Routledge Handbook of Motor Control and Motor Learning

Albert Gollhofer, Wolfgang Taube, Jens Bo Nielsen, Albert Gollhofer, Wolfgang Taube, Jens Bo Nielsen

• Publisher: Routledge
• Year: 2013
• ISBN:
  9781136477935
• Edition: 1
• Topic: Ciencias biológicas
• Subtopic: Neurociencia

The Routledge Handbook of Motor Control and Motor Learning is the first book to offer a comprehensive survey of neurophysiological, behavioural and biomechanical aspects of motor function. Adopting an integrative approach, it examines the full range of key topics in contemporary human movement studies, explaining motor behaviour in depth from the molecular level to behavioural consequences.

The book contains contributions from many of the world´s leading experts in motor control and motor learning, and is composed of five thematic parts:

• Theories and models

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• Basic aspects of motor control and learning

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• Motor control and learning in locomotion and posture

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• Motor control and learning in voluntary actions

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• Challenges in motor control and learning

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Mastering and improving motor control may be important in sports, but it becomes even more relevant in rehabilitation and clinical settings, where the prime aim is to regain motor function. Therefore the book addresses not only basic and theoretical aspects of motor control and learning but also applied areas like robotics, modelling and complex human movements. This book is both a definitive subject guide and an important contribution to the contemporary research agenda. It is therefore important reading for students, scholars and researchers working in sports and exercise science, kinesiology, physical therapy, medicine and neuroscience.

Part I

Theories and Models

1

Theoretical Models of Motor Control and Motor Learning

Adrian M. Haith¹ and John W. Krakauer ²

¹NEUROLOGY / BIOMEDICAL ENGINEERING, JOHNS HOPKINS UNIVERSITY, BALTIMORE, USA

²DEPARTMENTS OF NEUROLOGY AND NEUROSCIENCE, JOHNS HOPKINS UNIVERSITY, BALTIMORE, USA

Introduction

The ease with which one is able to walk, talk, manipulate objects and play sports belies the fact that generating coordinated movement is a tremendously complex task. We have to control our bodies through a muscular system that is highly redundant, nonlinear and unreliable. Furthermore, we are reliant on sensory feedback that is also unreliable and substantially delayed. Yet many tasks that robotic systems achieve either cumbersomely or not at all are routine to us. Expert performers push the limits of performance even further. Our advantage over synthetic manipulators and – arguably – a professional sportsperson’s advantage over a rookie, lies not so much in the hardware performing the task, but in the way it is controlled.

A theoretical approach to motor control and motor learning seeks to explain regularities in behavior in terms of underlying principles. This typically entails formulating mathematical models that describe the mechanics of the body or task, the way in which appropriate motor commands are selected, or the way in which prior experience influences future behavior. Many theories are mechanstic in nature – appealing to computations or plasticity occurring at the level of individual neurons or synapses in order to explain observations at the behavioral level. More abstract theories may not necessarily refer to any specific neural substrate but instead seek to explain behavior in terms of the way in which information can be represented and transformed. In both approaches, predictions about behavior stem largely from constraints imposed by the assumed circuitry or algorithm. Note that these two modelling approaches are similar to the implementational and algorithmic levels of analysis discussed by Marr (1982).

An alternative approach is to set aside questions about mechanism or algorithms and attempt to characterize and understand motor system function purely at the behavioral level. The sheer flexibility of the motor system makes it seem unlikely that underlying mechanisms place a significant constraint on the kinds of movement that can be generated. Instead, it seems that regularities in behavior are mostly dictated by … mostly dictated by features of the task at hand rather than by features of the underlying implementational mechanism. A normative modeling approach seeks to explain behavior by first understanding the precise computational problem that the brain faces, and then asking what, theoretically, is the best possible way to solve it (akin to Marr’s computational level of analysis). Finding solutions to such problems typically leverages ideas from control theory or machine learning. Mechanistic and normative approaches are far from mutually exclusive endeavors – breakthroughs in normative models of behavior often inspire and help guide mechanistic models. A deeper mechanistic understanding can help to constrain normative models. The normative point of view effectively assumes that the underlying neural mechanisms have omnipotent capacity. Consequently, aspects of the task itself, rather than the underlying mechanisms responsible for implementing the solution, are what primarily dictate our patterns of behavior.

In this chapter, we provide an introduction to the core concepts that underlie most recent theoretical models of motor control, state estimation and motor learning. We examine the assumptions – many of which often go unchallenged – underlying these models and discuss common pitfalls in their application. Finally, we discuss important unanswered questions and consider possible future directions for research.

Theoretical Models of Control

The fundamental problem the motor system faces is to decide upon appropriate motor commands to bring about a desired outcome in the environment. For example, suppose you want to move your hand to push a button to call an elevator. What makes this problem difficult is that it is not enough to simply know the location of the elevator button in space. Changing the position of the arm can only be done very indirectly by using the muscles to generate forces that cause acceleration about the joints of the arm. Thus the dynamics of our bodies place a fundamental constraint on how we are able to move. Furthermore, these dynamics are highly nonlinear – the exact same motor commands may lead to a very different acceleration depending on the state of the arm and muscles. As a result, even an apparently simple task like a point-to-point movement actually requires a complex sequence of motor commands to achieve success.

Compounding the fact that task goals are distally and nonlinearly related to motor commands, motor execution itself is highly unreliable – forces generated by a muscle are inherently variable. Though there are many potential mechanisms that contribute to this variability (Faisal et al., 2008), the net effect appears to be that force variability grows linearly with force magnitude (Jones et al., 2002) – a phenomenon known as signal-dependent or multiplicative noise. Managing this noise to minimize its negative impact is a major theme in models of the motor system. Since execution noise acts at every instant, its effects will, if unchecked, accumulate over the course of a movement so that even moderate variability can end up significantly interfering with task goals.

In addition to the problems of acting through potentially complex dynamics and noise, a further factor that complicates the control problem is redundancy. Although a movement goal might be specified by a unique point in space, there is no such unique set of controls to get there. The movement may take many potential paths through space, may take any amount of time and vary in speed during movement in infinitely many ways, all of which must be achieved using very different muscle activations. Even for a given trajectory, many different combinations of muscle activations can lead to exactly the same kinematic outcome, just with varying degrees of co-contraction. The importance of redundancy in the motor system has long been recognized. Since the time of Bernstein (1967), who dubbed the need to resolve redundancy as ‘the degrees-of-freedom problem’, it has been common to regard redundancy as a nuisance that the motor system has to deal with on top of all the other factors that complicate control. However, far from viewing redundancy as a problem, redundancy should actually be regarded as a positive thing. It makes it easier to find solutions to a given task and allows goals to be achieved more flexibly and robustly. Redundancy, therefore, makes life easier for the motor system to develop adequate means of control and in general enables superior control strategies. However, redundancy complicates life for the motor system in the sense that it leads to a more complex and challenging control problem if one wants to exploit it intelligently.

The considerable redundancy in a task such as a point-to-point reaching movement means that, in principle, the same task could be successfully performed by two different people in totally different ways. Yet experimental data show that point-to-point reaching movements tend to have highly consistent characteristics across individuals. For example, Morasso (1981) found that kinematics of point-to-point movements were similar across individuals as well as across different directions, different amplitudes and in different parts of one’s workspace. All movements followed a more or less Cartesian straight path and showed a characteristic bell-shaped velocity profile. One possible explanation for this regularity is that it is a consequence of a particular, idiosyncratic control mechanism that is common across individuals. In other words, regularities across the population may be arbitrary and purely a consequence of a shared motor heritage. For example, some models have attempted to explain regularities in the way we move as emerging from a simplistic controller coupled to the intrinsic dynamical properties of the musculoskeletal system (Gribble et al., 1998). An alternative view, and one that is adopted by the majority of recent theories of motor control, is that we possess sophisticated controllers that select the particular movements we make because they optimize some aspect of our behavior. Regularity across individuals emerges due to common properties of the underlying task. Explaining features of behavior as being the result of an optimization process has the advantage that, in principle, a range of behaviors can be explained through a single set of principles. Exactly what aspect of behavior should be optimized in such models is difficult to say, since it is something that the motor system – or, at least, evolutionary pressures – dictates. In most cases, one assumes that the motor system aims to minimize a cost function that reflects some combination of effort, variability, or the satisfaction of task goals. As we will see, in many cases it can be shown that a rational underlying principle can offer a parsimonious explanation for observed features of movement and generate novel predictions about features that our movements should possess.

A fundamental concern with normative models of control is that it might be possible to frame any regular behavior as optimizing something. Adhering to cost functions that make some ecological sense provides some protection against this concern. However, it is impossible to say in any principled way what kinds of cost functions should and should not be allowable. And, in any case, this cannot completely avoid the possibility of inferring spurious cost functions from behavior that may not truly be optimizing anything. It is therefore important to – where possible – specify cost functions a priori rather than reverse-engineering a cost function based on observed behavior. That said, there is reason to believe that behavior truly does reflect a process of optimization. When subjects are asked to control an unfamiliar object with complex dynamics, each individual initially adopts an idiosyncratic way of solving the task. With extended practice, however, all subjects gradually converged on almost identical patterns of behavior (Nagengast et al., 2009). This convergence is naturally explained by the idea of an optimization process.

Optimal Control

The motor system can be modeled mathematically at many different levels of detail. Most simply, one can model the end-effector as a point mass subject to accelerations in one-, two- or three-dimensional Cartesian space. A more realistic model replaces the point mass dynamics with a multi-link rigid body subject to torques around each joint. More detailed models still replace torques with the combined action of individual muscles generating forces across joints and may encompass intrinsic properties of the muscles themselves, such as the nonlinear relationship between muscle length, muscle velocity and muscle force. There is no single ‘correct’ level of detail to adopt. A point mass serves as an excellent model of the oculomotor system (Robinson et al., 1986), but may be overly simplistic in other settings. A more detailed musculoskeletal model may be unnecessarily cumbersome for modeling some behaviors, but can in certain cases prove to enlighten our understanding of how a task is performed (Todorov, 2000). The appropriate level of modeling detail is largely a matter of judgment. However, for the sake of both parsimony and transparency, it is generally best to work with the simplest model possible that is able to explain a particular phenomenon of interest.

Mathematically, regardless of the level of detail employed, we can represent the state of the body at time t by the vector x_t. This will typically contain the position and velocity of an end-effector or set of joints (e.g. the shoulder and elbow angles of the arm), but may also include things such as intrinsic states of each muscle. The motor commands themselves, which we denote by the time-varying vector u_t, may correspond to joint torques, muscle forces or motor neuronal activity that only indirectly leads to changes in muscle force. The dynamics of the system – the way in which motor commands change the state – can be expressed in terms of a forward dynamics equation:

This describes how changes in the state, represented as a derivative, depend in a particular way on the current state and on the current outgoing motor commands. The change in state is represented as a derivative – though note that this is the change in state of all components of the state. If the vector x_t contains position and velocity, then ẋ_t contains velocity and acceleration. This equation describes mathematically the properties of the apparatus under control.

The role of the controller is to specify the motor commands u_t. Typically, the process of motor command selection is described mathematically in terms of a control policy – a mapping π from some relevant variable, such as time or state of the body, to controls u_t. A control policy can be either purely feedforward (open-loop), in which case the control policy is a mapping from time to motor commands

or feedback (closed-loop), in which case the motor commands may depend also on the current...