Manifold reaching paradigm: how do we handle target redundancy?

Human arm redundancy: a new approach for the inverse kinematics problem

The inverse kinematics (IK) problem addresses how both humans and robotic systems coordinate movement to resolve redundancy, as in the case of arm reaching where more degrees of freedom are available at the joint versus hand level. This work focuses on which coordinate frames best represent human movements, enabling the motor system to solve the IK problem in the presence of kinematic redundancies. We used a multi-dimensional sparse source separation method to derive sets of basis (or source) functions for both the task and joint spaces, with joint space represented by either absolute or anatomical joint angles. We assessed the similarities between joint and task sources in each of these joint representations, finding that the time-dependent profiles of the absolute reference frame's sources show greater similarity to corresponding sources in the task space. This result was found to be statistically significant. Our analysis suggests that the nervous system represents multi-joint arm movements using a limited number of basis functions, allowing for simple transformations between task and joint spaces. Additionally, joint space seems to be represented in an absolute reference frame to simplify the IK transformations, given redundancies. Further studies will assess this finding's generalizability and implications for neural control of movement.

Feasibility of using the Leap Motion Controller to administer conventional motor tests: a proof-of-concept study

Although upper-limb movement impairments are common, the primary tools for assessing and tracking impairments in clinical settings are limited. Markerless motion capture (MMC) technology has the potential to provide a large amount of quantitative, objective movement data in routine clinical use. Many past studies have focused on whether MMC are sufficiently accurate. However, another necessary step is to create meaningful clinical tests that can be administered via MMC in a robust manner. Four conventional upper-limb motor tests common in clinical assessments (visually guided movement, finger tapping, postural tremor, and reaction time) were modified so they can be administered via a particular MMC sensor, the Leap Motion Controller (LMC). In this proof-of-concept study, we administered these modified tests to 100 healthy subjects and present here the successes and challenges we encountered. Subjects generally found the LMC and the graphical user interfaces of the tests easy to use. The LMC recorded movement with sufficiently high sampling rate (>106 samples/s), and the rate of LMC malfunctions (mainly jumps in time or space) was low, so only 1.9% of data was discarded. However, administration of the tests also revealed some significant weaknesses. The visually guided movement test was easily implemented with the LMC; the modified reaction time test worked reasonably well with the LMC but is likely more easily implemented with other existing technologies; and the modified tremor and finger tapping tests did not work well because of the limited bandwidth of the LMC. Our findings highlight the need to develop and evaluate motor tests specifically suited for MMC. The real strength of MMC may not be in replicating conventional tests but rather in administering new tests or testing conditions not possible with conventional clinical tests or other technologies.

Motor invariants in action execution and perception

The nervous system is sensitive to statistical regularities of the external world and forms internal models of these regularities to predict environmental dynamics. Given the inherently social nature of human behavior, being capable of building reliable predictive models of others' actions may be essential for successful interaction. While social prediction might seem to be a daunting task, the study of human motor control has accumulated ample evidence that our movements follow a series of kinematic invariants, which can be used by observers to reduce their uncertainty during social exchanges. Here, we provide an overview of the most salient regularities that shape biological motion, examine the role of these invariants in recognizing others' actions, and speculate that anchoring socially-relevant perceptual decisions to such kinematic invariants provides a key computational advantage for inferring conspecifics' goals and intentions.

Upper limb joint coordination preserves hand kinematics after a traumatic brachial plexus injury

Background

Traumatic brachial plexus injury (TBPI) causes a sensorimotor deficit in upper limb (UL) movements.

Objective

Our aim was to investigate the arm–forearm coordination of both the injured and uninjured UL of TBPI subjects.

Methods

TBPI participants (n = 13) and controls (n = 10) matched in age, gender, and anthropometric characteristics were recruited. Kinematics from the shoulder, elbow, wrist, and index finger markers were collected, while upstanding participants transported a cup to their mouth and returned the UL to a starting position. The UL coordination was measured through the relative phase (RP) between arm and forearm phase angles and analyzed as a function of the hand kinematics.

Results

For all participants, the hand transport had a shorter time to peak velocity (p < 0.01) compared to the return. Also, for the control and the uninjured TBPI UL, the RP showed a coordination pattern that favored forearm movements in the peak velocity of the transport phase (p < 0.001). TBPI participants' injured UL showed a longer movement duration in comparison to controls (p < 0.05), but no differences in peak velocity, time to peak velocity, and trajectory length, indicating preserved hand kinematics. The RP of the injured UL revealed altered coordination in favor of arm movements compared to controls and the uninjured UL (p < 0.001). Finally, TBPI participants' uninjured UL showed altered control of arm and forearm phase angles during the deceleration of hand movements compared to controls (p < 0.05).

Conclusion

These results suggest that UL coordination is reorganized after a TBPI so as to preserve hand kinematics.

Kinematic Changes in the Uninjured Limb After a Traumatic Brachial Plexus Injury

Background: Traumatic brachial plexus injury (TBPI) typically causes sensory, motor and autonomic deficits of the affected upper limb. Recent studies have suggested that a unilateral TBPI can also affect the cortical representations associated to the uninjured limb.

Objective: To investigate the kinematic features of the uninjured upper limb in participants with TBPI.

Methods: Eleven participants with unilateral TBPI and twelve healthy controls matched in gender, age and anthropometric characteristics were recruited. Kinematic parameters collected from the index finger marker were measured while participants performed a free-endpoint whole-body reaching task and a cup-to-mouth task with the uninjured upper limb in a standing position.

Results: For the whole-body reaching task, lower time to peak velocity (p = 0.01), lower peak of velocity (p = 0.003), greater movement duration (p = 0.04) and shorter trajectory length (p = 0.01) were observed in the TBPI group compared to the control group. For the cup-to-mouth task, only a lower time to peak velocity was found for the TBPI group compared to the control group (p = 0.02). Interestingly, no differences between groups were observed for the finger endpoint height parameter in either of the tasks. Taken together, these results suggest that TBPI leads to a higher cost for motor planning when it comes to movements of the uninjured limb as compared to healthy participants. This cost is even higher in a task with a greater postural balance challenge.

Conclusion: This study expands the current knowledge on bilateral sensorimotor alterations after unilateral TBPI and should guide rehabilitation after a peripheral injury.

Costs of position, velocity, and force requirements in optimal control induce triphasic muscle activation during reaching movement

The nervous system activates a pair of agonist and antagonist muscles to determine the muscle activation pattern for a desired movement. Although there is a problem with redundancy, it is solved immediately, and movements are generated with characteristic muscle activation patterns in which antagonistic muscle pairs show alternate bursts with a triphasic shape. To investigate the requirements for deriving this pattern, this study simulated arm movement numerically by adopting a musculoskeletal arm model and an optimal control. The simulation reproduced the triphasic electromyogram (EMG) pattern observed in a reaching movement using a cost function that considered three terms: end-point position, velocity, and force required; the function minimised neural input. The first, second, and third bursts of muscle activity were generated by the cost terms of position, velocity, and force, respectively. Thus, we concluded that the costs of position, velocity, and force requirements in optimal control can induce triphasic EMG patterns. Therefore, we suggest that the nervous system may control the body by using an optimal control mechanism that adopts the costs of position, velocity, and force required; these costs serve to initiate, decelerate, and stabilise movement, respectively.

Stochastic optimal feedforward-feedback control determines timing and variability of arm movements with or without vision

Human movements with or without vision exhibit timing (i.e. speed and duration) and variability characteristics which are not well captured by existing computational models. Here, we introduce a stochastic optimal feedforward-feedback control (SFFC) model that can predict the nominal timing and trial-by-trial variability of self-paced arm reaching movements carried out with or without online visual feedback of the hand. In SFFC, movement timing results from the minimization of the intrinsic factors of effort and variance due to constant and signal-dependent motor noise, and movement variability depends on the integration of visual feedback. Reaching arm movements data are used to examine the effect of online vision on movement timing and variability, and test the model. This modelling suggests that the central nervous system predicts the effects of sensorimotor noise to generate an optimal feedforward motor command, and triggers optimal feedback corrections to task-related errors based on the available limb state estimate.

Optimality Principles in Human Point-to-Manifold Reaching Accounting for Muscle Dynamics

Human arm movements are highly stereotypical under a large variety of experimental conditions. This is striking due to the high redundancy of the human musculoskeletal system, which in principle allows many possible trajectories toward a goal. Many researchers hypothesize that through evolution, learning, and adaption, the human system has developed optimal control strategies to select between these possibilities. Various optimality principles were proposed in the literature that reproduce human-like trajectories in certain conditions. However, these studies often focus on a single cost function and use simple torque-driven models of motion generation, which are not consistent with human muscle-actuated motion. The underlying structure of our human system, with the use of muscle dynamics in interaction with the control principles, might have a significant influence on what optimality principles best model human motion. To investigate this hypothesis, we consider a point-to-manifold reaching task that leaves the target underdetermined. Given hypothesized motion objectives, the control input is generated using Bayesian optimization, which is a machine learning based method that trades-off exploitation and exploration. Using numerical simulations with Hill-type muscles, we show that a combination of optimality principles best predicts human point-to-manifold reaching when accounting for the muscle dynamics.

Stochastic optimal open-loop control as a theory of force and impedance planning via muscle co-contraction

Understanding the underpinnings of biological motor control is an important issue in movement neuroscience. Optimal control theory is a leading framework to rationalize this problem in computational terms. Previously, optimal control models have been devised either in deterministic or in stochastic settings to account for different aspects of motor control (e.g. average behavior versus trial-to-trial variability). While these approaches have yielded valuable insights about motor control, they typically fail in explaining muscle co-contraction. Co-contraction of a group of muscles associated to a motor function (e.g. agonist and antagonist muscles spanning a joint) contributes to modulate the mechanical impedance of the neuromusculoskeletal system (e.g. joint viscoelasticity) and is thought to be mainly under the influence of descending signals from the brain. Here we present a theory suggesting that one primary goal of motor planning may be to issue feedforward (open-loop) motor commands that optimally specify both force and impedance, according to noisy neuromusculoskeletal dynamics and to optimality criteria based on effort and variance. We show that the proposed framework naturally accounts for several previous experimental findings regarding the regulation of force and impedance via muscle co-contraction in the upper-limb. Stochastic optimal (closed-loop) control, preprogramming feedback gains but requiring on-line state estimation processes through long-latency sensory feedback loops, may then complement this nominal feedforward motor command to fully determine the limb’s mechanical impedance. The proposed stochastic optimal open-loop control theory may provide new insights about the general articulation of feedforward/feedback control mechanisms and justify the occurrence of muscle co-contraction in the neural control of movement.

This study presents a novel computational theory to explain the planning of force and impedance (e.g. viscoelasticity) in the neural control of movement. It assumes that one main goal of motor planning is to elaborate feedforward motor commands that determine both the force and the impedance required for the task at hand. These feedforward motor commands (i.e. that are defined prior to movement execution) are designed to minimize effort and variance costs considering the uncertainty arising from sensorimotor or environmental noise. A major outcome of this mathematical framework is the explanation of muscle co-contraction (i.e. the concurrent contraction of a group of muscles involved in a motor function). Muscle co-contraction has been shown to occur in many situations but previous modeling works struggled to account for it. Although effortful, co-contraction contributes to increase the robustness of motor behavior (e.g. small variance) upstream of sophisticated optimal closed-loop control processes that require state estimation from delayed sensory feedback to function. This work may have implications regarding our understanding of the neural control of movement in computational terms. It also provides a theoretical ground to explain how to optimally plan force and impedance within a general and versatile framework.

Kinematic Analysis of Mae-Geri Kicks in Beginner and Advanced Kyokushin Karate Athletes

Background: Each of the techniques used in sport is a complex technique requiring a combination of neuromuscular conduction, motor anticipation, and extremely developed proprioception. This is especially the case in martial arts when we deal with a kick or a blow to a specific target. Methods: The main purpose of this study was to determine the kinematic differences in the tested movement pattern among athletes with different levels of advancement in the conditions of kicking: in the air, at a target (a shield), and in direct contact with a competitor. Comparative analysis was performed among 26 players: 13 advanced (group G1) and 13 beginners (group G2). Kinematic data was recorded using an optical motion capture system. The examination consisted of performing three tests of mae-geri kick in sequences of three kicks in three different conditions (without a target, with a static target, and with an opponent). The examination was performed with the back leg and only the moment of kick was analyzed. Results: The most significant differences were observed in the movement of head, torso, hip, knee, and ankle segments, especially during a kick at a shield. Based on the conducted analysis, we can assume that karate training changes the strategy of neuromuscular control, promoting improvement of mobility pattern efficiency. Conclusion: Acquiring this type of knowledge can lead to better results, elimination of errors in training, especially in the initial period of training, and the prevention of possible injuries that occur during exercise or competition.

An Inverse Optimal Control Approach to Explain Human Arm Reaching Control Based on Multiple Internal Models

Human motor control is highly efficient in generating accurate and appropriate motor behavior for a multitude of tasks. This paper examines how kinematic and dynamic properties of the musculoskeletal system are controlled to achieve such efficiency. Even though recent studies have shown that the human motor control relies on multiple models, how the central nervous system (CNS) controls this combination is not fully addressed. In this study, we utilize an Inverse Optimal Control (IOC) framework in order to find the combination of those internal models and how this combination changes for different reaching tasks. We conducted an experiment where participants executed a comprehensive set of free-space reaching motions. The results show that there is a trade-off between kinematics and dynamics based controllers depending on the reaching task. In addition, this trade-off depends on the initial and final arm configurations, which in turn affect the musculoskeletal load to be controlled. Given this insight, we further provide a discomfort metric to demonstrate its influence on the contribution of different inverse internal models. This formulation together with our analysis not only support the multiple internal models (MIMs) hypothesis but also suggest a hierarchical framework for the control of human reaching motions by the CNS.

Control strategy of hand movement depends on target redundancy

Reaching toward a point target has been intensively studied in human motor control. However, little is known about reaching toward a redundant target, such as grasping a bar, in which the grasping point is irrelevant to the achievement of a task. We examined whether humans could solve the target-redundancy and control problems in a serial fashion or control their body without solving the target-redundancy problem. We equalized the target ranges between two reaching tasks: a point-to-point reaching task without target-redundancy and a point-to-bar reaching task with target-redundancy. In the both tasks, we measured hand viscoelasticity at movement end as parameters that reflect the adopted control strategy. As a result, the hand viscoelasticity in the point-to-bar reaching task was smaller than that in the point-to-point reaching task, even under the same kinematics. These results indicate that the hand viscoelasticity was modulated depending on the target-redundancy. Moreover, it is suggested that a human reaches toward a redundant target by effectively utilizing information of target redundancy rather than explicitly solving the target-redundancy problem.

Adaptive use of interaction torque during arm reaching movement from the optimal control viewpoint

The study aimed at investigating the extent to which the brain adaptively exploits or compensates interaction torque (IT) during movement control in various velocity and load conditions. Participants performed arm pointing movements toward a horizontal plane without a prescribed reach endpoint at slow, neutral and rapid speeds and with/without load attached to the forearm. Experimental results indicated that IT overall contributed to net torque (NT) to assist the movement, and that such contribution increased with limb inertia and instructed speed and led to hand trajectory variations. We interpreted these results within the (inverse) optimal control framework, assuming that the empirical arm trajectories derive from the minimization of a certain, possibly composite, cost function. Results indicated that mixing kinematic, energetic and dynamic costs was necessary to replicate the participants' adaptive behavior at both kinematic and dynamic levels. Furthermore, the larger contribution of IT to NT was associated with an overall decrease of the kinematic cost contribution and an increase of its dynamic/energetic counterparts. Altogether, these results suggest that the adaptive use of IT might be tightly linked to the optimization of a composite cost which implicitly favors more the kinematic or kinetic aspects of movement depending on load and speed.

Direction-dependent arm kinematics reveal optimal integration of gravity cues

The brain has evolved an internal model of gravity to cope with life in the Earth's gravitational environment. How this internal model benefits the implementation of skilled movement has remained unsolved. One prevailing theory has assumed that this internal model is used to compensate for gravity's mechanical effects on the body, such as to maintain invariant motor trajectories. Alternatively, gravity force could be used purposely and efficiently for the planning and execution of voluntary movements, thereby resulting in direction-depending kinematics. Here we experimentally interrogate these two hypotheses by measuring arm kinematics while varying movement direction in normal and zero-G gravity conditions. By comparing experimental results with model predictions, we show that the brain uses the internal model to implement control policies that take advantage of gravity to minimize movement effort.

On the nature of motor planning variables during arm pointing movement: Compositeness and speed dependence

The purpose of this study was to investigate the nature of the variables and rules underlying the planning of unrestrained 3D arm reaching. To identify whether the brain uses kinematic, dynamic and energetic values in an isolated manner or combines them in a flexible way, we examined the effects of speed variations upon the chosen arm trajectories during free arm movements. Within the optimal control framework, we uncovered which (possibly composite) optimality criterion underlays at best the empirical data. Fifteen participants were asked to perform free-endpoint reaching movements from a specific arm configuration at slow, normal and fast speeds. Experimental results revealed that prominent features of observed motor behaviors were significantly speed-dependent, such as the chosen reach endpoint and the final arm posture. Nevertheless, participants exhibited different arm trajectories and various degrees of speed dependence of their reaching behavior. These inter-individual differences were addressed using a numerical inverse optimal control methodology. Simulation results revealed that a weighted combination of kinematic, energetic and dynamic cost functions was required to account for all the critical features of the participants' behavior. Furthermore, no evidence for the existence of a speed-dependent tuning of these weights was found, thereby suggesting subject-specific but speed-invariant weightings of kinematic, energetic and dynamic variables during the motor planning process of free arm movements. This suggested that the inter-individual difference of arm trajectories and speed dependence was not only due to anthropometric singularities but also to critical differences in the composition of the subjective cost function.

Evidence for subjective values guiding posture and movement coordination in a free-endpoint whole-body reaching task

When moving, humans must overcome intrinsic (body centered) and extrinsic (target-related) redundancy, requiring decisions when selecting one motor solution among several potential ones. During classical reaching studies the position of a salient target determines where the participant should reach, constraining the associated motor decisions. We aimed at investigating implicit variables guiding action selection when faced with the complexity of human-environment interaction. Subjects had to perform whole body reaching movements towards a uniform surface. We observed little variation in the self-chosen motor strategy across repeated trials while movements were variable across subjects being on a continuum from a pure 'knee flexion' associated with a downward center of mass (CoM) displacement to an 'ankle dorsi-flexion' associated with an upward CoM displacement. Two optimality criteria replicated these two strategies: a mix between mechanical energy expenditure and joint smoothness and a minimization of the amount of torques. Our results illustrate the presence of idiosyncratic values guiding posture and movement coordination that can be combined in a flexible manner as a function of context and subject. A first value accounts for the reach efficiency of the movement at the price of selecting possibly unstable postures. The other predicts stable dynamic equilibrium but requires larger energy expenditure and jerk.

Implicit guidance to stable performance in a rhythmic perceptual-motor skill

Feedback about error or reward is regarded essential for aiding learners to acquire a perceptual-motor skill. Yet, when a task has redundancy and the mapping between execution and performance outcome is unknown, simple error feedback does not suffice in guiding the learner toward the optimal solutions. The present study developed and tested a new means of implicitly guiding learners to acquire a perceptual-motor skill, rhythmically bouncing a ball on a racket. Due to its rhythmic nature, this task affords dynamically stable solutions that are robust to small errors and noise, a strategy that is independent from actively correcting error. Based on the task model implemented in a virtual environment, a time-shift manipulation was designed to shift the range of ball-racket contacts that achieved dynamically stable solutions. In two experiments, subjects practiced with this manipulation that guided them to impact the ball with more negative racket accelerations, the indicator for the strategy with dynamic stability. Subjects who practiced under normal conditions took longer time to acquire this strategy, although error measures were identical between the control and experimental groups. Unlike in many other haptic guidance or adaptation studies, the experimental groups not only learned, but also maintained the stable solution after the manipulation was removed. These results are a first demonstration that more subtle ways to guide the learner to better performance are needed especially in tasks with redundancy, where error feedback may not be sufficient.

Reach endpoint formation during the visuomotor planning of free arm pointing

Volitional motor control generally involves deciding 'where to go' and 'how to go there'. Understanding how these two constituent pieces of motor decision coordinate is an important issue in neuroscience. Although the two processes could be intertwined, they are generally thought to occur in series, whereby visuomotor planning begins with the knowledge of a final hand position to attain. However, daily activities are often compatible with an infinity of final hand positions. The purpose of the present study was to test whether the reach endpoint ('where') is an input of arm motor planning ('how') in such ecological settings. To this end, we considered a free pointing task, namely arm pointing to a long horizontal line, and investigated the formation of the reach endpoint through eye-hand coordination. Although eye movement always preceded hand movement, our results showed that the saccade initiation was delayed by ~ 120 ms on average when the line was being pointed to as compared with a single target dot; the hand reaction time was identical in the two conditions. When the latency of saccade initiation was relatively brief, subjects often performed double, or even triple, saccades before hand movement onset. The number of saccades triggered was found to significantly increase as a function of the primary saccade latency and accuracy. These results suggest that knowledge about the reach endpoint built up gradually along with the arm motor planning process, and that the oculomotor system delayed the primary reach-related saccade in order to gain more information about the final hand position.

Computational model of motor learning and perceptual change

Motor learning in the context of arm reaching movements has been frequently investigated using the paradigm of force-field learning. It has been recently shown that changes to somatosensory perception are likewise associated with motor learning. Changes in perceptual function may be the reason that when the perturbation is removed following motor learning, the hand trajectory does not return to a straight line path even after several dozen trials. To explain the computational mechanisms that produce these characteristics, we propose a motor control and learning scheme using a simplified two-link system in the horizontal plane: We represent learning as the adjustment of desired joint-angular trajectories so as to achieve the reference trajectory of the hand. The convergence of the actual hand movement to the reference trajectory is proved by using a Lyapunov-like lemma, and the result is confirmed using computer simulations. The model assumes that changes in the desired hand trajectory influence the perception of hand position and this in turn affects movement control. Our computer simulations support the idea that perceptual change may come as a result of adjustments to movement planning with motor learning.

Kinematics of the coordination of pointing during locomotion

In natural motor behaviour arm movements, such as pointing or reaching, often need to be coordinated with locomotion. The underlying coordination patterns are largely unexplored, and require the integration of both rhythmic and discrete movement primitives. For the systematic and controlled study of such coordination patterns we have developed a paradigm that combines locomotion on a treadmill with time-controlled pointing to targets in the three-dimensional space, exploiting a virtual reality setup. Participants had to walk at a constant velocity on a treadmill. Synchronized with specific foot events, visual target stimuli were presented that appeared at different spatial locations in front of them. Participants were asked to reach these stimuli within a short time interval after a "go" signal. We analysed the variability patterns of the most relevant joint angles, as well as the time coupling between the time of pointing and different critical timing events in the foot movements. In addition, we applied a new technique for the extraction of movement primitives from kinematic data based on anechoic demixing. We found a modification of the walking pattern as consequence of the arm movement, as well as a modulation of the duration of the reaching movement in dependence of specific foot events. The extraction of kinematic movement primitives from the joint angle trajectories exploiting the new algorithm revealed the existence of two distinct main components accounting, respectively, for the rhythmic and discrete components of the coordinated movement pattern. Summarizing, our study shows a reciprocal pattern of influences between the coordination patterns of reaching and walking. This pattern might be explained by the dynamic interactions between central pattern generators that initiate rhythmic and discrete movements of the lower and upper limbs, and biomechanical factors such as the dynamic gait stability.

Energy-related optimal control accounts for gravitational load: comparing shoulder, elbow, and wrist rotations

We permanently deal with gravity force. Experimental evidences revealed that moving against gravity strongly differs from moving along the gravity vector. This directional asymmetry has been attributed to an optimal planning process that optimizes gravity force effects to minimize energy. Yet, only few studies have considered the case of vertical movements in the context of optimal control. What kind of cost is better suited to explain kinematic patterns in the vertical plane? Here, we aimed to understand further how the central nervous system (CNS) plans and controls vertical arm movements. Our reasoning was the following: if the CNS optimizes gravity mechanical effects on the moving limbs, kinematic patterns should change according to the direction and the magnitude of the gravity torque being encountered in the motion. Ten subjects carried out single-joint movements, i.e., rotation around the shoulder (whole arm), elbow (forearm), and wrist (hand) joints, in the vertical plane. Joint kinematics were analyzed and compared with various theoretical optimal model predictions (minimum absolute work-jerk, jerk, torque change, and variance). We found both direction-dependent and joint-dependent variations in several kinematic parameters. Notably, directional asymmetries decreased according to a proximodistal gradient. Numerical simulations revealed that our experimental findings could be attributed to an optimal motor planning (minimum absolute work-jerk) that integrates the direction and the magnitude of gravity torque and minimizes the absolute work of forces (energy-related cost) around each joint. Present results support the general idea that the CNS implements optimal solutions according to the dynamic context of the action.

Trial-to-trial dynamics and learning in a generalized, redundant reaching task

If humans exploit task redundancies as a general strategy, they should do so even if the redundancy is decoupled from the physical implementation of the task itself. Here, we derived a family of goal functions that explicitly defined infinite possible redundancies between distance (D) and time (T) for unidirectional reaching. All [T, D] combinations satisfying any specific goal function defined a goal-equivalent manifold (GEM). We tested how humans learned two such functions, D/T = c (constant speed) and D·T = c, that were very different but could both be achieved by neurophysiologically and biomechanically similar reaching movements. Subjects were never explicitly shown either relationship, but only instructed to minimize their errors. Subjects exhibited significant learning and consolidation of learning for both tasks. Initial error magnitudes were higher, but learning rates were faster, for the D·T task than for the D/T task. Learning the D/T task first facilitated subsequent learning of the D·T task. Conversely, learning the D·T task first interfered with subsequent learning of the D/T task. Analyses of trial-to-trial dynamics demonstrated that subjects actively corrected deviations perpendicular to each GEM faster than deviations along each GEM to the same degree for both tasks, despite exhibiting significantly greater variance ratios for the D/T task. Variance measures alone failed to capture critical features of trial-to-trial control. Humans actively exploited these abstract task redundancies, even though they did not have to. They did not use readily available alternative strategies that could have achieved the same performance.

Energy margins in dynamic object manipulation

Many tasks require humans to manipulate dynamically complex objects and maintain appropriate safety margins, such as placing a cup of coffee on a coaster without spilling. This study examined how humans learn such safety margins and how they are shaped by task constraints and changing variability with improved skill. Eighteen subjects used a manipulandum to transport a shallow virtual cup containing a ball to a target without losing the ball. Half were to complete the cup transit in a comfortable target time of 2 s (a redundant task with infinitely many equivalent solutions), and the other half in minimum time (a nonredundant task with one explicit cost to optimize). The safety margin was defined as the ball energy relative to escape, i.e., as an energy margin. The first hypothesis, that subjects converge to a single strategy in the minimum-time task but choose different strategies in the less constrained target-time task, was not supported. Both groups developed individualized strategies with practice. The second hypothesis, that subjects decrease safety margins in the minimum-time task but increase them in the target-time task, was supported. The third hypothesis, that in both tasks subjects modulate energy margins according to their execution variability, was partially supported. In the target-time group, changes in energy margins correlated positively with changes in execution variability; in the minimum-time group, such a relation was observed only at the end of practice, not across practice. These results show that when learning a redundant object manipulation task, most subjects increase their safety margins and shape their movement strategies in accordance with their changing variability.

Catching a ball at the right time and place: individual factors matter

Intercepting a moving object requires accurate spatio-temporal control. Several studies have investigated how the CNS copes with such a challenging task, focusing on the nature of the information used to extract target motion parameters and on the identification of general control strategies. In the present study we provide evidence that the right time and place of the collision is not univocally specified by the CNS for a given target motion; instead, different but equally successful solutions can be adopted by different subjects when task constraints are loose. We characterized arm kinematics of fourteen subjects and performed a detailed analysis on a subset of six subjects who showed comparable success rates when asked to catch a flying ball in three dimensional space. Balls were projected by an actuated launching apparatus in order to obtain different arrival flight time and height conditions. Inter-individual variability was observed in several kinematic parameters, such as wrist trajectory, wrist velocity profile, timing and spatial distribution of the impact point, upper limb posture, trunk motion, and submovement decomposition. Individual idiosyncratic behaviors were consistent across different ball flight time conditions and across two experimental sessions carried out at one year distance. These results highlight the importance of a systematic characterization of individual factors in the study of interceptive tasks.