Dynamic primitives in the control of locomotion

Sounds like a basic building block that we should start with to recover our motor control again. Ask your therapist how to utilize this.
http://www.frontiersin.org/computational_neuroscience/10.3389/fncom.2013.00071/full?
Some great equations in the article, ask about them. Special html to print that equation.

${\dot{x}}_j(t)={\hat{v}}_j\sigma (t),j=1\dots n$

Humans achieve locomotor dexterity that far exceeds the capability of modern robots, yet this is achieved despite slower actuators, imprecise sensors, and vastly slower communication. We propose that this spectacular performance arises from encoding motor commands in terms of dynamic primitives. We propose three primitives as a foundation for a comprehensive theoretical framework that can embrace a wide range of upper- and lower-limb behaviors. Building on previous work that suggested discrete and rhythmic movements as elementary dynamic behaviors, we define submovements and oscillations: as discrete movements cannot be combined with sufficient flexibility, we argue that suitably-defined submovements are primitives.

As the term “rhythmic” may be ambiguous, we define oscillations as the corresponding class of primitives. We further propose mechanical impedances as a third class of dynamic primitives, necessary for interaction with the physical environment. Combination of these three classes of primitive requires care. One approach is through a generalized equivalent network: a virtual trajectory composed of simultaneous and/or sequential submovements and/or oscillations that interacts with mechanical impedances to produce observable forces and motions. Reliable experimental identification of these dynamic primitives presents challenges: identification of mechanical impedances is exquisitely sensitive to assumptions about their dynamic structure; identification of submovements and oscillations is sensitive to their assumed form and to details of the algorithm used to extract them. Some methods to address these challenges are presented. Some implications of this theoretical framework for locomotor rehabilitation are considered.

Introduction

In a recent publication, we asserted a pressing need for a fundamental mathematical theory to help organize and structure the prodigious volume of knowledge about sensorimotor control (Hogan and Sternad, 2012). We contend that such a theory has come within reach, though we anticipate that its development will require a process of continuous and incremental revision. While it is common practice to develop mathematical models for narrowly-specified sensorimotor tasks, to establish a reliable theoretical foundation it is necessary to take a broader perspective and consider the widest feasible range of behaviors—even if for no other reason than to uncover and confront facts that might prove embarrassing to a narrowly-formulated theory. Previously we outlined a theoretical framework for upper-extremity motor control that could encompass those quintessentially human behaviors, object manipulation and the use of tools. The goal of this essay is to extend this framework to lower-extremity motor control. To illustrate the potential value of such a theory we consider some of its possible implications for locomotor rehabilitation.

Of course, we acknowledge that an integrated theory of upper- and lower-extremity motor control is ambitious, but it ought to be possible—after all, there is only one central nervous system (CNS). Moreover, many commonplace actions require integrated control and coordination of upper and lower extremities, indeed of the entire body. For example, drilling a horizontal hole in a vertical wall using a hand-held drill is commonly performed in a standing position. Therefore, the force exerted by the hand on the drill and wall necessitates tangential force on the ground at the feet. In fact, almost all of the body's degrees of freedom must be coordinated—essentially everything between the hands and feet. The horizontal force results in an overturning moment that must be offset by displacing the center of gravity from the center of pressure below the feet, and a sufficiently strong hand force is typically accomplished by moving the center of gravity far beyond the base of support—i.e., by leaning hard into the push or pull (Dempster, 1958; Rancourt and Hogan, 2001). 

That is a common cause of falls if the horizontal force exceeds the frictional force between feet and ground and the feet slip (Grieve, 1983). Moreover, with feet together in this leaning posture, an unstable dynamic zero is introduced such that the hand force cannot decrease without transiently increasing, and vice-versa (Rancourt and Hogan, 2001). With feet far apart, that dynamic zero can be eliminated. The essential point is that the configuration of the feet dictates the dynamics of force exertion by the hands.

Even aside from the need to integrate upper- and lower-extremity motor control, the spectacular agility of human locomotion demands explanation. Even walking, that most mundane of behaviors, is a subtle and complex dynamic process. Despite intensive and ongoing research, the dynamics of human walking have yet to be reproduced by robots, even though they have actuators faster than muscle by factors of tens to thousands, and communication faster than neurons by a factor of a million or more (Kandel et al., 2000; Hogan and Sternad, 2012). But locomotor behavior is far more versatile than walking. For example, soccer, arguably the world's most popular sport, not only requires agile high-speed maneuvering to avoid equally agile opponents, but controlling the ball requires dexterity with the legs and feet comparable to that of the hands and fingers. In comparison, robot soccer—though fun, highly motivating, and a superb enticement to study science and engineering—is a pale shadow of the “beautiful game.”

Much more at link.