M.I. Jordan, Computational Aspects of Motor Control and Motor Learning. In H. Heuer and S.W. Keele (Eds.) Handbook of Perception and Action Vol 2:Motor skills (1996).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....simple feedback cannot offer a proper explanation for the control of fast movement. Thus, it was suggested that the nervous system contains an inverse model of the musculo skeletal system that is contextually being updated [7] For reviews of recent modeling with artificial neural networks, see [10,14]. Two methods for learning this inverse model are distal supervised learning [11] and feedback error learning [16] These methods do not confront the MTO problem. They choose an arbitrary solution that is the closest to the training set and to the initial conditions of the network. In some cases ....

M.I. Jordan, Computational Aspects of Motor Control and Motor Learning. In H. Heuer and S.W. Keele (Eds.) Handbook of Perception and Action Vol 2:Motor skills (1996).

.... of linear systems was presented by Widrow et al. 1979) For nonlinear systems, the inverse model can be learned by an artificial neural network (ANN) There are numerous papers on using ANN for control, see e.g. Narendra Parthasarathy, 1990) Barto (1990) Kawato (1990) Bullock et al. 1993) Jordan (1996) Karniel Inbar (2000) and many references therein. Figure 1 describes the control problem which is to find the control signal X, such that F(X) will be close to a given desired goal, Yd. F(X) characterizes the controlled system. The input and output spaces can be scalars, vectors, continuous ....

....best model, and then inverts this model. We call the model that is learned by this method the inverse of the best estimator (IBE) model. Narendra mentioned the superiority of the indirect learning scheme (here IBE) since it minimizes the output error; see, e.g. Narendra Parthasarathy (1990) Jordan (1996) clearly demonstrates the erroneous results that might occur using the direct inverse learning (BEI) for redundant systems. However, the direct inverse learning approach still appears in numerous papers and software toolboxes without clear manifestation of its drawbacks, even for the simplest ....

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Jordan M.I. (1996) Computational aspects of motor control and motor learning. In: Heuer H, Keele SW (eds.) Handbook of Perception and Action Vol 2:Motor skills.

....simple feedback cannot offer a proper explanation for the control of fast movement. Thus, it was suggested that the nervous system contains an inverse model of the musculo skeletal system that is contextually being updated [7] For reviews of recent modeling with artificial neural networks, see [10,14]. Two methods for learning this inverse model are distal supervised learning [11] and feedback error learning [16] These methods do not confront the MTO problem. They choose an arbitrary solution that is the closest to the training set and to the initial conditions of the network. In some cases ....

M.I. Jordan, Computational Aspects of Motor Control and Motor Learning. In H. Heuer and S.W. Keele (Eds.) Handbook of Perception and Action Vol 2:Motor skills (1996).

....of the system, the desired state of the system and the predicted state of the system. i) Predictors ( forward models) Predictors model aspects of the external world and of the motor system in order to capture the forward or causal relationship between actions and their outcomes (Ito 1970; Jordan 1996; Wolpert et al. 1995) Every time a motor command is issued to make a movement, an eerence copy of the motor command is produced inparallel. Based on the eerence copy, the predictor estimates the sensory consequences of the ensuing movement. Thisprediction can be used in several ways (Miall ....

Jordan, M. I. 1996 Computational aspects of motor control and motor learning. In Handbook of p erception and action: motor skills (ed. E. H. Heuer & E. S. Keele), pp.71^118. New York: Academic Press.

....model was learned by our algorithm, even when contaminated with irrelevant and redundant inputs. 2 The Curse of Dimensionality Both in research of biological and robotic motor control, the need for internal models has been emphasized in order to achieve accurate control of fast movements ( 8] [9]) For models with only few input dimensions, learning approaches have been quite successful (e.g, 10] 11] 12] However, for higher dimensional learning tasks, it has been unclear whether learning approaches can succeed. For instance, we are interested in learning the inverse dynamics model ....

M. I. Jordan, "Computational aspects of motor control and motor learning," in Handbook of perception and action, H. Heuer and S. W. Keele, Eds. New York: Academic Press, 1996.

....scheme. Another problem appears in trying to learn the inverse of a redundant system (i.e. the problem of mapping an MTO system) Most of the learning algorithm will converge to the average of all the possible solutions, but the average of correct solutions is not always a correct solution (see [20]) A second problem in inverting an MTO system is how to represent all the solutions and which solution to choose. This problem is dealt with in Section V. One major problem in trying to train a controller that is attached to the controlled system is how to transform the error from the output ....

M. I. Jordan, "Computational aspects of motor control and motor learning," in Handbook of Perception and Action. ser. Motor Skills, H. Heuer and S. W. Keele, Eds, New York: Academic, 1996, vol. 2.

.... grip force; virtual reality; bimanual coordination The ability to predict the consequences of our own actions using an internal model of both the motor system and the external world has emerged as an important theoretical concept in motor control (Kawato et al. 1987; Jordan and Rumelhart, 1992; Jordan, 1995; Wolpert et al. 1995; Miall and Wolpert, 1996; Wolpert, 1997) Such models are known as forward models because they capture the forward or causal relationship between actions, as signaled by efference copy (Sperry, 1950; von Holst, 1954; Jeannerod et al. 1979) and outcomes. Such forward models ....

Jordan MI (1995) Computational aspects of motor control and motor learning. In: Handbook of perception and action: motor skills. (Heuer H, Keele S, eds). New York: Academic.

....process, has emerged as an important theoretical concept in motor control. There are two varieties of internal model, forward and inverse models. Forward models capture the forward or causal relationship between inputs to the system, e.g. the arm, and the outputs (Ito, 1970; Kawato et al. 1987; Jordan, 1995). A forward dynamic model of the arm, for example predicts the next state (e.g. position and velocity) given the current state and motor command. Such models have been proposed to be used in motor learning (Sutton and Barto, 1981; Jordan and Rumelhart, 1992) state estimation (Wolpert et al. ....

Jordan, M.I. (1995). Computational aspects of motor control and motor learning. In H. Heuer & S. Keele (Eds.), Handbook of perception and action: Motor skills. New York: Academic Press.

....motor output plays the role of error signal. The interest of such an approach stems from the following points: ffl The desired plant output is used both for control and training, hence allowing an on line learning. Instead, in other approaches such as direct inverse modeling (as described by Jordan (1992)) the controller has to be trained off line because the input of the controller is the actual plant output, and not the desired plant output. ffl Although the training data that the system receives pairs of actual plant inputs and desired plant outputs are not samples of the inverse ....

....the feedback controller does not require the implementation of an explicit plant model but rather a qualitative knowledge of the plant. Besides, it is shown that the performance of an error correcting controller is generally rather insensitive to the exact value of the gain that is chosen (Jordan 1992). ffl Under assumptions that are fully detailed by Gomi Kawato (1993) the global convergence of the scheme can be proven, using German s theorem and Lyapunov s second method. The two main conditions are: 1) a guaranteed asymptotic convergence of the learning phase (role of the gain in the ....

Jordan, M.I. (1992). Computational Aspects of Motor Control and Motor Learning (Technical Report TR-9206). Massachusetts Institute of Technology, Department of Brain and Cognitive Sciences, USA.

....4. 2 Properties of the desired trajectory The desired performance of a controlled system is usually established by a criterion, or optimization principle, expressed in a particular coordinate system (e.g. the coordinate system of the task, cf. Flash and Hogan 1985, Jordan and Rumelhart 1992, Jordan 1993). For skilled movements of the arm, this criterion appears to be one of smoothness. Specifically, in the context of reaching movements in the horizontal plane, Flash and Hogan (1985) have noted that the hand s trajectory is well described by a function which maximizes a measure of smoothness. In a ....

.... 1990) For example, for the task of motor learning, combinations of non linear basis functions have been used to implement an internal model which represents the inverse dynamics of a multi joint limb (Raibert and Wimberly 1984, Kawato 1989, Jordan 1990, Shadmehr 1990, Kawato and Gomi 1992, Jordan 1993), mapping from states of the limb to an output force (e.g. Eq. 6) These results have provided an algorithm by which an internal model may be constructed. However, little has been learned regarding the properties of the computational elements with which the nervous system might be performing ....

Jordan MI (1993) Computational aspects of motor control and motor learning, In: Handbook of Perception and Action: Motor Skills (Heuer H, Keele S, eds), Academic: NY, pp. 87--146.

....how decision makers use this model to learn to improve their performance when interacting with the environment. Casting dynamic decision making in terms of control theory allows for the transfer of insights from other related domains (Hogarth, 1986) In motor learning, Jordan and Rumelhart (1992; Jordan, 1992, in press) address issues very similar to those addressed by Brehmer. The key to applying their approach to dynamic decision making is to divide the learning problem into two interdependent subproblems: 1) learning how actions affect the environment, and (2) learning what actions to take to ....

Jordan, M. I. (in press). Computational aspects of motor control and motor learning. In H. Heuer, & S. Keele (Eds.), Handbook of perception and action: Motor skills. New York: Academic Press. Jordan, M. I., & Rumelhart, D. E. (1992). Forward models: Supervised learning with a distal teacher. Cognitive Science, 16(3), 307--354.

....possible articulatory states, but each of those articulatory states maps only to silence. From the perspective of control theory, the mapping from proximal domain (articulation) to the distal domain (acoustics) is termed the forward mapping, whereas the reverse is termed the inverse mapping (see Jordan, 1992, 1996). When the inverse mapping is many to one, as in this case, it constitutes a motor equivalence problem. This problem must be solved if the link between articulation and acoustics is to support the acquisition of speech production. Our solution to the motor equivalence problem is based on a ....

....that the necessary articulatory feedback for the production system is derived from the comprehension system. Specifically, proximal (articulatory) error is derived from the distal (acoustic and phonological) consequences of articulation via a learned articulatory acoustic forward model (also see Jordan, 1996; Perkell et al. 1995) The simulation demonstrates that a model instantiating these properties can, in fact, learn to cope with time varying, variable speech in comprehension, and use the resulting knowledge to guide production effectively in imitation and intentional naming. Moreover, its ....

Jordan, M. I. (1996). Computational aspects of motor control and motor learning. In H. Heuer, & S. Keele (Eds.), Handbook of perception and action: Motor skills. New York: Academic Press.

.... perceptual systems (e.g. Nakayama Shimojo 1992) One difference between perceptual and sensorimotor systems is that, in the latter, the observer may also need to dynamically integrate reafferent sensory signals and copies of motor efference that arise during movement (Wolpert, Ghahramani Jordan 1995b) We explore this from a computational perspective in section 2.2.1 and report on one relevant experiment in section 4. 2 The Computational Model The presence of information common to multiple sensory modalities poses two challenging computational problems for the CNS. First, the signals from ....

....of linear dynamical control systems. We first outline how these problems are addressed in the Kalman filter model, before reviewing some recent results testing this model s predictions regarding the temporal propagation of errors in localizing the hand during a movement (Wolpert, Ghahramani Jordan 1995b) For the sensorimotor system, one key aspect of the coordinate transformation problem is that, whereas sensory signals may directly cue the location of the hand, motor outflow ( efference copy ) generally does not. Knowing the sequence of torques applied to an arm, for example, does not ....

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Jordan, M. I. (1995). Computational aspects of motor control and motor learning, in H. Heuer & S. Keele (eds), Handbook of Perception and Action: Motor Skills, Academic Press, New York.

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Jordan MI (1996) Computational Aspects of Motor Control and Motor Learning. In Heuer H, Keele SW (eds.) Handbook of Perception and Action Vol 2.

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