<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta name="GENERATOR" content="Mozilla/4.75 [en] (WinNT; U) [Netscape]"> <meta name="Author" content="Dr. Chris Kirtley (Kwok Kei Chi)"> <title>CGA FAQ: Control of Locomotion</title> </head> <body> <h2> CGA FAQ: Inverse Dynamics &amp; Control of Locomotion</h2> <pre>Dear All, Happy New Year! Chris Kirtley switched the topics of  centrifugal forces to a more important question on how the nervous system perceives and controls movements. I reproduce here his question:  As far as I know, we have no sensors for segment acceleration - only (conceivably) joint angular acceleration, via spindles, joint afferents and skin receptors. Would this variable be sufficient, I wonder, for the CNS to compute the inverse dynamics? I would like to point out that the term  inverse dynamics hypothesis (in the most explicit form formulated by Hollerbach but the idea is as old as Newton s mechanics) implies that the nervous system pre-plans the desired movement kinematics and then, based on some intrinsic representation of equations of motion, computes and specifies the electromyographic activity, muscle forces and torques, which are necessary to actualise the movement plan. Chris s question implies that the nervous system does compute the  inverse dynamics . I suppose that the majority of those who work in the field of biomechanics and maybe somewhat smaller %&nbsp; of physiologists share this view. I would be pleased to know if this is an exaggeration since I belong to those who, following the implicit arguments of Von Holst (1969/1973) and very explicit arguments of Bernstein (1967), are convinced that the nervous system cannot and does not need to compute inverse dynamics to produce perfect movements. &nbsp;The inverse computational strategy works well for robotics. I would like to point out some simple physical and physiological principles that bring us directly to the conclusion that the inverse dynamics control strategy cannot be realised in biological systems. &nbsp;&nbsp;&nbsp;&nbsp; 1. Many human actions consist of movements from one stable posture to another. A stable posture is associated not only with the equilibrium position at which all forces are balanced but also with the ability of the system to generate forces resisting deflections from this position. &nbsp;&nbsp;&nbsp; 2. According to a general rule of physics (e.g., Glansdorff &amp; Prigogine 1971),&nbsp; the spatial coordinates at which the equilibrium is established in any physical system are determined not by output variables (like EMG, forces, torques) but independently of them, by the system s parameters. For example, in a pendulum, the equilibrium (vertical) position is determined not by variable forces but the parameters of the pendulum, such as the length of the rope at which the pendulum s mass is suspended, the coordinates of the suspension point, and the direction of gravity. Since these parameters are constant, the equilibrium position of the pendulum remains the same even when the system is put in motion. Thus, the ability of the nervous system to change the equilibrium position implies that the nervous system has the capacity not only to maintain but also to change appropriate parameters or determinants of the equilibrium position and thus produce active movements. &nbsp;&nbsp;&nbsp;&nbsp; 3. Suppose control levels computed and specified EMG signals and forces according to the planned kinematics, as suggested in the inverse-dynamic approach. If the system left the parameters that determine the equilibrium position unchanged, the programmed forces would drive the system from the existing (initial) equilibrium position. The inverse dynamic approach does not account for the fact that, like in a pendulum, the system will produce additional, resisting forces trying to return the system to the initial position and thus destroy the programmed action. Even if the inverse-dynamic specifications of the computed forces were combined with a shift in the equilibrium position, the emerging, additional forces arising due to the difference between the initial position and the new equilibrium position would also interfere with the computed forces. As a result, the programmed motion would again be destroyed. The idea of EMG and force programming thus conflicts with the natural physical tendency of the system to generate, without programming, muscle activity and forces associated with deflections from equilibrium. Briefly, the inverse dynamic approach conflicts with the natural dynamics of biological systems. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4. Experimentally, one parameter (lambda) controlling the equilibrium position of the system has been found by Asatryan and Feldman (1965). &nbsp;&nbsp;&nbsp; I am looking forward to seeing reactions to my comments. In my view, the inverse-dynamic approach is just a revival of our old illness - the mechanistic tradition of thinking inspired by remarkable successes in robotics. The robotics view may, however, be misleading in educating, especially, young scientists on how movements are controlled in living systems. Best wishes in the New Millenium! -- Dr. Anatol Feldman Professor Neurological Science Research Center Department of Physiology University of Montreal and Rehabilitation Institute of Montreal 6300 Darlington, Montreal, Quebec, Canada H3S 2J4 feldman@med.umontreal.ca Tel (514) 340 2078 ext. 2192 Fax (514) 340 2154 Web Site: http://www.crosswinds.net/~afeldman/ <hr WIDTH="100%"></pre> <pre>&nbsp;Dear all, Just to paddle into the debate..... How would you compute the inverse dynamics of the tongue, considering it has no joints? Cheers, Gary. ******************************************************* Gary Ellem. School of Science &amp; Technology Central Coast Campus University of Newcastle Ourimbah NSW 2258 Australia Ph:&nbsp;&nbsp;&nbsp; +61 2&nbsp; 43494489 FAX:+61 2&nbsp; 4348 4145 <hr WIDTH="100%">Hello, I think perhaps this conversations started on CGA and is wandering.&nbsp; I have refrained from entering debates on religion, politics and dynamical systems, but I resolved to be less shy in the new millennium. 1.&nbsp; Where are the equilibrium states in walking and running? 2 and 3. I think control theory has long recognized that the dynamics of the system are part of the control loop. 3, 4 and follow-up. Stonehenge, ancient diagrams of circles and epicycles, and Keppler's equations attest to the fact you can describe undisturbed motion accurately without Newtonian mechanics.&nbsp; If everything worked as well as the moon and stars, science could be an intellectual exercise.&nbsp; However, fortunately, we live in a world where we want to do things that have never been done before; and, unfortunately, we live in a world where many people cannot move according to the heavenly plan.&nbsp; For both problems, you need f=ma physics.&nbsp; I doubt that the Druids or Ptolemy or Keppler or the lambda hypothesis could have put people on the moon and got them back.&nbsp; I hope we do not update the education of young scientist and engineers to the point that we totally loose the ability to solve real problems. As to Chris's question.&nbsp; I doubt that you need to measure accelerations. What you get out of the various joint organs appears to be some sort of modulated measure of velocity and force.&nbsp; Sounds like momentum to me. Impulse and momentum control determines where you're going, not where you are.&nbsp; Advantageous for a control system with long delays.&nbsp; Watch a child learning to walk or a quasi-adult (athlete) learning to bat, pitch or swing a golf club.&nbsp; They practice to get the feel of the movement.&nbsp; That "feel" is a sense of the dynamics not the kinematics. Yours, Pat -------------------------------------- Patrick O. Riley, PhD Harvard/SRH CRS Ph.:&nbsp;&nbsp; (617) 573 2731 FAX: (617) 573 2769 Email: priley@partners.org &lt;mailto:priley@partners.org> <hr WIDTH="100%"></pre> <pre>Dear all, I think Pat Riley has had a touch too much Christmas spirit! This discussion actually started on BIOMCH-L - to recap, it sort of went: centrifugal force -> end-point hypothesis -> inverse dynamics. I'm not complaining - this is turning into a classical BIOMCH-L debate a la Woltring. Sorry for the cross-posting - and I suggest we keep the debate on BIOMCH-L after this. As it happens, I'm a bit of fan of megaliths, and a member of the archaeoastronomy group at the University of Maryland &lt;http://www.wam.umd.edu/~tlaloc/archastro> and I have to say that we don't really know how much the builders of these extraordinary monuments knew about physics. I suspect it was more than we think, and I do know that we haven't been to the moon for a generation - I'm not entirely sure that we will ever manage to go back there. After the quite embarassing series of Mars missions, with one crash due to incorrect conversion of inches to millimeters, I agree with Pat that we are in no position to be complacent about the state of our engineering skills - this from an Englishman, who can't even build footbridges or run railways anymore :( My point about the segmental accelerations was simply that Ton and Paolo had discussed the problems of measurement in non-inertial frames, and I wondered how the nervous system copes with this problem since whilst we have (perhaps) joint position/velocity sensors, we have no natural segmental accelerometers. Ton responded that, although we don't conceivably possess segmental acceleration receptors in the limbs, we have one in the head. I confess I wasn't really convinced by this reply - it seems to place a lot of reliance on one sensor, and people with vestibular disorders, whilst clearly inconvenienced, aren't as disbleed as you'd expect if the vestibule were so vital. So, we are left with the original question, and now I suppose Pat and Anatol are both saying that the CNS doesn't use inverse dynamics. I'm not in one camp or the other, but I think the question gets to the heart of motor control. For too long people have been bluffing over this question - one reads, for example, in most textbooks, that the cerebellum is responsible for "coordination" of movements. What does that mean? What have we learned from a century of motor control since Sherrington? In my view (and I expect to be flamed for this!) not very much. We seem to be still discussing controversies that William James contemplated. I will go further and suggest that it is only when we engineer humanoid robots that we will really understand the nature of the problem. I am thinking of some work I saw last week from the MIT group (Gill Pratt and Hugh Herr) on walking robots using series-elastic actuators and actin-myosin machines. I know that Pat is working with this group, so perhaps he can tell us more? I'll now standby for the flames... Happy New Year to all BIOMCH-L and CGAers! Chris -- Dr. Chris Kirtley MD PhD Associate Professor HomeCare Technologies for the 21st Century (Whitaker Foundation) NIDRR Rehabilitation Engineering Research Center on TeleRehabilitation Dept. of Biomedical Engineering, Pangborn 105B Catholic University of America <hr WIDTH="100%"></pre> <pre>Here are my responses to the comments (quated here) by Pat Riley, point by point. 1. Where are the equilibrium states in walking and running? Response. A single step is a transition from one postural (equilibrium) state to another. One can also say that a step results from changes in specific parameters that transform the equilibrium configuration of the body&nbsp; in such a way that eventually the body establishes approximately the same (initial) posture but in another part of external space. All forces (torques) required for such a transition emerge in response to the shifts in the equilibrium body configuration and are not programmed by the nervous system. The faster the shifts, the faster the step. If you repeat the control shifts, you get walking. By speeding the shifts, you get running. For more details, please consult section Response in our article (Feldman &amp; Levin 1995). 2 &amp;3.&nbsp; I think control theory has long recognized that the dynamics of the system are part of the control loop. &nbsp;Comment. Generally, you are right but we discuss not a general but a specific theory called the inverse dynamics. My point was that this theory is inconsistent with the intrinsic dynamics of the neuromuscular system and, therefore, it is an example of a theory which failed to make  the dynamics as a part of the control loop . 3, 4 Stonehenge, ancient diagrams of circles and epicycles, and Keppler's equations attest to the fact you can describe undisturbed motion accurately without Newtonian mechanics.&nbsp; If everything worked as well fortunately, we live in a world where we want to do things that have never been done before; and, unfortunately, we live in a world where many people cannot move according to the heavenly plan.&nbsp; For both problems, you need f=ma physics. I doubt that the Druids or Ptolemy or Keppler or the lambda hypothesis could have put people on the moon and got them back.&nbsp; I hope we do not update the education of young scientist and engineers to the point that we totally loose the ability to solve real problems. Comments. I did not understand the point of this philosophy. The famous names you listed&nbsp; were the precursors of&nbsp; Newton s and modern science. In particular, Newton first tested his laws by looking whether or not they were consistent with Keppler s laws. So to be fare, we should blame not only Newton but also Kepler for what  we could put people on the moon and get them back . Concerning the lambda hypothesis, do not you want to use this theory to simulate locomotion?&nbsp; Maybe, this is a way to advance our knowledge on how the brain controls it? This might be not only theoretically significant but might give you the practical ability you want -&nbsp;  to solve real problems , such as the understanding of basic movement pathologies (I heard the opinion that this is more essential than putting people on the moon). Somebody can use inverse dynamics to create walking robots. Fine. In fact, we have already thechnical realizations- airplans-&nbsp; immitating&nbsp; locomotion of birds. Beyond airodynamics, the creation of airplains did not advance our understanding of how the brain of birds controls flight.&nbsp; This is an essential lesson showing that technical immitations of biological phenomena are devices that are helpless without the brain of the driver. All best -- Dr. Anatol Feldman Professor Neurological Science Research Center Department of Physiology University of Montreal and Rehabilitation Institute of Montreal 6300 Darlington, Montreal, Quebec, Canada H3S 2J4 feldman@med.umontreal.ca Tel (514) 340 2078 ext. 2192 Fax (514) 340 2154 Web Site: http://www.crosswinds.net/~afeldman/ <hr WIDTH="100%"></pre> <pre>Anatol Feldman wrote: &nbsp;&nbsp;&nbsp; I also disagree with Yildirim Hurmuzlu^s suggestion that locomotion is a limit cycle. A specific case of locomotion - a single step - is not a periodic process, which conflicts with the notion of limit cycle. During continuous walking or running, a state variable - the position of the body in space - changes monotoniously, which also conflicts with the notion of limit cycle. If you consider only relative motion of the body segments you may reduce the phenomenon of locomotion to a limit cycle but in this case you ignore the explanation of the most important aspect of locomotion - the displacement of the body in the environment. Mariano Garcia responds: If this were true, then one would expect people to walk much differently on treadmills than they do on a hard surface, which is probably not true. Mariano Garcia, Ph.D. 2250 North Triphammer Rd. Apt H-2B Ithaca NY 14850 ph: 607-257-3509, email: garcia@tam.cornell.edu still associated with the Polypedal Lab, Dept. Of Integrative Biology University of California Berkeley <hr WIDTH="100%"></pre> <pre>Previously, I outlined an explanation of locomotion (a single step, walking and running) in terms of the equilibrium point (EP) hypothesis: &nbsp; A single step is a transition from one postural (equilibrium) state to another. One can also say that a step results from changes in specific parameters that transform the equilibrium configuration of the body in such a way that eventually the body establishes approximately the same (initial) posture but in another part of external space. All forces (torques) required for such a transition emerge in response to the shift in the equilibrium body configuration and are not programmed by the nervous system. The faster the shift, the faster is the step. If you repeat the control shift, you get walking. By speeding the shift, you get running. For more details, please consult section Response in our article (Feldman &amp; Levin 1995) . &nbsp;&nbsp;&nbsp; Yildirim Hurmuzlu's&nbsp; reaction to this explanation is an interesting example of a rejection of the EP hypothesis. I think his arguments are largely flawed since they are based, in particular, on the misconception that the term  equilibrium position implies static. Dynamic essence of the concept equilibrium position has been emphasized in one of my previous messages posted on the Biomech-L:  A stable posture is associated not only with the equilibrium position at which all forces are balanced but also with the ability of the system to generate forces resisting deflections from this position . &nbsp;&nbsp;&nbsp; If one thinks that  equilibrium position implies  static", please make the following exercise. Show that for a pendulum (take for simplicity a pendulum without friction), [equilibrium position] = [actual position] - k [acceleration], where coefficient k is proportional to the squared period of oscillations. This equation implies, first, that the equilibrium position may be considered a virtual position that exists at any moment of the pendulum's motion. Second, it implies that the equilibrium position is an invariant of motion, meaning that kinematic variables are summed in some way to produce the same value (= equilibrium position) at any instant of motion. In fact, knowing that the equilibrium position is an invariant, one can derive the equation of motion of the pendulum and, as a consequence, other invariants of motion (e.g., energy). Static is just a specific case of this law, when &nbsp;[equilibrium position] = [actual position]. &nbsp;&nbsp;&nbsp; In general, with some reservations, the concepts of equilibrium position and EP (they are not identical) resemble the concept of&nbsp;  point attractor in dynamic systems theory and as such they are not less  dynamical than, say, the concept of limit cycle. &nbsp;&nbsp;&nbsp; The EP hypothesis strengthens the dynamical essence of the EP concept by suggesting that the nervous system may change system's parameters to shift the EP of the body and thus produce active movements, an idea fully applied to locomotion as was outlined in the beginning of this message. &nbsp;&nbsp;&nbsp; I also disagree with Yildirim Hurmuzlu s suggestion that locomotion is a limit cycle. A specific case of locomotion - a single step - is not a periodic process, which conflicts with the notion of limit cycle. During continuous walking or running, a state variable - the position of the body in space - changes monotoniously, which also conflicts with the notion of limit cycle. If you consider only relative motion of the body segments you may reduce the phenomenon of locomotion to a limit cycle but in this case you ignore the explanation of the most important aspect of locomotion - the displacement of the body in the environment. &nbsp;&nbsp;&nbsp; On a positive side, the criticisms of Yildirim Hurmuzlu and my response may be helpful in clarification of some aspects of the EP hypothesis. I feel that clarifications are necessary since, at least for now, all rejections of the EP hypothesis have been based on misconceptions. Some of them are discussed in our paper (Feldman et al. 1998). Are there any other rejections of the EP hypothesis in the cyberspace? We can discuss them! &nbsp; Best wishes to All! -- Dr. Anatol Feldman Professor Neurological Science Research Center Department of Physiology University of Montreal and Rehabilitation Institute of Montreal 6300 Darlington, Montreal, Quebec, Canada H3S 2J4 feldman@med.umontreal.ca Tel (514) 340 2078 ext. 2192 Fax (514) 340 2154 Web Site: http://www.crosswinds.net/~afeldman/ <hr WIDTH="100%"></pre> <pre>I would like to comment on the remarks of Professor Feldman regarding the equilibrium states in walking and running. > > 1. Where are the equilibrium states in walking and running? > > Response. A single step is a transition from one postural (equilibrium) > state to another. One can also say that a step results from changes in > specific parameters that transform the equilibrium configuration of the > body&nbsp; in such a way that eventually the body establishes approximately > the same (initial) posture but in another part of external space. The equilibrium in running/walking is a dynamic one. One cannot describe it as a transition from one postural equilibrium to another. The postural equilibrium is a static one (I assume that&nbsp; it means the biped is standing). By definition, a static equilibrium&nbsp; is "static". So, once a system is in a static equilibrium , it should not be moving anywhere. According to the theory of nonlinear dynamical systems, the dynamic equilibria in running and walking are described as limit cycles. The limit cycle is a periodic motion that can repel (unstable) or attract (stable) other motions that start from&nbsp; neighboring&nbsp; initial conditions. In addition, there is one set of parameter values that are associated with each equilibrium state. The only things that vary in time are the state variables. Anything else that changes can be expressed as a function of these variables. One cannot have an equilibrium state that consists of transition from one equilibrium state to another by varying the parameters. Best regards, Yildirim Hurmuzlu =================================== Yildirim Hurmuzlu Professor of Mechanical Engineering Southern Methodist University Dallas, TX 75275 Phone&nbsp; : (214) 768-3498 Fax&nbsp;&nbsp;&nbsp; : (214) 768-1473 e-mail : hurmuzlu@seas.smu.edu web&nbsp;&nbsp;&nbsp; : http://cyborg.seas.smu.edu/~hurmuzlu/ <hr WIDTH="100%">PART 2 - Inverse dynamics. &nbsp;Chris Kirtley asked if the CNS could do inverse dynamics to control &nbsp;the motor system. My first response was the same as Ton's but having &nbsp;thought about it some more, let me offer a different perspective. The &nbsp;CNS not only can do that but does do that. But it does not do it &nbsp;explicitly, the way we do it with our equations and Matlab. It does &nbsp;it implicitly in the patterns of forces it generates in the muscles. &nbsp;Think back, those of you old enough, to the time of analog computers &nbsp;when a few amplifiers, diodes, resistors and capacitors and wires &nbsp;could generate the solution to any nonlinear equation. Could not one &nbsp;do that with a few million neurons? And I suggest that that is how &nbsp;one should look at the force pattern generators in my schemes, the &nbsp;forward models in Shadmehr's, the force fields of &nbsp;Mussa-Ivaldi and Giszter and the dynamic forces of Ghez, Sainburg, &nbsp;Bastian and others (This is my opinion and I am not speaking for any &nbsp;of the above). &nbsp;The joint torques are the solutions to the inverse dynamic equations, &nbsp;even if we never explicitly write them out. &nbsp;The immediate objection to this is that even (or especially) analog &nbsp;computer solutions are only as accurate as their ability to integrate &nbsp;accurately which always is difficult and especially in a noisy &nbsp;environment. They drift and require frequent calibration. That is not &nbsp;a problem because we can recalibrate every time we make contact with &nbsp;an object or look at our limbs. Just as importantly, our &nbsp;neuromuscular system is not an ideal force generator but one with &nbsp;intrinsic elastic properties created especially by muscle &nbsp;co-contraction and also by reflex action. If you look at the block &nbsp;diagrams (or consider the implications of a converging force field), &nbsp;there are two inputs; the force input (the solution to the ID &nbsp;equations) and a position input that combines with length feedback. &nbsp;If the force input is well planned, that second input does nothing. &nbsp;But this elastic property makes the endpoint insensitive to errors in &nbsp;that dynamic force input. &nbsp;So I think Chris's question ties in very nicely with the issues of &nbsp;what are real forces. If you think that there is a fundamental &nbsp;difference between classes of forces, that some are real and some are &nbsp;reactions to real forces, then you come to a different conclusion &nbsp;about control and about pathology than you do if you think all force &nbsp;components have similar stature. This is another long and potentially &nbsp;interesting discussion but not this year. &nbsp;CONSUMER WARNING: The above views express the opinions of the writer &nbsp;and are not universally shared. Some of this was discussed&nbsp; here a &nbsp;couple of years ago and we ended up agreeing to disagree. That has &nbsp;not changed. &nbsp;However, the evidence from this discussion is that educated people &nbsp;can make careers in this line of work on either side of the fence so &nbsp;I will just wish all you monists and dualists out there, Happy &nbsp;Chanukah, Merry Christmas and May the Force be with you. &nbsp;-- &nbsp;&nbsp; ___________________________________________________________________ &nbsp;|&nbsp;&nbsp; Gerald Gottlieb&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (617) 358-0719 &nbsp;|&nbsp;&nbsp; NeuroMuscular Research Center&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 353-9757 &nbsp;|&nbsp;&nbsp; Boston University&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; fax&nbsp; 353-5737 &nbsp;|&nbsp;&nbsp; 19 Deerfield&nbsp; St. &nbsp;|&nbsp;&nbsp; Boston MA 02215 <hr WIDTH="100%"></pre> Want to know more? 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