Does the brain use sliding variables for the control of movements?

Abstract

Delays in the transmission of sensory and motor information prevent errors from being instantaneously available to the central nervous system (CNS) and can reduce the stability of a closed-loop control strategy. On the other hand, the use of a pure feedforward control (inverse dynamics) requires a perfect knowledge of the dynamic behavior of the body and of manipulated objects. Sensory feedback is essential both to accommodate unexpected errors and events and to compensate for uncertainties about the dynamics of the body. Experimental observations concerning the control of posture, gaze and limbs have shown that the CNS certainly uses a combination of closed-loop and open-loop control. Feedforward components of movement, such as eye saccades, occur intermittently and present a stereotyped kinematic profile. In visuo-manual tracking tasks, hand movements exhibit velocity peaks that occur intermittently. When a delay or a slow dynamics are inserted in the visuo-manual control loop, intermittent step-and-hold movements appear clearly in the hand trajectory. In this study, we investigated strategies used by human subjects involved in the control of a particular dynamic system. We found strong evidence for substantial nonlinearities in the commands produced. The presence of step-and-hold movements seemed to be the major source of nonlinearities in the control loop. Furthermore, the stereotyped ballistic-like kinematics of these rapid and corrective movements suggests that they were produced in an open-loop way by the CNS. We analyzed the generation of ballistic movements in the light of sliding control theory assuming that they occurred when a sliding variable exceeded a constant threshold. In this framework, a sliding variable is defined as a composite variable (a combination of the instantaneous tracking error and its temporal derivatives) that fulfills a specific stability criterion. Based on this hypothesis and on the assumption of a constant reaction time, the tracking error and its derivatives should be correlated at a particular time lag before movement onset. A peak of correlation was found for a physiologically plausible reaction time, corresponding to a stable composite variable. The direction and amplitude of the ongoing stereotyped movements seemed also be adjusted in order to minimize this variable. These findings suggest that, during visually guided movements, human subjects attempt to minimize such a composite variable and not the instantaneous error. This minimization seems to be obtained by the execution of stereotyped corrective movements.

Ageing of internal models: from a continuous to an intermittent proprioceptive control of movement

“…Intermittency is characterised by sub-movements which are triggered by an error crossing a threshold (Asai et al 2009;Hanneton et al 1997;Miall et al 1993;Wolpert et al 1992). In both self-selected and fast speed conditions, the weak correlations observed between the peak velocity and the constant error suggested that the young adults used adjustments to reach the endpoint position (Messier and Kalaska 1999).…”

Internal models in sensorimotor integration: perspectives from adaptive control theory

“…Nevertheless, the two algorithms use different adaptation laws: adaptive sliding control uses the sliding variable, whereas feedback error learning uses a neural network controller. Hanneton et al (Hanneton, Berthoz et al 1997) proposed that the experimental data of human control of movement are consistent with the predictions of adaptive sliding control.…”

Event-Based Data Acquisition and Reconstruction—Mathematical Background

“…The rationale for intermittent control is that it confers online flexibility and adaptability. This rationale has caused many investigators to consider whether intermittent control is an appropriate paradigm for understanding biological motor control (Craik, 1947a,b;Vince, 1948;Bekey, 1962;Navas and Stark, 1968;Neilson et al, 1988;Miall et al, 1993a;Hanneton, Berthoz, Droulez, and Slotine, 1997;Neilson and Neilson, 2005;Loram and Lakie, 2002).…”

“…The existence of discontinuities within the control signal has been interpreted as submovements or serially planned control sequences (Navas and Stark, 1968;Poulton, 1974;Miall et al, 1993a;Miall, Weir, and Stein, 1986;Hanneton et al, 1997;Loram and Lakie, 2002), 2. Constancy in the modal rate of discontinuities, typically around 2-3 per second, has been interpreted as evidence for a central process with a well defined timescale (Navas and Stark, 1968;Poulton, 1974;.…”