Animal Inspired Motion Control Mechanism.

Transcription

1 Animal Inspired Motion Control Mechanism. Minayori Kumamoto Professor Emeritus of Kyoto University Abstract The two-joint link mechanism provided with one antagonistic pair of the bi-articular actuators in addition to two antagonistic pairs of the mono-articular actuators could demonstrate perfect coordination of these actuators with only single command signal informing output force direction, and could lead smooth, rapid and precise movements without use of positional feedback signal from the endpoint, i.e. an open loop control. Further, the mechanism could demonstrate stable postural control against external disturbances, and dissolve contact task.. INTRODUCTION Link movements of so-called humanoid arm robots or even the most sophisticated bipedal walking robot are still clumsier than that of human or animal. Unique characteristics of human and animal movements would be summarized as follows. 1, Smooth, rapid and precise movements without use of positional feedback signal from the endpoint of extremity, i.e. an open loop control. 2, Distinguishably stable postural control ability against external disturbances. 3, The central nervous system of fundamental locomotion is intrinsically located at the spinal level [1]. 4, Even tiny ganglion of insects is enough to produce grooming with individual leg. An essential difference between motor link systems in conventional robots and human extremities is the existence of the antagonistic bi-articular muscles acting on the both end joints simultaneously in addition to the mono-articular muscles in human. As to control properties induced by the antagonistic pair of the bi-articular muscles, N. Hogan has reported that the pair could contribute to impedance control of the endpoint of the extremity[2,3], and J. McIntyre and E. Bizzi have proposed the Equilibrium Point Control Model wherein the pair could contribute to positional control of the endpoint [4]. Whereas, we have reported that the antagonistic pair of the bi-articular muscles could contribute to stiffness and trajectory control of the endpoint of the extremity, resulting in smooth, rapid and precise movement without use of position feedback signal from the endpoint [5]. Further, we have proposed the Coordination Control Model wherein three pairs of the antagonistic muscles, including one pair of the bi-articular muscles and two pairs of the mono-articular muscles, demonstrated perfectly coordinating activity pattern, and contributed to output force control and output force direction control at the endpoint [6,7]. In a hand-arm mechanism of human upper extremity, fine finger movements are directly controlled from the motor cortex, and only seen in mammals. Whereas, an arm mechanism consisted of three segments and two joints is driven by three pairs of antagonistic muscles, and seen commonly in not only mammals, but also birds, reptiles and amphibians. Even in insects, we could confirm the existence of the bi-articular muscles as well as the mono-articular muscles in their exoskeletal link system[8]. Thus, arm movements might be controlled with much more simple control system than that of fingers, and by a lower level neural network than the central motor cortex. In this paper, our recent reports dealing with the control properties of the two-joint link mechanism provided with three pairs of antagonistic muscles/actuators will be reviewed.. OUTPUT FORCE DIRECTION CONTROL At first, how antagonistic muscles are acting during arm movements was analyzed in terms of EMG kinesiology, second; the EMG results obtained were theoretically analyzed utilizing two joint muscle-skeletal model, and further, the EMG results were experimentally confirmed utilizing two-joint robot arm provided with three pairs of actuators. EMG kinesiology analysis Multichannel EMGs were recorded by conventional surface electrode method utilizing 14 channel multipurpose electroencephalography (Sanei Co. Tokyo). Subjects employed were 8 healthy young adults, and were requested to exert output forces at the wrist joint (W) in all round direction of 360 degrees, under isometric condition, and with the maximum efforts in horizontal plane as shown in Fig. 1. Muscles tested were the deltoideus anterior portion (Da) and the pectoralis major clavicular portion (Pc) of the mono-articular shoulder 1

2 flexors, and the deltoideus posterior portion (Ds) and the teres major (Tm) of the mono-articular shoulder extensors, the brachialis (Br) of the mono-articular elbow flexor and the triceps brachii lateral head (Tla) of the mono-articular elbow extensor, and the biceps brachii long head (Blo) and the triceps brachii long head (Tlo) of the antagonistic pair of the bi-articular muscles as shown in Fig. 1. Selected angles of shoulder and elbow joints were 60 and 60, 45 and 90, and 30 and 120, respectively. superimposed as shown in Fig. 3. It should be noted that the antagonistic pairs of the mono-articular shoulder muscles, the mono-articular elbow muscles and the bi-articular muscles demonstrated perfect inter muscular coordination, and all pairs of the antagonistic muscles changed their activity levels twice and covered 360 degrees. S E Fig. 1 Experimental posture and muscles tested. Upper body of the subject was tightly fixed on an iron frame and the wrist joint, W was fixed to a force detector attached on the frame. S: Shoulder joint. E: Elbow joint. Direction a-d is passing through the shoulder joint, S and the wrist joint, W, direction b-e, alongthelowerarm, and direction c-f, parallel to the upper arm. Abbreviations of muscle name, see in thetext. W A representative example of raw EMG recording was shown in Fig. 2. As shown here, in each pair of the antagonistic muscles, when one muscle showed remarkable electrical activities, the other antagonistic muscle showed almost none or very low electrical activities, and they were changing their activity levels around particular force directional ranges. force direction Fig. 3. IEMG. All IEMG recordings of all subjects, regardless of their postural changes, were superimposed. Force directional rages were normalized. Ordinate: IEMG in %, abscissa: output force direction. output force direction Fig.2 A representative example of raw EMG recordings. Output force direction, a-f, arethesameasshowninfig1. Detailed explanations, see in the text.. All EMG recordings obtained from all subjects, regardless of their postural changes, showed almost the same patterns as shown in Fig. 2. Therefore, when the electrical activities were integrated and expressed in percentage and force direction ranges were normalized, all EMG recordings were able to be Theoretical link model analysis Human upper extremity has very complicate muscular arrangement. However, the elbow joint can do only extension flexion movements for positional determination of the wrist joint in three dimensional free space, because of its joint structural feature[9]. Although origin of the deltoideus is spreading widely and many of the mono-articular shoulder extensors exist, only muscle bundles locating in the elbow extension-flexion movement plane, which is including the shoulder joint (S), the elbow joint (E) and the wrist joint (W) as shown in Fig. 4, are effectively acting for positional determination or force development at the endpoint W. Further, the both origins and insertions of the antagonistic bi-articular muscles are locating almost in this movement plane. Therefore, the complicate muscular arrangement of human upper extremity could be simplified into three pairs six muscles as shown in Fig. 4. The three pairs six muscles (fi, ei; i=1,2,3) 2

3 were defined as functionally different effective muscle, FEM. Mono-articular antagonistic pair FEMs (f1, e1) are acting on the shoulder joint S and (f2, e2), on the elbow joint E. Bi-articular antagonistic pair FEMs (f3, e3) are acting on the both end joints S and E simultaneously. In Fig. 4, supposing that six muscles (fi, ei; i=1,2,3) have the same contractile property and equal contractile force, and joint moment arms (r) and link lengths (l) are the same, activation levels of six muscles to exert the maximum output force at the endpoint W were theoretically calculated and plotted into Fig. 5. In Fig. 5, each pair of antagonistic muscles changed their activity levels twice between particular force directional ranges, and in the other force directional ranges, while one muscle showed full activity, the other antagonistic muscle showed zero activity. Three pairs of antagonistic muscles changed their activity levels twice and covered 360 degrees. The activation level pattern shown in Fig. 5 is quite similar to IEMG pattern shown in Fig.3. Experimental robot arm analysis A robot arm installed with 3pairs 6 actuators via sprockets and chains was built up on a horizontal table as shown in Fig. 6. Actuators installed were pneumatic controlled artificial rubber actuators (Bridgestone Co. RUB 5158). Rotary encoders were fitted at the joints S and E, and the shoulder and elbow joint angles were measured. A road cell and a position sensor were set at the endpoint W of the robot arm, so that the force and displacement exerted at the endpoint W could be measured. Three pairs of six actuators of the robot arm were driven according to the activation level pattern shown in Fig. 5. c b S d e W f a E g Fig. 6. Robot arm built for experimental analysis. :Bi-articular actuator f3 :Sprocket and chain :Bi-articular actuator e3 :Rotary encoder :Mono-articular actuator f1 :Mono-articular actuator e1 :Load cell and Position sensor :Mono-articular actuator f2 :Mono-articular actuator e2 3

4 The maximum output forces developed at the endpoint W of the robot arm demonstrated hexagonal distributions as shown in Fig. 7. It is obviously confirmed that the inter muscular coordination pattern shown in Fig. 5 could perform perfect output force direction control. g A spinal level neural network proposed EMGs recorded from muscles are electrical discharges of the muscles prior to the muscular contraction, and directly reflecting excitation of α-motoneurons innervating the muscles. Since at least four motor units in each muscle will be enough to reproduce alternation of activation levels between the antagonistic muscles, a spinal level neural network was proposed, where the network was simply consisted of excitatory and inhibitory interneurons as shown in Fig. 8. A command signal informing output force direction was represented by a switch board as shown also in Fig. 8. In Fig. 8, since alternation of activity levels of antagonistic muscles produced between output force directions a and b, the network was designed for the antagonistic bi-articular muscles. When three switch boards were rotated 60 degrees each from the others, and built up in one block, only single command g g 4

5 signal informing output force direction could perfectly reproduce the inter muscular coordinating activation pattern of 3pairs six muscles as shown in Fig. 3 or 5. The possible neural network proposed here, although such a real physiological neural network was not reported yet, might support the idea in which locomotion generating sub center can be located in spinal level [1]. Since neuronal signals are electrical excitation, the neural network proposed can be simply substituted by electric circuits as shown in Fig. 9. This circuit will be simply built in PC. One of our cooperation companies has succeeded to develop a two joint link Coordination Control Model provided with electric motors and this force direction controller. TRAJECTORY and STIFFNESS CONTROL Visco-elestic properties of the endpoint An elastic ellipse can be derived from the relation between the potential energy at the endpoint W and the elastic coefficient, and an elastic coefficient (ke) at the endpoint W in any direction can be indicated on the ellipse as shown in Fig. 10. The elastic ellipse consists of three parameters; the lengths of the long and short axes (Be, Ae) and inclination (θe). Trajectory and output force Since output force direction was determined by the activation level pattern of three pairs of the antagonistic muscles (Fig. 5), and three parameters of elastic ellipse were determined by compliances of three pairs of antagonistic muscles, it can be possible to change output force direction while shape and inclination of elastic ellipse remained unchanged. Fig.10. Elastic ellipse. If the lengths of the links and radii of the pulleys are held constant, the relation between the three parameters of the elastic ellipse (Ae, Be, θe) and compliances of three pairs of antagonistic muscles (C1, C2, C3) indicates that the elastic ellipse exerted at the endpoint W can be controlled by the sum of muscular contractile forces of any pair of antagonistic muscles. Three pairs of antagonistic muscles, including monoand bi-articular muscles, are sufficient for adjusting the three parameters of the elastic ellipse. Therefore, shape and inclination of the elastic ellipse can be determined independently as shown in Fig. 11. Viscous properties at the endpoint are completely the same as the elastic properties mentioned here. 5

6 Relation between trajectory and output force direction exerted at the endpoint W was recorded, while the sum of each pair of antagonistic muscles was kept constant (Fig. 12). In Fig. 12(a), the output force direction exerted at the endpoint W coincides with the major axis of the elastic ellipse, resulting almost perfect coincidence of the trajectory of the endpoint W and the output force exerted at the endpoint W. However, in Fig. 12(b) and (c), the output force direction do not coincide with the major axes of the elastic ellipses, and the trajectories do not coincide with the output force directions. Thus, the relation between trajectory and output force direction is affected by the axis of the elastic ellipse exerted at the endpoint W. The existence of the antagonistic pairs of the bi-articular muscles in addition to the antagonistic pairs of the mono-articular muscles made it possible to determine the parameters of elastic ellipse independently, and consequently, the perfect coincidence of the output force direction and the trajectory exerted at the endpoint W could be induced. These results mentioned here indicate that the arbitrary control of the output force direction, and elastic and viscous ellipses at the endpoint W can move the endpoint W precisely to any desired target point without use of positional feedback signal, that is a possibility of an open loop control [10]. Even simple spring model could dissolve contact task. A two joint link model was installed with simple linear springs as shown in Fig. 13, where both ends of bi-articular springs (f3, e3) were connected to the both first and second joints (S and E), mono-articular springs (f2, e2) were connected to the second joint (E) and other mono-articular springs (f1, e1) were connected to the first joint (S). equipped without bi-articular springs, the endpoint W shifted away from the original position, W W W as shown in Fig. 14 right panel[11]. When this model (A in Fig. 14) was vertically touched to smooth surface board, and the basement S was pushed down toward the endpoint W, the endpoint W did not shift from the original position as shown in Fig. 14 left panel. Whereas, in the model B in Fig. 14, in which only mono-articular springs were Stiffness control and postural stability Contact task experiment demonstrated in Fig. 14 is also suggesting excellent postural stability of the Coordination Control Model which is provided with antagonistic pair of the 6

7 bi-articular muscles as well as two antagonistic pairs of the mono-articular muscles. Relation between trajectory of the endpoint of the two joint link model and output force exerted at the endpoint was well discussed in terms of visco-elastic properties of the model in the previous sessions. Stiffness ellipse of the link model can be also changed by conditions whether the model was equipped with the bi-articular muscles in addition to the mono-articular muscles or not (Fig. 15). In Fig. 15 A, if the model was equipped with the bi-articular muscles in addition to to the mono-articular muscles, i.e. Coordination Control Model, stiffness ellipse exerted at the endpoint of the model did not change with changes in output force direction exerted at the endpoint. In Figs 15 B and C, if the models equipped with only the mono-articular muscles without the bi-articular muscle, stiffness ellipses changed with changes in the output force direction exerted at the endpoint. Thus, existence of the bi-articular muscle could induce distinguishably stable postural stability[5]. The most fastest conduction velocity of nerve is about 100m/sec at a nerve trunk, but it takes about 1msec through a synaps. Signal processing for feedback procedure, for instance landing, needs more than 2 synapses from the sole to the leg muscles via the spinal cord. Postural control mechanism supported by existence of the bi-articular muscle could skip feedback procedure and overcome such a synaptic delay, and made it possible to perform beautiful ski airial landing, but could not escape from a pitfall. HUMAN SIMULATION MODEL WITH OUTPUT FORCE CHARACTERISTICS Unique characteristics of hexagonal output force distribution Output forces exerted at the endpoint W of the upper extremity demonstrated hexagonal distribution as shown in Fig. 16. In Fig. 16, side lines A-B and D-E are parallel to the upper arm S-E, side lines B-C and E-F are parallel to the line which is passing through the shoulder joint S and the endpoint (wrist joint) W and side lines C-D and F-A are along the lower arm E-W. Length of side lines A-B and D-E is equal to sum of the muscular strengths of the antagonistic bi-articular muscles f3 and e3 and length of side lines B-C and E-F is equal to sum of the muscular strengths of the antagonistic mono-articular muscles f2 and e2, and length of side lines C-D and F-A is equal to sum of the muscular strengths of the antagonistic mono-articular muscles f1 and e1[12]. It is hard to measure strengths of FEM (fi, ei; i=1,2,3) directly, but referring to the unique properties of hexagonal output force distribution mentioned above, we could estimate individual strength of FEMs (FEMS) from measured output force values developed at the wrist joint W to four directions [13]. The last version of FEMS Program, which is developed by one of our cooperation companies, is able to give substantial training advise to disabled patients or sport athletes based on individual personal FEMS data. So far, physical performance was mainly discussed in terms of joint torque or joint moment and analyzed with reverse dynamics based on motion capture data. Joint torques or joint moments of adjacent joints are inevitably including output force of the same bi-articular muscle. Physical performance is a product of coordinating activities of the mono- and bi-articular muscles. Therefore, to discuss physical performance with joint torque or joint moment itself, as a logical consequences, includes big contradiction. Reverse dynamics was introduced to kinesiology or biomechanics fields from conventional mechanical dynamics, where idea of bi-articular actuator has never introduced. Physical performance should be discussed in terms of Coordination Control Model including the bi-articular muscle/actuator functions. Difference of direction between the maximum output forces of two joint link models with or without the bi-articular muscle. The almost all human simulation models (HSM) developed, so far, are motion capture base and only copied the outside images, but have never been referring the inside unique functions of coordination control mechanism. If output forces exerted at the endpoint was calculated with conventional kinetics based on joint coordinate system, in which idea of bi-articular muscle has never been introduced into calculation procedure, output force distribution of human extremities will become quadrilateral. Difference of direction between the maximum output forces of two joint link models with or without the bi-articular muscles, under the same conditions, was significant [12]. As far as HMS was applied on usual 7

8 motion analysis or so, such an angular difference will not induce any serious problem. When HSM is applied on, for instance a master-slave surgical operation system, or top athlete motion analysis, how much angular difference between output force characteristics of the slave model and the master human extremity will be allowed? Development of a motivation base HSM operating with FEMS is now under going. Human-friendly design Up until now, ergonomics design was based on only morphological measurement. Data base for human characteristics were obtained by external measurement, such as height, length, girth and so on, and human output force characteristics were obtained as usual back strength, squeeze strength and so on. Such a data will be enough for geometrical design of work station or living space, but does not make any sense for functional design of machine operation. For such a functional design, for instance a faucet for serious disabled, handlebars and a steering wheel for aged people and so on, output force distribution patterns changed with changes in posture, as shown in Fig. 17, will be applicable. Concept of Human-friendly Design, we proposed, is based on human output force characteristics. properties of a hexagon. This means that if one muscle/actuator deteriorated, the other muscles/actuators will change their activation level to keep the total output force distribution pattern unchanged. This is the outstanding adaptability of animal survived through countless centuries under hazardous environment. A locomotive machine, such as patrol robots, provided with 3 antagonistic pairs 6 actuators including the bi-articular actuators will have great advantages in dangerous and hazardous environment. Conventional robots provided with one motor on each joint could not have such an advantage. ANIMAL INSPIRED MECHANISMS In Fig. 18 (a), human and monkey have a complete set of one antagonistic pair of the bi-articular muscles and two antagonistic pairs of the mono-articular muscles at the thigh. However, they have the bi-articular Gastrocnemius (Gs) muscle alone at the back of shank, no bi-articular muscle at the front of shank [14]. INFINITE FLEXIBILITY In Fig. 16, it should be noted that combination of fi: ei, where i=1, 2, 3, will exist infinitely, because of unique According to anthropologist, lack of the bi-articular muscles at the front of the shank might suggest that a common ancestor of human and monkey originally live in woods, and 8

9 their lower leg adapted ant gravitational life style on tree. As to a unique function of the Gs, it has been just revealed utilizing a jump robot that the Gs could effectively transmit kinetic energy produced by the upper body part to the toe via the ankle joint, and produce stable airborne movement [15]. In Fig. 18 (b), hoofed animal and cats and dogs have complete sets of three pairs of the antagonistic muscles on both thigh and shank. It is noteworthy that a part of distal tendon of the biceps femoris (f3) branched off and goes down, and attached to the calcaneus, and a part of the f3, the f3 branched off from proximal tendon of the f3 goes down to front of the thigh and attached to the patella. These unique muscular arrangements certainly allow them high jump [14,16]. In Fig. 18 (c), they lost the mono-articular hip extensor (f1) and the mono-articular knee flexor (f2), and the bi-articular muscle at the front of shank, but had the pair of big bi-articular muscles. The output force distributions exerted at the ankle joint and the toe were suggesting that they well adapted to swim [14]. We can not explain yet, but would like to show following case, according to one of our colleagues, if patients stayed in bed fairly long, their mono-articular muscles deteriorated first, but their bi-articular muscles remained unchanged. We have to learn Animal Inspired Technologies more, because Nature created nothing without purpose. (Aristotle, BC) Acknowledgements The author gratefully acknowledges all of my colleagues for their excellent research works and remarkable developments on this new field. REFERENCES [1] S. Grillner, Neurobiological basis of human locomotion. M. Shimamura, S. Grillner and V.R. Egerton, Eds. Japan Scientific Societies Press, Tokyo, pp [2] N. Hogan. Adaptive control of mechanical impedance by coactivation of antagonistic muscles IEEE Transaction on automatic control, AC-29 (8), pp [3] N. Hogan. Impedance control: An approach to manipulation: Part - Impedance J. Dynamic Systems, Measurement and Control. Vol.107, pp.8-16, [4] J. McIntyre, E. Bizzi. Servo hypotheses for the biological control of movement. J. of Motor Behavior. Vol. 25-3, pp [5] M. Kumamoto, T. Oshima, T. Yamamoto. Control properties induced by the existence of antagonistic pairs of bi-articular muscles Mechanical engineering model analyses. Human Movement Science. Vol. 13, 1994, pp [6] T. Fujikawa, T. Oshima, M. Kumamoto and N. Yokoi, Functional coordination control of pairs of antagonistic muscles. Transactions of the Japan Society of Mechanical Engineers. Vol.63, pp , [7] T. Fujikawa, T. Oshima, M. Kumamoto and N. Yokoi, Output force at the endpoint in human upper extremities and coordinating activities of each antagonistic pair of muscles. Transactions of the Japan Society of Mechanical Engineers. Vol.65, pp , [8] R. Matsuda, Morphology and evolution of the insect thorax. The Entomological Society of Canada, Ottawa, 1970, pp [9]E. N. Duvall, Kinesiology. The anatomy of motion. Prentice-Hall, INC., NJ, [10] M. Kumamoto. T. Oshima, T. Fujikawa. Control properties of a two-joint link mechanism equipped with mono- and bi-articular actuators. Proceedings of the 2000 IEEE International Workshop on Robot and Human Interactive Communication. Osaka, Japan, 2000, pp [11] T. Fujikawa, T. Oshima, M. Kumamoto. Proposal of a humanlike two-joint link mechanism provided with the bi-articular and the mono-articular actuators. Part 2: Trajectory control: Contact task was dissolved. Proceedings of 5 th Franco-Japanese Congress & 3 rd European-Asian Congress of Mechatronics, Besançon, France, 2001, pp [12] T. Oshima, T. Fujikawa, O. Kameyama, M. Kumamoto. Robotic analyses of output force distribution developed by human limbs. Proceedings of the 2000 IEEE International Workshop on Robot and Human Interactive Communication. Osaka, Japan, 2000, pp [13] T. Oshima, T. Fujikawa and M. Kumamoto. Functional Evaluation of Effective Muscular Strength Based on a Muscle Coordinate System Composed of Bi-articular and Mono-articular Muscles Simplified Measurement Technique of Output Force Distribution- J. of the Japan Society for Precision Engineering, Vol.67-6, pp , [14] T. Oshima, T. Fujikawa and M. Kumamoto. Kinematic Analyses for the Various Muscular Arrangements of Animals Transactions of the Japan Society of Mechanical Engineers. Vol.65 pp , [15] K. Toriumi, T. Oshima, T. Fujikawa, M. Kumamoto and N. Momose, Effect of the Articular Gastrocnemius Muscle of Human on the Jump Movement of the Model. Transactions of the Japan Society of Mechanical Engineers. Vol.69 pp , [16] Y. Kato, S. Yamauchi. Atlas of comparative anatomy of domestic animals. Yokendo Ltd., Tokyo, 1996, p