Analysis of kinematic invariances of multijoint reaching movement

 There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joint angle or intrinsic space in the general condition of joint redundancy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate systems. We show that the cartesian trajectory can be planned based on the task parameters (target coordinates, etc.) prior to and independently of angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in cartesian and angular spaces simultaneously is proposed. Due to joint redundancy, each cartesian trajectory corresponds to a family of angular trajectories which can account for the substantial variability of the latter. A set of strategies for multijoint motor control following from this model is considered; one of them coincides with the frog wiping reflex model and resolves the kinematic inverse problem without inversion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, straight end-point paths, bell-shaped tangential velocity profiles, speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajectory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb configuration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian space. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control used in planning. All the results are given analytically and, in order to compare the model with experimental results, by computer simulations. Received: 6 April 1994/Accepted in revised form: 25 April 1995     

Mechanisms underlying the generation of averaged modified trajectories

In this work we have studied what mechanisms might possibly underlie arm trajectory modification when reaching toward visual targets. The double-step target displacement paradigm was used with inter-stimulus intervals (ISIs) in the range of 10-300 ms. For short ISIs, a high percentage of the movements were found to be initially directed in between the first and second target locations (averaged trajectories). The initial direction of motion was found to depend on the target configuration, and on : the time difference between the presentation of the second stimulus and movement onset. To account for the kinematic features of the averaged trajectories two modification schemes were compared: the superposition scheme and the abort-replan scheme. According to the superposition scheme, the modified trajectories result from the vectorial addition of two elemental motions: one for moving between the initial hand position and an intermediate location, and a second one for moving between that intermediate location and the final target. According to the abort-replan scheme, the initial plan for moving toward the intermediate location is aborted and smoothly replaced by a new plan for moving from the hand position at the time the trajectory is modified to the final target location. In both tested schemes we hypothesized that due to the quick displacement of the stimulus, the internally specified intermediate goal might be influenced by both stimuli and may be different from the location of the first stimulus. It was found that the statistically most successful model in accounting for the measured data is based on the superposition scheme. It is suggested that superposition of simple independent elemental motions might be a general principle for the generation of modified motions, which allows for efficient, parallel planning. For increasing values of the inferred locations of the intermediate targets were found to gradually shift from the first toward the second target locations along a path that curved toward the initial hand position. These inferred locations show a strong resemblance to the intermediate locations of saccades generated in a similar double-step paradigm. These similarities in the specification of target locations used in the generation of eye and hand movements may serve to simplify visuomotor integration. Received: 22 June 1994 / Accepted in revised form: 15 September 1994     

Choosing goals, not rules: deciding among rule-based action plans

In natural situations, movements are often directed toward locations different from that of the evoking sensory stimulus. Movement goals must then be inferred from the sensory cue based on rules. When there is uncertainty about the rule that applies for a given cue, planning a movement involves both choosing the relevant rule and computing the movement goal based on that rule. Under these conditions, it is not clear whether primates compute multiple movement goals based on all possible rules before choosing an action, or whether they first choose a rule and then only represent the movement goal associated with that rule. Supporting the former hypothesis, we show that neurons in the frontoparietal reach areas of monkeys simultaneously represent two different rule-based movement goals, which are biased by the monkeys' choice preferences. Apparently, primates choose between multiple behavioral options by weighing against each other the movement goals associated with each option.     

Activity in the lateral prefrontal cortex reflects multiple steps of future events in action plans

To achieve a behavioral goal in a complex environment, we must plan multiple steps of motor behavior. On planning a series of actions, we anticipate future events that will occur as a result of each action and mentally organize the temporal sequence of events. To investigate the involvement of the lateral prefrontal cortex (PFC) in such multistep planning, we examined neuronal activity in the PFC of monkeys performing a maze task that required the planning of stepwise cursor movements to reach a goal. During the preparatory period, PFC neurons reflected each of all forthcoming cursor movements, rather than arm movements. In contrast, in the primary motor cortex, most neuronal activity reflected arm movements but little of cursor movements during the preparatory period, as well as during movement execution. Our data suggest that the PFC is involved primarily in planning multiple future events that occur as a consequence of behavioral actions.     

A Sensorimotor Model for Computing Intended Reach Trajectories

The presumed role of the primate sensorimotor system is to transform reach targets from retinotopic to joint coordinates for producing motor output. However, the interpretation of neurophysiological data within this framework is ambiguous, and has led to the view that the underlying neural computation may lack a well-defined structure. Here, I consider a model of sensorimotor computation in which temporal as well as spatial transformations generate representations of desired limb trajectories, in visual coordinates. This computation is suggested by behavioral experiments, and its modular implementation makes predictions that are consistent with those observed in monkey posterior parietal cortex (PPC). In particular, the model provides a simple explanation for why PPC encodes reach targets in reference frames intermediate between the eye and hand, and further explains why these reference frames shift during movement. Representations in PPC are thus consistent with the orderly processing of information, provided we adopt the view that sensorimotor computation manipulates desired movement trajectories, and not desired movement endpoints.     

Sub-Optimal Allocation of Time in Sequential Movements

The allocation of limited resources such as time or energy is a core problem that organisms face when planning complex actions. Most previous research concerning planning of movement has focused on the planning of single, isolated movements. Here we investigated the allocation of time in a pointing task where human subjects attempted to touch two targets in a specified order to earn monetary rewards. Subjects were required to complete both movements within a limited time but could freely allocate the available time between the movements. The time constraint presents an allocation problem to the subjects: the more time spent on one movement, the less time is available for the other. In different conditions we assigned different rewards to the two tokens. How the subject allocated time between movements affected their expected gain on each trial. We also varied the angle between the first and second movements and the length of the second movement. Based on our results, we developed and tested a model of speed-accuracy tradeoff for sequential movements. Using this model we could predict the time allocation that would maximize the expected gain of each subject in each experimental condition. We compared human performance with predicted optimal performance. We found that all subjects allocated time sub-optimally, spending more time than they should on the first movement even when the reward of the second target was five times larger than the first. We conclude that the movement planning system fails to maximize expected reward in planning sequences of as few as two movements and discuss possible interpretations drawn from economic theory.     

Active inference unifies intentional and conflict-resolution imperatives of motor control

The field of motor control has long focused on the achievement of external goals through action (e.g., reaching and grasping objects). However, recent studies in conditions of multisensory conflict, such as when a subject experiences the rubber hand illusion or embodies an avatar in virtual reality, reveal the presence of unconscious movements that are not goal-directed, but rather aim at resolving multisensory conflicts; for example, by aligning the position of a person’s arm with that of an embodied avatar. This second, conflict-resolution imperative of movement control did not emerge in classical studies of motor adaptation and online corrections, which did not allow movements to reduce the conflicts; and has been largely ignored so far in formal theories. Here, we propose a model of movement control grounded in the theory of active inference that integrates intentional and conflict-resolution imperatives. We present three simulations showing that the active inference model is able to characterize movements guided by the intention to achieve an external goal, by the necessity to resolve multisensory conflict, or both. Furthermore, our simulations reveal a fundamental difference between the (active) inference underlying intentional and conflict-resolution imperatives by showing that it is driven by two different (model and sensory) kinds of prediction errors. Finally, our simulations show that when movement is only guided by conflict resolution, the model incorrectly infers that is velocity is zero, as if it was not moving. This result suggests a novel speculative explanation for the fact that people are unaware of their subtle compensatory movements to avoid multisensory conflict. Furthermore, it can potentially help shed light on deficits of motor awareness that arise in psychopathological conditions.     

Action generation and action perception in imitation: an instance of the ideomotor principle

We review a series of behavioural experiments on imitation in children and adults that test the predictions of a new theory of imitation. Most of the recent theories of imitation assume a direct visual-to-motor mapping between perceived and imitated movements. Based on our findings of systematic errors in imitation, the new theory of goal-directed imitation (GOADI) instead assumes that imitation is guided by cognitively specified goals. According to GOADI, the imitator does not imitate the observed movement as a whole, but rather decomposes it into its separate aspects. These aspects are hierarchically ordered, and the highest aspect becomes the imitator's main goal. Other aspects become sub-goals. In accordance with the ideomotor principle, the main goal activates the motor programme that is most strongly associated with the achievement of that goal. When executed, this motor programme sometimes matches, and sometimes does not, the model's movement. However, the main goal extracted from the model movement is almost always imitated correctly.     

Formation and control of optimal trajectory in human multijoint arm movement

In this paper, we study trajectory planning and control in voluntary, human arm movements. When a hand is moved to a target, the central nervous system must select one specific trajectory among an infinite number of possible trajectories that lead to the target position. First, we discuss what criterion is adopted for trajectory determination. Several researchers measured the hand trajectories of skilled movements and found common invariant features. For example, when moving the hand between a pair of targets, subjects tended to generate roughly straight hand paths with bell-shaped speed profiles. On the basis of these observations and dynamic optimization theory, we propose a mathematical model which accounts for formation of hand trajectories. This model is formulated by defining an objective function, a measure of performance for any possible movement: square of the rate of change of torque integrated over the entire movement. That is, the objective function CT is defined as follows: (formula; see text) We overcome this difficult by developing an iterative scheme, with which the optimal trajectory and the associated motor command are simultaneously computed. To evaluate our model, human hand trajectories were experimentally measured under various behavioral situations. These results supported the idea that the human hand trajectory is planned and controlled in accordance with the minimum torque-change criterion.     

Internal models and intermittency: A theoretical account of human tracking behavior

This paper concerns the use of tracking studies to test a theoretical account of the information processing performed by the human CNS during control of movement. The theory provides a bridge between studies of reaction time and continuous tracking. It is proposed that the human CNS includes neuronal circuitry to compute inverse internal models of the multiple input, multiple output, dynamic, nonlinear relationships between outgoing motor commands and their resulting perceptual consequences. The inverse internal models are employed during movement execution to transform preplanned trajectories of desired perceptual consequences into appropriate outgoing motor commands to achieve them. A finite interval of time is required by the CNS to preplan the desired perceptual consequences of a movement and it does not commence planning a new movement until planning of the old one has been completed. This behavior introduces intermittency into the planning of movements. In this paper we show that the gain and phase frequency response characteristics of the human operator in a visual pursuit tracking task can be derived theoretically from these assumptions. By incorporating the effects of internal model inaccuracy and of speed-accuracy trade-off in performance, it is shown that various aspects of experimentally measured tracking behavior can be accounted for.     

Prediction of a moving target's position in fast goal-directed action

 Subjects made fast goal-directed arm movements towards moving targets. In some cases, the perceived direction of target motion was manipulated by moving the background. By comparing the trajectories towards moving targets with those towards static targets, we determined the position towards which subjects were aiming at movement onset. We showed that this position was an extrapolation in the target’s perceived direction from its position at that moment using its perceived direction of motion. If subjects were to continue to extrapolate in the perceived direction of target motion from the position at which they perceive the target at each instant, the error would decrease during the movements. By analysing the differences between subjects’ arm movements towards targets moving in different (apparent) directions with a linear second-order model, we show that the reduction in the error that this predicts is not enough to explain how subjects compensate for their initial misjudgements. Received: 10 February 1995/Accepted in revised form: 30 May 1995     

Action planning and control under uncertainty emerge through a desirability-driven competition between parallel encoding motor plans

Living in an uncertain world, nearly all of our decisions are made with some degree of uncertainty about the consequences of actions selected. Although a significant progress has been made in understanding how the sensorimotor system incorporates uncertainty into the decision-making process, the preponderance of studies focus on tasks in which selection and action are two separate processes. First people select among alternative options and then initiate an action to implement the choice. However, we often make decisions during ongoing actions in which the value and availability of the alternatives can change with time and previous actions. The current study aims to decipher how the brain deals with uncertainty in decisions that evolve while acting. To address this question, we trained individuals to perform rapid reaching movements towards two potential targets, where the true target location was revealed only after the movement initiation. We found that reaction time and initial approach direction are correlated, where initial movements towards intermediate locations have longer reaction times than movements that aim directly to the target locations. Interestingly, the association between reaction time and approach direction was independent of the target probability. By modeling the task within a recently proposed neurodynamical framework, we showed that action planning and control under uncertainty emerge through a desirability-driven competition between motor plans that are encoded in parallel.     

Language comprehension in the balance: the robustness of the action-compatibility effect (ACE)

How does language comprehension interact with motor activity? We investigated the conditions under which comprehending an action sentence affects people''s balance. We performed two experiments to assess whether sentences describing forward or backward movement modulate the lateral movements made by subjects who made sensibility judgments about the sentences. In one experiment subjects were standing on a balance board and in the other they were seated on a balance board that was mounted on a chair. This allowed us to investigate whether the action compatibility effect (ACE) is robust and persists in the face of salient incompatibilities between sentence content and subject movement. Growth-curve analysis of the movement trajectories produced by the subjects in response to the sentences suggests that the ACE is indeed robust. Sentence content influenced movement trajectory despite salient inconsistencies between implied and actual movement. These results are interpreted in the context of the current discussion of embodied, or grounded, language comprehension and meaning representation.     

Three-dimensional hand movements during the execution of ball juggling: Effect of expertise in street performers

To determine expertise-related differences in performance and movement variability during the execution of closed skill codified tasks, we quantitatively assessed the 3D hand movements of two groups of jugglers with different levels of expertise: six advanced (who could juggle up to 7 balls) and six intermediate jugglers (who could juggle at most with 5 balls).All participants performed three trials for each 3-, 4- and 5-ball juggling schemes. The coordinates of the middle fingers were recorded by an optoelectronic motion analyzer (sampling rate 120 Hz), and were analyzed and compared between groups, number of juggled balls and the spatial decomposition of hand trajectories.The higher the level of expertise, the more stable the hand movements, as the number of juggled balls increased. Advanced jugglers also exhibited lower execution frequencies than intermediate jugglers in each scheme.When the level of difficulty rises, a slower play may be one of the factors accounting for the capability of the advanced jugglers to limit movement variability at the end-effector, and juggle a higher number of balls.     

Applying trait‐based models to achieve functional targets for theory‐driven ecological restoration

Manipulating community assemblages to achieve functional targets is a key component of restoring degraded ecosystems. The response‐and‐effect trait framework provides a conceptual foundation for translating restoration goals into functional trait targets, but a quantitative framework has been lacking for translating trait targets into assemblages of species that practitioners can actually manipulate. This study describes new trait‐based models that can be used to generate ranges of species abundances to test theories about which traits, which trait values and which species assemblages are most effective for achieving functional outcomes. These models are generalisable, flexible tools that can be widely applied across many terrestrial ecosystems. Examples illustrate how the framework generates assemblages of indigenous species to (1) achieve desired community responses by applying the theories of environmental filtering, limiting similarity and competitive hierarchies, or (2) achieve desired effects on ecosystem functions by applying the theories of mass ratios and niche complementarity. Experimental applications of this framework will advance our understanding of how to set functional trait targets to achieve the desired restoration goals. A trait‐based framework provides restoration ecology with a robust scaffold on which to apply fundamental ecological theory to maintain resilient and functioning ecosystems in a rapidly changing world.     

Corrections in grasp posture in response to modifications of action goals

There is ample evidence that people plan their movements to ensure comfortable final grasp postures at the end of a movement. The end-state comfort effect has been found to be a robust constraint during unimanual movements, and leads to the inference that goal-postures are represented and planned prior to movement initiation. The purpose of this study was to examine whether individuals make appropriate corrections to ensure comfortable final goal postures when faced with an unexpected change in action goal. Participants reached for a horizontal cylinder and placed the left or right end of the object into the target disk. As soon as the participant began to move, a secondary stimuli was triggered, which indicated whether the intended action goal had changed or not. Confirming previous research, participants selected initial grasp postures that ensured end-state comfort during non-perturbed trials. In addition, participants made appropriate on-line corrections to their reach-to-grasp movements to ensure end-state comfort during perturbed trials. Corrections in grasp posture occurred early or late in the reach-to-grasp phase. The results indicate that individuals plan their movements to afford comfort at the end of the movement, and that grasp posture planning is controlled via both feedforward and feedback mechanisms.     

Rhythm Patterns Interaction - Synchronization Behavior for Human-Robot Joint Action

Interactive behavior among humans is governed by the dynamics of movement synchronization in a variety of repetitive tasks. This requires the interaction partners to perform for example rhythmic limb swinging or even goal-directed arm movements. Inspired by that essential feature of human interaction, we present a novel concept and design methodology to synthesize goal-directed synchronization behavior for robotic agents in repetitive joint action tasks. The agents’ tasks are described by closed movement trajectories and interpreted as limit cycles, for which instantaneous phase variables are derived based on oscillator theory. Events segmenting the trajectories into multiple primitives are introduced as anchoring points for enhanced synchronization modes. Utilizing both continuous phases and discrete events in a unifying view, we design a continuous dynamical process synchronizing the derived modes. Inverse to the derivation of phases, we also address the generation of goal-directed movements from the behavioral dynamics. The developed concept is implemented to an anthropomorphic robot. For evaluation of the concept an experiment is designed and conducted in which the robot performs a prototypical pick-and-place task jointly with human partners. The effectiveness of the designed behavior is successfully evidenced by objective measures of phase and event synchronization. Feedback gathered from the participants of our exploratory study suggests a subjectively pleasant sense of interaction created by the interactive behavior. The results highlight potential applications of the synchronization concept both in motor coordination among robotic agents and in enhanced social interaction between humanoid agents and humans.     

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.     

Stochastic modelling of animal movement

Modern animal movement modelling derives from two traditions. Lagrangian models, based on random walk behaviour, are useful for multi-step trajectories of single animals. Continuous Eulerian models describe expected behaviour, averaged over stochastic realizations, and are usefully applied to ensembles of individuals. We illustrate three modern research arenas. (i) Models of home-range formation describe the process of an animal ‘settling down’, accomplished by including one or more focal points that attract the animal''s movements. (ii) Memory-based models are used to predict how accumulated experience translates into biased movement choices, employing reinforced random walk behaviour, with previous visitation increasing or decreasing the probability of repetition. (iii) Lévy movement involves a step-length distribution that is over-dispersed, relative to standard probability distributions, and adaptive in exploring new environments or searching for rare targets. Each of these modelling arenas implies more detail in the movement pattern than general models of movement can accommodate, but realistic empiric evaluation of their predictions requires dense locational data, both in time and space, only available with modern GPS telemetry.