Probabilistic Models of Motor Production

N. Bernstein defined the ability of the central neural system (CNS) to control many degrees of freedom of a physical body with all its redundancy and flexibility as the main problem in motor control. He pointed at that man-made mechanisms usually have one, sometimes two degrees of freedom (DOF); when the number of DOF increases further, it becomes prohibitively hard to control them. The brain, however, seems to perform such control effortlessly. He suggested the way the brain might deal with it: when a motor skill is being acquired, the brain artificially limits the degrees of freedoms, leaving only one or two. As the skill level increases, the brain gradually "frees" the previously fixed DOF, applying control when needed and in directions which have to be corrected, eventually arriving to the control scheme where all the DOF are "free". This approach of reducing the dimensionality of motor control remains relevant even today. One the possibles solutions of the Bernstetin's problem is the hypothesis of motor primitives (MPs) - small building blocks that constitute complex movements and facilitite motor learnirng and task completion. Just like in the visual system, having a homogenious hierarchical architecture built of similar computational elements may be beneficial. Studying such a complicated object as brain, it is important to define at which level of details one works and which questions one aims to answer. David Marr suggested three levels of analysis: 1. computational, analysing which problem the system solves; 2. algorithmic, questioning which representation the system uses and which computations it performs; 3. implementational, finding how such computations are performed by neurons in the brain. In this thesis we stay at the first two levels, seeking for the basic representation of motor output. In this work we present a new model of motor primitives that comprises multiple interacting latent dynamical systems, and give it a full Bayesian treatment. Modelling within the Bayesian framework, in my opinion, must become the new standard in hypothesis testing in neuroscience. Only the Bayesian framework gives us guarantees when dealing with the inevitable plethora of hidden variables and uncertainty. The special type of coupling of dynamical systems we proposed, based on the Product of Experts, has many natural interpretations in the Bayesian framework. If the dynamical systems run in parallel, it yields Bayesian cue integration. If they are organized hierarchically due to serial coupling, we get hierarchical priors over the dynamics. If one of the dynamical systems represents sensory state, we arrive to the sensory-motor primitives. The compact representation that follows from the variational treatment allows learning of a motor primitives library. Learned separately, combined motion can be represented as a matrix of coupling values. We performed a set of experiments to compare different models of motor primitives. In a series of 2-alternative forced choice (2AFC) experiments participants were discriminating natural and synthesised movements, thus running a graphics Turing test. When available, Bayesian model score predicted the naturalness of the perceived movements. For simple movements, like walking, Bayesian model comparison and psychophysics tests indicate that one dynamical system is sufficient to describe the data. For more complex movements, like walking and waving, motion can be better represented as a set of coupled dynamical systems. We also experimentally confirmed that Bayesian treatment of model learning on motion data is superior to the simple point estimate of latent parameters. Experiments with non-periodic movements show that they do not benefit from more complex latent dynamics, despite having high kinematic complexity. By having a fully Bayesian models, we could quantitatively disentangle the influence of motion dynamics and pose on the perception of naturalness. We confirmed that rich and correct dynamics is more important than the kinematic representation. There are numerous further directions of research. In the models we devised, for multiple parts, even though the latent dynamics was factorized on a set of interacting systems, the kinematic parts were completely independent. Thus, interaction between the kinematic parts could be mediated only by the latent dynamics interactions. A more flexible model would allow a dense interaction on the kinematic level too. Another important problem relates to the representation of time in Markov chains. Discrete time Markov chains form an approximation to continuous dynamics. As time step is assumed to be fixed, we face with the problem of time step selection. Time is also not a explicit parameter in Markov chains. This also prohibits explicit optimization of time as parameter and reasoning (inference) about it. For example, in optimal control boundary conditions are usually set at exact time points, which is not an ecological scenario, where time is usually a parameter of optimization. Making time an explicit parameter in dynamics may alleviate this

Passive Motion Paradigm: An Alternative to Optimal Control

In the last years, optimal control theory (OCT) has emerged as the leading approach for investigating neural control of movement and motor cognition for two complementary research lines: behavioral neuroscience and humanoid robotics. In both cases, there are general problems that need to be addressed, such as the “degrees of freedom (DoFs) problem,” the common core of production, observation, reasoning, and learning of “actions.” OCT, directly derived from engineering design techniques of control systems quantifies task goals as “cost functions” and uses the sophisticated formal tools of optimal control to obtain desired behavior (and predictions). We propose an alternative “softer” approach passive motion paradigm (PMP) that we believe is closer to the biomechanics and cybernetics of action. The basic idea is that actions (overt as well as covert) are the consequences of an internal simulation process that “animates” the body schema with the attractor dynamics of force fields induced by the goal and task-specific constraints. This internal simulation offers the brain a way to dynamically link motor redundancy with task-oriented constraints “at runtime,” hence solving the “DoFs problem” without explicit kinematic inversion and cost function computation. We argue that the function of such computational machinery is not only restricted to shaping motor output during action execution but also to provide the self with information on the feasibility, consequence, understanding and meaning of “potential actions.” In this sense, taking into account recent developments in neuroscience (motor imagery, simulation theory of covert actions, mirror neuron system) and in embodied robotics, PMP offers a novel framework for understanding motor cognition that goes beyond the engineering control paradigm provided by OCT. Therefore, the paper is at the same time a review of the PMP rationale, as a computational theory, and a perspective presentation of how to develop it for designing better cognitive architectures

Muscleless Motor synergies and actions without movements : From Motor neuroscience to cognitive robotics

Emerging trends in neurosciences are providing converging evidence that cortical networks in predominantly motor areas are activated in several contexts related to ‘action’ that do not cause any overt movement. Indeed for any complex body, human or embodied robot inhabiting unstructured environments, the dual processes of shaping motor output during action execution and providing the self with information related to feasibility, consequence and understanding of potential actions (of oneself/others) must seamlessly alternate during goal-oriented behaviors, social interactions. While prominent approaches like Optimal Control, Active Inference converge on the role of forward models, they diverge on the underlying computational basis. In this context, revisiting older ideas from motor control like the Equilibrium Point Hypothesis and synergy formation, this article offers an alternative perspective emphasizing the functional role of a ‘plastic, configurable’ internal representation of the body (body-schema) as a critical link enabling the seamless continuum between motor control and imagery. With the central proposition that both “real and imagined” actions are consequences of an internal simulation process achieved though passive goal-oriented animation of the body schema, the computational/neural basis of muscleless motor synergies (and ensuing simulated actions without movements) is explored. The rationale behind this perspective is articulated in the context of several interdisciplinary studies in motor neurosciences (for example, intracranial depth recordings from the parietal cortex, FMRI studies highlighting a shared cortical basis for action ‘execution, imagination and understanding’), animal cognition (in particular, tool-use and neuro-rehabilitation experiments, revealing how coordinated tools are incorporated as an extension to the body schema) and pertinent challenges towards building cognitive robots that can seamlessly “act, interact, anticipate and understand” in unstructured natural living spaces

Muscle synergies in neuroscience and robotics: from input-space to task-space perspectives

In this paper we review the works related to muscle synergies that have been carried-out in neuroscience and control engineering. In particular, we refer to the hypothesis that the central nervous system (CNS) generates desired muscle contractions by combining a small number of predefined modules, called muscle synergies. We provide an overview of the methods that have been employed to test the validity of this scheme, and we show how the concept of muscle synergy has been generalized for the control of artificial agents. The comparison between these two lines of research, in particular their different goals and approaches, is instrumental to explain the computational implications of the hypothesized modular organization. Moreover, it clarifies the importance of assessing the functional role of muscle synergies: although these basic modules are defined at the level of muscle activations (input-space), they should result in the effective accomplishment of the desired task. This requirement is not always explicitly considered in experimental neuroscience, as muscle synergies are often estimated solely by analyzing recorded muscle activities. We suggest that synergy extraction methods should explicitly take into account task execution variables, thus moving from a perspective purely based on input-space to one grounded on task-space as well

Neurally Plausible Model of Robot Reaching Inspired by Infant Motor Babbling

In this dissertation, we present an abstract model of infant reaching that is neurally-plausible. This model is grounded in embodied artificial intelligence, which emphasizes the importance of the sensorimotor interaction of an agent and the world. It includes both learning sensorimotor correlations through motor babbling and also arm motion planning using spreading activation. We introduce a mechanism called bundle formation as a way to generalize motions during the motor babbling stage. We then offer a neural model for the abstract model, which is composed of three layers of neural maps with parallel structures representing the same sensorimotor space. The motor babbling period shapes the structure of the three neural maps as well as the connections within and between them; these connections encode trajectory bundles in the neural maps. We then investigate an implementation of the neural model using a reaching task on a humanoid robot. Through a set of experiments, we were able to find the best way to implement different components of this model such as motor babbling, neural representation of sensorimotor space, dimension reduction, path planning, and path execution. After the proper implementation had been found, we conducted another set of experiments to analyze the model and evaluate the planned motions. We evaluated unseen reaching motions using jerk, end effector error, and overshooting. In these experiments, we studied the effect of different dimensionalities of the reduced sensorimotor space, different bundle widths, and different bundle structures on the quality of arm motions. We hypothesized a larger bundle width would allow the model to generalize better. The results confirmed that the larger bundles lead to a smaller error of end-effector position for testing targets. An experiment with the resolution of neural maps showed that a neural map with a coarse resolution produces less smooth motions compared to a neural map with a fine resolution. We also compared the unseen reaching motions under different dimensionalities of the reduced sensorimotor space. The results showed that a smaller dimension leads to less smooth and accurate movements

Comparative evaluation of approaches in T.4.1-4.3 and working definition of adaptive module

The goal of this deliverable is two-fold: (1) to present and compare different approaches towards learning and encoding movements us- ing dynamical systems that have been developed by the AMARSi partners (in the past during the first 6 months of the project), and (2) to analyze their suitability to be used as adaptive modules, i.e. as building blocks for the complete architecture that will be devel- oped in the project. The document presents a total of eight approaches, in two groups: modules for discrete movements (i.e. with a clear goal where the movement stops) and for rhythmic movements (i.e. which exhibit periodicity). The basic formulation of each approach is presented together with some illustrative simulation results. Key character- istics such as the type of dynamical behavior, learning algorithm, generalization properties, stability analysis are then discussed for each approach. We then make a comparative analysis of the different approaches by comparing these characteristics and discussing their suitability for the AMARSi project