This chapter describes the motivation for the study of human motor
control and introduces the subject of this thesis. The main problem
and thesis are stated, the organization of this dissertation is outlined
and illustrated, and the contribution of each chapter is briefly specified.
Three different reasons motivate the study of human motor control: the patient, the robot and the brain: (i) Crippled and paralyzed patients can improve their quality of life by artificial limbs or with external stimulation of their muscles. In order to design these aids, one needs a model of the biological motor control system. (ii) Robots are inferior to people and animals in many aspects. One of the promising directions of improving our technology is by imitating nature and learning from its ingenious solutions. (iii) The main outputs of the nervous system are the muscles, and motor control is the salient evolutionary drive for the development of the brain. Therefore, the act of modeling and understanding the motor control system can be symbolized as polishing the window to the secrets of the brain.
Two salient features of the biological system are adaptation and redundancy. The quality of adaptation allows us to develop the optimal behavior and to be able to respond to changes in the environment and in ourselves. A child has to learn how to move and how to perform simple and complex motor skills. Children and adults have a superb ability to learn new motor tasks and to adapt to changes in the environment and in their own body. Adaptation in the wide sense is one of the most important characteristics of all living things (see Holland 1995)
The quality of redundancy improves our flexibility and reliability.
We have excess resources in many parts of our body, and this property allows
us to perform the same task in many different possible ways. The
Russian physiologist Bernstein considered redundancy as the most remarkable
feature of the biological system (see Bernstein 1967, and Latash and Turvey
1996)
Therefore, as the name of this dissertation implies, we suggest a model
for learning motor control of redundant systems. We describe its
relation to the biological system and supply analytical tools and a theoretical
framework to analyze it and examine its performance.
We concentrate on open loop feed-forward control. This view is justified for rapid movements where there is no time for effective use of the sensory information due to the large delays in the biological system.
In this setup, we examine two different approaches to the problem.
The first puts the emphasis on the dynamic properties of the muscles and
the spinal cord, and the second approach emphasizes the higher nervous
system and computational methods to learn the control commands. We
suggest that there is no contradiction between these approaches since we
locate them in different places in the motor control hierarchy.
We address the properties of the lower level dynamics and their role
in simplifying the control that is needed at the higher level. We
then suggest an algorithm to learn all the possible control commands for
redundant systems, and an architecture that can represent these control
commands in a parametric fashion that allows using and switching between
different solutions in real time.
We use engineering and mathematical tools in order to develop a model
of the biological system. In this combination we aim to contribute
to both disciplines: to the biological motor control research by introducing
rigorous definitions and analyzable models, and to control engineering
by new ideas of using the system dynamics and exploiting the redundancy.
Chapter 2 reviews the current state of the art in the field of human
motor control, biological and artificial. Parts of this chapter appear
in Karniel and Inbar (2000)
Chapter 3 introduces the general model and this is its main contribution.
It also contains a unique definition of redundancy and redundancy types
from a functional point of view and a special perspective on learning and
adaptation. Parts of this chapter appear in Karniel and Inbar (2000)
and in Karniel et al. (1999)
Chapter 4 describes two simulations. The models were already presented in the literature. The novelty in this chapter is in demonstrating that these biologically plausible models can explain some well-observed properties of rapid human movements with a simple control scheme. The first simulation work was presented in my M.Sc. thesis, see Karniel (1996) and Karniel and Inbar (1997); it is brought here as an additional example. It is the first time that the stereotypical relationships between the parameters of rapid movements are shown to be reproducible by a simple biologically plausible mechanical model, the one-fifth-power law. Parts of this chapter appear in Karniel and Inbar (1999a)
Chapter 5 introduces a new architecture and algorithms for many-to-one
function approximation and inversion. There are some minor improvements
in the description and implementation of the hinging hyperplanes algorithm
of Breiman (1993). An algorithm is developed to transform the parameters
of the hinging hyperplanes to the PMLE parameters. The main contribution
of this chapter is in the PMLE architecture and in the description and
proof of its properties. Parts of this chapter appear in Karniel
et al. (1998), and in Karniel et al. (1999).
Chapter 6 contributes in two directions. It provides some extensions
to the field of learning theory by defining an error measure for one-to-many
“function” approximation and by showing some basic bounds.
It also rigorously shows the difference between two methods for learning
inverse model for control. This observation is important in order
to use the best method for control purposes and avoid errors in the estimation.
Parts of this chapter appear in Karniel et al. (1999).
Chapter 7 discusses the issues of this dissertation with many references
to related work and suggestions of some prospective direction for future
research.
Figure 1: The Structure of this dissertation. The arrows
represent possible sequences of reading.