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

PAMPC: Perception-Aware Model Predictive Control for Quadrotors

We present the first perception-aware model predictive control framework for quadrotors that unifies control and planning with respect to action and perception objectives. Our framework leverages numerical optimization to compute trajectories that satisfy the system dynamics and require control inputs within the limits of the platform. Simultaneously, it optimizes perception objectives for robust and reliable sens- ing by maximizing the visibility of a point of interest and minimizing its velocity in the image plane. Considering both perception and action objectives for motion planning and control is challenging due to the possible conflicts arising from their respective requirements. For example, for a quadrotor to track a reference trajectory, it needs to rotate to align its thrust with the direction of the desired acceleration. However, the perception objective might require to minimize such rotation to maximize the visibility of a point of interest. A model-based optimization framework, able to consider both perception and action objectives and couple them through the system dynamics, is therefore necessary. Our perception-aware model predictive control framework works in a receding-horizon fashion by iteratively solving a non-linear optimization problem. It is capable of running in real-time, fully onboard our lightweight, small-scale quadrotor using a low-power ARM computer, to- gether with a visual-inertial odometry pipeline. We validate our approach in experiments demonstrating (I) the contradiction between perception and action objectives, and (II) improved behavior in extremely challenging lighting conditions

Models for the Effects of G-seat Cuing on Roll-axis Tracking Performance

Including whole-body motion in a flight simulator improves performance for a variety of tasks requiring a pilot to compensate for the effects of unexpected disturbances. A possible mechanism for this improvement is that whole-body motion provides high derivative vehicle state information whic allows the pilot to generate more lead in responding to the external disturbances. During development of motion simulating algorithms for an advanced g-cuing system it was discovered that an algorithm based on aircraft roll acceleration producted little or no performance improvement. On the other hand, algorithms based on roll position or roll velocity produced performance equivalent to whole-body motion. The analysis and modeling conducted at both the sensory system and manual control performance levels to explain the above results are described

Perception of Human Movement Based on Modular Movement Primitives

People can identify and understand human movement from very degraded visual information without effort. A few dots representing the position of the joints are enough to induce a vivid and stable percept of the underlying movement. Due to this ability, the realistic animation of 3D characters requires great skill. Studying the constituents of movement that looks natural would not only help these artists, but also bring better understanding of the underlying information processing in the brain. Analogous to the hurdles in animation, the efforts of roboticists reflect the complexity of motion production: controlling the many degrees of freedom of a body requires time-consuming computations. Modularity is one strategy to address this problem: Complex movement can be decomposed into simple primitives. A few primitives can conversely be used to compose a large number of movements. Many types of movement primitives (MPs) have been proposed on different levels of information processing hierarchy in the brain. MPs have mostly been proposed for movement production. Yet, modularity based on primitives might similarly enable robust movement perception. For my thesis, I have conducted perceptual experiments based on the assumption of a shared representation of perception and action based on MPs. The three different types of MPs I have investigated are temporal MPs (TMP), dynamical MPs (DMP), and coupled Gaussian process dynamical models (cGPDM). The MP-models have been trained on natural movements to generate new movements. I then perceptually validated these artificial movements in different psychophysical experiments. In all experiments I used a two-alternative forced choice paradigm, in which human observers were presented a movement based on motion-capturing data, and one generated by an MP-model. They were then asked to chose the movement which they perceived as more natural. In the first experiment I investigated walking movements, and found that, in line with previous results, faithful representation of movement dynamics is more important than good reconstruction of pose. In the second experiment I investigated the role of prediction in perception using reaching movements. Here, I found that perceived naturalness of the predictions is similar to the perceived naturalness of movements itself obtained in the first experiment. I have found that MP models are able to produce movement that looks natural, with the TMP achieving the highest perceptual scores as well highest predictiveness of perceived naturalness among the three model classes, suggesting their suitability for a shared representation of perception and action

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

Robot training using system identification

This paper focuses on developing a formal, theory-based design methodology to generate transparent robot control programs using mathematical functions. The research finds its theoretical roots in robot training and system identification techniques such as Armax (Auto-Regressive Moving Average models with eXogenous inputs) and Narmax (Non-linear Armax). These techniques produce linear and non-linear polynomial functions that model the relationship between a robot’s sensor perception and motor response. The main benefits of the proposed design methodology, compared to the traditional robot programming techniques are: (i) It is a fast and efficient way of generating robot control code, (ii) The generated robot control programs are transparent mathematical functions that can be used to form hypotheses and theoretical analyses of robot behaviour, and (iii) It requires very little explicit knowledge of robot programming where end-users/programmers who do not have any specialised robot programming skills can nevertheless generate task-achieving sensor-motor couplings. The nature of this research is concerned with obtaining sensor-motor couplings, be it through human demonstration via the robot, direct human demonstration, or other means. The viability of our methodology has been demonstrated by teaching various mobile robots different sensor-motor tasks such as wall following, corridor passing, door traversal and route learning

Computational physics of the mind

In the XIX century and earlier such physicists as Newton, Mayer, Hooke, Helmholtz and Mach were actively engaged in the research on psychophysics, trying to relate psychological sensations to intensities of physical stimuli. Computational physics allows to simulate complex neural processes giving a chance to answer not only the original psychophysical questions but also to create models of mind. In this paper several approaches relevant to modeling of mind are outlined. Since direct modeling of the brain functions is rather limited due to the complexity of such models a number of approximations is introduced. The path from the brain, or computational neurosciences, to the mind, or cognitive sciences, is sketched, with emphasis on higher cognitive functions such as memory and consciousness. No fundamental problems in understanding of the mind seem to arise. From computational point of view realistic models require massively parallel architectures