Contributed articleBiomimetic gaze stabilization based on feedback-error-learning with nonparametric regression networks
Introduction
The goal of our research is to investigate the interplay between oculomotor control, visual processing, and limb control in humans and primates by exploring the computational issues of these processes with a humanoid robotic system and by comparing predictions of our theories with data from neurobiology. In this paper, we will present the first step towards these goals, focusing on oculomotor control. In many biological organisms, oculomotor is the interface to one of the most important sensory systems, the visual system, and through this system it affects biological information processing in various ways. Firstly, oculomotor control is needed to select which visual information should be processed by the limited sensory resources of the eye and the following brain circuits. This role is particularly important in primates that employ foveal vision. Furthermore, as eye movements must be executed in a sequential manner, it is crucial to focus visual attention at the right time on the right targets such that subsequent information processes, in particular motor planning and execution, receive relevant information sufficiently fast to update ongoing computations. Secondly, in order to obtain full understanding of limb motor control or whole-body control, it may be necessary to study oculomotor control because oculomotor control may be a crucial constraint in how movements of other body parts are planned. Recent physiological research provides several insights that are consistent with the above statements. For instance, Gauthier, Fercher, Mussa Ivaldi and Marchetti (1988) demonstrated a tight coupling of oculomotor and limb motor systems through oculo-manual tracking experiments of visual target, and Miyashita, Kato, Miyauchi and Hikosaka (1996) showed that anticipatory saccades in sequential procedural learning in monkeys are tightly coupled to the limb–motor system.
Many artificial vision systems (Aloimonos et al., 1988, Ballard and Brown, 1993) have been developed to include oculomotor control techniques. To contrast these ‘moving’ vision systems from research conducted using purely ‘static’ vision systems, the term ‘active’ vision was introduced (Ballard & Brown, 1993). Although most of these approaches are inspired by biology’s active vision (Berthouze et al., 1996a, Capurro et al., 1996, Ferrell, 1996, Murray et al., 1992, Takanishi et al., 1995), only a few implementations of oculomotor systems can be found that try to emphasize biological plausibility.
In this paper, we will focus on an active vision system that employs as many as possible of the computational mechanisms that have been discovered in neurophysiological research on primates. We will restrict our scope to the most basic oculomotor behaviors, the stabilization of visual information by means of oculomotor reflexes. Successful visual perception requires that retinal images remain constant, at least for a certain amount of time. Since an oculomotor system usually resides in a moving body, one of the most basic and phylogenetically oldest functions of oculomotor control is visual stabilization, an area that has been studied intensively in neurobiology and that is known to be implemented as a combination of reflexes.
Our work is particularly inspired by research in the vestibulocerebellum that suggested the idea of feedback-error-learning (FEL) as a biologically plausible and control theoretically sound adaptive control concept (Kawato, 1990). While FEL has been pursued in several robotic studies (e.g. Berthouze et al., 1996b, Bruske et al., 1997), there has never been any emphasis on developing synthetic FEL learning approaches that consider fast nonlinear learning and coping with unknown delays in the sensory feedback pathway.
In the context of learning oculomotor reflexes, we will demonstrate in this paper how nonparametric regression networks in conjunction with FEL can be employed to learn a biomimetic oculomotor controller that leads to accurate control performance and very fast learning convergence for a nonlinear oculomotor plant with temporal delays in the feedback loop. For this purpose, first, we will review some of the elementary principles of biological gaze stabilization reflexes. Second, we will focus on exploring how, from a computational point of view, efficient learning of these reflexes could be achieved based on parallels that have been developed in research on the vestibulocerebellum. Finally, we describe the experimental setup we have developed to explore the feasibility of biomimetic oculomotor control and results obtained with this system.
Section snippets
The VOR and the OKR
When we have our hand in front of our eyes at a moderate frequency, it seems blurred, while there is no blurring when we look at the non-moving hand during movement of our head at a similar frequency. The former phenomenon involves the Opto-Kinetic Response (OKR), one of the basic reflexes to stabilize images on the retina. As sensory input, the OKR receives retinal slip information. Retinal slip is usually defined as the overall velocity with which an image drifts on the retina. As the goal of
Research objectives
From a control theoretic point of view, the VOR-OKR system corresponds to a negative feedback controller based on retinal slip information, augmented with a feedforward controller based on vestibular input. Control with such a system is straightforward if the dynamics of the eye system is known and the feedback pathways have no delays. However, the opposite is true for biological and even artificial oculomotor systems: retinal slip information is significantly delayed due to the overhead of
Sources of nonlinearity in oculomotor control
There are three sources of nonlinearities both in biology and artificial oculomotor systems: (i) muscle nonlinearities or nonlinearities added by the actuators and the usually heavy cable attached to the cameras; (ii) perceptual distortion due to foveal vision; and (iii) off-axis effects. Off-axis effects result from the non-coinciding axes of rotation of eyeballs and the head and require a nonlinear adjustment of the feedforward controller as a function of local length, eye, and head position.
Experimental set up
We implemented an on-line learning system of the VOR-OKR controller for our humanoid robot. Each DOF of the robot is actuated hydraulically out of a torque control loop. Each eye of the robot’s oculomotor system consists of two cameras, a wide angle (100° view-angle horizontally) color camera for peripheral vision, and second camera for foveal vision, providing a narrow-viewed (24° view-angle horizontally) color image. This setup mimics the foveated retinal structure of primates, and it is also
Discussion
Our research objective is to study the computational processes of oculomotor control, visual processing, limb control, and the interdependencies of these three modalities by using a humanoid robot. This paper took a first step towards this goal by exploring adaptive gaze stabilization in a biomimetic artificial oculomotor system. We presented how the strategy of FEL together with a state-of-the-art statistical learning network can be used to construct a control theoretically principled learning
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