The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements

An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements, this model has the particularity of using a cost function that is not smooth. First, a mathematical theory related to both direct and inverse optimal control approaches is presented. The first theoretical result is the Inactivation Principle, according to which minimizing a term similar to the absolute work implies simultaneous inactivation of agonistic and antagonistic muscles acting on a single joint, near the time of peak velocity. The second theoretical result is that, conversely, the presence of non-smoothness in the cost function is a necessary condition for the existence of such inactivation. Second, during an experimental study, participants were asked to perform fast vertical arm movements with one, two, and three degrees of freedom. Observed trajectories, velocity profiles, and final postures were accurately simulated by the model. In accordance, electromyographic signals showed brief simultaneous inactivation of opposing muscles during movements. Thus, assuming that human movements are optimal with respect to a certain integral cost, the minimization of an absolute-work-like cost is supported by experimental observations. Such types of optimality criteria may be applied to a large range of biological movements

Do muscle synergies reduce the dimensionality of behavior?

The muscle synergy hypothesis is an archetype of the notion of Dimensionality Reduction (DR) occurring in the central nervous system due to modular organisation. Towards validating this hypothesis, it is however important to understand if muscle synergies can reduce the state-space dimensionality while suitably achieving task control. In this paper we present a scheme for investigating this reduction, utilising the temporal muscle synergy formulation. Our approach is based on the observation that constraining the control input to a weighted combination of temporal muscle synergies instead constrains the dynamic behaviour of a system in trajectory-specific manner. We compute this constrained reformulation of system dynamics and then use the method of system balancing for quantifying the DR; we term this approach as Trajectory Specific Dimensionality Analysis (TSDA). We then use this method to investigate the consequence of minimisation of this dimensionality for a given task. These methods are tested in simulation on a linear (tethered mass) and a nonlinear (compliant kinematic chain) system; dimensionality of various reaching trajectories is compared when using idealised temporal synergies. We show that as a consequence of this Minimum Dimensional Control (MDC) model, smooth straight-line Cartesian trajectories with bell-shaped velocity profiles are obtained as the solution to reaching tasks in both of the test systems. We also investigate the effect on dimensionality due to adding via-points to a trajectory. The results indicate that a synergy basis and trajectory-specific DR of motor behaviours results from usage of muscle synergy control. The implications of these results for the synergy hypothesis, optimal motor control, developmental skill acquisition and robotics are then discussed

Reinforcement learning control of a biomechanical model of the upper extremity

Among the infinite number of possible movements that can be produced, humans are commonly assumed to choose those that optimize criteria such as minimizing movement time, subject to certain movement constraints like signal-dependent and constant motor noise. While so far these assumptions have only been evaluated for simplified point-mass or planar models, we address the question of whether they can predict reaching movements in a full skeletal model of the human upper extremity. We learn a control policy using a motor babbling approach as implemented in reinforcement learning, using aimed movements of the tip of the right index finger towards randomly placed 3D targets of varying size. We use a state-of-the-art biomechanical model, which includes seven actuated degrees of freedom. To deal with the curse of dimensionality, we use a simplified second-order muscle model, acting at each degree of freedom instead of individual muscles. The results confirm that the assumptions of signal-dependent and constant motor noise, together with the objective of movement time minimization, are sufficient for a state-of-the-art skeletal model of the human upper extremity to reproduce complex phenomena of human movement, in particular Fitts' Law and the 2/3 Power Law. This result supports the notion that control of the complex human biomechanical system can plausibly be determined by a set of simple assumptions and can easily be learned.Comment: 19 pages, 7 figure

Optimality Principles and Motion Planning of Human-Like Reaching Movements

The paper deals with modeling of human-like reaching movements. Several issues are under study. First, we consider a model of unconstrained reaching movements that corresponds to the minimization of control effort. It is shown that this model can be represented by the wellknown Beta function. The representation can be used for the construction of fractional order models and also for modeling of asymmetric velocity proï¬les. Next, we address the formation of boundary conditions in a natural way. From the mathematical point of view, the structure of the optimal solution is deï¬ned not only by the form of the optimality criterion but also by the boundary conditions of the optimization task. The natural boundary conditions, deï¬ned in this part of the paper, can also be used in modeling asymmetric velocity proï¬les. Finally, addressing the modeling of reaching movements with bounded control actions, we consider the minimum time formulation of the optimization problem and (for the n-th order integrator) ï¬nd its analytical solution

A Simple and Accurate onset Detection Method for a Measured Bell-shaped Speed Profile

Motor control neuroscientists measure limb trajectories and extract the onset of the movement for a variety of purposes. Such trajectories are often aligned relative to the onset of individual movement before the features of that movement are extracted and their properties are inspected. Onset detection is performed either manually or automatically, typically by selecting a velocity threshold. Here, we present a simple onset detection algorithm that is more accurate than the conventional velocity threshold technique. The proposed method is based on a simple regression and follows the minimum acceleration with constraints model, in which the initial phase of the bell-shaped movement is modeled by a cubic power of the time. We demonstrate the performance of the suggested method and compare it to the velocity threshold technique and to manual onset detection by a group of motor control experts. The database for this comparison consists of simulated minimum jerk trajectories and recorded reaching movements

Evidence for Composite Cost Functions in Arm Movement Planning: An Inverse Optimal Control Approach

An important issue in motor control is understanding the basic principles underlying the accomplishment of natural movements. According to optimal control theory, the problem can be stated in these terms: what cost function do we optimize to coordinate the many more degrees of freedom than necessary to fulfill a specific motor goal? This question has not received a final answer yet, since what is optimized partly depends on the requirements of the task. Many cost functions were proposed in the past, and most of them were found to be in agreement with experimental data. Therefore, the actual principles on which the brain relies to achieve a certain motor behavior are still unclear. Existing results might suggest that movements are not the results of the minimization of single but rather of composite cost functions. In order to better clarify this last point, we consider an innovative experimental paradigm characterized by arm reaching with target redundancy. Within this framework, we make use of an inverse optimal control technique to automatically infer the (combination of) optimality criteria that best fit the experimental data. Results show that the subjects exhibited a consistent behavior during each experimental condition, even though the target point was not prescribed in advance. Inverse and direct optimal control together reveal that the average arm trajectories were best replicated when optimizing the combination of two cost functions, nominally a mix between the absolute work of torques and the integrated squared joint acceleration. Our results thus support the cost combination hypothesis and demonstrate that the recorded movements were closely linked to the combination of two complementary functions related to mechanical energy expenditure and joint-level smoothness

The Fourier analysis of saccadic eye movements

This thesis examines saccadic eye movements in the frequency domain and develops sensitive tools for characterising their dynamics. It tests a variety of saccade models and provides the first strong empirical evidence that saccades are time-optimal. By enabling inferences on the neural command, it also allows for better clinical differentiation of abnormalities and the evaluation of putative mechanisms for the development of congenital nystagmus. Chapters 3 and 4 show how Fourier transforms reveal sharp minima in saccade frequency spectra, which are robust to instrument noise. The minima allow models based purely on the output trajectory, purely on the neural input, or both, to be directly compared and distinguished. The standard, most commonly accepted model based on bang-bang control theory is discounted. Chapter 5 provides the first empirical evidence that saccades are time-optimal by demonstrating that saccade bandwidths overlap across amplitude onto a single slope at high frequencies. In Chapter 6, the overlap also allows optimal (Wiener) filtering in the frequency domain without a priori assumptions. Deconvolution of the aggregate neural driving signal is then possible for current models of the oculomotor plant. The final two chapters apply these Fourier techniques to the quick phases of physiological (optokinetic) nystagmus and of pathological (congenital) nystagmus. These quick phases are commonly assumed to be saccadic in origin. This assumption is thoroughly tested and found to hold, but with subtle differences implying that the smooth pursuit system interacts with the saccade system during the movement. This interaction is taken into account in Chapter 8 in the assessment of congenital nystagmus quick phases, which are found to be essentially normal. Congenital nystagmus models based on saccadic abnormalities are appraised

Theories for Skilled Limb Movements .

Some of the theories that have been advanced to perform skilled limb movements are reviewed in this paper. The aspects discussed in brief include alpha-gamma control, choice of control variables in limb movements, equilibrium point hypotheses, experimental observations from simple movement studies and explanations proposed, in particular the dual strategy hypothesis. The single mechanical degree-of-freedom movements may be controlled by one of two strategies: a speed-insensitive strategy or a speed-sensitive strategy. The term strategy implies a set of rules which specify in terms of task variables and subject instructions how to choose the excitation signal, the controlling signal at the alpha motoneuron level. The two strategies differ in that speed-insensitive strategy is a result of duration modulation of the excitation pulse, whereas the speed-sensitive strategy is a result from amplitude modulation. Finally, the problem of multi-degrees of freedom movements and the role of higher motor control centres are discussed in brief