A model of open-loop control of equilibrium position and stiffness of the human elbow joint

According to the equilibrium point theory, the control of posture and movement involves the setting of equilibrium joint positions (EP) and the independent modulation of stiffness. One model of EP control, the α-model, posits that stable EPs and stiffness are set open-loop, i.e. without the aid of feedback. The purpose of the present study was to explore for the elbow joint the range over which stable EPs can be set open-loop and to investigate the effect of co-contraction on intrinsic low-frequency elbow joint stiffness (

New control strategies for neuroprosthetic systems

The availability of techniques to artificially excite paralyzed muscles opens enormous potential for restoring both upper and lower extremity movements with\ud neuroprostheses. Neuroprostheses must stimulate muscle, and control and regulate the artificial movements produced. Control methods to accomplish these tasks include feedforward (open-loop), feedback, and adaptive control. Feedforward control requires a great deal of information about the biomechanical behavior of the limb. For the upper extremity, an artificial motor program was developed to provide such movement program input to a neuroprosthesis. In lower extremity control, one group achieved their best results by attempting to meet naturally perceived gait objectives rather than to follow an exact joint angle trajectory. Adaptive feedforward control, as implemented in the cycleto-cycle controller, gave good compensation for the gradual decrease in performance observed with open-loop control. A neural network controller was able to control its system to customize stimulation parameters in order to generate a desired output trajectory in a given individual and to maintain tracking performance in the presence of muscle fatigue. The authors believe that practical FNS control systems must\ud exhibit many of these features of neurophysiological systems

Control of position and movement is simplified by combined muscle spindle and Golgi tendon organ feedback

Whereas muscle spindles play a prominent role in current theories of human motor control, Golgi tendon organs (GTO) and their associated tendons are often neglected. This is surprising since there is ample evidence that both tendons and GTOs contribute importantly to neuromusculoskeletal dynamics. Using detailed musculoskeletal models, we provide evidence that simple feedback using muscle spindles alone results in very poor control of joint position and movement since muscle spindles cannot sense changes in tendon length that occur with changes in muscle force. We propose that a combination of spindle and GTO afferents can provide an estimate of muscle-tendon complex length, which can be effectively used for low-level feedback during both postural and movement tasks. The feasibility of the proposed scheme was tested using detailed musculoskeletal models of the human arm. Responses to transient and static perturbations were simulated using a 1-degree-of-freedom (DOF) model of the arm and showed that the combined feedback enabled the system to respond faster, reach steady state faster, and achieve smaller static position errors. Finally, we incorporated the proposed scheme in an optimally controlled 2-DOF model of the arm for fast point-to-point shoulder and elbow movements. Simulations showed that the proposed feedback could be easily incorporated in the optimal control framework without complicating the computation of the optimal control solution, yet greatly enhancing the system's response to perturbations. The theoretical analyses in this study might furthermore provide insight about the strong physiological couplings found between muscle spindle and GTO afferents in the human nervous system. © 2013 the American Physiological Society

On the intrinsic control properties of muscle and relexes: exploring the interaction between neural and musculoskeletal dynamics in the framework of the equilbrium-point hypothesis

The aim of this thesis is to examine the relationship between the intrinsic dynamics of the body and its neural control. Specifically, it investigates the influence of musculoskeletal properties on the control signals needed for simple goal-directed movements in the framework of the equilibriumpoint (EP) hypothesis. To this end, muscle models of varying complexity are studied in isolation and when coupled to feedback laws derived from the EP hypothesis. It is demonstrated that the dynamical landscape formed by non-linear musculoskeletal models features a stable attractor in joint space whose properties, such as position, stiffness and viscosity, can be controlled through differential- and co-activation of antagonistic muscles. The emergence of this attractor creates a new level of control that reduces the system’s degrees of freedom and thus constitutes a low-level motor synergy. It is described how the properties of this stable equilibrium, as well as transient movement dynamics, depend on the various modelling assumptions underlying the muscle model. The EP hypothesis is then tested on a chosen musculoskeletal model by using an optimal feedback control approach: genetic algorithm optimisation is used to identify feedback gains that produce smooth single- and multijoint movements of varying amplitude and duration. The importance of different feedback components is studied for reproducing invariants observed in natural movement kinematics. The resulting controllers are demonstrated to cope with a plausible range of reflex delays, predict the use of velocity-error feedback for the fastest movements, and suggest that experimentally observed triphasic muscle bursts are an emergent feature rather than centrally planned. Also, control schemes which allow for simultaneous control of movement duration and distance are identified. Lastly, it is shown that the generic formulation of the EP hypothesis fails to account for the interaction torques arising in multijoint movements. Extensions are proposed which address this shortcoming while maintaining its two basic assumptions: control signals in positional rather than force-based frames of reference; and the primacy of control properties intrinsic to the body over internal models. It is concluded that the EP hypothesis cannot be rejected for single- or multijoint reaching movements based on claims that predicted movement kinematics are unrealistic

Is equilibrium point control feasible for fast goal-directed single-joint movements?

Several types of equilibrium point (EP) controllers have been proposed for the control of posture and movement. EP controllers are appealing from a computational perspective because they do not require solving the "inverse dynamic problem" (i.e., computation of the torques required to move a system along a desired trajectory). It has been argued that EP controllers are not capable of controlling fast single-joint movements. To refute this statement, several extensions have been proposed, although these have been tested using models in which only the tendon compliance, force-length-velocity relation, and mechanical interaction between tendon and contractile element were not adequately represented. In the present study, fast elbow-joint movements were measured and an attempt was made to reproduce these using a realistic musculoskeletal model of the human arm. Three types of EP controllers were evaluated: an open-loop α-controller, a closed-loop λ-controller, and a hybrid open- and closed-loop controller. For each controller we considered a continuous version and a version in which the control signals were sent out intermittently. Only the intermittent hybrid EP controller was capable of generating movements that were as fast as those of the subjects. As a result of the nonlinear muscle properties, the hybrid EP controller requires a more detailed representation of static muscle properties than generally assumed in the context of EP control. In sum, this study shows that fast single-joint movements can be realized without explicitly solving the inverse dynamics problem, but in a less straightforward manner than implied by proponents of conventional EP controllers. Copyright © 2006 The American Physiological Society

A robotic model to investigate human motor control

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Inter-Joint Coordination Deficits Revealed in the Decomposition of Endpoint Jerk During Goal-Directed Arm Movement After Stroke

It is well documented that neurological deficits after stroke can disrupt motor control processes that affect the smoothness of reaching movements. The smoothness of hand trajectories during multi-joint reaching depends on shoulder and elbow joint angular velocities and their successive derivatives as well as on the instantaneous arm configuration and its rate of change. Right-handed survivors of unilateral hemiparetic stroke and neurologically-intact control participants held the handle of a two-joint robot and made horizontal planar reaching movements. We decomposed endpoint jerk into components related to shoulder and elbow joint angular velocity, acceleration, and jerk. We observed an abnormal decomposition pattern in the most severely impaired stroke survivors consistent with deficits of inter-joint coordination. We then used numerical simulations of reaching movements to test whether the specific pattern of inter-joint coordination deficits observed experimentally could be explained by either a general increase in motor noise related to weakness or by an impaired ability to compensate for multi-joint interaction torque. Simulation results suggest that observed deficits in movement smoothness after stroke more likely reflect an impaired ability to compensate for multi-joint interaction torques rather than the mere presence of elevated motor noise

Conclusions on motor control depend on the type of model used to represent the periphery

Within the field of motor control, there is no consensus on which kinematic and kinetic aspects of movements are planned or controlled. Perturbing goal-directed movements is a frequently used tool to answer this question. To be able to draw conclusions about motor control from kinematic responses to perturbations, a model of the periphery (i.e., the skeleton, muscle-tendon complexes, and spinal reflex circuitry) is required. The purpose of the present study was to determine to what extent such conclusions depend on the level of simplification with which the dynamical properties of the periphery are modeled. For this purpose, we simulated fast goal-directed single-joint movement with four existing types of models. We tested how three types of perturbations affected movement trajectory if motor commands remained unchanged. We found that the four types of models of the periphery showed different robustness to the perturbations, leading to different predictions on how accurate motor commands need to be, i.e., how accurate the knowledge of external conditions needs to be. This means that when interpreting kinematic responses obtained in perturbation experiments the level of error correction attributed to adaptation of motor commands depends on the type of model used to describe the periphery

Modeling of equilibrium point trajectory control in human arm movements

The underlying concept of the Equilibrium Point Hypothesis (EPH) is that the CNS provides a virtual trajectory of joint motion, representing spacing and timing, with actual movement dynamics being produced by interactions of limb inertia, muscle viscosity and speed/position feedback from muscle spindles. To counter criticisms of the EPH, investigators have proposed the use of complex virtual trajectories, non-linear damping, stiffness and time varying stiffness to the EPH model. While these features allow the EPH to adequately produce human joint velocities, they conflict with the EPH’s premise of simple pre-planned monotonic control of movement trajectory. As a result, this study proposed an EPH based method, which provides a simpler mechanism in motor control without conflict with the core advantages of the original approach. This work has proposed relative damping as an addition to the EPH model to predict the single and two joint arm movements. This addition results in simulated data that not only closely match experimental angle data, but also match the experimental joint torques. In addition, it is suggested that this modified model can be used to predict the multi-joint angular trajectories with fast and normal velocities, without the need for time varying or non-linear stiffness and damping, but with simple monotonic virtual trajectories. In the following study, this relative damping model has been further enhanced with an EMG-based determination of the virtual trajectory and with physiologically realistic neuromuscular delays. The results of unobstructed voluntary movement studies suggest that the EPH models use realistic impedance values and produce desired joint trajectories and joint torques in unperturbed voluntary arm movement. A subsequent study of obstructed voluntary arm movement extended the relative damping concept, and incorporated the influential factors of the mechanical behavior of the neural, muscular and skeletal system in the control and coordination of arm posture and movement. A significant problem of the study is how this information should be used to modify control signals to achieve desired performance. This study used an EPH model to examine changes of controlling signals for arm movements in the context of adding perturbation/load in the form of forces/torques. The mechanical properties and reflex actions of muscles of the elbow joint were examined. Brief unexpected torque/force pulses of identical magnitude and time duration were introduced at different stages of the movement in a random order by a pre-programmed 3 degree of freedom (DOF) robotic arm (MOOG FCS HapticMaster). The results show that the subjects may maintain the same control parameters (virtual trajectory, stiffness and damping) regardless of added perturbations that cause substantial changes in EMG activity and kinematics

Real-time simulation of three-dimensional shoulder girdle and arm dynamics

Electrical stimulation is a promising technology for the restoration of arm function in paralyzed individuals. Control of the paralyzed arm under electrical stimulation, however, is a challenging problem that requires advanced controllers and command interfaces for the user. A real-time model describing the complex dynamics of the arm would allow user-in-the-loop type experiments where the command interface and controller could be assessed. Real-time models of the arm previously described have not included the ability to model the independently controlled scapula and clavicle, limiting their utility for clinical applications of this nature. The goal of this study therefore was to evaluate the performance and mechanical behavior of a real-time, dynamic model of the arm and shoulder girdle. The model comprises seven segments linked by eleven degrees of freedom and actuated by 138 muscle elements. Polynomials were generated to describe the muscle lines of action to reduce computation time, and an implicit, first-order Rosenbrock formulation of the equations of motion was used to increase simulation step-size. The model simulated flexion of the arm faster than real time, simulation time being 92% of actual movement time on standard desktop hardware. Modeled maximum isometric torque values agreed well with values from the literature, showing that the model simulates the moment-generating behavior of a real human arm. The speed of the model enables experiments where the user controls the virtual arm and receives visual feedback in real time. The ability to optimize potential solutions in simulation greatly reduces the burden on the user during development