Forward Inverse Relaxation Model Incorporating Movement Duration Optimization.
ABSTRACT: A computational trajectory formation model based on the optimization principle, which introduces the forward inverse relaxation model (FIRM) as the hardware and algorithm, represents the features of human arm movements well. However, in this model, the movement duration was defined as a given value and not as a planned value. According to considerable empirical facts, movement duration changes depending on task factors, such as required accuracy and movement distance thus, it is considered that there are some criteria that optimize the cost function. Therefore, we propose a FIRM that incorporates a movement duration optimization module. The movement duration optimization module minimizes the weighted sum of the commanded torque change term as the trajectory cost, and the tolerance term as the cost of time. We conducted a behavioral experiment to examine how well the movement duration obtained by the model reproduces the true movement. The results suggested that the model movement duration was close to the true movement. In addition, the trajectory generated by inputting the obtained movement duration to the FIRM reproduced the features of the actual trajectory well. These findings verify the use of this computational model in measuring human arm movements.
Project description:When deciding between alternative options, a rational agent chooses on the basis of the desirability of each outcome, including associated costs. As different options typically result in different actions, the effort associated with each action is an essential cost parameter. How do humans discount physical effort when deciding between movements? We used an action-selection task to characterize how subjective effort depends on the parameters of arm transport movements and controlled for potential confounding factors such as delay discounting and performance. First, by repeatedly asking subjects to choose between 2 arm movements of different amplitudes or durations, performed against different levels of force, we identified parameter combinations that subjects experienced as identical in effort (isoeffort curves). Movements with a long duration were judged more effortful than short-duration movements against the same force, while movement amplitudes did not influence effort. Biomechanics of the movements also affected effort, as movements towards the body midline were preferred to movements away from it. Second, by introducing movement repetitions, we further determined that the cost function for choosing between effortful movements had a quadratic relationship with force, while choices were made on the basis of the logarithm of these costs. Our results show that effort-based action selection during reaching cannot easily be explained by metabolic costs. Instead, force-loaded reaches, a widely occurring natural behavior, imposed an effort cost for decision making similar to cost functions in motor control. Our results thereby support the idea that motor control and economic choice are governed by partly overlapping optimization principles.
Project description:Trajectory optimization with musculoskeletal models can be used to reconstruct measured movements and to predict changes in movements in response to environmental changes. It enables an exhaustive analysis of joint angles, joint moments, ground reaction forces, and muscle forces, among others. However, its application is still limited to simplified problems in two dimensional space or straight motions. The simulation of movements with directional changes, e.g. curved running, requires detailed three dimensional models which lead to a high-dimensional solution space. We extended a full-body three dimensional musculoskeletal model to be specialized for running with directional changes. Model dynamics were implemented implicitly and trajectory optimization problems were solved with direct collocation to enable efficient computation. Standing, straight running, and curved running were simulated starting from a random initial guess to confirm the capabilities of our model and approach: efficacy, tracking and predictive power. Altogether the simulations required 1 h 17 min and corresponded well to the reference data. The prediction of curved running using straight running as tracking data revealed the necessity of avoiding interpenetration of body segments. In summary, the proposed formulation is able to efficiently predict a new motion task while preserving dynamic consistency. Hence, labor-intensive and thus costly experimental studies could be replaced by simulations for movement analysis and virtual product design.
Project description:Animal behaviour arises through a complex mixture of biomechanical, neuronal, sensory and control constraints. By focusing on a simple, stereotyped movement, the prey capture strike of a weakly electric fish, we show that the trajectory of a strike is one which minimizes effort. Specifically, we model the fish as a rigid ellipsoid moving through a fluid with no viscosity, governed by Kirchhoff's equations. This formulation allows us to exploit methods of discrete mechanics and optimal control to compute idealized fish trajectories that minimize a cost function. We compare these with the measured prey capture strikes of weakly electric fish from a previous study. The fish has certain movement limitations that are not incorporated in the mathematical model, such as not being able to move sideways. Nonetheless, we show quantitatively that the computed least-cost trajectories are remarkably similar to the measured trajectories. Since, in this simplified model, the basic geometry of the idealized fish determines the favourable modes of movement, this suggests a high degree of influence between body shape and movement capability. Simplified minimal models and optimization methods can give significant insight into how body morphology and movement capability are closely attuned in fish locomotion.
Project description:How to move efficiently is an optimal control problem, whose computational complexity grows exponentially with the horizon of the planned trajectory. Breaking a compound movement into a series of chunks, each planned over a shorter horizon can thus reduce the overall computational complexity and associated costs while limiting the achievable efficiency. This trade-off suggests a cost-effective learning strategy: to learn new movements we should start with many short chunks (to limit the cost of computation). As practice reduces the impediments to more complex computation, the chunking structure should evolve to allow progressively more efficient movements (to maximize efficiency). Here we show that monkeys learning a reaching sequence over an extended period of time adopt this strategy by performing movements that can be described as locally optimal trajectories. Chunking can thus be understood as a cost-effective strategy for producing and learning efficient movements.
Project description:The central nervous system plans human reaching movements with stereotypically smooth kinematic trajectories and fairly consistent durations. Smoothness seems to be explained by accuracy as a primary movement objective, whereas duration seems to economize energy expenditure. But the current understanding of energy expenditure does not explain smoothness, so that two aspects of the same movement are governed by seemingly incompatible objectives. Here, we show that smoothness is actually economical, because humans expend more metabolic energy for jerkier motions. The proposed mechanism is an underappreciated cost proportional to the rate of muscle force production, for calcium transport to activate muscle. We experimentally tested that energy cost in humans (N = 10) performing bimanual reaches cyclically. The empirical cost was then demonstrated to predict smooth, discrete reaches, previously attributed to accuracy alone. A mechanistic, physiologically measurable, energy cost may therefore explain both smoothness and duration in terms of economy, and help resolve motor redundancy in reaching movements.
Project description:A long-standing challenge in motor neuroscience is to understand the relationship between movement speed and accuracy, known as the speed-accuracy tradeoff. Here, we introduce a biomechanically realistic computational model of three-dimensional upper extremity movements that reproduces well-known features of reaching movements. This model revealed that the speed-accuracy tradeoff, as described by Fitts' law, emerges even without the presence of motor noise, which is commonly believed to underlie the speed-accuracy tradeoff. Next, we analyzed motor cortical neural activity from monkeys reaching to targets of different sizes. We found that the contribution of preparatory neural activity to movement duration (MD) variability is greater for smaller targets than larger targets, and that movements to smaller targets exhibit less variability in population-level preparatory activity, but greater MD variability. These results propose a new theory underlying the speed-accuracy tradeoff: Fitts' law emerges from greater task demands constraining the optimization landscape in a fashion that reduces the number of 'good' control solutions (i.e., faster reaches). Thus, contrary to current beliefs, the speed-accuracy tradeoff could be a consequence of motor planning variability and not exclusively signal-dependent noise.
Project description:Objective: To date, motion trajectory prediction (MTP) of a limb from non-invasive electroencephalography (EEG) has relied, primarily, on band-pass filtered samples of EEG potentials i.e., the potential time-series model. Most MTP studies involve decoding 2D and 3D arm movements i.e., executed arm movements. Decoding of observed or imagined 3D movements has been demonstrated with limited success and only reported in a few studies. MTP studies normally use EEG potentials filtered in the low delta (~1 Hz) band for reconstructing the trajectory of an executed or an imagined/observed movement. In contrast to MTP, multiclass classification based sensorimotor rhythm brain-computer interfaces aim to classify movements using the power spectral density of mu (8-12 Hz) and beta (12-28 Hz) bands. Approach: We investigated if replacing the standard potentials time-series input with a power spectral density based bandpower time-series improves trajectory decoding accuracy of kinesthetically imagined 3D hand movement tasks (i.e., imagined 3D trajectory of the hand joint) and whether imagined 3D hand movements kinematics are encoded also in mu and beta bands. Twelve naïve subjects were asked to generate or imagine generating pointing movements with their right dominant arm to four targets distributed in 3D space in synchrony with an auditory cue (beep). Main results: Using the bandpower time-series based model, the highest decoding accuracy for motor execution was observed in mu and beta bands whilst for imagined movements the low gamma (28-40 Hz) band was also observed to improve decoding accuracy for some subjects. Moreover, for both (executed and imagined) movements, the bandpower time-series model with mu, beta, and low gamma bands produced significantly higher reconstruction accuracy than the commonly used potential time-series model and delta oscillations. Significance: Contrary to many studies that investigated only executed hand movements and recommend using delta oscillations for decoding directional information of a single limb joint, our findings suggest that motor kinematics for imagined movements are reflected mostly in power spectral density of mu, beta and low gamma bands, and that these bands may be most informative for decoding 3D trajectories of imagined limb movements.
Project description:Stable label movement and smooth label trajectory are critical for effective information understanding. Sudden label changes cannot be avoided by whatever forced directed methods due to the unreliability of resultant force or global optimization methods due to the complex trade-off on the different aspects. To solve this problem, we proposed a hybrid optimization method by taking advantages of the merits of both approaches. We first detect the spatial-temporal intersection regions from whole trajectories of the features, and initialize the layout by optimization in decreasing order by the number of the involved features. The label movements between the spatial-temporal intersection regions are determined by force directed methods. To cope with some features with high speed relative to neighbors, we introduced a force from future, called temporal force, so that the labels of related features can elude ahead of time and retain smooth movements. We also proposed a strategy by optimizing the label layout to predict the trajectories of features so that such global optimization method can be applied to streaming data. <h4>Electronic Supplementary Material</h4> Supplementary material is available in the online version of this article at 10.1007/s41095-021-0231-y.
Project description:Humans show a spontaneous tendency to increase the velocity of their movements depending on the linear extent of their trajectory in order to keep execution time approximately constant. Termed the isochrony principle, this compensatory mechanism refers to the observation that the velocity of voluntary movements increases proportionally with their linear extension. Although there is a wealth of psychophysical data regarding isochrony in humans, there is none regarding non-human primates. The present study attempts to fill that gap by investigating reach-to-grasp movement kinematics in free-ranging macaques. Video footage of monkeys grasping objects located at different distances was analyzed frame-by-frame using digitalization techniques. The amplitude of arm peak velocity was found to be correlated with the distance to be covered, and total movement duration remained invariant although target distances varied. Like in humans, the "isochrony principle" seems to be operative as there is a gearing down/up of movement velocity that is proportional to the distance to be covered in order to allow for a relatively constant movement duration. Based on a centrally generated temporal template, this mode of motor programming could be functional in macaques given the high speed and great instability of posture and joint kinematics characterizing their actions. The data presented here take research in the field of comparative motor control a step forward as they are based on precise measurements of spontaneous grasping movements by animals living/acting in their natural environment.
Project description:Various optimality principles have been proposed to explain the characteristics of coordinated eye and head movements during visual orienting behavior. At the same time, researchers have suggested several neural models to underly the generation of saccades, but these do not include online learning as a mechanism of optimization. Here, we suggest an open-loop neural controller with a local adaptation mechanism that minimizes a proposed cost function. Simulations show that the characteristics of coordinated eye and head movements generated by this model match the experimental data in many aspects, including the relationship between amplitude, duration and peak velocity in head-restrained and the relative contribution of eye and head to the total gaze shift in head-free conditions. Our model is a first step towards bringing together an optimality principle and an incremental local learning mechanism into a unified control scheme for coordinated eye and head movements.