Acquisition of Humanoid Walking Motion. Considering Characteristics of Servo Modules

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1 Acquisition of Humanoid Walking Motion Using Genetic Algorithm Considering Characteristics of Servo Modules Fuminori Yamasaki, Ken Endo Λ, Hiroaki Kitano and Minoru Asada Kitano Smbiotic Sstems Project, EATO, Japan Science and Technolog Corp. Graduate School of Engineering, Osaka Universit, * Graduate School of Science and Technolog, Keio Universit, Son Computer Science Laboratories, Inc. Suite 6A, Jingumae, Shibua-ku, Toko 5-, Japan Tel: , Fa: amasaki,endo,kitano@smbio.jst.go.jp, asada@ams.eng.osaka-u.ac.jp Abstract This paper presents a method for humanoid walking acquisition with less energ consumption based on a two-stage genetic algorithm. In the first phase of genetic algorithm, in order to acquire the continuous walking motion, the fitness function consists ofawalking distance (longer is better). In the second phase, the fitness function consists of a walking distance (longer) and energ consumption(less) for acquisition of highl energ-efficientwalking. Further, we restrain the relationship among some joints and keep knee joint straight on supporting leg in order to ensure the less energ consumption. We appl the method to our platform PINO which has low-torque actuators owing to the servo modules. In order to realie a genetic process, we encode the scaling parameter of the joint movements and the phase difference between the joints into the computational simulation which considers the characteristics of the servo module used in our platform, PINO. The evolved results are applied to a real PINO and its smooth and stable walking with less energ consumption is verified. Kewords Humanoidwalking, Genetic algorithm, Less energ consumption I. Introduction Stable biped walking generall requires highl precise control and powerful actuator sstems []. It forces the use of epensive actuators and gear sstems, therefore, the total cost of the robot tends to be ver high. The are ver different from normal human walking. It should be noted that most of the eisting control methods for humanoid walking are designed independent of the structural properties of the robot hardware. On the other hand, McGeer has studied Passive Dnamic Walk (PDW), in which the simplest leg-like structure can walk down a gentle slope without an actuators to control it [2]. In such methods, walking motions are determined b the relationship between a gravit potential effect and the parameters of the robot mechanical structure. Therefore, no control of walking behaviors such as speed or dnamic change in step sie is possible as its name stands for. Motors that are affordable for man researchers have onl limited torque and accurac. Development ofa method that allows biped walking using low-cost components would have a major impact on the research communit aswell as industr [3]. Therefore, we have developed the humanoid PINO [4] which isalow-cost humanoid platform for various kinds of research issues. It is intentionall designed to have low-torque motors and low-precision mechanical structures because such motors and mechanical structures significantl reduce production cost. Figure shows the whole view and the mechanical architecture of PINO. PINO has 26 degrees of freedom (DOF) and these components consist of low cost and off-the-shelf components. Especiall, actuators of PINO are for radio control models of which maimum torque is 2.45 [N m]. It is considered that the use of genetic algorithm enables humanoids with high DOFs to acquire highl energ-efficient and natural walking motion in a real environment [5],[6]. In these bi-ped walking algorithms, however, knees are alwas bended, therefore, knee joint motors are highl loaded continuousl. It is known that the keeping a knee joint straight and the periodical matching between the motion of lateral plane and sagittal plane enable a humanoid to reduce the energ consumption. If a robot, however, evolve its walking locomotion performed b awalking distance and energ consumption simultaneousl, a individual which doesnotmove is selected. In this paper, therefore, we applatwo-stage genetic algorithm for acquisition of stable and smooth walking trajectories with less energ consumption. In the first phase of genetic algorithm, the fitness func-

2 In the first phase of the evolution, the total walking distance during one trial should be evaluated for acquisition of the continuous walking motion without falling down. A fitness function of this phase is given b, f = l walk ; (2) where l walk is a distance from the start point [m]. In the net phase, the energ consumption and the walking distance from the start point should be evaluated using results of first phase, because the natural and smooth walking motion needs less energ. Therefore, a fitness function is given b, 2 Fig.. (a) A whole view (b) A half skelton view Picture and mechanism of Our Platform, PINO tion consists of a walking distance (longer is better) to acquire the continuous walking motion. In the second phase, the fitness function consists of a walking distance (longer) and energ consumption(less) for acquisition of highl energ-efficient walking, and the best results of first phase are used as initial individuals. Further, we restrain the relationship among some joints and keep knee joint straight on supporting leg in order to ensure the less energ consumption. Also, the specification of the each servo module is identified b the sstem identification, b which we epect the reliabilit of the computational simulation against the real robot. Finall,we appl the computational results acquired b the genetic algorithm to our platform PINO, and its smooth and stable walking with less energ consumption is verified. II. Genetic Algorithm for Humanoid Walking In order to simplif the problem, we assume that the locomotion of right and left legs are smmetr and periodical. Further, the phase difference is ß [rad]. Here, we adopt combination of sinusoidal and cosine function to represent such locomotion as follows: _ (i) = ff i sin (!t + (i) )+fi i cos (!t + 2(i) ); () where ff i and fi i denote the gains, and (i) and 2(i) denote the phase difference of sinusoidal and cosine waveforms, respectivel. Also,! represents the angular velocit.!, ff i, fi i, (i) and 2(i) are parameters for each individual, and each parameter is represented b 7bits. f = l walk E consumption ; (3) where E consumption are energ consumption during total walking [J], and this fitness function denotes the moving efficience of a robot. An energ consumption is calculated as, E consumption = XZ t walk fi i _ i dt; (4) where t walk, fi i, i _ denote the total walking [sec], a torque and angular velocit ofthe i th joint, respectivel. Table shows the condition of genetic algorithm. The crossover module creates new individuals b com- TABLE I Condition of genetic algorithm Population 5 Generation 5 Crossover ratio.9 Mutation ratio.2 bining segments of the string of parents. The mutation module replaces the segments of the string of another one. Also, the best individual is stored to the net generation, and the elitest scheme is alwas selected. The crossover module and mutation module function are shown in Figure 2. III. Conditions and Simulations A. Sstem Identification for Servo Module Sstem A computational simulation should have high accurac against the real world. Especiall, a characteristic of an actuator is one of the most important parameters. It is clear that the servo module for radio control model has a PD control sstem inside. Therefore we

3 Crossorver Mutation Fig. 2. The crossover and mutation module function assume that a servo module has the sstem as equation (5), K( dt t ) C _ t = I t ; (5) where I, C and K denotes a moment of inertia, viscosit coefficient and damper coefficient, respectivel. In order to obtain these parameters, we had the sstem identification. From preliminar eperiments, we obtain the time series of angular acceleration, angular velocit and angle at the output ais when we input the desired angle. From equation (5), parameter matri [C; K] T is obtained b, h i t _ ; t [C; K] T = I t [C; K] T = h _ t ; t i + I t ; (6) h i + where t _ ; t denotes the pseudo inverse matri of h a matri t _ ; t i. To verif the validit of these parameters, stabilit of this sstem are discriminated. As a result, it is verified that these parameters of servo module are valid, because a real part of these eigenvalues isbeleftsidein the comple plane, that is, this sstem is stable model. B. Condition of Dnamical Simulation Dnamical simulations are analed b the fourth unge - Kutta method, and the time interval is.2 [ms]. The dnamic equation of this model can be represented as follow: o o [M( )]n +[C( )]n _ 2 +[K( )] = [fi] ; (7) where [M( )], [C( )] and [K( )] denote the parameter matrices of the mechanism and angular positions of the links, and [fi] denotes feedback torque vector. Desired angles of each joint are simultaneousl updated at 3.5 [ms] interval which is same to servo module one. In computational simulations, the floor force is calculated based on spring - dumper contact model. Local feedback torque are given b, fi i = k( di i ) k v _ i ; (8) θ θ 2 θ 3 θ 4 θ 5 θ 6 ight Leg l l2 l3 l4 l5 l6 l Left leg ll ll ll2 ll3 ll4 ll5 ll6 θ L θ L2 θ L3 θ L4 θ L5 θ L Σ 7 7 Σ E 2 Σ,, 2 Σ 3 Σ 4 Σ 6 E p E E 7 E Σ p LE LE Σ L, L, L2 Fig. 3. Coordinate frames of legs of the robot where k and k v are the control gain of servo modules, and di denotes the desired angle of i. k and k v are obtained b the sstem identification of servo module. Also, a maimum torque of servo module is defined as ±2.45 [N m]. The trial of each individual runs for 2 [sec]. If the robot walk for 2 [sec] or falls down halfwa, the trial is finished and the individual is evaluated b fitness function. In order to keep the foot plate parallel against the ground and avoid collision between the swing leg and the ground, following equations are defined, = L =[rad] 2 = 6 = L2 = L = 4 L3 + L5 = L4 4 = ß[rad] (at supporting phase) L4 = ß[rad] (at supporting phase) 3 (!t) = L3 (!t + ß) (dela half period) 4 (!t) = L4 (!t + ß) (dela half period) 5 (!t) = L5 (!t + ß) (dela half period); Σ L3 Σ L4 Σ LE L L3 L4 Σ L6 L6 Σ L7 L7 LE L 3 (9) where each i denotes the desired angle of each joint and correspond with the Figure 3 number. IV. Eperiments A. esults of Computational Simulation In the result of the first phase of genetic algorithm, the best and average of fitness value changes shown in Figure 4,,which indicates transitions of best fitness value and average fitness value of each generation. The second phase of genetic algorithm is evolved using the results of first phase. Figure 5 indicates transitions of best fitness value L L3 L4 L6 L7 LE L2 L L2

4 2 Maimum TABLE II Walking period and step sie 4 Fitness f.5 Average Initial motion Evolutional motion Period [sec]..49 Step sie [m] Fig. 4. Fitness f Generation Maimum and average fitness value in the first phase. Maimum Average Generation Fig. 5. Maimum and average fitness value in the second phase and average fitness value of each generation of the second phase. Also, a walking step period and a sie of one step on the initial and evolutional motion are shown in table. 2. B. esults at eal obot The results of computational simulations are performed b the real robot. The time series of desired joint angle of each joints are given, which is 3.5 [ms] interval. From the eperimental results, PINO realie the walking motion smoothl. Besides, we had the eperiments to make PINO walk in the real environment using conventional control method, whose locomotion are obtained b inverse kinematics, and ero moment point are controlled b moving into support surface [4],[7]. In this time, PINO achieve onl the unstable Total torque [ N m ] Ave. of Inital data Ave. of Evolutionar data Inital data Evolutionar data Time [ sec ] Fig. 7. Time series of total torque walking motion because motors are highl loaded continuousl, and sometimes PINO fells down. Figure 6 shows the time series of walking motion of real PINO using conventional control method and results of genetic algorithm. From these figures, the walking pattern obtained b genetic algorithm realies fewer distortion of upper bod than that of conventional control method, that is, this walking motion needs less energ consumption and achieve the smooth locomotion. V. Discussion Time series of the total torque for two seconds of initial human designed walking motion and evolved walking motion are shown in Figure 7. Also, average of these data are shown in it. Further, the differencial total torque of them are shown in Figure 8. Evolved locomotion needs less energ consumption against the initial locomotion and conventional control method one. At the point ofspike torque in Figure 7, the swing leg touches down with the ground and the knee of supporting leg is locked straight. This spike torqueofevolved locomotion etremel reduces against initial one. In Figure8, it is verified that the deviation of torque of evolved locomotion is smaler than that of initial one, that is, this locomotion achive the smooth and stable walking.

5 5 (a) Walking motion of a real robot (Conventional control method) (b) Walking motion of a real robot (Genetic algorithm) Fig. 6. Eperimental result Total torque [ N m ] Fig. 8. Inital data Evolutionar data Time [ sec ] Time series of differencial total torque TABLE III Torque consumption in each condition [N m] Initial motion Evolutional motion each [m] each [sec] each [step] It is shown in table 3 a torque consumptions in each [m],each [sec] and each [step], walk period and step sie from Figure 7. From these results, it is verified that evolved walking motion achieves the highl energ-efficience. Also, humanoids with limited torque like PINO can realie a walking motion which is acquired from genetic algorithm.

6 VI. Conclusion This paper present the method for humanoid walking acquisition with less energ consumption with genetic algorithm. In order to realie smooth and stable walking with less energ consumption, in the first phase of genetic algorithm, the fitness function consistsofawalking distance (longer is better) to acquire the continuous walking motion. In the second phase, the fitness function consists of a walking distance (longer) and energ consumption(less) for acquisition of highl energ-efficient walking. Further, we restrain the relationship among some joints and keep knee joint straight on supporting leg in order to ensure the less energ consumption. We appl the method to our platform PINO which has low-torque actuators owing to the servo modules. As a result, the evolved results are applied to a real PINO and its smooth and stable walking with less energ consumption is verified. As future work, we plan to generate various kinds of behaviors using this method. VII. Acknowledgements The dnamic simulator is developed b Mr. Masaki Ogino of Osaka Universit. The authors acknowledge him and members of Asada Laborator of graduate school of engineering, Osaka universit, and members of smbiotic intelligence group of Kitano Smbiotic Sstems Project, EATO, Japan Science and Technolog Corporation. eferences [] Hashimoto, S, Narita, S, Kasahara, K, Shirai, K, Kobaashi, T, Takanishi, A, Sugano, S, et. al, Humanoid obots in Waseda Universit Hadal-2 and WABIAN", Proc. of The First IEEE-AS International Conference on Humanoid obots, CD-OM, 2. [2] T. McGeer, Passive dnamic walking", The International Journal of obotics esearch, Vol.8, No.6, pp.62 82, CD- OM, 99. [3] Inaba, M, Kanehiro, F, Kagami, S and Inoue, H, Twoarmed Bipedal obot that can Walk, oll Over and Stand up", Proc. of International Conference on Intelligent obots and Sstems,995. [4] Yamasaki, F, Matsui, T, Miashita, T and Kitano, H., PINO The Humanoid that Walk", Proc. of The First IEEE-AS International Conference on Humanoid obots, CD-OM, 2. [5] Arakawa, T., Fukuda, T., Natural Motion Generation of Biped Locomotion Using Hierarchical Trajector Generation Method Consisting of GA,EP Laers", Proc. of IEEE International Conference on obotics & Automation, pp. 2-26, 997. [6] Fukuda, T., Komata, Y., Arakawa, T., Stabiliation Control of Biped Locomotion obot Based Learning with Gas having Self-adaptive Mutation and ecurrent Neural Netwrok" Proc. of IEEE International Conference on obotics & Automation, pp , 997. [7] M. Vukobratović, B. Borovac and D. Surdilović, Zero- Moment Point Propoer Interpretation and New Apprications", Proc. of The Second IEEE-AS International Conference on Humanoid obots, CD-OM, 2. 6