ARTICLE
International Journal of Advanced Robotic Systems
A Bio-Inspired Approach to the Realization of Sustained Humanoid Motion
Invited Paper
Miomir Vukobratović1,†, Branislav Borovac2,*, Aleksandar Rodić1, Duško Katić1 and Veljko Potkonjak3
1 Institute „M. Pupin“, Belgrade, Serbia 2 Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia 3 Faculty of Electrical Engineering, University of Belgrade, Belgrade, Serbia † Professor Miomir Vukobratović passed away before the publication of this article * Corresponding author E-mail: [email protected]
Accepted 16 Aug 2012
DOI: 10.5772/52419
© 2012 Vukobratović et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract This paper overviews some author’s biome‐ motion trying to re‐establish posture and dynamic chanical inspiration for the development of an approach balance where jeopardized by perturbation). which enables the realization of bipedal artificial motion. First, we introduce the notion of dynamic balance, which Keywords Humanoids, biped locomotion, dynamic is a basic prerequisite for the realization of any task by balance, ground reference points humanoids. Then, as ground reference points, important indicators of a humanoid’s state were introduced and discussed. Particular attention was paid to ZMP, which is 1. Introduction the most important indicator of robot dynamic balance. As defined in [1] “Biomechanics1 is the study of the Issues of modelling of the complex mechanical systems structure and function of biological systems by means of (humanoids belonging to this class) were also discussed. the methods of mechanics.ʺ However, in engineering we Such software should allow humanoid modelling, either often want to build up a replica of a biological system, without any contact with the environment (such as flying imitating its “natural” behaviour and trying to make the freely in space, for example, during jumping) or having replica as close as possible2 to its biological paragon. To contact with ground or any other supporting object. It achieve this engineering has to be bio‐inspired. There are also should be enough general to cover different humanoids’ structures, postures, and allow the 1 From the Ancient Greek: βίος ʺlifeʺ and μηχανική ʺmechanics.ʺ calculation of all relevant dynamic characteristics. Some 2 In this paper, we will not discuss issue why this similarity is examples are presented in this paper (e.g., the modelling welcomed and needed. The need for human‐likeness will simply of a goalkeeper catching a ball, the replication of human be assumed. www.intechopen.com Miomir Vukobratović, Branislav Borovac, AleksandarInt JRodić, Adv Robotic Duško KatićSy, 2012, and VeljkoVol. 9, Potkonjak: 201:2012 1 A Bio-Inspired Approach to the Realization of Sustained Humanoid Motion many examples where design has been inspired by 2. Ground reference points and dynamic balance biological systems, but we will focus on humanoid robots and, in particular, biped locomotion. 2.1 General – the notion of dynamic balance
Let us begin with history. Concepts akin to todayʹs robot In this paper, we will try to demonstrate the biome‐ can be found as long ago as 450 B.C., when the Greek chanical inspiration for the development of an approach mathematician Tarentum [2] postulated a mechanical which enables the realization of biped artificial motion bird which he called ʺThe Pigeonʺ and which was (posture realization, gait synthesis and realization). In all propelled by steam. Al‐Jazari (1136‐1206), a Turkish [2] these activities, the maintenance of a humanoid upright inventor, designed and constructed automatic machines position (i.e., dynamic balance) is a task that is constantly such as water clocks, kitchen appliances and musical present during any kind of motion and, thus, of basic automatons powered by water. One of the first recorded importance for any kind of humanoid activity while designs of a humanoid robot was made by Leonardo da standing. This is why we will first pay attention to this Vinci [2], around 1495. Da Vinciʹs notebooks, extremely important issue. rediscovered in the 1950s, contain detailed drawings of a mechanical knight able to sit up, wave its arms and move The motion of bipedal robotic systems is realized by a its head and jaw. The first known functioning human‐like synchronized motion of the joints in robot’s legs, arms robot was created in 1738 by Jacques de Vaucanson [2], and trunk ‐ i.e., by the change of the robotʹs internal who made an android that played the flute, as well as a coordinates. The validity of the motion performed is mechanical duck that reportedly ate and defecated. In verified with respect to the environment (external 1893, George Moor [2] created a steam man. He was coordinates). In order that the preset goals can be realized powered by a 0.5 hp gas fired boiler and attained a speed by the humanoid system’s motion, a unique and of 9 mph (14 km/h). Westinghouse made a humanoid bidirectional correspondence must exist between the robot known as Electro. It was exhibited at the 1939 and movements performed in internal (joint) coordinates and 1940 World’s Fairs. It is also important to mention their external effect regarding the environment ‐ i.e., another not so well known scientist, Nikolai between internal and external synergies. In other words, Aleksandrovich Bernstein [3]. He began his research at the action realized by the moving robot’s mechanism the beginning of the 1920s by studying voluntary joints will attain the goal if the mechanism is “properly” movements. At that time, he significantly refined the supported. This notion of “proper contact with the classic methods of recording movements [4, 5], and ground” needs clarification. already in 1926 his first book ʺGeneral Biomechanicsʺ [6] came out. He made a significant contribution to the study Let us focus on the humanoid robot sketched in Fig. 1. of biomechanics and especially of the modes of human [25]. Let the coordinate frame representing the motion, such as walking and running. Moreover, environment to which external synergy has been defined Bernstein was the first in world science who studied be xGR OGR zGR (Fig. 1a) and let it be fixed to the ground. motion from the viewpoint of the knowledge of the Also, let the internal synergy be defined with respect to
regularity of brain functioning. While the scientists before the coordinate frame xF OF zF fixed to the foot tip (Fig. 1a). Bernstein studied human motion with the objective of Both coordinate frames are presented only in the sagittal merely describing it, Professor Bernstein began the study plane (the y‐axis not being shown in either of the cases). of this motion to establish how it was controlled [7‐12]. He thought that a researcher who wants to understand the brain’s functions could hardly find a more worthwhile object for such study than by controlling movement.
The most important bio‐inspired notion regarding biped locomotion is the Zero‐Moment Point (ZMP), which was first introduced by Vukobratovic and his associates [13– 19]. The first application of the ZMP was made by Japanese researchers in the middle of the 1970s, headed Figure 1. Illustration of the relationship between internal and by the late professor Kato. At Waseda University, they external synergy. developed biped WL 12 which, for the first time in the world, performed fully dynamic walking [20]. Later on, Let us further suppose that the humanoid is walking (Fig. 1 there were a number of examples of biped walking robots shows the single‐support phase) while trying to reach the using ZMP as a basis for gait realization: e.g., Wabian [21] object O shown in Fig. 1b. The object position requires that and Asimo [22, 23]. Let us also mention example of first the hand tip (represented by the point H) approaching the
exoskeletons for the restoration of walking function [24]. trajectory is parallel to the x‐axis of the frame xF OF zF. In
2 Int J Adv Robotic Sy, 2012, Vol. 9, 201:2012 www.intechopen.com case, the foot realizes ʺproperʺ contact with the ground (i.e., Let us look more closely at the notion of dynamic balance contact over the surface, not the line or the point) and the [26]. It is clear that any change of the system dynamics coordinate frames xGR OGR zGR and xF OF zF will coincide while will cause a change in any reactions between the foot and hand trajectory will also be parallel to the x‐axis of the the ground. Let us first consider a static single‐support external coordinate frame xGR OGR zGR. Suppose further that a case – a robot “standing upright” on one leg, without disturbance occurred and that the humanoid started falling moving – and let the resultant of the gravitational forces forward by rotating about the front foot edge (Fig. 1d). In pierces the ground plane at a point which is inside the such a case, the frames xGR OGR zGR and xF OF zF will not support area. The piercing point is called the centre of coincide any more (Fig. 1e). They are being rotated by the pressure (CoP). Looking from the opposite direction, one angle φ. If the humanoid is continuing to realize the joints’ may say that the CoP is the point where the resultant trajectories exactly as before, the occurrence of the ground reaction force pierces the supporting surface. The disturbance of the hand trajectory will remain parallel to condition that the CoP is inside the support area the x‐axis of the frame xF OF zF but will not be parallel to the guarantees the static balance. In addition, in static case x‐axis of the external frame xGR OGR zGR. In other words, in the this condition means that the centre of mass projection case of any ʺnon‐properʺ foot‐ground contact, the internal (CMP) is inside the support area (edges excluded). and external synergies will not coincide. This means that now the hand trajectory with respect to the environment Now suppose that the humanoid starts to move, still (external synergy) will not depend solely on the joint relying on one leg. As an examples, one may might angles qi, i=1, ... n but also on the angle φ between the foot imagine a gymnastic exercise or a single‐support phase during walking. In this dynamic case, and in addition to and the ground. We think it is obvious that this non‐ the gravitational and external forces, there also appear coincidence of the hand trajectories is caused by the foot inertial forces generated by the robot’s motion. The rotation relative to the ground and that it influences the piercing point now concerns the resultant of all the forces: behaviour of the overall system. Thus, we can say that in gravitational, external, and inertial. For the piercing point the case of biped locomotion a unique relationship between internal and external synergies is ensured by the relative (CoP), it holds that the sum of all moments about around immobility of the robotʹs foot (more precisely, the legsʹ two horizontal axes equal zero. If the piercing point is terminal links3) and the environment in contact. If this within the support polygon (excluding the edges) it is holds, the robot is dynamically balanced. This means that if called the Zero‐Moment Point (ZMP); note that in this a proper internal synergy results in the proper external case, the ZMP and the CoP are actually the same point. If synergy, we say that the robot is dynamically balanced or, so, we say that the system is dynamically balanced – the more specifically, that dynamic balance can be represented foot maintains its surface‐to‐surface contact with the ground. If, however, the piercing point finds itself on the by the relative immobility of the coordinate frames xGR OGR edge, indicating that the foot is turning, then the term zGR and xF OF zF representing internal and external synergies. CoP still applies while the ZMP is not used. The system is As the contact with the ground is realized through the no longer dynamically balanced and the surface‐to‐ feet, this means that “proper” contact with the ground surface contact is replaced by a line (or point) contact. So, requires that the terminal link of the supporting leg(s)4 the term ZMP is reserved for dynamically balanced does not move with respect to the ground. Since the bipedʹs states. contact between the foot and the ground is unilateral 2.2.2 Double support posture – ZMP related to CoPleft and (there is no constraint or resistance to prevent a foot CoPright lifting from the ground), it is necessary that the biped during motion does not generate forces that would cause While notions of ZMP and CoP look quite similar in the the turning of the foot about its edge. above described single‐support situation, the difference being almost formal, their true relevance and the difference 2.2 Ground reference points will become fully apparent when the double‐support 2.2.1 CoP, MCP, and ZMP situation is considered. Bearing in mind that statics is just a special case of dynamics, we move our attention 3 In the case of a single‐link foot, the terminal link is the whole immediately to a dynamic double‐support problem. foot, while with the two‐link foot only the toes’ link is considered Suppose that a humanoid performs some movement while terminal. Although all the future discussion will actually apply supported on both feet. As examples, one may imagine a to the “terminal link”, for simplicity we will often say “foot”.4 In double‐support phase of walking or some appropriate a single‐support phase, the whole body relies on one leg, while actions in sports (karate, gymnastics, etc.). Regarding the in a double‐support phase booth feet are in contact with the ground reaction forces and the centre of pressure, one has ground. to distinguish between two foot‐specific points, one 4 In a single‐support phase, the whole body relies on one leg, while in a double‐support phase booth feet are in contact with defined for the left foot and the other for the right foot: the ground. CoPleft and CoPright. The role of these two points is to www.intechopen.com Miomir Vukobratović, Branislav Borovac, Aleksandar Rodić, Duško Katić and Veljko Potkonjak: 3 A Bio-Inspired Approach to the Realization of Sustained Humanoid Motion indicate the kind of contact existing between a particular is not so uncommon with humans and it is overcome in the foot and the ground. If CoPleft is inside the contact area of way that unbalanced and thus partly uncontrolled motion is the left foot, excluding edges, the foot keeps its surface‐to‐ seen as acceptable if re‐establishing the balance and full surface contact with the ground. If, however, the point control is expected in the next double‐support phase when finds itself on the edge, it means that the foot starts turning. the deviation will be corrected. An analogous discussion holds for the right foot. While with the single‐support posture for the turning of the foot means that the posture was compromised, the double‐ support posture is much more flexible. If one or both feet start turning, the posture need not be “lost”. To explore this, we use the ZMP concept. Since the ZMP is defined above as the point inside support area where the resultant moments of external and inertial forces about two horizontal axes equal zero, it is a unique characteristic point representing motion of the whole robot. The ZMP is not foot‐specific but rather is related to CoPleft and CoPright, as shown in Fig. 2. To conclude, the ZMP is the indicator of dynamic balance. If it is within the convex support polygon created by the feet (the grey area in Fig. 2), we say that the humanoid is dynamically balanced. If the ZMP comes to the edge of the support area, the balance will be lost and the entire robot will start falling down, overturning about Figure 3. Double‐support phase of the gait. It starts with the heel strike – (a). If we adopt single‐link feet, the overall shaded zone the edge. shows the support area created by the entire rear foot and the heel of the front foot that has just ended the swing phase and landed. In the case of two‐link feet, the double‐support phase direction also begins also with the heel strike, but the rear foot is in contact of walk with the ground by its toe link only. The support area is now shown as darker shaded. Later, the entire front foot will contact the ground, ‐ as shown in (b), ) ‐ thus enlarging the support area. The overall shaded area shows the support if the feet are of a CoPright single‐link type. The darker shaded zone represents the support area for the two‐link feet.
ZMP
CoPleft
Figure 2. Relation between the ZMP and the foot‐specific CoP points in the double‐support state.
Fig. 3 shows how the support area changes during the double‐support phase of the regular bipedal gait. Figure 4 presents two examples of an irregular gate. In case (b), a man has a wounded sole, and thus can only support just himself on the outer edge of this foot. Case (a) shows a more seriously injured man who walks with a crutch. In both cases, there exists a supporting area offering the possibility of dynamic balance in the double support phase. The common characteristic of these irregular gaits is that the left and right single‐support phases will not be symmetric. When the healthy right foot is on the ground, the support
area will exist and the dynamic balance will be likely. Figure 4. Two examples of an irregular gait. (a) The right foot However, when supporting on the wounded left foot or the makes the full contact while the left leg is replaced with a crutch crutch, the area will disappear, reducing to a line or a point, making a point contact.(b) The right foot is in full contact and the and thus preventing any possibility of balance. This situation left one makes a line contact.
4 Int J Adv Robotic Sy, 2012, Vol. 9, 201:2012 www.intechopen.com Let us point out that ZMP is an instant indicator of F M r y y y z x MC dynamic balance – it can answer whether a system is ZMP MC F m g MC F Mg balanced or not at the current time instant but it cannot z t z say whether it will maintain the balance in the immediate where mt is the total mass; Fx and Fy are the components future. Let us illustrate this by example, where the a of the resultant inertial force (given above); and are the humanoid is walking fast when suddenly the need to components of the resultant inertial moment about the stop arises. If the momentum is large, the generated CM, and g is the gravitational constant. inertial forces (due to the deceleration while stopping) may cause the loss of the dynamic balance. In the single‐support phase of the gait (only one foot is in
contact with the ground), the ZMP obtained by Eq. (1) The further generalization of the ZMP notion can lead to refers to the supporting foot and its contact area. Its different complex human/humanoid motions, like as in existence in the support region (excluding the edges) sports. One can imagine a posture where a gymnast prevents turning about the edge of the foot. In the stands on his head and hands while the his legs are up. double‐support phase, the support area is enlarged and it Clearly, there would be three CoP points and a unique can be done in many different ways. ZMP defining the dynamic balance.
Note that the ZMP and the CoP actually represent the Mathematically, the ZMP can be defined in several ways. same point while located inside the support area Consider a Cartesian frame with the x and y axes being (excluding the edges), ‐ i.e., while the system is in tangential to the flat ground and the z‐axis being normal. dynamic balance. If this point reaches an edge, turning For a dynamically balanced bipedal walker, there is about the edge will begin and the dynamic balance will always a unique reference point for which it holds that: be lost. The system dynamics radically changes since a new degree of freedom appears. Accordingly, the Mx 0 and My 0 calculation of the dynamics must switch to the appropriately modified model. The term ZMP is where summation is made for all the moments generated exclusively used for dynamically balanced states and can by the ground reaction forces, arising from the foot‐ not be applied for collapsing biped. The CoP will keep its ground contacts. For a dynamically balanced system, this location on the edge while the foot is turning. If the point is inside the support area and is called the ZMP. calculation finds the ZMP out of the support region, this Therefore, the ZMP represents the point where the means that the algorithm was too rough to precisely resulting reaction force acts (if the ZMP is positioned indicate the moment when the ZMP reached the edge and between the feet, the total ground reaction force is a sum thus missed to switch to the modified dynamic model. of two reaction forces under the feet and formally acts as More details can be found in [25, 26]. the ZMP). The ZMP position inside the support area (ex‐ cluding the edges) guarantees that the system will not 2.2.3 CMP rotate about the edge of the support region. The Centroidal Moment Pivot (CMP) [27‐32] is a ground Alternatively, instead of summing up the forces “under” reference point whose position defines the existence of the moment acting about the system’s mass center CM. the contact surface (i.e., the reaction forces), one may sum the forces “above” the contact. The ZMP is then thought The CMP location, rCMP , is defined as the point where a of as that point inside the support area at which the sum line parallel to the ground reaction force, passing through of moments due to all forces (gravitational, forces the whole‐body CM, intersects with the ground surface. induced by the mechanism’s motion, and external forces, This condition can be expressed mathematically as: if they exist) has no component along the horizontal axes. (r r ) F 0 (2) This is mathematically described by above expression, CMP CM hor where Mx and My are now interpreted as the moments of all acting forces. When the CMP departs from the ZMP, there exist nonzero horizontal CM moments, causing variations in The ZMP, as a function of the centre of mass (CM) whole‐body angular momentum. While the ZMP cannot position, the resultant inertial force, and the resultant leave the ground support area, the CMP can, but this will inertial moment about the (CM), can be expressed and happen only when horizontal moments act about the CM. calculated as: The zero CM moment (ZMP = CMP) is not a general F M r feature across all human movement tasks. For some x y MC xZMP xMC zMC (1) movement patterns, humans purposefully generate Fz mt g Fz Mg angular momentum to enhance stability and
www.intechopen.com Miomir Vukobratović, Branislav Borovac, Aleksandar Rodić, Duško Katić and Veljko Potkonjak: 5 A Bio-Inspired Approach to the Realization of Sustained Humanoid Motion manoeuvrability [31‐33]. By actively rotating body more of them) of the flier is geometrically constrained in segments (arms, torso, legs), CM moments can be its motion. An example is the gait, where the foot is in generated which cause horizontal moment forces to act contact with a non‐deformable support. With a soft on the CM. This strategy allows humans to perform contact, there is no geometric constraint imposed on the movement tasks that would not otherwise be possible. system motion, but the strong elastic forces between the For example, while balancing on one leg, humans are contacted link and some external object make the link capable of repositioning the CM just above the stance foot motion close to the object. An example of such contact is from an initial body state where the CM velocity is zero, walking on a support covered with an elastic layer. In and the ground CM projection is outside the foot support view of limitations, we restrict our consideration to the envelope. rigid case.
Figure 5. The CMP and the relation between the ZMP and the CMP.
3. Dynamic model of general human/humanoid motion Figure. 6. Unconstrained (free flier) and constrained systems 3.1 The concept 3.2 Mathematics In the above discussion on of the ground reference points, we tried to make their definitions general. Previously, the 3.2.1 Free‐Flier Motion reference points were introduced to allow for the We consider a flier as an articulated system consisting of modelling and synthesis of the bipedal robot gait. the a basic body (the torso in this case) and several branches Accordingly, their application was based on dynamic (head, arms and legs), as shown in Figure 6. Joints have models restricted to walking. However, the relevance of one degree of freedom (DOF) each. Let the joint angles be the reference points goes beyond this application. They described by the n‐vector: q [,,]q q T . The main actually apply to any humanoid motion and any kind of 1 n body needs six coordinates to describe its spatial position: ground contact: running and jumping, gymnastic X [,,,,,]x y z T defines the position of the mass centre exercises, other motions in sports, posture analysis, etc. and orientation angles (roll, pitch, and yaw). Now, the To exploit such possibilities and apply the reference overall number of DOFs for the system is N6 n , and points in such a general way, we need the a dynamic the system position is defined by: model which is sufficiently universal to cover any humanoid motion task. The method presented in [34‐36] Q[,][,,,,,,,,] XTTT q x y z q q T (3) and proposed for sporting motions in [37] offers a solid 1 n foundation for this. The contact analysis, ‐ essential in this We now consider the drives. It is assumed that each joint method, ‐ follows the theory explained in [38]. has its own drive – the torque j . Note that, in this analysis, there is no drive associated to with the basic‐ The proposed general approach starts by considering a body coordinates X. The vector of the joint drives is humanoid that ʺfliesʺ without constraints (meaning that it τ [,,] T , and the generalized drive vector (N‐ is not connected to the ground or to any object in its 1 n dimensional) is Τ[0 , τTT ] [0, ,0, , , ]T . environment – see Fig. X1). The term flier is suggested. 1 6 1 n
Such a situation occurs in running, jumping, trampoline The dynamic model of the free flier has the general form: exercise, etc., but it is less common than the situation where the human‐humanoid is in contact with the ground H()(,) Q Q h Q Q Τ or some other supporting object. or Let us introduce the contact of the flier and some external H X H q h 0 OBJECT (the term object includes the ground). A contact X, X X, q X (4) can be rigid or soft. With a rigid contact, one LINK (or Hq,, X X H q q q h q τ
6 Int J Adv Robotic Sy, 2012, Vol. 9, 201:2012 www.intechopen.com The dimensions of the inertial matrix and its submatrices We show the motion of the foot after the “heel strike”. are: H()NN , HXX, (6 6) , HX, q(6 n ) , Hq, X(n 6) , and Case (a) is the motion of a woman’s shoe with a high heel. Hq, q()n n . The dimensions of the column vectors Case (b) is a rectangular robot foot. Later, the “flat foot” containing the centrifugal, Coriolis’ and gravity effects phase of the gait will constrain all six foot coordinates (case (c)). However, if the foot begins to turn about its are: h()N , hX(6) , and hq()n . edge, like as in the case of lost balance (case (d)), a free 3.2.2 Contact Motion coordinate will appear again (coordinate ψ in the figure).
Let us consider a LINK that has to establish a contact with The motion of the external object (to be contacted) has to some external OBJECT. In example of walking, it is the be either known or calculable from the appropriate foot moving towards the ground and ready to land (in walking or running). In the example of a soccer game, one mathematical model, and then the s‐frame fixed to the may consider the foot or the head moving towards a ball object is introduced to describe the relative position of the in order to hit. The external object may be immobile (like link in the most appropriate manner. Thus, in a the the ground), an individual moving body (like a ball), or a general case, the s‐frame is mobile. As the link is part of some other complex dynamic system. approaching the object, some of the s‐coordinates reduce and finally reach zero. The zero value means that the In order to express the coming contact mathematically, contact is established. These functional coordinates T we introduce relative coordinates s [,,]s1 s 6 to define (which reduce to zero) are called restricted coordinates and c the position of the link with respect to the object to be they form the subvector s of dimension m . The other contacted. Let us call them functional coordinates (often functional coordinates are free and they form the f referred to as s‐coordinates). The choice is normally made subvector s of dimension 6 m . Some examples are in accordance with the expected contact – to support its shown in Fig. 7. Now, one may write: mathematical description. cTf T T cTf T T [,]s s s or [,]s s Rs (5) A consequence of the rigid (no elastic deformation) link‐ object contact the link and the object move, along certain where R is a 6 6 matrix used, when necessary, to axes, together. These are constrained (restricted) directions. rearrange the functional coordinates (elements of the Let there be m such directions, m being a characteristic of vector s) and bring the restricted ones to the first a particular contact. The relative position along these axes positions. does not change. Along other axes, relative displacement is possible. These are unconstrained (free) directions. In The relative s‐coordinates, depend on link motion (thus order to get a simple mathematical description of the on the flier motion Q, being N‐dimensional) and the on contact, s‐coordinates are introduced so as to describe object motion Q being Nb‐dimensional (the index “b” relative positioning. A zero value of for some coordinate b will stand for “object”): indicates existance of the contact along the corresponding axis. For a better understanding, we use a well‐known s s(,) Q Q (6) example (Figure 7) coming from a biped gait. b When speaking about a moving object, one may distinguish between two cases. The first case assumes that the object motion is given and cannot be influenced by the flier dynamics. An immobile object is included in this case. Such a situation appears if the object mass is considerably larger than the flier mass (thus, the flier influence may be neglected), or if the object is driven by so strong actuators that they can overcome any influence on the object motion. An example would be walking on the ground, ‐ i.e., contact between the foot and the ground. The ground is the large immobile object. Another example is walking on a large ship. The ship is a large object whose motion is practically independent of the walker. The ship is a
dynamic system but it cannot be influenced by the Figure 7. Foot‐ground contact in a bipedal gait: (a) heel strike walker, and so, from the standpoint of the walker, the phase – woman’s shoe with a high heel; (b) heel strike phase – ship motion may be considered as given. Accordingly, rectangular robot foot; (c) “flat foot” phase of the gait; (d) foot one may say that Qb()t is known: it is either prescribed overturning due to lost balance. or calculated from the object model. www.intechopen.com Miomir Vukobratović, Branislav Borovac, Aleksandar Rodić, Duško Katić and Veljko Potkonjak: 7 A Bio-Inspired Approach to the Realization of Sustained Humanoid Motion The other case refers to the object being a ʺregularʺ dynamic Now, (9), (10), and (11) describe the dynamics of a flier‐ system, so that the flier dynamics can have an effect on it. The plus‐object contact motion, allowing one to calculate the example would be walking on a small boat. The boat accelerations Q and Qb , and the reaction F. This enables behaviour depends upon the motion of the walker. Here, the integration of the differential equations and the
the time history of Qb is a new unknown in the joint flier‐ calculation of the system’s motion. object model. Under some of the conditions discussed above, the object The relation (6) can be written in the second‐order model (11) can be considered as to be independent of the Jacobian form (separation (x3) included): flier dynamics. Accordingly, it can be solved separately and the solution used to resolve the flier model (9), (10). c c c c s Jl(,)(,) Q Q b Q J b Q Q b Q b A (7) 3.2.3 Impact sf Jf (,)(,) Q Q Q Jf Q Q Q A f (8) l b b b b One may might recognize the three phases of a contact task: approaching, impact, and regular contact motion. The dimensions of the Jacobian matrices are: Jc()m N , l Jc ()m N , J f ((6m ) N ) , J f ((6m ) N ) , where N b b l b b b Approaching means that the link moves towards the is the number of DOFs in the object, and the adjoint object. From the standpoint of mathematics, approaching c f vectors’ dimensions are: A (m 1) and A ((6m ) 1) . is an unconstrained (and thus free) motion. Although all of coordinates from the vector s are free, we use the Due to space limitation, we restrict the consideration to separation (5) since the subvector sc is intended to durable (lasting) contacts. This means that the two bodies describe the coming contact and gradually reduces to (link and object), ) ‐ after they have touched each other zero. Strictly speaking, the restricted coordinates and when the impact is over, ‐ continue to move together (elements of sc ) reach zero one by one. Accordingly, a for some finite time. An example is walking. When the complex contact is established as a series of simpler foot touches the ground, it maintains contact for some contact effects. Let us assume, for simplicity, that all of time before it moves up again. the coordinates sc attain zero simultaneously and establish a complex contact instantaneously. The contact‐dynamics model is obtained by introducing contact reactions into the free‐flier model (4). Reactions The flier dynamics during approaching is are described appear along the restricted directions sc . Reaction forces by the model (4). The model represents the set of N scalar appear along the linear coordinates and the reaction equations that can be solved for N scalar unknowns – the moments along the angular ones. In total, there are m acceleration vector Q (thus enabling the integration and reactions forming the reaction vector F. Introducing F into calculation of the flier motion Q()t ). The object motion is (4), one obtains: solved separately: first Qb and then Qb()t . The relations (7) and (8) allow us to calculate the link’s functional c T H( Q ) Q h ( Q , Q ) Τ (JQQFl ( , b )) (9) trajectory: s and s()t .
Due to the m‐component reaction F, in order to solve the Let us discuss the desired (reference) motion s *()t (the model one needs m additional scalar conditions that sign * will be used to denote the reference values of a describe the contact. variable). It might be planned so as to make a zero‐ c velocity contact at the instant tc * : s * (tc *) 0 and c The rigid contact is described by the m‐dimensional s * (tc *) 0 . An example of such collision‐free reference c would be grasping a glass of wine. However, due to the condition s 0 . Starting from (7), this condition can be control system, tracking errors will appear and the actual written in the Jacobian form: motion s will differ from the reference, causing an f undesired collision and impact. In other examples, the sc J c( Q , Q ) Q Jc ( Q , Q ) Q A 0 (10) l b b b b reference motion of the link might be planed so as to hit the object (like in volleyball or in landing after a jump). In Now, relations (9) and (10) involves N+m scalar this case, the collision is intentional. In any case, it is equations. Let us list the unknowns: N scalar unknowns necessary to monitor the actual coordinates sc and detect in Q , m in F, and N unknowns in Q . As such, the flier b b the contact as the instant t when sc reduces to zero model can be solved if joined with the object model. To c ( sc(t ) 0 ). It will be t t * . Note that the actual keep the discussion general, we assume that the object c c c contact velocity will not be zero: s c(t ) 0 . dynamics is described by the N ‐dimensional model: c b During the approaching phase, the integration of the MQQCQQ()(,)(,)b b b b Τ b DQQF b (11) system coordinates Q and Qb is performed. As such, at
8 Int J Adv Robotic Sy, 2012, Vol. 9, 201:2012 www.intechopen.com the instant of collision, there will be some known system momentum Ft is determined as well. The new state state: QQ(tc ), ( t c ) , for the flier, and QQb(t c ), b ( t c ) , for the QQ, , QQb, b represents the initial condition for the object. third phase, the regular contact motion.
In the case of a rigid impact, there exists a finite or 3.3 Simulation Experiment infinitely short period while the system velocities change In order to support the potentials of the proposed general so as to meet the geometrical constraints imposed by the method, we present the results of the simulation of a contact – this is the impact interval. Let it be [,]t t . At t c c c complex sporting motion – e.g., a soccer goalkeeper’s approaching finishes and at t the regular contact motion c action. Figure 8 shows the snapshot of the action. described by (9), (10), and (11) starts. The shorter the impact interval, the higher the impact forces. For this The following phases can be distinguished in this analysis, we adopt the an infinitely short impact: example. t t t 0 . Hence, infinitely high impact forces are c c expected. Next, we assume a plastic impact (the durable contact mentioned above) where the connected bodies - In Phase 1, the goalkeeper moves slowly to the left with both feet on the ground – this is a double maintain contact for some finite time, moving together. support state (Figure 8 a‐c). Finally, we assume that all the m coordinates forming sc - Phase 2, the single support state, starts begins when reduce to zero simultaneously. Impact The impact model means the those equations that allow the calculation of the right foot leaves the ground (at t = 0.213s, Figure the change in the system’s velocities. 8 d). Accordingly, the take‐off is mainly up to the left leg. We now integrate the dynamic models (9) and (11) over - When the left foot leaves the ground (at t = 0.2782s, the infinitely short impact interval t , thus obtaining: Figure 8 f), ) Phase 3, ‐ free flight towards the ball, begins. c T - Phase 4 is the impact (at t = 0.722s, Figure 8 i). – the HQJF ()l t (12) goalkeeper catches the ball. and: - Falling down represents Phase 5.
MQDFb t (13) where:
QQQQQ ()()tc t c and QQQb b b (14)
The system state at the instant tc , (i.e., QQQQ, ,,b b ) is considered known. The position does not change during t 0 , ‐ i.e.,: QQQ()tc and QQb b . Accordingly, it is possible to calculate the model matrices HJMD,,,c l in the equations (12) and (13).
Now, the model (12), ) and (13) contains NN b scalar equations with N Nb m scalar unknowns: the change in velocities across the impact, Q (of dimension N ) and Qb (dimension Nb ), and the impact momentum Ft (dimension m). The additional m equations needed to allow the solution are obtained by rewriting the constraint relation (9) into the first‐order form and applying it for tc :
c c c c c c JQJQl b b 0 => JQJQJQJQl b b l b b (15)
The augmented set of equations, (12), (13) and (15), allow us to solve the impact. The change QQ, b is found and then (14) enables one to calculate the velocities after the impact (i.e., Q and Qb ). As such, the new state (in tc ) is Figure 8 The sSnapshot of the human/humanoid goalkeeper found starting from the known state in tc . The impact motion. www.intechopen.com Miomir Vukobratović, Branislav Borovac, Aleksandar Rodić, Duško Katić and Veljko Potkonjak: 9 A Bio-Inspired Approach to the Realization of Sustained Humanoid Motion All of the relevant dynamic characteristics could be has to abandon the realization of the previous calculated, like such as joints and main‐body coordinates, reference motion and, for example, step by one leg in joint driving torques, total reactions in joints, impact the direction of falling, achieve support on it, and ‐ in effects, power requirements, and energy consumptions, the few steps ‐ return to the reference trajectory. etc. In all three cases, the task of control is to minimize the 4. Ground reference points – case study deviations of the real humanoid state from the reference one for all the joints while preserving the dynamic 4.1 ZMP control of the regular gait in the presence of balance, whereby in Case 2) ‐ and especially in Case 3), ) ‐ disturbances the priority task is to prevent the system from falling (i.e., Under real conditions, the realization of motion is always preserve its dynamic balance). accompanied by disturbances, and some deviation from ideal (reference) motion always exists. The deviation in In practice, small disturbances are most common, so such tracking reference trajectories at the joints causes the that the problem of gait control reduces to Case 1), which deviation of ZMP from its reference position. An has been investigated most thoroughly in [39]. Hence, we especially undesirable situation arises when the ZMP will not elaborate it in detail and we will instead give only comes too close to the edge of the support area, ‐ when it a brief account of it, just for the sake of completeness of our might happen that the humanoid loses its balance, ‐ and discussion. In this case, the control has to minimize the deviations in all the joints and, when the attained motion is starts to rotate about the support area edge, and close to the reference one, the real ZMP will be close to its collapsing. The control has to ensure the approaching to reference position. However, the compensatio‐nal actions the reference trajectories of all the powered joints while at the joints have as a side effect the change of the linksʹ constantly preserving dynamic balance. accelerations (differing from the reference ones), and this
further leads directly to the change of the intensity and In order to better comprehend better the complex issues direction of the inertial forces (and, consequently, the ZMP related to control and ‐ later ‐ to defining the stability of position). Thus, by correcting the internal synergy, the humanoid motion, let us consider three characteristic external one can be upset. To prevent the appearance of cases due to disturbance effect. In all three cases, it is unpowered DOFs, it is necessary to constantly measure assumed that the humanoid in the beginning of the [15] the real ZMP position and endeavour to bring it during considered period performs a reference motion and then the motion most closely to its reference position. disturbances begin to operate. Information about the ZMP position is fundamental, both for the synthesis of the reference motion (the reference 1. Due to the external disturbance force (smaller ZMP position) and control of the real motion of the intensity), the ideal tracking of the joint trajectories is humanoid (the real ZMP position). disturbed, ‐ as well as the ZMP position, ‐ but so that it still remains within a ʺsafety zoneʺ. In the case of small disturbances, the deviations can be Appropriate control actions can return the system to compensated for in two ways: the reference trajectory. 2. Assume now that a disturbance force of medium a) local feedbacks at each joint attempt to bring the intensity is involved. In this case too, the force causes trajectory of the joint motion as close as possible to that the ideal tracking of the joint trajectories is to be the reference one, whereby care is taken of the disturbed, and the deviation of the ZMP from its compensation ʺintensityʺ (i.e., of the generated reference position is increased. To preserve dynamic accelerations because of which the real inertial balance, the humanoid must undertake a ʺmore forces will differ from the reference ones), in order resoluteʺ action (e.g., arms swinging), in order to to avoid the side effect of jeopardizing dynamic enusre ensure that the ZMP remains within the balance, and ʺsafety zoneʺ and also to return the system again to b) apart from the local feedbacks acting at each joint, the reference motion. an additional task can be assigned to a joint or a 3. In the case of a high‐intensity disturbance, group of joints to prevent inadmissible excursions of unpowered (passive) DOFs arise, and the system as a the ZMP, even at the expense of ʺspoilingʺ the whole begins to rotate about the edge of the support quality of the tracking reference trajectories at the area. The attempt to minimize the deviations of joint joints. Compensational actions to prevent the loss of trajectories and resume reference motion is senseless dynamic balance of the humanoid are defined solely if the system has lost dynamic balance. Hence, it is of on the basis of measuring the real ZMP position. highest interest to preserve (or re‐establish) dynamic balance, taking no care at the moment of the joints’ Cases 2) and 3) differ from Case 1) only in respect of trajectories tracking. Because of that, the humanoid disturbance intensity; the larger is the disturbance, the
10 Int J Adv Robotic Sy, 2012, Vol. 9, 201:2012 www.intechopen.com more endangered is the dynamic balance. Hence, the and finally to compare the recorded and simulated most urgent task is to prevent the humanoid from falling, motion to verify the applied control. and, when this danger is eliminated, the system can turn to minimizing joint deviations and bringing the motion as Healthy adults volunteered for the study. Each close as possible to the reference one. Because of that, in participant was asked to stand on his left foot and lean to the first phase of compensating larger disturbances, the his left until his shoulder touched a vertical support wall. humanoidʹs part that is not directly involved in the The support wall was a flat force sensor and the motion (e.g., the arms) has to abandon the tracking of the participant was asked to lean until this sensor measured reference trajectories for a while, and, by an energetic approximately 20 N of force. This level of force action (e.g., of the arms or the trunk), ʺensureʺ dynamic corresponded to a leaning posture where the CM pro‐ balance, whereby the legs’ links do not significantly jection on the ground surface fell outside the stance foot envelope. The support was then suddenly pulled away change their trajectories. After that, the system switches and the motion recorded. to the algorithm similar to that described for Case 1), so as to return fully to the reference motion. In other words, The three‐dimensional motion of the whole body was part of the system is abandoning the realization of recorded by an infrared camera system (the precision of internal synergy in order to prevent overturning and the detecting marker position was ~ 1mm) and the whole‐ preserve the possibility of walking continuation, and then body CM position was computed from the kinematic returns to tracking the external reference synergy. data. The ZMP and the ground reaction force intensity were obtained from the force plate (the measured ZMP). If the disturbance is of such intensity that it causes the The ground reaction forces were measured instantaneous appearance of unpowered DOFs and the synchronously with the kinematic data at a sampling rate overturning of the humanoid, then the overall system has of 120 Hz using a force platform. The force intensity and to abandon the tracking of internal synergy and attempt its acting point position (the ZMP location) were to resume dynamic balance, (e.g., to step in the direction measured at a precision of ~0.1 N and ~2 mm, re‐ of the systemʹs fall, gain support on that leg, re‐establish spectively. However, the position of the ZMP was also dynamic equilibrium, and, in the next few steps, return to computed on the basis of a model of a human and the reference motion [39]). compared with the measured ZMP position.
It should be noted that the disturbance described in Case It should be pointed out that the reordered movement 3) results in the degeneration of the humanoid‐ground changes significantly from beginning to end and it was contact area to a line or point, and the sensory not possible to control the system in same way during the information about the contact force is lost. The ZMP, whole movement. This was the reason the movement was then, does not exist. In order to take any decision about a split into three phases, each having different compensational action, even on passing to a new internal characteristics. The phases were defined in the following synergy, some other sensory information about the way: relevant coordinates of the instantaneous state of the system is needed, ‐ especially about the relative position Phase 1 is characterized by the agile motion of of the humanoid in its environment. In a similar situation, the whole body. Here, the primary aim is to pre‐ a man receives the necessary information from the serve dynamic balance ‐ i.e., prevent the fall. equilibrium sensors, the visual system, and the like, while This phase begins with the occurrence of the in the case of the humanoid, similar information could be disturbance and ends with the CM projection obtained either from a gyroscope [21], vision, an comes “significantly” closer to the ZMP position inclinometer, etc. In any case, additional sensory ‐ i.e., when the ZMP position deviation from its information is needed. reference becomes less than 0.003 m. As the reference was adopted, the ZMP position before 4.2 Ground reference points ‐ disturbed motion and its perturbation occurred. compensation Phase 2 is the “calming down” phase. It lasts until the deviation of the instantaneous ZMP Following experiment [40]5 we can introduce additional position from its reference reaches less than insight into as to this issue. The basic idea of the 0.001 m. experiment was to record “natural” responses of humans In Phase 3, the system returns to the “normal” on unexpected perturbations, than to replicate, as close as position of standing on one (the left) leg. In the possible, this motion by simulation (please note that case of a dynamically balanced humanoid control should be appropriately defined and applied); posture, the ZMP and the CoP coincide.
5 The basic idea was to gain an insight into biological principles of control selection embedded into in the “natural” behavior of As already pointed out, to replicate the motion, each humans. phase will require a different control. An example of the www.intechopen.com Miomir Vukobratović, Branislav Borovac, Aleksandar Rodić, Duško Katić and Veljko Potkonjak: 11 A Bio-Inspired Approach to the Realization of Sustained Humanoid Motion results (the recorded and computed data) is shown in Theoretically, the measured and computed ZMP Figure 9. The trajectories of the ZMP (measured by the positions should coincide. However, there is a difference force plate and computed), the CM and the CMP between them, for two reasons. The first is discrepancies (computed) are shown in Figure 9 a) while the stick between the model of the human used in simulation and diagram of the motion during the first phase is shown in the human subject itself. The second one is the accuracy Figure 9 b). The motion during the second and third of recordered (and replayed) motion in simulation. phases is not shown.
(a) ( b) Figure 9. a) Positions of the ZMP, the CMP and the ground projection of the system’s CM and measured CoP (ZMP)6 in all three phases, b) the sequence of postures in reaching the final posture at the end of the first phase.
(a) (b) (c) (d) Figure 10. Mutual relationships between the ZMP, the CMP and the CM projection on the ground: (a) beginning of the first phase, (b) middle of the first phase, (c) beginning of the second phase, and (d) beginning of the third phase.
But, in spite of the fact that the computed ZMP position second and the third phase. At the beginning (Fig. 5(a)), does not coincide with the measured ones, we can derive the CMP and the CM projection coincide. This may occur some important conclusions. The first impression about only if the reaction force is vertical or very close to the Figure 9 is that, in spite of the “large scale movement”, vertical. This is obviously so if we bear in mind that the the measured ZMP position is located in a very narrow human was initially immobile, standing on one leg, and area. This is witnesses about to the extreme skill of that the foot area was very small. Besides this, in the humans in preserving dynamic balance. initial moment the CM projection is outside the support area, which unambiguously speaks of the necessity to of Let us consider in more detail the mutual relationships applying a compensating action as soon as the human has between the ZMP, the CMP and the CM projection on the lost support. ground during the whole experiment. In Fig. 10 are shown the calculated positions of the ZMP, the CMP and The compensating action that was applied drove the the ground CM projection, as well as the ZMP position CMP and the CM closer to the centre of the support area, acquired in the experiment with the human subject in and their positions in the middle of the first phase are four different time instants: at the beginning and in the shown in Fig. 10(b). It is evident that the CMP moved middle of the first phase, and at the beginning of the faster. This only means that there appeared a more
12 Int J Adv Robotic Sy, 2012, Vol. 9, 201:2012 www.intechopen.com significant horizontal component of the reaction force, of the paper, we see this as justified. A detailed list of which is understandable since the humanoid, ‐ while body parameters is given in [37]. performing the compensating action, ‐ also moves. Over the course of the second and third phases, the mutual convergence of the ZMP, the CMP and the CM continued, approaching the reference ZMP position.
4.3 ZMP and foot‐specific CoP points in the evaluation of posture robustness evaluation
In this case, the study of the simulation is applied to a problem that is important for both humans and humanoid robots, namely, the behaviour of a posture (keeping stability or collapsing) when subject to different disturbances. For the numerical elaboration, typical postures from every‐day life and sports can be selected, such as: upright standing, squatting (and partial squatting), and some characteristic karate postures. In this paragraph, one characteristic example is considered to support the theoretical considerations presented in the previous sections. Two sorts of disturbances are applied: external impulse and permanent external force. This example does not aim to suggest a new control strategy but develops and as a preliminary verifies the dynamic model and the simulation algorithm, thus constituting a tool for optimizing a posture under disturbance. Since the test posture that was selected is “well known”, the Figure 11. Configuration of the body mechanism (n = 31 DOFs). agreement of the simulation results with the available experience from every‐day life (a squat is more robust to The arms, neck and spine joints and their influence to on disturbances than up‐right standing) and sports (some posture stability will not be discussed here, but they will karate postures are more appropriate for one direction of be assumed as fixed in a proper position (depending on disturbances whilst while the others are more robust in the example). The waist will move with three DOFs. other directions) is considered a satisfactory preliminary These simplifications do not compromise the conclusions verification. that will come out of the simulation experiments.
Figure 11 shows the mechanism which is used to model We now examine a postures that is “designed” to be the human/humanoid body. It has n = 31 degrees of highly resistant to disturbances. For many years, karate freedom (DOFs) in its joints. The total body mass is techniques have been improved. Stable postures have 71.23kg and the total height is 1.75m. Among other body always been among the key factors for a successful fight. data, we specify here the foot shape and dimensions. The As such, it is supposed that one such posture possesses foot is rectangular, 26cm long and 10cm wide. This shape, an inherent stability and can withstand strong normal for humanoids, may be considered as an disturbances. The Hangetsu dachi (Fig. 12) karate posture approximation of a human foot. Having in mind the goal is considered in this case study. It is assumed that the pelvis height is h=0.84m. The torso is strictly vertical.
2 2 -1
1.5 1.5 2 -0.5 1.5 1 1 0 1
0.5 0.5 0.5 0.5 0 -1 0 0 1 -1 0 -1 -0.5 0 0.5 1 0 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 1 1
Figure 12. Karate posture – hangetsu dachi. www.intechopen.com Miomir Vukobratović, Branislav Borovac, Aleksandar Rodić, Duško Katić and Veljko Potkonjak: 13 A Bio-Inspired Approach to the Realization of Sustained Humanoid Motion -0.5 0.1 0.05 0 0 0 -0.4 -0.2 0 0.5 -0.2 0 0.5 0.2t=0.06s 0.2t=0.202s (a) (b)
-0.5 0.1 0.05 0 0 0 -0.4 -0.2 0 0.5 -0.2 0 0.5 0.2t=0.273s 0.2t=0.305s (c) (d)
-0.5 0.1 0.05 0 0 0 -0.4 -0.2 0 0.5 -0.2 0 0.5 0.2t=0.377s 0.2t=0.537s (e) (f)
-0.5 0 -0.2 0 0.5 0.2t=0.598s (g)
Figure 13. The feet and their contacts with the ground. The entire support area (gray grey colour) changes as the ground points CoPleft, CoPright, and the ZMP change their positions.
The impulse disturbance, ‐ i.e., short‐term external occurs and the right foot starts rotating about its rear momentum ‐ is applied upon the humanoid. A body, like a edge, re‐establishing the line contact. The support heavy ball, hits the human/humanoid who catches it. The area partly recovers. Due to the mutual positions of ball comes horizontally, from the imposed side, and with the feet, this recovery, although qualitatively clear, a different velocity. In the simulation example, the ball increases the area size a little. Regardless of the small mass of 5kg and the velocity of 7m/s are checked. improvement in the support, it looks like “things start moving in a good direction.”. We consider the hangetsu posture (Fig. 12) under the However, the recovery was short. At te = 0.377s, the impulse disturbance. The ball comes with the highest CoPleft reaches the right lateral edge of the left foot velocity, 7m/s, from the a direction of ‐22.5 degrees, (the inward edge of the rear foot) and the foot starts contrary counter‐clockwise with respect to the sagittal rotating. The support area reduces. direction. Figures 13 shows the behaviour of the At tf = 0.537s (the instant (f) in the Figure 13), the human/humanoid after the impact. The time right foot again starts again rotating about its rear measurement begins such that the disturbance appears left corner (CoPright comes to the corner as shown in with a delay of 60ms. Fig. 13(f)). This rotation is presented in Fig. 13(f), too. The support area further reduces. Note that for all At ta = 60ms = 0.06s (the instant (a) in Fig. 13), the the this time the ZMP has been within the support perturbed behaviour starts. The body, found in the area, meaning that the human/humanoid has been position of Fig. 12, begins inclining, while the feet dynamically balanced. keep their full contact with the ground (Fig. 13(a), Finally, at tg = 0.598s, the left foot began rotating left) and the corresponding support area (right). about its rear right corner (CoPleft comes to the At tb = 0.202s, the CoPright reaches the left lateral edge corner). The support area disappears, reducing to a of the right foot (the inward edge of the front foot). line connecting two corners and all three ground The right foot begins rotating about this edge. The points, CoPleft, CoPright, and the ZMP, are now located support area defined by the feet reduces. The CoPright on this rotation axis. After this event, the now starts moving along the rotation axis, the left human/humanoid is no longer dynamically edge of the right foot, towards the heel. balanced. We consider the posture as being definitely At tc = 0.273s (the instant (c) in the Fig. 13), the lost since the human/humanoid will unavoidably fall CoPright reaches the heel, ‐ i.e., the left rear corner of down on the back. The conclusion is that the the right foot. Accordingly, the right foot starts considered posture cannot stand the imposed rotating about the corner (see Fig. 13(c), right). The disturbance. support area reduces once again. At td = 0.305s, an interesting phenomenon, induced The algorithm described in the paper enables the by the ball weight, occurs. The trunk has already dynamic modelling and simulation of the human‐or‐ started to rotate around the waist, moving down to humanoid movements provoked by some external the ball, and, as a consequence, the right heel has disturbance. The final goal of the movements taken is to moved back down to strike the ground. The impact face successfully the disturbance, ‐ i.e., to keep the a
14 Int J Adv Robotic Sy, 2012, Vol. 9, 201:2012 www.intechopen.com stable posture and avoid collapsing. The result of this [4] Bernstein, N. A. The origin of species in technics (to attempt depended upon the chosen posture. We have the railway centenary), J. Iskra, No. 9 (in Russian), proved the expectation, by use using the proposed 1925. methodology, that some postures are less robust to [5] Bernstein, N. A. Die Kymocyclographische Methode disturbance. der Bewegungs‐Untersuchung, Hdb. d. bioI. Arbeitsmethoden, Vol. 5, Pt. Sa, Abderhalden, 1927. The developed tool for modelling and simulation is [6] Bernstein, N. A., General Biomechanics, Monograph general; it covers all possible postures and allows the (in Russian), Publ. VCSPS, Moscow, 1926. calculation of all relevant dynamic characteristics. The [7] Bernstein, N. A. Studies of the biomechanics of goal was to show the potentials of this simulation tool walking and running, Questions of the Dynamics of and to as a preliminary to verify it via a comparative Bridges, Res. of the Scient. Committee of the Peopleʹs analysis of the robustness of some postures which more Commissariat of Transport, No. 63 (in Russian), 1927. or less could be judged by experience. [8] Bernstein, N.A., Popova, T.S. Untersuchung der Bio‐ dynamik des Klavieranschlags, Arbeitsphysiologie 1, 5. Conclusion 5, 1929. [9] Bernstein, N. A. Clinical Ways of Modern Biomecha‐ In this paper has been elaborated a bio‐inspired approach nics, Coll. of papers of the Inst. for Medical to the realization of sustained humanoid motion. These Improvement, Kazan, 1929. approaches do not suppose the just mere simple recording and replication of natural organisms’ [10] Bernstein, N. A. Analyse der Korper‐bewegungen movements and motions. It is of particular interest to und Stellungen im Raummittels Spiegel‐ understand thoroughly the control mechanisms of Stereoaufnahmen. Arbeitsphysiologie 3, 3, 1930. complex systems (humanoids certainly belonging to this [11] Bernstein, N. A. and Dementev, E. Ein Zeit‐Okular zu class) to be able to realize sustained motion. Dynamic der Zeitlupe, Arbeitsphysiologie 6, 4, 1933. balance is a basic prerequisite for the realization of any [12] Bernstein, N. A. et al. Studies of the Biodynamics of task by humanoids (particularly distained locomotion) Locomotions (Normal Gait, Load and Fatigue), Inst. and considerable attention was paid to it. The ground of the experim. Medicine, Moscow (in Russian), 1935. reference points (important indicators of a humanoid’s [13] M. Vukobratović, D. Juričić, Contribution to the state in a dynamic sense) were introduced and discussed, synthesis of biped gait, Proc. IFAC Symp. on Tech‐ as well. Particular attention was focused on the ZMP due nical and Biological Problem on Control, Erevan, to the fact that it is the most important indicator of a USSR (1968). robot’s dynamic balance. The issue of the appropriate [14] M. Vukobratović, Legged Locomotion Systems and modelling (either with or without contacts with the Anthropomorphic Mechanisms, monograph edited environment) of humanoids was also discussed, too. by Mihajlo Pupin Institute, Belgrade, also published Some characteristic examples were presented. The in Japanese, Nikkan Shimbun Ltd. Tokyo, in Russian, described tool for modelling/simulation tool is general “MIR”, Moscow (1975) in Chinese, Beijing (1983). and covers a wide class of body postures, allowing the [15] M. Vukobratović, B. Borovac, Zero‐moment point — calculation of the relevant dynamic characteristics. Thirty five years of its life, Int. J. Human. Robot. 1(1) (2004) 157–173. 6. Acknowledgments [16] M. Vukobratović, B. 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