Interactions between body mechanical properties and sensorimotor feedback 

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Functional spinal synergies must be learned

The most conclusive evidence that spinal synergies are not fixed comes from the study of spinalized animals, the very same experimental paradigm that was used to initially develop the notion of spinal synergies (Bizzi et al., 1991). In these initial experiments, the learning process was not considered: the frogs used in the experiments were already able to wipe away painful stimuli before they were spinalized. It was subsequently assumed that the observed spinal synergies did not change during learning.
The withdrawal reflex in the rat is functionally analogous to the wiping reflex in the frog: when the skin of the paw of one of the hind limbs is pinched or heated, the rat raises that paw from the ground by contracting the hind limb flexor muscles (Schouenborg and Kalliomäki, 1990). Similarly to the frog wiping reflex, this functional behaviour persists in the spinalized rat (Schouenborg et al., 1992). This behaviour is not immediately functional at birth: in certain new-born rats, painful stimulation of the paw elicits muscle activity which presses the paw against the painful stimulus, rather than withdrawing it (Holmberg and Schouenborg, 1996). The appropriate pattern of muscular contraction develops over the first few weeks after birth. However if the rat is spinalized at birth, then the appropriate pattern does not develop (Levinsson et al., 1999). Thus, supra-spinal input is necessary to learn the appropriate muscular contraction pattern, which can then be retained after spinalization. Moreover, this acquired pattern of muscular contraction depends on the muscle’s mechanical action: thus, if the mechanical action of a muscle is altered by surgically displacing the point of attachment of a muscle’s tendon at birth, then the pattern of muscular contraction elicited by painful stimulation of the paw changes according to this new action so as to raise the paw away from the painful stimulus (Holmberg et al., 1997). Thus, the learning process does not consist in the supra-spinal centres finding better ways to combine fixed, functional spinal synergies. Indeed the very existence of functional spinal synergies depends on motor learning and requires the supra-spinal centres.
Even after development, when functional spinal synergies have been learned, the supra-spinal centres retain the capacity to alter these synergies in order to achieve a task. An artificial motor learning paradigm, developed by Wolpaw and colleagues and applied to humans, primates, rats and mice, shows that the amplitude of the H-reflex can be increased (or decreased) by repeatedly eliciting the H-reflex and rewarding the animal every time its amplitude is above (or below) a certain threshold (Wolpaw, 2010). If the axons projecting from the cortex to the spinal cord are severed, then this change cannot be learned. However, if the animal is spinalized after learning, then the change in the H-reflex is retained and persists for several days (Chen and Wolpaw, 2002). The difference in behaviour between animals spinalized before and after learning shows that learning has induced changes within the spinal cord itself. This suggests that adjustments in the H-reflex do not rely entirely on supra-spinal centres calculating and setting the appropriate feedback gain. Thus, the intelligent use of feedback by the spinal cord emerges over the course of learning. Therefore, the motor modules that are retained after spinalization cannot be the basis for learning: learning cannot consist in finding better combinations of fixed building blocks, since the building blocks themselves must be learned.

Adaptation in spinalized animals

Moreover, learning has also been shown to be possible in spinalized animals. Thus, spinalized cats can be trained to step with their hind limbs when these are placed on a backwards-moving treadmill (Figure 1.6). When they are first placed on the treadmill after spinalization, their hind limbs are unable to support their weight, and the animal’s trunk must therefore be supported. Also, at first the legs might not step forwards if the treadmill moves too fast and may simply end up being dragged backwards onto their paws. However, with repeated practice on the treadmill, the animals become increasingly able to support their own weight, and the number of steps they are able to perform in a row increases, as well as the speed at which they can step (de Leon et al., 1998).

Improvements in performance through the adjustment of body dynamics

An extensive literature in sports science has provided evidence that improvements in performance rely on changes in the body dynamics that occur over the course of learning. A recent development in robotics, the embodied robotics approach, has shown that if the engineer designs the mechanical properties of a robot in accordance with the task assigned to the robot, then the control of such a robot requires minimal knowledge of the robot dynamics and can be implemented without internal models or centralized computation. This has sparked renewed interest in the interactions between the nervous system and the body dynamics in the generation of animal and human movement. I propose to develop this neuro-mechanical approach one step further by exploring how the nervous system may adjust body mechanics to the task at hand. I therefore present the rationale for my thesis, which is to study the role of postural adjustments in motor coordination.

How the way we move shapes our body

Mobility, the ability to move and perform physical activities, relies on the ability to shape the contact forces with the ground. Indeed, these contact forces are what allows a person to accelerate, decelerate and turn. Thus, sprinting requires large forwards acceleration, obtained by pushing backwards with the legs on the ground, whereas jumping requires large vertical forces, obtained by pushing downwards with the legs on the ground.
Consequently, to improve in skills which require fast and ample movements, athletes may train to increase the maximal forces they can exert with their limbs (Duchateau and Baudry, 2010).

Implications for motor learning

Sensorimotor learning by the nervous system occurs within a body whose sensory and motor aspects change at multiple timescales, from the long timescales of growth and aging to the short timescales of adaptation and fatigue. Within existing sensorimotor learning theories, the changes in the sensory and motor aspects of the body are either ignored, or considered as a nuisance to be overcome, typically through elaborate inference algorithms.
However, as I have presented, the changes which occur throughout exercise in the structure of a person’s bones and muscles are functional, and improve the person’s ability to perform the movements they practice. Thus, bone density responds to weight-bearing, muscle mass responds to resistance training, and muscle fibre properties respond to endurance training. If a sprinter’s calf muscles are too slow and too weak to produce fast and strong impact forces, then whatever command the nervous system issues to the muscles, it will not allow the person to win the race. If the person’s muscles are strong enough but their bones are too weak to withstand the impact forces, then they may break (Court-Brown et al., 2008), and the person may still not win the race. Thus, skill learning does not consist only in finding the best motor command for a given body. Through practice, the body itself changes such that the motor command for a strong, smooth, ample movement might not even exist for the stiff, weak, brittle-boned novice. Thus, after skill learning, the body itself can be thought of as embodying knowledge about the movement to be performed.
This suggests a different way of considering the role of the nervous system in motor learning. Its task is not only to find better ways of controlling the body, for example by acquiring knowledge about the body and environmental dynamics. It must also guide changes within the body itself so as to adjust the body mechanical properties to the task being practiced.

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How much knowledge is necessary for motor control?

In traditional robotics, improvements in performance are obtained by improving the control of movement, either through better approximations for inverse models, or through online adjustment of feedback gains. A more recent approach, the embodied robotics approach, suggests a radically different alternative: if the body itself embodies knowledge about the movement to be performed, then the controller does not need this knowledge. Indeed, this approach has demonstrated that stark improvements in the robustness, agility and performance of legged robots running in natural environments can be achieved by improving the design of the robotic bodies themselves (Pfeifer and Bongard, 2006).

Weight for propulsion

The first striking demonstration of the importance of the body dynamics was provided by McGeer’s passive dynamic walker (McGeer, 1990) (Figure 1.10.A), later improved on by (Collins et al., 2001) (Figure 1.10.B). The passive walker has no motors. Its legs are made of two rigid segments articulated at the knee, and the two legs are articulated at the hips. The shape and weight of the walker’s segments have been designed so that the walker steps from foot to foot: when one leg is in contact with the ground, the other leg swings forwards like a pendulum from its own weight, until it touches the ground and the first leg then starts swinging forwards. Such a mechanical device is very stable in the forwards direction, but not in the lateral direction: it can very easily topple on its side. Therefore, in McGeer’s implementation, each leg is actually composed of two legs constrained to swing together (Figure 1.10.A). This four-legged device is stable in both the forwards and lateral directions. Collins and colleagues then developed a laterally stable biped: they improved the walker’s balance by equipping it with wide feet, elastic heels, and counter-swinging arm, as shown in Figure 1.10.B (Collins et al., 2001). These walkers have no motors: their motion is therefore determined by their mechanical properties rather than their (non-existent) control. Yet, the resulting walking pattern is stable, and has a very natural feel to it (Pfeifer and Bongard, 2006).
Since the walker uses its own weight for propulsion, its gait is very energy efficient. The passive walker loses energy every time one of its heels strikes the ground, and must therefore walk down a slope in order to maintain steady walking. Minimal actuation can be added to allow the walker to walk on flat ground: for example, by detecting heel strike in the forwards leg and using it to trigger ankle push-off from the backwards leg. This allows the robot to walk on flat ground with at least ten times less energy consumption than more traditional robots with motors controlling each joint (Collins et al., 2005). This approach has yielded much insight into the energetic efficiency of human walking (Kuo and Donelan, 2010).

Elasticity for robustness to perturbations

The design of running quadruped robots has also been shown to benefit from an improvement of the robot’s morphology. Thus, the quadruped robots Puppy (Iida and Pfeifer, 2004) and Cheetah-Cub (Spröwitz et al., 2014) (Figure 1.10.C) have a leg structure designed to imitate that of a cat or a dog, with two springs attached to each leg. The actuation is very simple, with motors at the hips and shoulders swinging the legs back and forth rhythmically. The elasticity of the legs allows them to adjust the ground contact forces to the height of the ground. Thus, although it has no sensors, Cheetah-Cub can run down a small step without falling (Spröwitz et al., 2014): its body mechanical properties are sufficient to provide robustness to small external perturbations.
Elasticity in a joint prevents the joint torque from being fully determined by the control signal (such as the external command to the motor for a robot, or muscular contraction for an animal), since the joint torque will also depend on the joint angle. Rather than hindering motor performance, here this lack of direct control actually improves performance, since the elasticity allows the joint torque to adjust to the actual contact forces.

Table of contents :

1. Introduction
I. Abstract
II. Optimal patterns of motor coordination
1. Feedback and feedforward control
2. Internal inverse models for feedforward control
3. Motor redundancy and the uncontrolled manifold
4. Stochastic optimal feedback control for redundant tasks
5. Adaptive control
6. Centralised knowledge
III. Where is the knowledge for motor control
1. Basic neuro-anatomy of motor control
2. Spinal organisation of movement
3. Learning and adaptation in spinal synergies
IV. Improvements in performance through the adjustment of body dynamics
1. How the way we move shapes our body
2. How much knowledge is necessary for motor control?
3. Adjustment of body mechanical properties for stability
V. Motivation and plan of the thesis
1. Motivation
2. Plan of the thesis
2. Postural adjustments for improving stability
I. Introduction
1. Muscular contraction response to a perturbation
2. Body mechanical properties
3. Interactions between body mechanical properties and sensorimotor feedback
II. Modelling results
1. Single inverted pendulum model of stance
2. Delayed feedback control of a single dimensional system
3. Generalisation to N dimensions
III. Discussion
1. Adjusting posture to decrease relative speed
2. Adjusting feedback gains to changed dynamics
3. Is immobility critical?
IV. Supplementary methods: Stability analysis
1. Propagation of exponential signals and derivation of the characteristic equation
2. Nyquist criterion
3. Application to our system
4. Simulations
V. Supplementary methods: Critical damping
1. Pade approximation
2. Generalisation of criticality
VI. Supplementary methods: generalisation to N dimensions
3. Mobility as the purpose of postural control
I. Abstract
II. Introduction
III. Adjustment of posture during stance
1. The standing posture allows for mobility
2. The standing posture is actively maintained
3. The standing posture is adjusted in anticipation of movement
4. Summary
IV. Adjustment of posture during voluntary movement
1. Initiation of voluntary movement
2. The ability to use one’s weight for movement requires practice
V. Balance requires mobility rather than immobility
1. Responding to external perturbations
2. Emergence over development and impairment with aging
VI. Discussion
1. Posture is adjusted in view of mobility rather than immobility
2. Mobility emerges through development and skill learning
VII. Supplementary methods
1. Limits to ankle torque
2. Horizontal acceleration of the CoM
4. Postural adjustments for mobility and immobility in aging
I. Introduction
1. Mobility in aging
2. Falls in aging and risk factors for falling
3. Clinical assessments of balance and mobility and prediction of fall risk
4. Laboratory based assessments of balance and mobility and prediction of fall risk
5. Postural adjustments
II. Methods
1. Protocol
2. Analysis
III. Results
1. Previously published results
2. Performance in the two tasks
3. Initial posture
4. Change in initial posture across tasks
5. Ankle stiffness
IV. Discussion
1. Adjustment of the initial position of the CoM
2. Adjustment of ankle stiffness
3. How to measure the adjustment of ankle stiffness
V. Supplementary methods
1. Success in the perturbation task
2. Position of the centre of mass
5. Discussion
I. Summary
II. Postural versatility
1. Adjustment of posture to the task
2. Postural allostasis
3. Fall risk in the elderly
III. Motor coordination
1. Redundancy in motor tasks
2. Change in coordination during learning
3. Postural modulation after learning
6. Appendix: Models of human stance
I. Ankle torque and body rotational momentum
1. Torques of the external forces
2. Lower leg muscle contraction changes the ground reaction torque
II. Double inverted pendulum model
1. Rotational momentum
2. Acceleration of the centre of mass
7. References


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