Reconstruction of equilibrium trajectories during whole-body movements

Towards physics of neural processes and behavior

Behavior of biological systems is based on basic physical laws, common across inanimate and living systems, and currently unknown physical laws that are specific for living systems. Living systems are able to unite basic laws of physics into chains and clusters leading to new stable and pervasive relations among variables (new physical laws) involving new parameters and to modify these parameters in a purposeful way. Examples of such laws are presented starting from the tonic stretch reflex. Further, the idea of control with referent coordinates is formulated and merged with the idea of hierarchical control and the principle of abundance. The notion of controlled stability of behaviors is linked to the idea of structured variability, which is a common feature across living systems and actions. The explanatory and predictive power of this approach is illustrated with respect to the control of both intentional and unintentional movements, the phenomena of equifinality and its violations, preparation to quick actions, development of motor skills, changes with aging and neurological disorders, and perception.

Synergies in the space of control variables within the equilibrium-point hypothesis

We use an approach rooted in the recent theory of synergies to analyze possible co-variation between two hypothetical control variables involved in finger force production based on the equilibrium-point (EP) hypothesis. These control variables are the referent coordinate (R) and apparent stiffness (C) of the finger. We tested a hypothesis that inter-trial co-variation in the {R; C} space during repeated, accurate force production trials stabilizes the fingertip force. This was expected to correspond to a relatively low amount of inter-trial variability affecting force and a high amount of variability keeping the force unchanged. We used the "inverse piano" apparatus to apply small and smooth positional perturbations to fingers during force production tasks. Across trials, R and C showed strong co-variation with the data points lying close to a hyperbolic curve. Hyperbolic regressions accounted for over 99% of the variance in the {R; C} space. Another analysis was conducted by randomizing the original {R; C} data sets and creating surrogate data sets that were then used to compute predicted force values. The surrogate sets always showed much higher force variance compared to the actual data, thus reinforcing the conclusion that finger force control was organized in the {R; C} space, as predicted by the EP hypothesis, and involved co-variation in that space stabilizing total force.

Closed-loop and open-loop control of posture and movement during human trunk bending

Closed-loop (CL) and open-loop (OL) types of motor control during human forward upper trunk bending are investigated. A two-joint (hip and ankle) biomechanical model of the human body is used. The analysis is performed in terms of the movements along eigenvectors of the motion equation ("eigenmovements" or "natural synergies"). Two analyzed natural synergies are called "H-synergy" (Hip) and "A-synergy" (Ankle) according to the dominant joint in each of these synergies. Parameters of CL control were estimated using a sudden support platform displacement applied during the movement execution. The CL gain in the H-synergy increased and in the A-synergy decreased during the movement as compared with the quiet standing. The analysis of the time course of OL control signal suggests that the H-synergy (responsible for the prime movement, i.e. bending per se) is controlled according to the EP theory whereas for the associated A-synergy (responsible for posture adjustment, i.e. equilibrium maintenance) muscle forces and gravity forces are balanced for any its final amplitude and therefore the EP theory is not applicable to its control.

MODEM: a multi-agent hierarchical structure to model the human motor control system

In this study, based on behavioral and neurophysiological facts, a new hierarchical multi-agent architecture is proposed to model the human motor control system. Performance of the proposed structure is investigated by simulating the control of sit to stand movement. To develop the model, concepts of mixture of experts, modular structure, and some aspects of equilibrium point hypothesis were brought together. We have called this architecture MODularized Experts Model (MODEM). Human motor system is modeled at the joint torque level and the role of the muscles has been embedded in the function of the joint compliance characteristics. The input to the motor system, i.e., the central command, is the reciprocal command. At the lower level, there are several experts to generate the central command to control the task according to the details of the movement. The number of experts depends on the task to be performed. At the higher level, a "gate selector" block selects the suitable subordinate expert considering the context of the task. Each expert consists of a main controller and a predictor as well as several auxiliary modules. The main controller of an expert learns to control the performance of a given task by generating appropriate central commands under given conditions and/or constraints. The auxiliary modules of this expert learn to scrutinize the generated central command by the main controller. Auxiliary modules increase their intervention to correct the central command if the movement error is increased due to an external disturbance. Each auxiliary module acts autonomously and can be interpreted as an agent. Each agent is responsible for one joint and, therefore, the number of the agents of each expert is equal to the number of joints. Our results indicate that this architecture is robust against external disturbances, signal-dependent noise in sensory information, and changes in the environment. We also discuss the neurophysiological and behavioral basis of the proposed model (MODEM).

Postural preparation to making a step: is there a 'motor program' for postural preparation?

We tested the hypothesis that a sequence of mechanical events occurs preceding a step that scales in time and magnitude as a whole in a task-specific manner, and is a reflection of a "motor program." Young subjects made a step under three speed instructions and four tasks: stepping straight ahead, down a stair, up a stair, and over an obstacle. Larger center-of-pressure (COP) and force adjustments in the anterior-posterior direction and smaller COP and force adjustments in the mediolateral direction were seen during stepping forward and down a stair, as compared with the tasks of stepping up a stair and over an obstacle. These differences were accentuated during stepping under the simple reaction time instruction. These results speak against the hypothesis of a single motor program that would underlie postural preparation to stepping. They are more compatible with the reference configuration hypothesis of whole-body actions.

Adjustment of the human arm viscoelastic properties to the direction of reaching

The viscoelastic properties of the human arm were measured by means of short force perturbations during fast reaching movements in two orthogonal directions. A linear spring model with time delay described the neuromuscular system of the human arm. The obtained viscoelastic parameters ensured movement stability in spite of the time delay of 50 ms. The stiffness and viscosity ellipses appeared to be predominantly orthogonal to the movement direction, which reduced the effect of force perturbation in the direction orthogonal to the reaching movement. Thus, it can be argued that the viscoelastic properties of the neuromuscular system of the human arm are adjusted to the direction of movement according to a "path preserving" strategy, which minimizes the deviation of the movement path from a straight line, when exposed to an unexpected external force.

Basic elements of arm postural control analyzed by unloading

To address the question of how arm posture is controlled, we analyzed shoulder-elbow unloading responses in the horizontal plane for different directions of the initial load. The initial load, produced by a double-joint manipulandum, was suddenly diminished to 1of 12 randomly presented levels (60 to -10% of the initial load; in 6 out of 12 cases the final load direction varied by +/-20 degrees ). Subjects were instructed "not to intervene" in response to unloading. Neither the unloading onset nor the final load level was predictable and we assumed that the responses to rapid unloading were involuntary. Unloading elicited a smooth hand movement characterized by a bell-shaped velocity profile. The changes in hand position, joint angles, and joint torques generally increased with greater amounts of unloading. For each direction of the initial load, tonic electromyographic activity of the shoulder and elbow muscles also changed, depending on the amount of unloading. The shoulder and elbow joint torques before and after unloading were a function of the difference between the actual configuration of the arm and its referent configuration (R) described by the angles at which each joint torque was zero. The R configuration changed depending on the direction of the initial load. Our electromyographic data imply that these changes result from a central modification of muscle activation thresholds. The nervous system may thus control the R configuration in a task-specific way by leaving it unchanged to generate involuntary responses to unloading or modifying it to accommodate a new load direction at the same initial position. It is concluded that the R configuration is a major variable in both intentional and involuntary control of posture.

Mechanical aspects of legged locomotion control

We review the mechanical components of an approach to motion science that enlists recent progress in neurophysiology, biomechanics, control systems engineering, and non-linear dynamical systems to explore the integration of muscular, skeletal, and neural mechanics that creates effective locomotor behavior. We use rapid arthropod terrestrial locomotion as the model system because of the wealth of experimental data available. With this foundation, we list a set of hypotheses for the control of movement, outline their mathematical underpinning and show how they have inspired the design of the hexapedal robot, RHex.

Why and how are posture and movement coordinated?

In most motor acts, posture and movement must be coordinated in order to achieve the goal of the task. The focus of this chapter is on why and how this coordination takes place. First, the nature of posture is discussed. Two of its general functions are recognized; an antigravity role, and a role in interfacing the body with its environment such that perception and action can ensue. Next addressed is how posture is controlled centrally. Two models are presented and evaluated; a genetic and a hierarchical one. The latter has two levels; internal representation and execution. Finally, we consider how central control processes might achieve an effective coordination between posture and movement. Is a single central control process responsible for both movement and its associated posture? Alternatively, is there a dual coordinated control system: one for movement, and the other for posture? We provide evidence for the latter, in the form of a biomechanical analysis that features the use of eigenmovement approach.