On the cost functions for the control of the human arm movement

The aim of our investigation is to understand the mechanisms which control the movement of the human arm. The arm is here considered as a redundant system: the shoulder, elbow and wrist joints, which provide three degrees of freedom, combine to move the hand in a horizontal plane, i.e. a two dimensional space. Thus the system has one extra degree of freedom. Earlier investigations of the static situation led to the hypothesis that independent cost functions were attached to each of the three joints and that the configuration chosen for a given target position is that which provides the minimum total cost (Cruse 1986). The aim of the current investigation was to look for measurable values corresponding to the hypothetical cost functions. Experiments using pointers of different lengths attached to the hand showed that the strategy in choosing the joint angles are independent of the limb length. The muscle force necessary to reach a given angle is increased by a spring mounted across a joint. In this situation the angles of the loaded joint are changed for a given target point to give way to the force effect. This leads to the conclusion that the hypothetical cost functions are not independent of the physiological costs necessary to hold the joint at a given angle. The cost functions seem to depend on joint angle and on the force which is necessary to hold the joint in a given position. Cost functions are measured by psychophysical methods. The results showU-shaped curves which can be approximated by parabolas. The position of minimum cost (maximum comfort) for one joint showed no or weak dependency on the angles of the other joints. For each subject these psychophysical cost functions are compared with the hypothetical cost functions. The comparison showed reasonable agreement. This supports the assumption that the psychophysically measured comfort functions provide a measure for the hypothetical cost functions postulated to explain the targeting movements. Targeting experiments using a four joint arm which has two extra degrees of freedom showed a much larger scatter compared to the three joint arm. Nevertheless, the results still conform to the hypothesis that also in this case the minimum cost principle is applied to solve the redundancy problem. As the cost function for the whole arm shows a large minimum valley, quite a large range of arm positions is possible of about equal total costs. The scatter does not result from pure randomness but seems to be mainly produced by the fact that the angles at the end of the movement depend on the value of the joint angles at the beginning of the movement.     

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.     

Active inference and agency: optimal control without cost functions

This paper describes a variational free-energy formulation of (partially observable) Markov decision problems in decision making under uncertainty. We show that optimal control can be cast as active inference. In active inference, both action and posterior beliefs about hidden states minimise a free energy bound on the negative log-likelihood of observed states, under a generative model. In this setting, reward or cost functions are absorbed into prior beliefs about state transitions and terminal states. Effectively, this converts optimal control into a pure inference problem, enabling the application of standard Bayesian filtering techniques. We then consider optimal trajectories that rest on posterior beliefs about hidden states in the future. Crucially, this entails modelling control as a hidden state that endows the generative model with a representation of agency. This leads to a distinction between models with and without inference on hidden control states; namely, agency-free and agency-based models, respectively.     

Analysis of an optimal control model of multi-joint arm movements

 In this paper, we propose a model of biological motor control for generation of goal-directed multi-joint arm movements, and study the formation of muscle control inputs and invariant kinematic features of movements. The model has a hierarchical structure that can determine the control inputs for a set of redundant muscles without any inverse computation. Calculation of motor commands is divided into two stages, each of which performs a transformation of motor commands from one coordinate system to another. At the first level, a central controller in the brain accepts instructions from higher centers, which represent the motor goal in the Cartesian space. The controller computes joint equilibrium trajectories and excitation signals according to a minimum effort criterion. At the second level, a neural network in the spinal cord translates the excitation signals and equilibrium trajectories into control commands to three pairs of antagonist muscles which are redundant for a two-joint arm. No inverse computation is required in the determination of individual muscle commands. The minimum effort controller can produce arm movements whose dynamic and kinematic features are similar to those of voluntary arm movements. For fast movements, the hand approaches a target position along a near-straight path with a smooth bell-shaped velocity. The equilibrium trajectories in X and Y show an ‘N’ shape, but the end-point equilibrium path zigzags around the hand path. Joint movements are not always smooth. Joint reversal is found in movements in some directions. The excitation signals have a triphasic (or biphasic) pulse pattern, which leads to stereotyped triphasic (or biphasic) bursts in muscle control inputs, and a dynamically modulated joint stiffness. There is a fixed sequence of muscle activation from proximal muscles to distal muscles. The order is preserved in all movements. For slow movements, it is shown that a constant joint stiffness is necessary to produce a smooth movement with a bell-shaped velocity. Scaled movements can be reproduced by varying the constraints on the maximal level of excitation signals according to the speed of movement. When the inertial parameters of the arm are altered, movement trajectories can be kept invariant by adjusting the pulse height values, showing the ability to adapt to load changes. These results agree with a wide range of experimental observations on human voluntary movements. Received: 4 December 1995 / Accepted in revised form: 17 September 1996     

Parallel movement planning is achieved via an optimal preparatory state in motor cortex

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Human movement data for malaria control and elimination strategic planning

ABSTRACT: Recent increases in funding for malaria control have led to the reduction in transmission in many malaria endemic countries, prompting the national control programmes of 36 malaria endemic countries to set elimination targets. Accounting for human population movement (HPM) in planning for control, elimination and post-elimination surveillance is important, as evidenced by previous elimination attempts that were undermined by the reintroduction of malaria through HPM. Strategic control and elimination planning, therefore, requires quantitative information on HPM patterns and the translation of these into parasite dispersion. HPM patterns and the risk of malaria vary substantially across spatial and temporal scales, demographic and socioeconomic sub-groups, and motivation for travel, so multiple data sets are likely required for quantification of movement. While existing studies based on mobile phone call record data combined with malaria transmission maps have begun to address within-country HPM patterns, other aspects remain poorly quantified despite their importance in accurately gauging malaria movement patterns and building control and detection strategies, such as cross-border HPM, demographic and socioeconomic stratification of HPM patterns, forms of transport, personal malaria protection and other factors that modify malaria risk. A wealth of data exist to aid filling these gaps, which, when combined with spatial data on transport infrastructure, traffic and malaria transmission, can answer relevant questions to guide strategic planning. This review aims to (i) discuss relevant types of HPM across spatial and temporal scales, (ii) document where datasets exist to quantify HPM, (iii) highlight where data gaps remain and (iv) briefly put forward methods for integrating these datasets in a Geographic Information System (GIS) framework for analysing and modelling human population and Plasmodium falciparum malaria infection movements.     

A genetic algorithm approach to the inverse problem of treatment planning for intensity-modulated radiotherapy

A genetic algorithm optimization approach for designing treatment plans in intensity-modulated radiotherapy is proposed. The approach determines the beam intensities of the pencil-beam dose model such that the optimized dose distribution closely matches the prescribed dose distribution. The approach indirectly inverts the ill-conditioned dose-projection matrix, which can be very large and extremely sparse. The beam intensities are treated as chromosomes that are encoded as binary strings. The approach was used to design treatment plans for two deceptive clinical test cases. In both case, cancerous tissues in the planning target region received at least 98% of the prescribed dose level while dose levels delivered to the organs at risk were well within safe limits, with a maximum exposure of 2.5 and 52.5% of the prescribed tolerance level for the brain and prostrate cancer cases, respectively. Dose levels delivered to the healthy tissues were small with a mean exposure of 22.8 and 23.5% of the prescribed tolerance level.     

An analytical approach to the problem of inverse optimization with additive objective functions: an application to human prehension

We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms.     

Towards a biomechanics-based technique for assessing myocardial contractility: an inverse problem approach

This work presents the initial development and implementation of a novel 3D biomechanics-based approach to measure the mechanical activity of myocardial tissue, as a potential non-invasive tool to assess myocardial function. This technique quantifies the myocardial contraction forces developed within the ventricular myofibers in response to electro-physiological stimuli. We provide a 3D finite element formulation of a contraction force reconstruction algorithm, along with its implementation using magnetic resonance (MR) data. Our algorithm is based on an inverse problem solution governed by the fundamental continuum mechanics principle of conservation of linear momentum, under a first-order approximation of elastic and isotropic material conditions. We implemented our technique using a subject-specific ventricle model obtained by extracting the left ventricular anatomical features from a set of high-resolution cardiac MR images acquired throughout the cardiac cycle using prospective electrocardiographic gating. Cardiac motion information was extracted by non-rigid registration of the mid-diastole reference image to the remaining images of a 4D dataset. Using our technique, we reconstructed dynamic maps that show the contraction force distribution superimposed onto the deformed ventricle model at each acquired frame in the cardiac cycle. Our next objective will consist of validating this technique by showing the correlation between the presence of low contraction force patterns and poor myocardial functionality.     

On optimal control policy for probabilistic Boolean network: a state reduction approach

Background

Probabilistic Boolean Network (PBN) is a popular model for studying genetic regulatory networks. An important and practical problem is to find the optimal control policy for a PBN so as to avoid the network from entering into undesirable states. A number of research works have been done by using dynamic programming-based (DP) method. However, due to the high computational complexity of PBNs, DP method is computationally inefficient for a large size network. Therefore it is natural to seek for approximation methods.

Results

Inspired by the state reduction strategies, we consider using dynamic programming in conjunction with state reduction approach to reduce the computational cost of the DP method. Numerical examples are given to demonstrate both the effectiveness and the efficiency of our proposed method.

Conclusions

Finding the optimal control policy for PBNs is meaningful. The proposed problem has been shown to be ${\sum }_2^p\mathsf{\text{ - hard}}$. By taking state reduction approach into consideration, the proposed method can speed up the computational time in applying dynamic programming-based algorithm. In particular, the proposed method is effective for larger size networks.

     

Carbon cost of root systems: an architectural approach

Root architecture is an important component of nutrient uptake and may be sensitive to carbon allocational changes brought about by rising CO₂. We describe a deformable geometric model of root growth, SimRoot, for the dynamic morphological and physiological simulation of root architectures. Using SimRoot, and measurements of root biomass deposition, respiration and exudation, carbon/phosphorus budgets were developed for three contrasting root architectures. Carbon allocation patterns and phosphorus acquisition efficiencies were estimated for Phaseolus vulgaris seedlings with either a dichotomous, herringbone, or empirically determined bean root architecture. Carbon allocation to biomass, respiration, and exudation varied significantly among architectures. Root systems also varied in the relationship between C expenditure and P acquisition, providing evidence for the importance of architecture in nutrient acquisition efficiency.     

Neuromechanics: an integrative approach for understanding motor control

Neuromechanics seeks to understand how muscles, sense organs,motor pattern generators, and brain interact to produce coordinatedmovement, not only in complex terrain but also when confrontedwith unexpected perturbations. Applications of neuromechanicsinclude ameliorating human health problems (including prosthesisdesign and restoration of movement following brain or spinalcord injury), as well as the design, actuation and control ofmobile robots. In animals, coordinated movement emerges fromthe interplay among descending output from the central nervoussystem, sensory input from body and environment, muscle dynamics,and the emergent dynamics of the whole animal. The inevitablecoupling between neural information processing and the emergentmechanical behavior of animals is a central theme of neuromechanics.Fundamentally, motor control involves a series of transformationsof information, from brain and spinal cord to muscles to body,and back to brain. The control problem revolves around the specifictransfer functions that describe each transformation. The transferfunctions depend on the rules of organization and operationthat determine the dynamic behavior of each subsystem (i.e.,central processing, force generation, emergent dynamics, andsensory processing). In this review, we (1) consider the contributionsof muscles, (2) sensory processing, and (3) central networksto motor control, (4) provide examples to illustrate the interplayamong brain, muscles, sense organs and the environment in thecontrol of movement, and (5) describe advances in both roboticsand neuromechanics that have emerged from application of biologicalprinciples in robotic design. Taken together, these studiesdemonstrate that (1) intrinsic properties of muscle contributeto dynamic stability and control of movement, particularly immediatelyafter perturbations; (2) proprioceptive feedback reinforcesthese intrinsic self-stabilizing properties of muscle; (3) controlsystems must contend with inevitable time delays that can simplifyor complicate control; and (4) like most animals under a varietyof circumstances, some robots use a trial and error processto tune central feedforward control to emergent body dynamics.     

A radial basis function network approach for the computation of inverse continuous time variant functions

This Paper presents an efficient approach for the fast computation of inverse continuous time variant functions with the proper use of Radial Basis Function Networks (RBFNs). The approach is based on implementing RBFNs for computing inverse continuous time variant functions via an overall damped least squares solution that includes a novel null space vector for singularities prevention. The singularities avoidance null space vector is derived from developing a sufficiency condition for singularities prevention that conduces to establish some characterizing matrices and an associated performance index.     

Biological control of cereal stem borers in Kenya: A cost benefit approach

Lepidopteran stem borers are the key pests of maize in Sub-Saharan Africa. In the lowland tropics, dry mid-altitude, dry transitional and the moist mid-altitude zones of Kenya, the invasive crambid Chilo partellus (Swinhoe) (Lepidoptera: Crambidae) causes up to 73% yield loss. The International Centre of Insect Physiology and Ecology (ICIPE) started a biological control (BC) program in 1991 to control stem borers in subsistence agriculture in Africa with emphasis on classical BC of C. partellus. The project released the braconid larval parasitoid Cotesia flavipes Cameron (Hymenoptera: Braconidae) in 1993 in coastal Kenya, where it got established and spread to other regions. This study assesses the economic impact of the introduced parasitoid. Temporal data on percentage parasitism by the introduced parasitoid and on stem borer density were collected between 1995 and 2004. Socio-economic data was collected through administration of questionnaires to 300 farmers. Economic impact of the project was calculated as the value of the yield loss abated by the parasitoid based on a model of expected stem borer density and parasitism level. Average annual parasitism increased linearly from the time of introduction to reach 20% parasitism by 2004. The net reduction in total stem borer density over the last 10 years was 33.7%, thus abating 47.3% of yield loss. The region will accumulate a net present value of US $ 183 million in economic benefits in 20 years since release of the parasitoid. Introduction of other parasitoid species targeting the egg and pupal stages of the stem borer life cycle stages would be required for biological control to push yield loss by stem borers to an insignificant level.     

Optimal compensation for temporal uncertainty in movement planning

Motor control requires the generation of a precise temporal sequence of control signals sent to the skeletal musculature. We describe an experiment that, for good performance, requires human subjects to plan movements taking into account uncertainty in their movement duration and the increase in that uncertainty with increasing movement duration. We do this by rewarding movements performed within a specified time window, and penalizing slower movements in some conditions and faster movements in others. Our results indicate that subjects compensated for their natural duration-dependent temporal uncertainty as well as an overall increase in temporal uncertainty that was imposed experimentally. Their compensation for temporal uncertainty, both the natural duration-dependent and imposed overall components, was nearly optimal in the sense of maximizing expected gain in the task. The motor system is able to model its temporal uncertainty and compensate for that uncertainty so as to optimize the consequences of movement.     

A novel model of motor learning capable of developing an optimal movement control law online from scratch

A computational model of a learning system (LS) is described that acquires knowledge and skill necessary for optimal control of a multisegmental limb dynamics (controlled object or CO), starting from knowing only the dimensionality of the objects state space. It is based on an optimal control problem setup different from that of reinforcement learning. The LS solves the optimal control problem online while practicing the manipulation of CO. The systems functional architecture comprises several adaptive components, each of which incorporates a number of mapping functions approximated based on artificial neural nets. Besides the internal model of the COs dynamics and adaptive controller that computes the control law, the LS includes a new type of internal model, the minimal cost (IM_mc) of moving the controlled object between a pair of states. That internal model appears critical for the LSs capacity to develop an optimal movement trajectory. The IM_mc interacts with the adaptive controller in a cooperative manner. The controller provides an initial approximation of an optimal control action, which is further optimized in real time based on the IM_mc. The IM_mc in turn provides information for updating the controller. The LSs performance was tested on the task of center-out reaching to eight randomly selected targets with a 2DOF limb model. The LS reached an optimal level of performance in a few tens of trials. It also quickly adapted to movement perturbations produced by two different types of external force field. The results suggest that the proposed design of a self-optimized control system can serve as a basis for the modeling of motor learning that includes the formation and adaptive modification of the plan of a goal-directed movement.     

Wide-field motion integration in fly VS cells: insights from an inverse approach

Fly lobula plate tangential cells are known to perform wide-field motion integration. It is assumed that the shape of these neurons, and in particular the shape of the subclass of VS cells, is responsible for this type of computation. We employed an inverse approach to investigate the morphology-function relationship underlying wide-field motion integration in VS cells. In the inverse approach detailed, model neurons are optimized to perform a predefined computation: here, wide-field motion integration. We embedded the model neurons to be optimized in a biologically plausible model of fly motion detection to provide realistic inputs, and subsequently optimized model neuron with and without active conductances (g(Na), g(K), g(K(Na))) along their dendrites to perform this computation. We found that both passive and active optimized model neurons perform well as wide-field motion integrators. In addition, all optimized morphologies share the same blueprint as real VS cells. In addition, we also found a recurring blueprint for the distribution of g(K) and g(Na) in the active models. Moreover, we demonstrate how this morphology and distribution of conductances contribute to wide-field motion integration. As such, by using the inverse approach we can predict the still unknown distribution of g(K) and g(Na) and their role in motion integration in VS cells.