On the control of biologically and kinematically redundant manipulators

How does computed tomography inform our understanding of shoulder kinematics? A structured review

The objective of this structured review was to review how computed tomography (CT) scanning has been used to measure the kinematics of the shoulder. A literature search was conducted using Evidence-based Medicine Reviews (Embase) and PubMed. In total, 29 articles were included in the data extraction process. Forty percent of the studies evaluated healthy participants' shoulder kinematics. The glenohumeral joint was the most studied, followed by the scapulothoracic, acromioclavicular, and sternoclavicular joints. Three-dimensional computed tomography (3DCT) and 3DCT with biplane fluoroscopy are the two primary imaging techniques that have been used to measure shoulder joints' motion under different conditions. Finally, many discrepancies in the reporting of the examined motions were found. Different authors used different perspectives and planes to report similar motions, which results in confusion and misunderstanding of the actual examined motion. The use of 3DCT has been widely used in the examination of shoulder kinematics in a variety of populations with varying methods employed. Future work is needed to extend these methodologies to include more diverse populations, to examine the shoulder complex as a whole, and to standardize their reporting of motion examined to make study to study comparisons possible.

A survey of human shoulder functional kinematic representations

In this survey, we review the field of human shoulder functional kinematic representations. The central question of this review is to evaluate whether the current approaches in shoulder kinematics can meet the high-reliability computational challenge. This challenge is posed by applications such as robot-assisted rehabilitation. Currently, the role of kinematic representations in such applications has been mostly overlooked. Therefore, we have systematically searched and summarised the existing literature on shoulder kinematics. The shoulder is an important functional joint, and its large range of motion (ROM) poses several mathematical and practical challenges. Frequently, in kinematic analysis, the role of the shoulder articulation is approximated to a ball-and-socket joint. Following the high-reliability computational challenge, our review challenges this inappropriate use of reductionism. Therefore, we propose that this challenge could be met by kinematic representations, that are redundant, that use an active interpretation and that emphasise on functional understanding.

Interaction against different environmental dynamics during a leg extension task is controlled by temporal rather than amplitude scaling of muscular activity

Force exertion against different mechanical environments can affect motor control strategies in order to account for the altered environmental dynamics and to maintain the ability to produce force. Here, we investigated the change of muscular activity of selected muscles of the lower extremities while the participants interacted with an external mechanical device of variable stability. Twenty-five healthy participants exerted force against the device by performing a unilateral ballistic leg extension task under 1 or 3 degrees of freedom (DoF). Directional force data and electromyographic responses from four leg muscles (TA, VM, GM, PL) were recorded. Muscle responses to the altered experimental conditions were analyzed by calculating time to peak electrical activity (TTP), peak electrical activity (PEA), slope of EMG-signal and muscle activity. It was found that neuromuscular system adjustments to the task are expressed mainly by temporal (TTP) rather than amplitude (PEA) scaling of muscular activity. This change was specific for the investigated muscles. Moreover, a selective increase of muscle activity occurred while increasing external DoF. This scheme was accompanied by a significant reduction of applicable force against the device in the unstable 3 DoF condition. The findings suggest that orchestration of movement control is linked to environmental dynamics also affecting the ability to produce force under dynamic conditions. The adjustments of the neuromuscular system are rather temporal in nature being consistent with the impulse timing hypothesis of motor control.

A novel two-stage framework for musculoskeletal dynamic modeling: an application to multifingered hand movement

In this paper, we present a new computational framework for biodynamic modeling of human movement. The framework decouples the conventional dynamic modeling process into two stages: in the first stage, two-component "agonist-antagonist" torque actuators under hypothesized and testable parametric control drive the forward dynamics, and parameters are identified by tracking both kinematics and kinetics; the second stage completes the mapping from the muscle-tendon forces to the predicted joint torques. An empirical test using multifinger grasping movement data was conducted to illustrate the application of the proposed framework and showed that the model reproduced the measurement accurately in both kinematics and kinetics. The torque components exhibited consistent spatial-temporal patterns across joints, digits, and subjects. The muscle-tendon forces computed based on the model-predicted kinematics and kinetics had the peak values within the same order of magnitude as in vivo data reported in the literature. The potential to predict was also demonstrated as we applied the control parameters of one subject to another and achieved close matches.

Review of models for the generation of multi-joint movements in 3-D

Most studies in motor control have focused on movements in two dimensions and only very few studies have systematically investigated movements in three dimensions. As a consequence, the large majority of modeling studies for motor control have tested the predictions of these models using movement data in 2D. As we will explain, movements in 3D cannot be understood from movements in 2D by adding just another dimension. The third dimension adds new and unexpected complexities. In this chapter we will explore the frames of reference, which are used in mapping sensory information about movement targets into motor commands and muscle activation patterns. Moreover, we will make a quantitative comparison between the predictions of various models in the literature with the outcome of 3D movement experiments. Quite surprisingly, none of the existing models is able to explain the data in different movement paradigms.

Stable Running with Segmented Legs

Spring-like leg behavior is found in both humans and animals when running. In a spring-mass model, running proves to be self-stable in terms of external perturbations or variations in leg properties (for example, landing angle). However, biological limbs are not made of springs, rather, they consist of segments where spring-like behavior can be localized at the joint level. Here, we use a two-segment leg model to investigate the effects of leg compliance originating from the joint level on running stability. Owing to leg geometry a non-linear relationship between leg force and leg compression is found. In contrast to the linear leg spring, the segmented leg is capable of reducing the minimum speed for self-stable running from 3.5 m s-1in the spring- mass model to 1.5 m s-1for almost straight joint configurations, which is below the preferred transition speed from human walking to running (≈2 m s-1). At moderate speeds the tolerated range of landing angle is largely increased (17° at 5 m s-1) compare with the linear leg spring model (2°). However, for fast running an increase in joint stiffness is required to compensate for the mechanical disadvantage of larger leg compression. This could be achieved through the use of non-linear springs to enhance joint stiffness in fast running.

Neuromuscular and biomechanical factors codetermine the solution to motor redundancy in rhythmic multijoint arm movement

How the CNS deals with the issue of motor redundancy remains a central question for motor control research. Here we investigate the means by which neuromuscular and biomechanical factors interact to resolve motor redundancy in rhythmic multijoint arm movements. We used a two-df motorized robot arm to manipulate the dynamics of rhythmic flexion-extension (FE) and supination-pronation (SP) movements at the elbow-joint complex. Participants were required to produce rhythmic FE and SP movements, either in isolation, or in combination (at the phase relationship of their choice), while we recorded the activity of key bi-functional muscles. When performed in combination, most participants spontaneously produced an in-phase pattern of coordination in which flexion is synchronised with supination. The activity of the Biceps Brachii (BB), the strongest arm muscle which also has the largest moment arms in both flexion and supination was significantly higher for FE and SP performed in combination than in isolation, suggesting optimal exploitation of the mechanical advantage of this muscle. In a separate condition, participants were required to produce a rhythmic SP movement while a rhythmic FE movement was imposed by the motorized robot. Simulations based upon a musculoskeletal model of the arm demonstrated that in this context, the most efficient use of the force-velocity relationship of BB requires that an anti-phase pattern of coordination (flexion synchronized with pronation) be produced. In practice, the participants maintained the in-phase behavior, and BB activity was higher than for SP performed in isolation. This finding suggests that the neural organisation underlying the exploitation of bifunctional muscle properties, in the natural context, constrains the system to maintain the "natural" coordination pattern in an altered dynamic environment, even at the cost of reduced biomechanical efficiency. We suggest an important role for afference from the imposed movement in promoting the "natural" pattern. Practical implications for the emerging field of robot-assisted therapy and rehabilitation are briefly mentioned.

Computational motor control: redundancy and invariance

The nervous system controls the behavior of complex kinematically redundant biomechanical systems. How it computes appropriate commands to generate movements is unknown. Here we propose a model based on the assumption that the nervous system: 1) processes static (e.g., gravitational) and dynamic (e.g., inertial) forces separately; 2) calculates appropriate dynamic controls to master the dynamic forces and progress toward the goal according to principles of optimal feedback control; 3) uses the size of the dynamic commands (effort) as an optimality criterion; and 4) can specify movement duration from a given level of effort. The model was used to control kinematic chains with 2, 4, and 7 degrees of freedom [planar shoulder/elbow, three-dimensional (3D) shoulder/elbow, 3D shoulder/elbow/wrist] actuated by pairs of antagonist muscles. The muscles were modeled as second-order nonlinear filters and received the dynamics commands as inputs. Simulations showed that the model can quantitatively reproduce characteristic features of pointing and grasping movements in 3D space, i.e., trajectory, velocity profile, and final posture. Furthermore, it accounted for amplitude/duration scaling and kinematic invariance for distance and load. These results suggest that motor control could be explained in terms of a limited set of computational principles.

Modeling 3D object manipulation: synchronous single-axis joint rotations?

In the present paper we introduce a movement planning model that is capable of predicting object manipulation movements in three dimensions. A basic assumption of this model is that the joint kinematics of the movement are optimized, which implies that joint rotations are synchronous. Synchronous joint rotations can be considered as a simplifying strategy to control arm movements, thus controlling the timing of several segments as a whole rather than for each joint separately. We will discuss evidence for synchronous joint rotations in 2D and explain why 3D synchrony is much more complex to substantiate. Different joint-angle representations and measures of asynchrony yield conflicting results. After showing that our model predicts realistic hand paths for various movement directions (the center-out task), we focus on a task that involves re-orientation of a hand-held cylinder, thus especially zooming in on those degrees of freedom not taken into account in 2D models. The more the cylinder needs to be rotated, the more curved the hand path is. With respect to 3D synchrony, a representation of shoulder and elbow rotations as single-axis rotations comes closest to synchronous joint rotations, which suggests that the brain plans a movement in joint space as a single postural transition.

Reliability of upper and lower limb three-dimensional kinematics in children with hemiplegia

The repeatability of both 3D kinematic measurements of arm movement during simple upper limb tasks and lower limb movement during gait analysis was evaluated in 10 children with hemiplegic cerebral palsy. All tasks were completed on two separate occasions, 1 week apart. The 3D lower limb gait analysis showed high levels of repeatability in the sagittal plane measures, with mean coefficient of multiple correlations (CMCs) greater than 0.92 between sessions. Transverse and frontal plane measures had mean CMCs greater than 0.7 between sessions. A 3D analysis of shoulder and elbow flexion/extension during the two functional tasks (hand to head and hand to mouth) was highly repeatable between sessions (mean CMCs, 0.87 to 0.95). Rotational measures at the shoulder and the elbow during the same tasks demonstrated moderate levels of inter-sessional repeatability (mean CMCs shoulder 0.49 to 0.63; elbow 0.63 to 0.74). Overall, the lower limb 3D kinematic analysis had similar levels of repeatability in both the hemiplegic limb and the limb with normal tone. The 3D kinematic analysis of movement of the hemiplegic upper limb during simple upper limb tasks also had moderate to good repeatability, suggesting it may be able to be used as an outcome measure in the hemiplegic upper limb.

Joint stiffness of the ankle and the knee in running

The spring-mass model is a valid fundament to understand global dynamics of fast legged locomotion under gravity. The underlying concept of elasticity, implying leg stiffness as a crucial parameter, is also found on lower motor control levels, i.e. in muscle-reflex and muscle-tendon systems. Therefore, it seems reasonable that global leg stiffness emerges from local elasticity established by appropriate joint torques. A recently published model of an elastically operating, segmented leg predicts that proper adjustment of joint elasticities to the leg geometry and initial conditions of ground contact provides internal leg stability. Another recent study suggests that in turn the leg segmentation and the initial conditions may be a consequence of metabolic and bone stress constraints. In this study, the theoretical predictions were verified experimentally with respect to initial conditions and elastic joint characteristics in human running. Kinematics and kinetics were measured and the joint torques were estimated by inverse dynamics. Stiffnesses and elastic nonlinearities describing the resulting joint characteristics were extracted from parameter fits. Our results clearly support the theoretical predictions: the knee joint is always stiffer and more extended than the ankle joint. Moreover, the knee torque characteristic on the average shows the higher nonlinearity. According to literature, the leg geometry is a consequence of metabolic and material stress limitations. Adapted to this given geometry, the initial joint angle conditions in fast locomotion are a compromise between metabolic and control effort minimisation. Based on this adaptation, an appropriate joint stiffness ratio between ankle and knee passively safeguards the internal leg stability. The identified joint nonlinearities contribute to the linearisation of the leg spring.

Interplay of biomechanical constraints and kinematic strategies in selecting arm postures

In this study, the authors examined the interplay between biomechanics and control strategies in the resolution of excess degrees of freedom at the joint level. Seven participants made aimed arm movements from 30 starting points and several starting postures to targets. Final arm postures for movements to a target exhibited substantial joint angle variation. Through regression modeling and by comparing observed final arm postures with biomechanically plausible postures, the authors identified 3 kinematic strategies: (a) Maintain deviations from the average angle at the starting point to the joint's final posture; (b) make torso rotations that are a fixed proportion of shoulder rotations; and (c) adopt a characteristic combination of 4 wrist-positioning approaches. The results demonstrated that kinematic strategies can account for substantial variance in final arm postures, if one takes into account 2 types of individual differences-those that arise inevitably from biomechanical constraints and those that reflect choices in movement strategy.

Evidence of motor equivalence in a pointing task involving locomotion

A pointing task was performed both while subjects stood beside and while subjects walked past targets that involved differing movement amplitudes and differing sizes. The hand kinematics were considered relative both to a fixed frame of reference in the movement environment (end effector kinematics) and to the subject's body (kinematics of the hand alone). From the former view, there were few differences between standing and walking versions of the task, indicating similarity of the kinematics of the hand. However, when the hand was considered alone, marked differences in the kinematics and spatial trajectories between standing and walking were achieved. Furthermore, kinematic analyses of the trunk showed that subjects used differing amounts of both flexion-extension and rotation movements at the waist depending on whether they were standing or walking as well as on the constraints imposed by target width and movement amplitude. The present results demonstrate the existence of motor equivalence in a combined upper and lower extremity task and that this motor equivalence is a control strategy to cope with increasing task demands. Given the complexity involved in controlling the arm, the torso, and the legs (during locomotion), the movements involved in the present tasks appear to be planned and controlled by considering the whole body as a single unit.

A behavior-based inverse kinematics algorithm to predict arm prehension postures for computer-aided ergonomic evaluation

In this paper, the computational problem of inverse kinematics of arm prehension movements was investigated. How motions of each joint involved in arm movements can be used to control the end-effector (hand) position and orientation was first examined. It is shown that the inverse kinematics problem due to the kinematic redundancy in joint space is ill-posed only at the control of hand orientation but not at the control of hand position. Based upon this analysis, a previously proposed inverse kinematics algorithm (Wang et Verriest, 1998a) to predict arm reach postures was extended to a seven-DOF arm model to predict arm prehension postures using a separate control of hand position and orientation. The algorithm can be either in rule-based form or by optimization through appropriate choice of weight coefficients. Compared to the algebraic inverse kinematics algorithm, the proposed algorithm can handle the non-linearity of joint limits in a straightforward way. In addition, no matrix inverse calculation is needed, thus avoiding the stability and convergence problems often occurring near a singularity of the Jacobian. Since an end-effector motion-oriented method is used to describe joint movements, observed behaviors of arm movements can be easily implemented in the algorithm. The proposed algorithm provides a general frame for arm postural control and can be used as an efficient postural manipulation tool for computer-aided ergonomic evaluation.