changes in order to estimate its next state (e.g., random walk process). With this estimate, the internal model predicts the sensory measurements. With this estimate, the internal model predicts the sensory measurements. The nervous system’s behavior will adapt to changing environmental conditions. Does the model adapt in the same way as the human postural control system? Van der Kooij (2001) was the first to propose an internal model of the environment as part of the postural control system (in response to translation / rotation of the support base). Van der Kooij (2001) was the first to propose an internal model of the environment as part of the postural control system (in response to translation / rotation of the support base). The internal model derives its prediction of the sensory signals not only by simulating the dynamics of the body and its sensors, but also by simulating the dynamics of the environment. The internal model derives its prediction of the sensory signals not only by simulating the dynamics of the body and its sensors, but also by simulating the dynamics of the environment. To implement a simulation of the environment, the nervous system must have a model of how it changes in order to estimate its next state (e.g., random walk process). To implement a simulation of the environment, the nervous system must have a model of how it changes in order to estimate its next state (e.g., random walk process). With this estimate, the internal model predicts the sensory measurements. With this estimate, the internal model predicts the sensory measurements. The nervous system’s behavior will adapt to changing environmental conditions. Does the model adapt in the same way as the human postural control system?

4Introduction In many respects, the model of Van der Kooij succeeded in reproducing the behavior of the human postural control system. In many respects, the model of Van der Kooij succeeded in reproducing the behavior of the human postural control system. Numerous studies (Peterka & Benolken 1995; Oie et al. 2002) have found that across different frequencies of sinusoidal stimulation, the gain with respect to the stimulus drops as the amplitude of the stimulus increases, but the phase remains roughly constant. Numerous studies (Peterka & Benolken 1995; Oie et al. 2002) have found that across different frequencies of sinusoidal stimulation, the gain with respect to the stimulus drops as the amplitude of the stimulus increases, but the phase remains roughly constant. The model of Van der Kooij did not reproduce these observations. The model of Van der Kooij did not reproduce these observations. In many respects, the model of Van der Kooij succeeded in reproducing the behavior of the human postural control system. In many respects, the model of Van der Kooij succeeded in reproducing the behavior of the human postural control system. Numerous studies (Peterka & Benolken 1995; Oie et al. 2002) have found that across different frequencies of sinusoidal stimulation, the gain with respect to the stimulus drops as the amplitude of the stimulus increases, but the phase remains roughly constant. Numerous studies (Peterka & Benolken 1995; Oie et al. 2002) have found that across different frequencies of sinusoidal stimulation, the gain with respect to the stimulus drops as the amplitude of the stimulus increases, but the phase remains roughly constant. The model of Van der Kooij did not reproduce these observations. The model of Van der Kooij did not reproduce these observations.

5Introduction This work tests more rigorously the hypothesis that an internal model of the environment underlies the adaptation of the human postural control system to changing environmental conditions, in other words: This work tests more rigorously the hypothesis that an internal model of the environment underlies the adaptation of the human postural control system to changing environmental conditions, in other words: To find a suitable postural model for a changing environment, To find a suitable postural model for a changing environment, To see if it contains an internal model of the visual environment or not, To see if it contains an internal model of the visual environment or not, To find if the model produces the observations of Peterka & Benolken (1995). To find if the model produces the observations of Peterka & Benolken (1995).

6Modeling The standing human body is modeled as an inverted pendulum. The standing human body is modeled as an inverted pendulum. Its stability is maintained by a PD controller that depends upon an estimate of the body’s position & velocity. Its stability is maintained by a PD controller that depends upon an estimate of the body’s position & velocity. Two groups of sensors are modeled (no dynamics): Visual & Non-visual Two groups of sensors are modeled (no dynamics): Visual & Non-visual 3 postural control models based on 3 internal models of the visual environment ( adaptation to changing environmental conditions ) an nth order linear stochastic process: 3 postural control models based on 3 internal models of the visual environment ( adaptation to changing environmental conditions ) an nth order linear stochastic process: ξ env is a Gaussian white noise with spectral density matrix D. The three internal models of the visual environment differed in how they represented A and D. One nonestimating postural model (no internal model of the visual environment): Minimize the mean square of the control signal. One nonestimating postural model (no internal model of the visual environment): Minimize the mean square of the control signal. The standing human body is modeled as an inverted pendulum. The standing human body is modeled as an inverted pendulum. Its stability is maintained by a PD controller that depends upon an estimate of the body’s position & velocity. Its stability is maintained by a PD controller that depends upon an estimate of the body’s position & velocity. Two groups of sensors are modeled (no dynamics): Visual & Non-visual Two groups of sensors are modeled (no dynamics): Visual & Non-visual 3 postural control models based on 3 internal models of the visual environment ( adaptation to changing environmental conditions ) an nth order linear stochastic process: 3 postural control models based on 3 internal models of the visual environment ( adaptation to changing environmental conditions ) an nth order linear stochastic process: ξ env is a Gaussian white noise with spectral density matrix D. The three internal models of the visual environment differed in how they represented A and D. One nonestimating postural model (no internal model of the visual environment): Minimize the mean square of the control signal. One nonestimating postural model (no internal model of the visual environment): Minimize the mean square of the control signal.

7 Conclusion The nonestimating model is the only scheme that reproduces the well-known experimental result that across frequencies the gain substantially drops but the phase remains roughly constant as a function of increasing stimulus amplitude. The nonestimating model is the only scheme that reproduces the well-known experimental result that across frequencies the gain substantially drops but the phase remains roughly constant as a function of increasing stimulus amplitude. The nonestimating model adapts to changing environmental conditions by adjusting sensory weights to minimize the mean square of the control signal. The nonestimating model adapts to changing environmental conditions by adjusting sensory weights to minimize the mean square of the control signal. Ravaioli (2004) reached a different conclusion concerning the response of the postural control system to translatory visual scene motion. In this case an internal model approach did well. Ravaioli (2004) reached a different conclusion concerning the response of the postural control system to translatory visual scene motion. In this case an internal model approach did well.

8 Conclusion This suggests that the nervous system may handle translatory stimuli differently than sinusoidal stimuli. This suggests that the nervous system may handle translatory stimuli differently than sinusoidal stimuli. The results of Ravaioli suggesting the presence of an internal model that compensates for a translating environment may reflect the fact that translating environments were indeed common in the environment in which humans evolved and that sinusoidal stimuli were not common. The results of Ravaioli suggesting the presence of an internal model that compensates for a translating environment may reflect the fact that translating environments were indeed common in the environment in which humans evolved and that sinusoidal stimuli were not common.