An organizing principle for a class of voluntary movements

By Neville Hogan. 1984

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.

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Citations in the corpus

Apprenticeship learning via inverse reinforcement learning (2004, background): “Examples include the minimum jerk principle to explain limb movement in primates (Hogan, 1984), and the minimum torque-change model to explain trajectories in human multijoint arm movement.”
Computational principles of movement neuroscience (2000, background): “One of the first proposals was that the CNS specifies spatial parameters and relies on the spring-like properties of muscles and reflex loops to move the lim”
Upper Limb Robot Mediated Stroke Therapy—GENTLE/s Approach (2003, methodology): “The empirical minimum jerk approach is the simplest to implement in a real-time system and such a model was first proposed for a single joint by Hogan (1984) and further developed for multi-joint movements by Flash and Hogan (1985).”
Geometrical Invariance and Smoothness Maximization for Task-Space Movement Generation (2016, background): “Therefore, (2) is a Euclidean cost (in Section IV, we discuss the properties of this model with respect to Euclidean and affine invariance).”
The Relationship between Curvature and Velocity in Two-Dimensional Smooth Pursuit Eye Movements (1997, methodology): “Second, the Two-Thirds Power Law can be derived from a principle of optimal control (Minimum-Jerk Principle, Viviani and Flash, 1995) that is supposed to legislate motor planning at the central level ( Hogan, 1984; Flash and Hogan, 1985; Flash, 1990).”
Forward Models: Supervised Learning with a Distal Teacher (1992, methodology): “The random control signal u in this equation acts as a " virtual " equilibrium position for the arm (Hogan, 1984) and the augmented dynamics can be used to generate training data for learning the forward model.”
Parabolic movement primitives and cortical states: merging optimality with geometric invariance (2009, methodology): “The model predicts maximally smooth trajectories, accountingformultiplekinematicfeaturesofsingle-jointmovements ( Hogan 1984 ), of two-joint movements (Flash and Hogan 1985) and of movements that follow prescribed geometricalpaths(theconstrainedminimum-jerkmodel,(Vivianiand Flash 1995;Todorov and Jo”
Dynamics systems vs. optimal control--a unifying view. (2007, background): “1) — acceleration is equivalent to the time derivative of z, € y ¼ _ z: In this example, the trajectories realize a minimum jerk trajectory (Hogan, 1984), a smooth trajectory as typically observed in human behavior (the ideal minimum jerk trajectory, which minimizes the integral of the squared jerk…”
Operational Space Control: A Theoretical and Empirical Comparison (2008, background): “The desired pointing movement is specified by a minimum-jerk trajectory (Hogan 1984).”
Short- and long-term changes in joint co-contraction associated with motor learning as revealed from surface EMG. (2002, background): “…(Mussa-Ivaldi et al. 1985), the CNS can control the limbs by simply commanding a series of stable equilibrium positions aligned along the desired movement trajectory (equilibrium-point control hypothesis) (Bizzi et al. 1984; Feldman 1966; Flanagan et al. 1993; Flash 1987; Hogan 1984).”
Signal-dependent noise determines motor planning (1998, background): “For arm movements, it has been suggested that trajectories are selected to optimize a cost that is integrated over the movement, such as jerk (rate of change of acceleration”
Persistence of motor adaptation during constrained, multi-joint, arm movements. (2000, background): “This movement plan dictates the desired shape and temporal profile of the movement (i.e., the movement kinematics) (Hogan 1984; Wolpert et al. 1995).”