Kinematic features of unrestrained vertical arm movements
TL;DR: Unrestrained human arm trajectories between point targets have been investigated using a three-dimensional tracking apparatus, the Selspot system, and movement regions were discovered in which the hand paths were curved.
Abstract: Unrestrained human arm trajectories between point targets have been investigated using a three-dimensional tracking apparatus, the Selspot system. Movements were executed between different points in a vertical plane under varying conditions of speed and hand-held load. In contrast to past results which emphasized the straightness of hand paths, movement regions were discovered in which the hand paths were curved. All movements, whether curved or straight, showed an invariant tangential velocity profile when normalized for speed and distance. The velocity profile invariance with speed and load is interpreted in terms of simplification of the underlying arm dynamics, extending the results of Hollerbach and Flash (Hollerbach, J. M., and T. Flash (1982) Biol. Cybern. 44: 67-77).
Citations
More filters
29 Nov 1995
TL;DR: The discrete Kalman filter as mentioned in this paper is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error.
Abstract: In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.
2,811 citations
TL;DR: In this article, the authors proposed a mathematical model which accounts for formation of hand trajectories by defining an objective function, a measure of performance for any possible movement: square of the rate of change of torque integrated over the entire movement.
Abstract: In this paper, we study trajectory planning and control in voluntary, human arm movements. When a hand is moved to a target, the central nervous system must select one specific trajectory among an infinite number of possible trajectories that lead to the target position. First, we discuss what criterion is adopted for trajectory determination. Several researchers measured the hand trajectories of skilled movements and found common invariant features. For example, when moving the hand between a pair of targets, subjects tended to generate roughly straight hand paths with bell-shaped speed profiles. On the basis of these observations and dynamic optimization theory, we propose a mathematical model which accounts for formation of hand trajectories. This model is formulated by defining an objective function, a measure of performance for any possible movement: square of the rate of change of torque integrated over the entire movement. That is, the objective function C T is defined as follows: $$C_T = \frac{1}{2}{}^t\int\limits_0^f {\sum\limits_{i = 1}^n {\left( {\frac{{{\text{d}}z_i }}{{{\text{d}}t}}} \right)^2 {\text{d}}t,} } $$ where z iis the torque generated by the i-th actuator (muslce) out of n actuators, and t fis the movement time. Since this objective function critically depends on the complex nonlinear dynamics of the musculoskeletal system, it is very difficult to determine the unique trajectory which yields the best performance. We overcome this difficult by developing an iterative scheme, with which the optimal trajectory and the associated motor command are simultaneously computed. To evaluate our model, human hand trajectories were experimentally measured under various behavioral situations. These results supported the idea that the human hand trajectory is planned and controlled in accordance with the minimum torquechange criterion.
1,584 citations
TL;DR: An operational meaning to ” controlled” and ”uncontrolled” is given and a method of analysis through which hypotheses about controlled and uncontrolled degrees of freedom can be tested is described, finding that, for the task of sit-to-stand, the position of the center of mass in the sagittal plane was controlled.
Abstract: The degrees of freedom problem is often posed by asking which of the many possible degrees of freedom does the nervous system control? By implication, other degrees of freedom are not controlled. We give an operational meaning to "controlled" and "uncontrolled" and describe a method of analysis through which hypotheses about controlled and uncontrolled degrees of freedom can be tested. In this conception, control refers to stabilization, so that lack of control implies reduced stability. The method was used to analyze an experiment on the sit-to-stand transition. By testing different hypotheses about the controlled variables, we systematically approximated the structure of control in joint space. We found that, for the task of sit-to-stand, the position of the center of mass in the sagittal plane was controlled. The horizontal head position and the position of the hand were controlled less stably, while vertical head position appears to be no more controlled than joint motions.
1,333 citations
Cites result from "Kinematic features of unrestrained ..."
...This conclusion has been supported by a number of other studies of reaching tasks in both humans (Atkeson and Hollerbach 1985; Flash and Hogan 1985; Haggard et al. 1995; Won and Hogan 1995) and animals (Georgopoulos et al. 1993; Martin et al. 1995)....
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TL;DR: It is shown that organization of postural movements into combinations of distinct strategies simplifies the interpretation of sensory inputs and provides a framework compatible with both mechanical and physiological information and amenable to experimental testing.
Abstract: A scheme for understanding the organization of human postural movements is developed in the format of a position paper. The structural characteristics of the body and the geometry of muscular actions are incorporated into a three-dimensional graphical representation of human movement mechanics in the sagittal plane. A series of neural organizational hypotheses limit a theoretically infinite number of combinations of muscle contractions and associated movement trajectories for performing postural corrections: (1) Controls are organized to use the minimum number of muscles; (2) frequently performed movements are organized to require a minimum of neural decision-making.These hypotheses lead to the prediction that postural movements are composed of muscle contractile strategies derived from a limited set of distinct contractile patterns. The imposition of two mechanical constraints related to the configuration of support and to requirements for body stability with respect to gravity predict the conditions under which individual movement strategies will be deployed.A complementary organizational scheme for the senses is developed. We show that organization of postural movements into combinations of distinct strategies simplifies the interpretation of sensory inputs. The fine-tuning of movement strategies can be accomplished by breaking down the complex array of feedback information into a series of scalar quantities related to the parameters of the movement strategies. For example, the magnitude, aim, and curvature of the movement trajectory generated by an individual strategy can be adjusted independently.The second half of the report compares theoretical predictions with a series of actual experimental observations on normal subjects and patients with known sensory and motor disorders. Actual postural movements conform to theoretical predictions about the composition of individual movement strategies and the conditions under which each strategy is used. Observations on patients suggest how breakdowns in individual steps within the logical process of organization can lead to specific movement abnormalities.Discussion focuses on the areas needing further experimentation and on the implications of the proposed organizational scheme. We conclude that although our organizational scheme is not new in demonstrating the need for simplifying the neural control of movement, it is perhaps original in imposing discrete logical control upon a continuous mechanical system. The attraction of the scheme is that it provides a framework compatible with both mechanical and physiological information and amenable to experimental testing.
1,081 citations
References
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TL;DR: Human subjects were instructed to point one hand to different visual targets which were randomly sequenced, using a paradigm which allowed two degrees of freedom, and trajectories of the hand in space were observed.
Abstract: Human subjects were instructed to point one hand to different visual targets which were randomly sequenced, using a paradigm which allowed two degrees of freedom (shoulder, elbow). The time course of the hand trajectory and the joint angular curves were observed. The latter exhibited patterns which change markedly for different movements, whereas the former preserve similar characteristics (in particular, a single peaked tangential velocity curve). The hypothesis is then formulated that the central command for these movements is formulated in terms of trajectories of the hand in space.
1,619 citations
TL;DR: A theory of motor-output variability that accounts for the relationship among the movement amplitude, movement time, the mass to be moved, and the resulting movement error is presented.
Abstract: Theoretical accounts of the speed-accuracy trade-off in rapid movement have usually focused on within-moveme nt error detection and correction, and have consistently ignored the possibility that motor-output variability might be predictably related to movement amplitude and movement time. This article presents a theory of motor-output variability that accounts for the relationship among the movement amplitude, movement time, the mass to be moved, and the resulting movement error. Predictions are derived from physical principles; empirical evidence supporting the principles is presented for three movement paradigms (single-aiming responses, reciprocal movements, and rapid-timing tasks); and the theory and data are discussed in terms of past theoretical accounts and future research directions. Examining the current level of understanding about the production and control of motor responses, many would no doubt be tempted to say that we have not come very far since the early writings of Woodworth (1899) and Hollingworth (1909). These writers were concerned with the basic laws of limb movements (analogous, perhaps to the basic laws of motion that were the cornerstone of physics) that denned the relationship between the simplest aspects of motor
1,605 citations
"Kinematic features of unrestrained ..." refers methods in this paper
...Schmidt et al. (1979) and Meyer et al. (1982) proposed different impulse variability models as alternatives to Fitts’ law; the latter model is notable for the derivation of a symmetric acceleration profile with a double inflection point from acceleration to deceleration....
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...Schmidt et al. (1979) and Meyer et al. (1982) proposed different impulse variability models as alternatives to Fitts’ law; the latter model is notable for the derivation of a symmetric acceleration profile with a double inflection point from acceleration to deceleration....
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TL;DR: A mathematical model is presented which predicts both the major qualitative features and, within experimental error, the quantitative details of a class of perturbed and unperturbed large-amplitude, voluntary movements performed at intermediate speed by primates.
Abstract: This paper presents a mathematical model which predicts both the major qualitative features and, within experimental error, the quantitative details of a class of perturbed and unperturbed large-amplitude, voluntary movements performed at intermediate speed by primates. A feature of the mathematical model is that a concise description of the behavioral organization of the movement has been formulated which is separate and distinct from the description of the dynamics of movement execution. Based on observations of voluntary movements in primates, the organization has been described as though the goal were to make the smoothest movement possible under the circumstances, i.e., to minimize the accelerative transients. This has been formalized by using dynamic optimization theory to determine the movement which minimizes the rate of change of acceleration (jerk) of the limb. Based on observations of muscle mechanics, the concept of a “virtual position” determined by the active states of the muscles is rigorously defined as one of the mechanical consequences of the neural commands to the muscles. This provides insight into the mechanics of perturbed and unperturbed movements and is a useful aid in the separation of the descriptions of movement organization and movement execution.
1,228 citations
1,184 citations
"Kinematic features of unrestrained ..." refers methods in this paper
...iterative corrections model (Keele, 1968; Crossman and Goodeve, 1983) which, however, is now discounted (Langolf et al....
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...One model of the movement segmentation has been an iterative corrections model (Keele, 1968; Crossman and Goodeve, 1983) which, however, is now discounted (Langolf et al., 1976; Jagacinski et al., 1978; Carlton, 1980)....
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TL;DR: A general-purpose computer program which is capable of designing a large Class of optimum (in the minimax sense) FIR linear phase digital filters and is shown to be exceedingly efficient.
Abstract: This paper presents a general-purpose computer program which is capable of designing a large Class of optimum (in the minimax sense) FIR linear phase digital filters. The program has options for designing such standard filters as low-pass, high-pass, bandpass, and bandstop filters, as well as multipassband-stopband filters, differentiators, and Hilbert transformers. The program can also be used to design filters which approximate arbitrary frequency specifications which are provided by the user. The program is written in Fortran, and is carefully documented both by comments and by detailed flowcharts. The filter design algorithm is shown to be exceedingly efficient, e.g., it is capable of designing a filter with a 100-point impulse response in about 20 s.
1,160 citations