Trajectory Formation of Vertical Arm Movements through a Via-Point: A Limit of Validity of the Minimum-Jerk Model

1993 ◽  
Vol 76 (3) ◽  
pp. 875-884 ◽  
Author(s):  
Taketo Furuna ◽  
Hiroshi Nagasaki

The minimum-jerk model predicts the smoothest trajectory for a class of human movements and so provides us with a kinematic measurement of skilled motor performance. To establish the limits of the model's validity, the predicted and experimentally defined movement trajectories and the joint coordination were compared in two-joint arm movements, bringing the hand from the initial position to the final position through a specified point (a via-point). Kinematic data of the movements were obtained through the SELSPOT system. The movement path, tangential velocity, and coordinated change in positions of the shoulder and elbow joints evidently deviated from those predicted by the model. These results suggest that the minimum-jerk model is not valid for movements under extreme conditions which are highly dependent on musculoskeletal dynamics.

2008 ◽  
Vol 20 (3) ◽  
pp. 779-812 ◽  
Author(s):  
Shay Ben-Itzhak ◽  
Amir Karniel

Rapid arm-reaching movements serve as an excellent test bed for any theory about trajectory formation. How are these movements planned? A minimum acceleration criterion has been examined in the past, and the solution obtained, based on the Euler-Poisson equation, failed to predict that the hand would begin and end the movement at rest (i.e., with zero acceleration). Therefore, this criterion was rejected in favor of the minimum jerk, which was proved to be successful in describing many features of human movements. This letter follows an alternative approach and solves the minimum acceleration problem with constraints using Pontryagin's minimum principle. We use the minimum principle to obtain minimum acceleration trajectories and use the jerk as a control signal. In order to find a solution that does not include nonphysiological impulse functions, constraints on the maximum and minimum jerk values are assumed. The analytical solution provides a three-phase piecewise constant jerk signal (bang-bang control) where the magnitude of the jerk and the two switching times depend on the magnitude of the maximum and minimum available jerk values. This result fits the observed trajectories of reaching movements and takes into account both the extrinsic coordinates and the muscle limitations in a single framework. The minimum acceleration with constraints principle is discussed as a unifying approach for many observations about the neural control of movements.


2014 ◽  
Vol 112 (5) ◽  
pp. 1040-1053 ◽  
Author(s):  
Natalia Dounskaia ◽  
Wanyue Wang

Redundancy of degrees of freedom (DOFs) during natural human movements is a central problem of motor control research. This study tests a novel interpretation that during arm movements, the DOF redundancy is used to support a preferred, simplified joint control pattern that consists of rotating either the shoulder or elbow actively and the other (trailing) joint predominantly passively by interaction and gravitational torques. We previously revealed the preference for this control pattern during nonredundant horizontal arm movements. Here, we studied whether this preference persists during movements with redundant DOFs and the redundancy is used to enlarge the range of directions in which this control pattern can be utilized. A free-stroke drawing task was performed that involved production of series of horizontal center-out strokes in randomly selected directions. Two conditions were used, with the arm's joints unconstrained (U) and constrained (C) to the horizontal plane. In both conditions, directional preferences were revealed and the simplified control pattern was used in the preferred and not in nonpreferred directions. The directional preferences were weaker and the range of preferred directions was wider in the U condition, with higher percentage of strokes performed with the simplified control pattern. This advantage was related to the usage of additional DOFs. We discuss that the simplified pattern may represent a feedforward control strategy that reduces the challenge of joint coordination caused by signal-dependent noise during movement execution. The results suggest a possibility that the simplified pattern is used during the majority of natural, seemingly complex arm movements.


2000 ◽  
Vol 83 (3) ◽  
pp. 1480-1501 ◽  
Author(s):  
William J. Kargo ◽  
Simon F. Giszter

The hindlimb wiping reflex of the frog is an example of a targeted trajectory that is organized at the spinal level. In this paper, we examine this reflex in 45 spinal frogs to test the importance of proprioceptive afferents in trajectory formation at the spinal level. We tested hindlimb to hindlimb wiping, in which the wiping or effector limb and the target limb move together. Loss of afferent feedback from the wiping limb was produced by cutting dorsal roots 7–9. This caused altered initial trajectory direction, increased ankle path curvature, knee-joint velocity reversals, and overshooting misses of the target limb. We established that these kinematic and motor-pattern changes were due mainly to the loss of ipsilateral muscular and joint afferents. Loss of cutaneous afferents alone did not alter the initial trajectory up to target limb contact. However, there were cutaneous effects in later motor-pattern phases after the wiping and target limb had made contact: The knee extension or whisk phase of wiping was often lost. Finally, there was a minor and nonspecific excitatory effect of phasic contralateral feedback in the motor-pattern changes after deafferentation. Specific muscle groups were altered as a result of proprioceptive loss. These muscles also showed configuration-based regulation during wiping. Biceps, semitendinosus, and sartorius (all contributing knee flexor torques) all were regulated in amplitude based on the initial position of the limb. These muscles contributed to an initial electromyographic (EMG) burst in the motor pattern. Rectus internus and semimembranosus (contributing hip extensor torques) were regulated in onset but not in the time of peak EMG or in termination of EMG based on initial position. These two muscles contributed to a second EMG burst in the motor pattern. After deafferentation the initial burst was reduced and more synchronous with the second burst, and the second burst often was broadened in duration. Ankle path curvature and its degree of change after loss of proprioception depended on the degree of joint staggering used by the frog (i.e., the relative phasing between knee and hip motion) and on the degree of motor-pattern change. We examined these variations in 31 frogs. Twenty percent (6/31) of frogs showed largely synchronous joint coordination and little effect of deafferentation on joint coordination, end-point path, or the underlying synchronous motor pattern. Eighty percent of frogs (25/31) showed some degree of staggered joint coordination and also strong effects of loss of afferents. Loss of afferents caused two major joint level changes in these frogs: collapse of joint phasing into synchronous joint motion and increased hip velocity. Fifty percent of frogs (16/31) showed joint-coordination changes of type (1) without type (2). This change was associated with reduction, loss, or collapse of phasing of the sartorius, semitendinosus and biceps (iliofibularis) in the initial EMG burst in the motor pattern. The remaining 30% (9/31) of frogs showed both joint-coordination changes 1 and 2. These changes were associated with both the knee flexor EMG changes seen in the other frogs and with additional increased activity of rectus internus and semimembranosus muscles. Our data show that multiple ipsilateral modalities all play some role in regulating muscle activity patterns in the wiping limb. Our data support a strong role of ipsilateral proprioception in the process of trajectory formation and specifically in the control of limb segment interactions during wiping by way of the regulation and coordination of muscle groups based on initial limb configuration.


1998 ◽  
Vol 11 (1) ◽  
pp. 574-574
Author(s):  
A.E. Gómez ◽  
S. Grenier ◽  
S. Udry ◽  
M. Haywood ◽  
V. Sabas ◽  
...  

Using Hipparcos parallaxes and proper motions together with radial velocity data and individual ages estimated from isochones, the velocity ellipsoid has been determined as a function of age. On the basis of the available kinematic data two different samples were considered: a first one (7789 stars) for which only tangential velocities were calculated and a second one containing 3104 stars with available U, V and W velocity components and total velocities ≤ 65 km.s-1. The main conclusions are: -Mixing is not complete at about 0.8-1 Gyr. -The shape of the velocity ellipsoid changes with time getting rounder from σu/σv/σ-w = 1/0.63/0.42 ± 0.04 at about 1 Gyr to1/0.7/0.62 ±0.04 at 4-5 Gyr. -The age-velocity-dispersion relation (from the sample with kinematical selection) rises to a maximum, thereafter remaining roughly constant; there is no dynamically significant evolution of the disk after about 4-5 Gyr. -Among the stars with solar metallicities and log(age) > 9.8 two groups are identified: one has typical thin disk characteristics, the other is older than 10 Gyr and lags the LSR at about 40 km.s-1 . -The variation of the tangential velocity with age(without selection on the tangential velocity) shows a discontinuity at about 10 Gyr, which may be attributed to stars typically of the thick disk populations for ages > 10 Gyr.


2004 ◽  
Vol 01 (04) ◽  
pp. 613-636 ◽  
Author(s):  
WINFRIED ILG ◽  
GÖKHAN H. BAKIR ◽  
JOHANNES MEZGER ◽  
MARTIN A. GIESE

In this paper we present a learning-based approach for the modeling of complex movement sequences. Based on the method of Spatio-Temporal Morphable Models (STMMs) we derive a hierarchical algorithm that, in a first step, identifies automatically movement elements in movement sequences based on a coarse spatio-temporal description, and in a second step models these movement primitives by approximation through linear combinations of learned example movement trajectories. We describe the different steps of the algorithm and show how it can be applied for modeling and synthesis of complex sequences of human movements that contain movement elements with a variable style. The proposed method is demonstrated on different applications of movement representation relevant for imitation learning of movement styles in humanoid robotics.


1988 ◽  
Vol 59 (6) ◽  
pp. 1814-1830 ◽  
Author(s):  
R. B. Stein ◽  
F. W. Cody ◽  
C. Capaday

1. To determine the form of human movement trajectories and the factors that determine this form, normal subjects performed wrist flexion movements against various elastic, viscous, and inertial loads. The subjects were instructed with visual and auditory feedback to make a movement of prescribed amplitude in a present period of time, but were free to choose any trajectory that fulfilled these constraints. 2. The trajectories were examined critically to determine if they corresponded to those which would minimize the root mean square (RMS) value of some kinematic variable or of energy consumption. The data agreed better with the trajectory that minimized the RMS value of jerk (the third derivative of length) than that of acceleration. However, systematic deviations from the minimum jerk predictions were consistently observed whenever movements were made against elastic and viscous loads. 3. Improved agreement could generally be obtained by assuming that the velocity profile varied according to a normal (Gaussian) curve. We conclude that minimization of jerk is not a general principle used by the nervous system in organizing voluntary movements, although movements may approach the predicted form, particularly under inertial loading conditions. 4. The EMG of the agonist muscles consisted of relatively simple waveforms containing ramplike increases and approximately exponential decays. The form of the movements could often be predicted quite well by using the EMG as an input to a linear second-order model of the muscle plus load. Rather than rigorously minimizing a kinematic variable or energy consumption, the nervous system may generate simple waveforms and adjust the parameters of these waveforms by trial and error until a trajectory is achieved that meets the requirements for a given load.


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