The coordination of arm movements: an experimentally confirmed mathematical model

By Tamar Flash, Neville Hogan. 1985

This paper presents studies of the coordination of voluntary human arm movements. A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multijoint arm movements. Coordination is modeled mathematically by defining an objective function, a measure of performance for any possible movement. The unique trajectory which yields the best performance is determined using dynamic optimization theory. In the work presented here, the objective function is the square of the magnitude of jerk (rate of change of acceleration) of the hand integrated over the entire movement. This is equivalent to assuming that a major goal of motor coordination is the production of the smoothest possible movement of the hand. Experimental observations of human subjects performing voluntary unconstrained movements in a horizontal plane are presented. They confirm the following predictions of the mathematical model: unconstrained point-to-point motions are approximately straight with bell-shaped tangential velocity profiles; curved motions (through an intermediate point or around an obstacle) have portions of low curvature joined by portions of high curvature; at points of high curvature, the tangential velocity is reduced; the durations of the low-curvature portions are approximately equal. The theoretical analysis is based solely on the kinematics of movement independent of the dynamics of the musculoskeletal system and is successful only when formulated in terms of the motion of the hand in extracorporal space. The implications with respect to movement organization are discussed.

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Citations in the corpus

Evidence for the Flexible Sensorimotor Strategies Predicted by Optimal Feedback Control (2007, methodology): “The ho-ReceivedMarch15 mogeneous cost could be energy consumption (Nelson, 1983; Anderson and Pandy, 2001), derivative of hand acceleration (Flash and Hogan, 1985), derivative of joint torque (Uno et al., 1989), endpoint variance (Harris and Wolpert, 1998).”
Upper Limb Robot Mediated Stroke Therapy—GENTLE/s Approach (2003, methodology): “In most of these studies, one characterisation of multi-joint planar reaching movements was found to be a straight path with a bell shaped velocity profile ( Flash and Hogan, 1985; Uno et al., 1989; Abend et al., 1982; Atkenson and Hollerbach, 1985).”
Task-Specific Generalization of Discrete and Periodic Dynamic Movement Primitives (2010, unknown): “resemble human-reaching trajectories [49].”
Learning Physical Collaborative Robot Behaviors From Human Demonstrations (2016, methodology): “The minimum jerk model [18] has also been an inspiration”
Segmenting sign language into motor primitives with Bayesian binning (2013, methodology): “, snap, crackle and so on (Flash and Hogan, 1985; Todorov and Jordan, 1998).”
Movement Timing and Invariance Arise from Several Geometries (2009, methodology): “Using only via points and end-points, the minimum jerk principle successfully accounted for both the trajectory path and velocity of curved and drawing movements [4,61].”
On the analysis of movement smoothness (2015, background): “For instance, point-topoint reaching movements through a via point performed by healthy subjects can exhibit sharp dips in the speed profile [12].”
Quantifying Generalization from Trial-by-Trial Behavior of Adaptive Systems that Learn with Basis Functions: Theory and Experiments in Human Motor Control (2003, methodology): “Some, like the minimum jerk trajectory that we used in our adaptive controller (Flash and Hogan, 1985), do indeed have these properties.”
Ergonomics Society of the Human Factors and Human Factors: The Journal (2014, unknown): “Flash and Hogan (1985) proposed that the motor system minimizes mean squared jerk (the mean squared third time derivative of position, or the rate of change in acceleration) over the duration of the movement.”
DexMV: Imitation Learning for Dexterous Manipulation from Human Videos (2021, background): “The reason is two-fold: (i) First, physiological study [22] shows that the motion of human hand is a minimum jerk trajectory, where the lowest effort is required during the movement.”