A cerebellar recurrent architecture for the head stabilization of a humanoid robot

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A cerebellar recurrent architecture for the head

stabilization controller of a humanoid robot

Author:

Francesca R

Supervisor:

Cecilia L

José S

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Co-Supervisor:

Egidio F

Lorenzo J

Acknowledgements ii

1 The Head Stabilization: State of Art and Physiological Models 1

1.1 The Vestibulocollicar Reflex . . . 2

1.1.1 The Vestibular System . . . 2

1.1.2 The Vestibulocollicar Reflex . . . 8

1.1.3 The Characteristics of VCR . . . 9

1.2 The Modelisation of VCR . . . 11

2 The Robotics Implementations for the Head Stabilization 15 2.1 Head stabilization for a humanoid robot . . . 16

2.1.1 FEL Architecture . . . 17

3 A new bio-inspired model 20 3.1 The role of the cerebellum . . . 20

3.2 The Recurrent Architecture . . . 21

3.3 The model . . . 23

3.4 The iCub robotic platform . . . 24

3.4.1 The Forward Kinematic . . . 25

4 Validation and discussion of the results 28 4.1 Training . . . 29

5 Conclusions 31

Chapter 1

The Head Stabilization: State of

Art and Physiological Models

Head stabilization is fundamental for many animals survival. Its posture and the way it compensates the movements of the other part of the body as the torso, especially during everyday basic movements like walking or running, are crucial to give a stable reference frame for the two essential perceptual systems for detection of self-motion relative to space: the visual and vestibular systems.

Vision is the most useful sensor for many animals to provide information about the surrounding environment and is an important function for protection from enemies.

The vestibular informations operate to create an inertial guidance system determining the spatial orientation in order to coordinate movements and balance.

Another advantage of head stabilization during movements and locomotion is in maintaining gaze stability and preserving visual acuity.

The head/trunk coordination helps the interpretation of the inputs from the sensors, as the visual and vestibular receptors are stimulated as soon as the head moves, in order to maintain equilibrium while standing or walking.

In vestibular injured patients however, this compensation was not observed. This brought to understand the role of the vestibular information for the head stabilization and the existence of the vestibulocollic reflex (VCR), a reflex loop wich stabilize the head in the inertial space.

This works is based on the analysis and the study of the existent models of this mechanism, both the biological ones and the robotic ones and presents a new bio-inspired controller for the iCub robot head based on above-mentioned study.

Figure 1.1: The vestibular system

1.1

The Vestibulocollicar Reflex

1.1.1

The Vestibular System

The origin of the vestibular system is seen in the outputs of the labyrinthine receptors, which flow to vestibular nuclei located in the brain stem. Many components of the vestibular system subserve a variety of postural reflexes, including those that make possible our upright, bipedal posture.

The vestibular system is a bilateral set of inertial sensors (Figure 1.1) involving inter-connected chambers called the labyrinth because the origin of the this system is seen in the outputs of the labyrinthine receptors, which flow to vestibular nuclei located in the brain stem. Chambers detect head motion in space to give a perception of self- movement and as well as the orientation of the head relative to gravity. In fact many components of the vestibular system subserve a variety of postural reflexes,including those that make possible our upright, bipedal posture. Each labyrinth is in the temporal bone and consists of three orthogonal semicircular canals and two orthogonal otolith membranes. The first ones (the horizontal, anterior and posterior) sense head rotation velocity and acceleration, and the two otoliths sense head translation acceleration and head tilt. Both labyrinths are mirrored copies of one another even if the two canals work in concert as antagonistic functional pairs [1].

The two vestibular labyrinths are mirror-symmetric structures within the inner ears. Each of them comprises five receptor organs that, complemented by those of the contralat-eral ear, can measure linear acceleration along any axis and angular acceleration about any axis: linear accelerations( including those produced by gravity and those resulting from body motions) are detected by the utricle and the saccule, angular accelerations (caused by

1.1 The Vestibulocollicar Reflex 3

Figure 1.2: Hair cells in the vestibular labyrinth transduce mechanical stimuli into neural signals [1].

rotation of the head or the body)are measured by the semicircular canals. The receptive organs are surrounded by the connective tissue that delineates the membranous labyrinth; The bony labyrinth, that is a layer of laminar bone, invests the membranous labyrinth and separates it from the cancellous bone of the skull. Although the labyrinth’s geometric complexity, the fundamental organization of the five constituent receptors is not dauntingly complicated :each organ is lined with a continuous sheet of epithelial cells. By the action of ion pumps, certain cells in this epithelium produce the endolymph, a special extracellularW fluid that bathes the apical cellular surfaces. This fluid,like cochlear endolymph, is rich in K+but relatively poor in Na+and Ca2+. During its development, the labyrinth progresses from a simple sac to a complex of interconnected organs:a junctional complex girdling the apex of each cell includes tight junctions that separate the endolymph from the ordinary extracellular fluid, the perilymph, that surrounds the membranous labyrinth and bathes the basolateral epithelial surfaces.Therefore each organ originates as an epithelium-lined pouch that buds from the otic cyst, and the endolymphatic spaces within the several organs remain continuous in the adult. The endolymphatic spaces of the vestibular labyrinth are also connected to the scala media of the cochlea through the ductus reuniens.

Among the epithelial cells lining the membranous labyrinth there are five clusters of hair cells, one cluster in each receptor organ.: The hair cells of the vestibular labyrinth are endowed with hair bundles that transduce mechanical stimuli into receptor potentials, like the hair cells that mediate hearing in the cochlea. Deflection of a hair bundle toward the kinocilium elicits a depolarization which in turn increases the release of synaptic transmitter. Deflection away from the kinocilium hyperpolarizes the hair cell and reduces neurotransmitter release (Figure 1.2).

The hair cells of the vestibular labyrinth send their outputs to the vestibular nuclei of the brain stem by 20,000 myelinated axons, which constitute the vestibular component of the eighth cranial nerve. The cell bodies of the vestibular neurons are clustered in the

Figure 1.3: The utricle is organized to detect tilt of the head [1].

vestibular ganglion.In some cells firing persists indefinitely, but in other cells the firing adapts during protracted stimulation. Vestibular afferents thus provide information about sustained stimulation, such as the acceleration from gravity, and about abrupt changes in bodily accelerations. The time-dependent decrease in vestibular afferents firing is likely to stem from adaptation at several levels, including that of mechanoelectrical transduction by hair cells and accommodation by the nerve fibers. Like most other hair cells, those of the human vestibular system receive efferent inputs from the brain stem: even if the effect of these inputs has not been extensively studied by recording from hair cells in situ, stimulation of the fibers from the brain stem has dramatic effects on the sensitivity of the afferent axons from the hair cells beacause it decreases the excitability of some hair cells, as would be expected if activation of the efferent fibers elicited inhibitory postsynaptic potentials in hair cells. In other hair cells, however, activation of the efferent fibers leads to increased excitability, the cause of which is unknown. The key to understanding how each vestibular organ operates lies in grasping how mechanical stimuli are delivered to the constituent hair cells,given that hair cells are essentially strain gauges. Distinctive mechanical linkages account for the contrasting sensitivities of the utricle and saccule, on the one hand, and the three semicircular canals, on the other.

The Otholits

The utricle and the saccule are simplest labyrinthine organs (or utriculus) (or sacculus), each of which consists of an ovoidal sac of membranous labyrinth about 3 mm in the longest dimension. The human utricle contains about 30,000 hair cells, while the saccule contains

1.1 The Vestibulocollicar Reflex 5

some 16,000. The complement of hair cells in each organ is localized to a roughly elliptical patch, called the macula. The hair bundle at the apex of each hair cell extends into the endolymphatic space of the utricle or saccule, where the bundle’s top is attached to a gelatinous sheet, the otolithic membrane, that covers the entire sensory macula (Figure 1.3). Embedded within and lying on the otolithic membrane are fine, dense particles, the otoconia; consisting of calcium carbonate in the form of the mineral calcite. Otoconia are typically 0.5-10 µm long and millions of these particles fill the endolymphatic cavities of the utricle and the saccule. The utricle and saccule are named the otolithic organs because of the prominence of otoconia,. When the head undergoes linear acceleration the membranous labyrinth moves along as well because it is fixed to the skull. The otoconial mass, however, is free to shift within the receptor organ and lags behind movement of the head,because of its inertia . The motion of the otoconia is communicated to the gelatinous otolithic membrane, which thus shifts with respect to the underlying epithelium. This motion in turn deflects the hair bundles that link the otolithic membrane to the macula, thus exciting an electrical response in the hair cells. The otolithic organs are arranged to provide the central nervous system with a unique pattern of signals for any acceleration within the physiological range,although a linear acceleration may be of any magnitude and may be oriented in any direction, . With the head in its normal position, the macula in each utricle is approximately horizontal: a substantial acceleration in the horizontal plane therefore deflects at least some hair bundles; a particular one maximally depolarizes one group of hair cells and maximally inhibits a complementary set because the various hair cells are so oriented that their axes of greatest mechano-sensitivity lie in all possible directions (Figure 1.4). Other hair cells, whose axes of sensitivity lie at various angles to the acceleration, are excited or inhibited according to their orientations. The afferent nerve fibers from each utricle therefore provide a rich and redundant representation of the magnitude and orientation of any acceleration in the horizontal plane. The brain receives additional information from the contralateral labyrinth, because the utricles are bilateral. The hair cells represent all possible orientations within the plane of each macula, but the maculas are oriented vertically in nearly parasagittal planes. The saccules are therefore especially sensitive to vertical accelerations, of which gravity is the most ubiquitous and the most important. Certain saccular hair cells also respond to accelerations in the horizontal plane; in particular, a saccule is sensitive to motions along the anterior-posterior axis. The operation of the paired saccules resembles that of the utricles.

The Semicircular Canals

Angular acceleration occurs whenever an object alters its rate of rotation about an axis. Our head therefore undergoes angular acceleration during turning or tilting motions of the head, rotatory body movements, and turning movements during active or passive locomotion. The three semicircular canals of each vestibular labyrinth detect these angular accelerations and report their magnitudes and orientations to the brain. Semicircular canal’s structure

Figure 1.4: The utricle is organized to detect tilt of the head [1].

is a roughly semicircular tube of membranous labyrinth extending from the utricle. The term canal is misleading, nearly 8 mm in overall diameter, and filled with endolymph. Like the otolithic organs, the semicircular canals detect accelerations by means of the inertia of their internal contents and it is the mass of endolymph itself that responds to accelerations. Considering the simplest case of a smoothly increasing rotatory motion, and from now a constant angular acceleration about an axis passing perpendicularly through the center of a semicircular canal one can observe that as the head rotates faster and faster it carries the bony and membranous labyrinths with it. Because of its inertia, however, the endolymph tends to lag behind and therefore rotates within the semicircular canal in a direction opposite that of the head. A cup of coffee can demonstrate the motion of endolymph in a semicircular canal: while gently twisting the cup about its vertical axis, a particular bubble is near the fluid’s outer boundary. As the cup begins to turn, the coffee tends to maintain its original orientation in space and thus counterrotates in the vessel. At the conclusion of the turning motion, when the cup decelerates, the coffee moves in the opposite direction. Fluid cannot freely move around the whole of a semicircular canal. Instead, the endolymphatic space of each canal is interrupted by a gelatinous diaphragm, the cupula, that extends across the canal in its widest region, a dilatation termed the ampulla (Figure 1.5).

Cupola’s perimeter is attached to the epithelium lining the canal: The portion contacting the ampullary crista, however, is less firmly anchored; there the cupula is penetrated by hair bundles extending from a patch of nearly 7000 hair cells.

When endolymph begins to move as the result of an acceleration, this fluid presses against one surface of the cupula and the cupula bows,because of its flexibility. The

1.1 The Vestibulocollicar Reflex 7

Figure 1.5: The organization of the ampulla of a semicircular canal [1].

margin into which the hair bundles insert also flexes, thus stimulating the associated hair cells. Angular acceleration in one direction depolarizes hair cells and excites afferent axons, while acceleration in the opposite direction hyperpolarizes the receptor cells and diminishes spontaneous neural activity,because all the hair bundles in each semicircular canal share a common orientation,. As with the other receptor organs of the internal ear, the magnitude of the response of the hair cells, as well as that of the afferent axons, is graded with the amplitude of stimulation. In each labyrinth the three canals are almost precisely perpendicular to one another, so that the canals represent accelerations about three mutually orthogonal axes . The planes in which the semicircular canals lie do not correspond with the head’s major anatomical planes.This canal is accordingly sensitive to rotations about a vertical axis, for example to twisting the neck:the horizontal semicircular canal of each ear lies nearly horizontally with the head in its ordinary, upright position. The vestibular labyrinths on the two sides of the head are systematically arranged with respect to one another. The two horizontal canals thus lie in a common plane and hence function together. Each anterior vertical canal, in contrast, lies in the same plane as the contralateral posterior vertical canal. The plane in which each anterior vertical semicircular canal lies is slanted about 45◦with respect to the coronal plane, so that the lateral extreme of each canal lies rostrally to the medial edge. The planes of the two posterior vertical canals are canted approximately 45◦in the opposite direction.

Actual human movements generally elicit a complex pattern of excitation and inhibition in several receptor organs on both sides of the body,although the actions of the vestibular

organs may be separated conceptually and experimentally, as may be the operation of the right and left vestibular labyrinths,. Consider, for example, the act of rising from the driver’s seat of an automobile:as one begins to swivel toward the door, both horizontal semicircular canals are strongly stimulated. The simultaneous lateral movement out the car’s door stimulates hair cells in both utricles in a pattern that changes continuously as the orientation of the turning head changes with respect to the direction of bodily movement. An appropriately oriented complement of hair cells in each of the saccules is excited, and an oppositely oriented group inhibited, by the vertical acceleration that accompanies rising to a standing position.So the maneuver’s conclusion involves linear and angular accelerations opposite to those at the inception. The coffee cup example again confirms the complex pattern of accelerations involved in even a simple movement. In fact examining the result of extending the cup from a position immediately in front of the body to one laterally and at arm’s length, the movements involved in serving another person. The angular component of acceleration causes the coffee to rotate within the cup, while the linear component causes the liquid to slosh toward the cup’s rim. Therefore there are contrary fluid motions that reflect linear and angular accelerations in the opposite direction.

The complementary and redundant pattern of stimulation of various receptor organs, both within one vestibular labyrinth and between the two internal ears, explains why lesions of the vestibular receptors and pathways can cause disorientation and vertigo: the central nervous system associates a particular pattern of neuronal activity with each motor action in our repertory of behavior. If a component of the vestibular system is excessively active or abnormally silent, the brain receives inappropriate information on acceleration and the reflexes driven by vestibular inputs understandably falter so we become consciously aware of the vestibular system at work. In the most severe cases a diseased labyrinth must be surgically destroyed in order to relieve the brain of erratic and disabling vestibular signals.

1.1.2

The Vestibulocollicar Reflex

The vestibular system combined with other multisensory inputs collaborating to a multitude of functions and reflexes that contributes to posture maintenance. In this regard there are three classes of reflexes:

1. the vestibulo-ocular reflex (VOR), which stabilizes the visual axis to minimize retinal image motion,

2. the vestibulocollic (VCR) reflex, which stabilizes the head in space through the activation of the neck musculature in response to vestibular inputs,

3. the cervico-collic (CCR) reflex, wich stabilizes the head on the torso, it is a neck-stretch reflex that acts in response to the neck muscle spindle receptors [2].

The VOR has been well characterized in many studies and is compen- satory in all frequency range can be encountered in everyday life [3].

1.1 The Vestibulocollicar Reflex 9

Figure 1.6: Pathways between ampullary nerves and neck motoneurons. Inhibitory vestibulocollic neurons and their terminals are shown in black; excitatory vestibulocollic neurons, in white [4].

The function of the VCR is less clear with two not mutually exclusive hypothesis about its function.

The first one is that the VCR stabilizes the head in space during active body movements, as during locomotion [5], for example. But if the VCR remains active during voluntary head movements, it would oppose voluntary motion. This has led to the hypothesis that the VCR is suppresed when the movement is under the voluntary control [6]. The other hypothesis is that the VCR could dampen head oscillations, which would otherwise occur during active head movements because of the large mass of the head [7] .

1.1.3

The Characteristics of VCR

The VCR helps stabilize the head relative to inertial space by generating a command moving the head in the direction opposite to that of the current head–in–space displacement. When the head is rotate in the plane of a semicircular canal, the canal is stimulated and the muscles are activated. This stimulation would produce a compensatory rotation of the head in the same plane. If more than one canal is activated,there is a combination of stimulus and that produces an appropiate reflex response.

The efficacy of the VCR appears to vary substantially across species. It is much more evident in animals that make minimal eye movements such as pigeons [8] and other birds. Its contribution to head stabilization has is instead less significant in macaque monkeys and human species that have large oculomotor ranges [9]

For example, when human subjects are distracted by mental arithmetic, that means the reduction of the influence of the voluntary control, the active yaw-axis stabilization at low frequencies (<1 Hz) is generated by longer-latency voluntary mechanisms, suggesting that the VCR contribution is negligible [9], [10] . This led to the hypothesis of the cancellation

Figure 1.7: The neck muscolature.

of VCR during voluntary head rotations. A possible explanation comes from recordings of secondary vestibular-only (VO) neurons in the vestibular nuclei; VO neurons, including some that project into vestibulospinal pathways, react to passive head movements, but their response to active head rotations is attenuated, on average by 70% [11], [6], [12]. The cancellation signal carried to VO neurons is due to a comparison of the expected afferent signal, built by the brain and based on the voluntary movement, with the actual neck-afferent signal [12].

The cancelation of the VCR during voluntary movements can be related [4] to the reafference theory by von Holst and Mittelstaedt [13] where a copy of the expected sensory consequences of a motor command (efference copy) is removed from the actual sensory signal (reafference) to create a sensation of external perturbations (termed exafference). In this way, the nervous system can separate sensory inputs arising from external origin and those resulting from self-generated movements.

The range of frequencies in wich the VCR is more active is 1 – 3 Hz [7],[10] where it would be most effective in coumpensate the underdamped mechanics of the head.

The VCR is mediate by a direct pathway, comprised of three neurons [14]: two central synapses, one on vestibulocollic neurons in the vestibular nuclei and the second on neck motoneurons (Figure 1.6), in addition there is the peripheral synapse.

Unlike the VOR, the VCR controls a complex musculature. The VOR involves six extraocular muscles, each pair acts around a single rotation axis. On the other hand, the neck has more than 30 muscles (Figure 1.7 ) controlling pitch, roll and yaw rotations [15]. The system could be considered underdetermined because there are more muscles than rotation axes. One consequence of this property is that the same head movement can be produced by the activation of different muscle patterns: this is the case for voluntary head movements, but not for the VCR where a particular head motion is related to a stereotyped

1.2 The Modelisation of VCR 11

Figure 1.8: The gait cycle.

muscle activation pattern [15].

The VCR role during locomotion

The neuroscientific studies conducted on human patients during locomotion evidence the contribution of the VCR for the head stabilization. During a normal straight walking 1.8 the head moves mainly in the sagittal plane, rotating around the pitch axes in a range of 0.3−8◦ and traslating between 0.8 - 90 cm [5], [16], [17] .

Some experiments were conducted at different walking velocities and there has been demostrated the contribution of the reflex in the head compensation, in particular the optimal stabilization is within a range of 1.2 - 1.8 m/s [18] that is coherent to a mean walking velocity. It happens both for the angular rotation, especially at low velocities, and the vertical translation – that is more evident with the increasing of the speed. During fixed-gaze treadmill walking, that is at fixed velocity, the coordination between the head and the trunk is dependent on the events in a gait cycle [19], although the trunk already damps many oscillation acting as a low pass filter [20], the role of the reflexes is still essential.

The influence of the reflexes depends also on the frequency of the stimulation. The high-frequency behavior seems to be dominated by passive head dynamics. At low-high-frequency be-havior, Goldberg and Peterson [21] explain that in alert cats VCR and CCR are in opposition, while the human studies [9], [10] suggest low-frequency behavior is regulated by voluntary control with minimal reflex ac- tivity. The reflex contributions provide the transition from voluntary to passive head control. This theory was supported by measurements of neck muscle electromyographic (EMG) datas at the transitional frequencies.

1.2

The Modelisation of VCR

Although there are many physiological models of the VOR and many robotic implementa-tions, it is not really the same for the VCR. Many of the existents models have incomplete characteristics or anyway are not suitable for a further robotic implementation. The current state of art provide two main important models for the reflex in this study. Both consider the VCR as a simple negative feedback but recent studies [22] demonstrates the engagement of the central nervous system in the modulations of feedback gains. That means the simple feedback is not enough to explain the mechanisms envolved in the head stabilization but

Figure 1.9: Neuromechanical model of head and neck movement in the horizontal plane [7].

there is some feedforward contribution.

The first model has been proposed by Peng [7] in 1996 1.9

The researchers presents a control model of yaw head rotations during perturbations of the torso, which for the first time combine a model of the human head with neural feedback controllers representing the vestibulocollic and the cervicocollic reflexes. The parameters of the modelare extracted directly from anthropomorphic, biomechanical and physiological studies. The model includes two negative-feedback reflexes, the VCR and CCR; a transfer function representing the mechanical properties of the neck and head; and a low-pass torque converter that transforms EMG data into mechanical torques.

It is a one degree of freedom model of the head for the movements in the transversal plane, derived assuming the head to be a rigid body rotating about the C1â ˘AˇTC2 joint in that plane.

The input of the model are the torso angular displacements in the yaw plane and the outputs are the relative head movement with respect to the trunk. The outputs from the head plant describes the compensatory head re- sponse to an input perturbation of the torso. The neck output provides direct input to the CCR. As the proper input to the VCR is a head movement in the inertial space, the torso input is added to the plant output to generate the appropriate signal. The VCR and CCR controller are constructed on the basis of current knowledge of VCR and neuroanatomy and physiology. It based the VCR controller on a simple neuronal pathway, it consists of a second-order trans- fer function describing the processing from an input head acceleration to an output neck EMG modulation. In the same

1.2 The Modelisation of VCR 13

Figure 1.10: Step response of the four models. The output displays the neck movement response over 2 s [7].

way the CCR controller is a second-order transfer function describing the processing from an input stretch of the neck to an output neck EMG modulation.

In the experiments they applied a step perturbation of 57.3◦to the torso, in 4 different ways: considering only the head plant, adding only the VCR controller, adding only the CCR controller and the full model.

Without considering the reflex contributions, the head and neck system produced a second-order underdamped response with a 5.2 dB resonant peak at 2.1 Hz. Adding the CCR com- ponent to the system dampened the response by approx- imately 7%; while the VCR controller dampened head oscillations by 75%. The VCR is also responsible of a low-frequency compensation by increasing the gain and phase lag, creating a phase minimum at 0.1 Hz and a phase peak at 1.1 Hz. Combining all three components (mechanics, VCR and CCR), the closed loop closely fits human data, and ex- plains quantitatively the characteristic phase peak often observed.In conclusion, the model confirms that the VCR plays a much more important role than the CCR in humans, and that the low-frequency behavior is shaped by the VCR.

The model proposed by Goldberg et al. [4] is nearthe same of the previous one but in addition there is the contribution of the voluntary control.

Were the VCR active during voluntary head movements, it could increase damping reducing the oscillations. But the VCR opposes the head movement, so its presence necessitates an increase in the voluntary command, referred to in the model as VOL. As explained in the previous sections there is the hypothesis that the VCR is canceled during voluntary head movements [23].

Figure 1.11: Block diagram of the presented neuromechanical model [4].

The model depends on the nature of the efference copy signal, that signal is the desired dampened head trajectory, not including the oscillations of the underdamped plant. Without external sensory inputs, the exafferent signal would only include oscillations and other perturbations from the desired movement. Not unexpectedly, the reduction of oscillations is as effective in the modified model (Figure 1.11) as in the original diagram.

Chapter 2

The Robotics Implementations for

the Head Stabilization

In nature we can found many complex systems from whom the robotics draws inspiration creating artificial systems which can perform assigned tasks very efficiently. The human body itself can be seen as a many-degree-of-freedom robotic system. The observation and the study of nature, especially from a neuroscientific point of view can help to find solutions to mechanical and control problems of the machines. On the other hand the study of some behaviours and characteristics implemented on the robots contributed to better understand the neuroscientifical or physiological feature.

That happened for the head and gaze stabilization essential for the animals survivor as important for the good operation of the robot.

From the robotic point of view there are some implementations of head stabilization model.

Yamada and colleagues [24] propose a method for the stabilization of the snake-like robot head, controlling the neck to cancel the undulation. The controller is based on the rejection of the disturbance of the body on the head using a continuous model.

Another controller [25] for the head stabilization has been implemented on the quadrupedal Sony AIBO robot 2.1. While a network of Central pattern Generators (CPGs) generates locomotion, giving the joint angles of the hip and knee joints in the sagittal plane. another network of CPGs in combination with a genetic algorithm generate the compensating head movement, specifing the planned neck tilt, pan and nod joint values. The CPGs are located in the spine of vertebrates and produce coordinated rhythmic movements for the locomotion. Here a CPG is modelled as coupled Hopf oscillators, that generate the rhythmic movements, the genetic algorithm create the best set of parameters that results close to the desired movement. Although the head movements were minimized especially in X and Y coordinates, the results show it is not totally eliminated during

Figure 2.1: The quadrupedal robot AIBO

locomotion.

The work of Marcinkiewicz [26] conducted on the AIBO robot usa a controller based on a machine learning algorithm able to learn the compensation for the head rotations when no stabilization mechanism is present.

2.1

Head stabilization for a humanoid robot

Talking about the head stabilization of a humanoid robot we can found the work of Gay [27]. The controller proposed is a system for stabilizing the head of a bipedal robot during locomotion, using only the optical flow information. It is based on Adaptive Frequency Oscillators to learn the frequency and phase shift of the optical flow and produce compensatory movements to minimize the head motion. Although the system can successfully stabilize the head of the robot during its locomotion, it doesn’t take in consideration the vestibular inputs.

The most close to the neurophysiological behaviour of the VCR is the controller proposed by Falotico [28] (Figure 2.2).

It is an adaptive model based on a feedback error learning (FEL) applied by Shaal and Shibata for the VOR [29], able to compensate the disturbance rapresented by the trunk rotations. In this way the model adapt itself to the dynamics of the head motion.

The block diagram (Figure 2.2) shows a feedback controller using the measured RPY angles (ν, φ, ψ) and able to follow a reference orientation around the three axes (νr, φr, ψr). The feedback controller performances, however, are not enough due to nonlinearities in the

2.1 Head stabilization for a humanoid robot 17

Figure 2.2: Block diagram of the Adaptive Head Stabilization model [28]

plant and delays in the feedback signals.

To enhance the performance, the model require a feedforward architecture, in this case the FEL.

Furthermore an Artificial Neural Network is use to solve the inverse kinematics problem without using the closed form solution because could result too complex and computation-ally heavy and could present multiple solutions.

2.1.1

FEL Architecture

The Feedback Error Learning Architecture, from the viewpoint of adaptive control, is a model-reference adaptive controller. The controller is assumed to have a stabilizing linear feedback controller because the feedback motor command is used as an error signal to train a neural network controller. Kawato [30] demonstrated the convergence of this adaptive control scheme and suggested its architecture as an abstract model of learning in the cerebellum.

The estimation af the trunk angular orientation ( bνt, bφt, bψt) and the error due to the

difference between the actual measured angles of the head and the reference orientation are the input for the FEL architecture. The output of this model is sent as input to a Neural Network which calculate the joint angles relative to the estimated orientation.

FEL is a principle of learning motor control, using an approximate way of mapping sensory errors into motor errors that, can be employed to train a neural network. This work in the same way as the work of Shibata for the VOR [29] adoperate the moidified recursive least squares (RLS) algorithm for FEL, a Newton-like method with very fast convergence, high robustness, and without the need for elaborate parameter adjustments.

P(t) = 1 λ h P(t−1) − P)(t−1)x(t)x(t)TP(t−1) λ+x(t)TP(t−1)x(t) i w(t) =w(t−1) + P(t)x(t) λ+x(t)TP(t)x(t)ψ e_{(t+1) =} ˆ ψ(t) =w(t)Tx(t) Where:

Figure 2.3: The FEL architecture [28]

• λ∈ [0, 1]is the forgetting factor

For λ = 1, no forgetting takes place, while for smaller values, the oldest values in the matrix P are exponentially forgotten. This forgetting strategy permit training data from the first stages of learning, where the feedback error was large and very inaccurate, to be neglected.

Figure 2.4: The results on the SABIAN robot relative to the pitch rotation [28] The model has been validated initally on Matlab Simulink,simulating the dynamics of the SABIAN head, then directly on the humanoid robot SABIAN (Sant’Anna BIped humANoid). SABIAN is a biped humanoid developed by the Robot-An Laboratory, at Scuola Superiore Sant’Anna. The SABIAN robot (Figure 2.5) has 7 DOF in each leg, 2 DOF in the waist, for a more agile stretched knee walking, 2 DOF in the trunk. Every DOF has a bio-inspired range of motion, related to human motion measurements. On the platform, the iCub head (see section ??) has been mounted.

2.1 Head stabilization for a humanoid robot 19

Figure 2.5: The SABIAN humanoid robot and its body kinematics [28]

The results demonstrate the head is stabilized compared to the trunk motion (Figure 2.4), indeed the peak to peak amplitude of the head is less than 2 degrees during the whole task execution.

A new bio-inspired model

On the bases of the previous discussion, this work consider the existent bio-inspired models af the Vestibulocollicar reflex and complete it with the model of the cerebellum, in a similar way as the Vestibuloocular reflex in [31]. The validation of the model has been done in Matlab Simulink using a rapresentation of the robotic humanoid platform iCub.

3.1

The role of the cerebellum

The cerebellum plays a fundamental role in adaptation of postural control. It is also an important component in adaptation of the vestibular reflex, but it is dubious which is its specific function in this adaptation. An interesting hypothesis, based on experimental studies of rabbits, has been proposed by Masao Ito [32].

In addition to the direct excitation of the vestibular nuclei in the brain stem, in the vestibular labyrinth the sensory neurons also stimulate Purkinje cells of the cerebellum flocculo-nodular lobes via a mossy and parallel fibers pathway. Then, the Purkinje cells in turn send an inhibitory influence back onto the vestibular nuclei. According to Itoâ ˘A ´Zs hypothesis,it is the alteration of the relative strengths of the direct excitatory and indirect

a) b)

3.2 The Recurrent Architecture 21

a) b)

Figure 3.2: Comparison between the two architectures a)Feedforward and b) Recurrent[31].

inhibitory pathways that adaptively modulates the gain of the vestibulo-ocular reflex [1]. On the other hand, David Marr proposed earlier that it is the concurrent action of a climbing fiber input that modified the synaptic efficacy of parallel fiber input to a specific Purkinje. Instead, Ito asserts that the modulation could be influenced by messages of retinal image slip, carried by the climbing fiber. Ito and his colleagues demonstrated that such a signal in the accessory optic pathway is transmitted from the retina to the inferior olivary nucleus and from the nucleus into climbing fiber pathways and then to the vestibular cerebellum.

Thus, it is the latter pathway that establishes the parameters for the adaptation between the parallel fiber and Purkinje cell synapse, like a â ˘AIJteachingâ ˘A˙I line. Infact, cerebellar lesions abolish the learning potential and, thanks to the mechanism of long-term depression, simultaneous electrical stimulation of related mossy and climbing fiber projections causes long-term changes in the efficacy of the synapse of the parallel fiber and the Purkinje cell.

Later, Frederick Miles and Stephen Lisberger [33] tested this interpretation. During experiments with monkeys, by the modulation of the Purkinje cell output only during the process of adaptive learning, the input returned to its original state after completion of the adaptation and didnâ ˘A ´Zt leave any trace in the cerebellar cortex. This work demonstrates that both Purkinje cell output and the climbing fiber input are the â ˘AIJteachingâ ˘A˙I line. For this reason, according to Miles and Lisberger, the site of adaptive learning is represented by the brain stem neurons targeted by the Purkinje cells and the cerebellum function is the construction of the signal that provides the parameters for adaptation

3.2

The Recurrent Architecture

As explained in Section 2.1.1 one of the interpretation of the cerebellar structure has been made with the FEL model, assuming the cerebellum as a one-layered neural network able to modify its own weights with a gradient descent learning. But this kind of learning needs the knowledge of the motor error,given by the difference between the actual motor command and the desired one. This value is not directly observable because the commands from the cerebellum pass trough the controlled motor plant. What we can measure is only the effect that these commands have on the system, the sensory error.

Figure 3.3: Schematic diagram of the organization of the cerebellar microcircuit [31].

However, sensory error would not be an adequate training signal for the same reason that the error at the output units of a multilayer artificial neural network is not appropriate training signal for units in the middle layers. This problem is called ’distal-error problem’.

One solution is the back-propagation architecture, consisting in a neural structure wich approssimate the motor system, using the inverse jacobian (reference structure) evaluated in a point nearby the current motor command. In this way back-propagating the sensory error and giving it as an input of the new block, an estimation of the motor error is possible, even if not directly osservable.

One of the weak point of this approach is the complexity of the structures required for stable learning is similar to the complexity of the system studied. Moreover, a motor-error teaching signal seems physiologically incompatible with the real nature of the sensorial properties of the Climbing Fibers.

For this reasons, Porril et al. [31] proposed a model whose structure was more biologically-inspired altough able to well stabilize the system. The architecture suggested is recurrent, this time the cerebellar input is the efferent copy of the motor command, directly available. It employs a decorrelation learning algorithm wich has a stronger physiological meaning, close to the structure described by Marr [34] and Albus [35]. The inputs of the system (Figure 3.3) (represented by the vector y) are carried by MossyFibers (MF), which converge in the Granule Cells (GC). Each GC receives input from several MFs and from recurrent connections (not shown) and its output is distributed along a Parallel Fiber (PF). Attached to the bundle of PFs there are Purkinje Cells (PC). Each PC re- ceives input from all the PFs and receives an additional input from a Climbing Fiber (CF). This additional input is assumed in Marr-Albus models to act as a teaching signal for the weights wij of the PC-PF synapse.

3.3 The model 23

Figure 3.4: The cerebellum as an adaptable linear filter [31].

If we see the model as an adaptive filter, Granule Cells are modelled as filters with transfer function Gi and PC perform a weighted sum of signals pi carried by Parallel Fibers. If we

consider this model for dynamic problems like adaptive filtering or control, the Giare actual

transfer function, whose value depend even on the past values of y. If we want to use this model to solve a "static" approximation problem, the Giare simply functions of the current

values of y.

The learning algorithm used in this approach is the decorreleà ˇnation control, implemented in the cerebellum block. The sensory error here is due to a incorrect motor response: when there is no more correlation between the two cerebellar input (sensory error and efferent motor copy) the learning stops because is no more possible reducing the sensory error.

In decorrelation control, mossy-fibre inputs are predictor variables, to be decorrelated from the target determined by the CF signal, processing of the MF input y(t)by the granule cell layer is meant as analysis by a bank of linear filters Gi so that the PFs carry signals

pi(t) = Giy(t). PC output is modelled as z(t) = ∑ wi∗pi(t) of these PF inputs, so the

PC implements a linear filter C = sumwi∗Gi . The CF input is interpreted as a training

signal e(t), which adapts synaptic weights using the anti-Hebbian heterosynaptic covariance learning rule δwi = −β∗e∗pi.

3.3

The model

Using this architecture in the cerebellar block in Figure 3.5 was possible to create a controller for the head of humanoid robot iCub (see section 3.4) really biologically inspired. Like the human head with is vestibular system, iCub head own an Inertial Measurement Unit (IMU) wich is able to sense the linear acceleration and the angular velocities around the three axes. Using the iCub kinematics and dynamics and the cerebellar architecture described above

Figure 3.5: Block diagram of the model.

was possible to implement in Matlab Simulink the controller. The model proposed is shown in the figure 3.5.

This model has as input the angular velocities of the head, more precisely the difference between a reference velocity vr and the one estimated by the cerebellum ˜v. The Inverse

Jacobian transforms the command from the operative space to the joint space and it goes as input to the robot. The error used as a teaching signal is the velocity measured by the inertial sensor. The reference velocity vr is an estimation of the torso velocity obtained by

the difference between the angular pitch velocity of the head and the one misured by the inertial sensor.

3.4

The iCub robotic platform

The humanoid robot iCub (Figure 3.6) was design and developed by Italian Institute of Tecnology in the european project RobotCub. The robot is about 104 cm tall and it has the sembiance and the dimensions of a 3.5 years old child. The final goal of the research around iCub is the study of the human cognitive system, trough the robotic implementation, of the learning process of every day actions as manipulation, grasping, locomotion finalized to the exploration and the interaction with the external environment [36].

One of the most evident characteristics and of the strong points of the icub project is the free access to the platform. Indeed the repositories, the design and the software are a free Open Source distribution, licensed under the GPL/FDL.

The robot is very complex, with 53 Dof in all the body wich make passible the motion of head, arms, hands, hips and legs. It was designed to simulate the sense of proprioception, of the configuration of its own body and movements, it has sensors that are its sense of sight, of hearing and touch.

3.4 The iCub robotic platform 25

Figure 3.6: ICub humanoid platform

This work take in consideration only the iCub head and the three rotational joints situated in the neck, because they are the ones directly involved in the VCR modelisation.

Icub head has six joints, three for the neck(roll, pitch, yaw) and three for the eyes (tilt, version and vergence) [37]. In this work we considered only the neck pitch joint.

The robot Inverse Jacobian and Direct Knematic were considered.

3.4.1

The Forward Kinematic

The origin of the root reference frame is a point on the axis of rotation of the torso pitch. The origin of the reference frame located in the middle of the robot in between the two legs (Figure 3.7).

• The z axis of the root reference frame is parallel to gravity but pointing upwards. • The x axis of the root reference frame points behind the robot.

• The y axis of the root reference frame points laterally and is chosen according to the right hand rule.

The head, more exactly the inertial sensor forward kinematics is obtainad using the Denavit-Hartenberg convention. The matrix that describes the transformation is:

T_RoIs = T_Ro0 * T_0n * T_nIs where:

• T_Ro0 represents the rigid roto-translation from the root reference frame to points in the 0th reference frame, just a rigid rotation which aligns the z-axis with the first joint of the waist.

Figure 3.7: The iCub root reference frame T_Ro0 =       0 −1 0 0 0 0 −1 0 1 0 0 0 0 0 0 1      

• T_0n is the roto-translation from the 0th reference frame to the nth reference frame where n the number of degrees of freedom, in this case it represent tge of the waist and neck forward kinematics. T_0n = T_01 T_12 ... T_(n-1)n

In table are the actual DH parameters which describe T_01, T_12, ... T_(n-1)n. Link i/H-D Ai(mm) di+1(mm) αi(rad) θi+1(deg)

i = 0 32 0 π 2 [−22, 84] i = 1 0 -5.5 π 2 −90+ [−39, 39] i = 2 2.31 -193.3 −π 2 −90+ [−59, 59] i = 3 33 0 π 2 90+ [−40, 30] i = 4 0 1 −π 2 −90+ [−70, 60] i = 5 2.5 100.5 −π 2 90+ [−55, 55]

• T_nls could be considered as a further virtual link located at the end of the chain and with its joint constantly kept at 0 value.

3.4 The iCub robotic platform 27

Figure 3.8: The CAD design of iCub head and Inertial Sensor

T_nls =       1 0 0 0 0 0 −1 0 0 1 0 6.6 0 0 0 1      

Validation and discussion of the

results

The properties of the model with the decorrelation control were tested trough a Matlab implementation.

a)

b) Figure 4.1: Head and torso angular velocities and error for a single sinusoid input at 1 Hz a and for a sum of sinusoids b).

4.1 Training 29

The validation of the model has been conducted on a single axis of rotation. It was done giving as a disturb for the system single sinusoids at different frequencies and also a sum of sinusoid. The range of frequency used is between 0.1 and 1 Hz that is the oscillatory range of frequency distinctive of the locomotion and with a time sampling of 100 Hz.

In the model we use 20 weights with a learning rate of 0.05.

Various experiments was done with a single sinusoid varying the frequency and also with a sum of sinusoids. Analysing the values assumed by the wheights of the model it has been noticed that the convergence is verified in the frequency range studied.

In the figure 4.1 we can see in red the error decreasing fo both the single sinusoid and the sum and the head velocity compensates the torso. In this range the system converges. The convergence time is a parameter we used to verify the quality of the system. It represent the time needed to the system to reach a stabile condition. In this case it increase when the frequency of the disturbs increase, but, at a given frequency, it results more or less the same for al the weights. Head pitch velocity compensates the torso pitch velocity, as happen in human body trough the VCR action.

4.1

Training

Figure 4.2: The evolution of the weights during the training set

The system was trained with training cycles of 100s with a sum of sinusoid as input signal. The coefficients of the weights obtained after the training (figure 4.2) were used to set the coefficient of a new session. Simulating the system with a single sinusoid at 0.5 Hz in input, we can notice that system is stabilised faster and reach easily the convergence. (Figure 4.3)

The behaviour of the learning algorithm and subsequently the values assumed from its weights, is not strictly dependent from the frequency of the input signal. The model, starting from a condition considered due to the previous dynamic assumed by the weights, react to the new signal trying to stabilise in a new condition, more suitable to the new contest.

That’s why the training set is very important: the values assumed at the end of the training include a wide range of dynamics wich are not new to the mode. It is the memory property of the algorithm, analogue to the cerebellar. The results analysed confirm that,

a)

b)

Figure 4.3: Head and torso angular velocities and error for a single sinusoid input at 0.5 Hz before a) and after the training b)

although the complex dinamics of the angular velocity of the head, the model is able to modify its own paramenters and reach the convergence.

Chapter 5

Conclusions and further steps

Studying the available literature of motion-captured head motion during hu- man walking, and analyzing the characteristics of the mechanisms involved, this work developed a simplified reference model of human-like head movement for humanoid robots.

The approach of this study was trying to find the corrispondences between the biological, neuromechanical and physiological systems and the robotic ones.

The VCR behaviour is therefore compared to a feedback controller, but it is not the only mechanism involved. From the neuroscientifical studies and experiment was evident the engagement of some elements of the central nervous system.

For this reason the model include the Recurrent Cerebellar Architecture network model to simulate the cerebellar influence on the controller.

Other improvements have to be done to make suitable the controller for more general porpouse, starting from the extension to all the three axes of rotation, to a generalization to any robot, using machine learning algorithms to learn the kinematics for example. Another step could be the integration of the modelization of the VCR with the VOR, to obtain a more stable and efficient system.

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