Experimental Approach for the Fast Walking by the Biped Walking Robot MARI-1

Transcription

1 Experimental Approach for the Fast Walking by the Bipe Walking Robot MARI-1 Youji Nakajima* Akira Yonemura Atsuo Kawamura Dept. of Elec. an Comp. Eng., Yokohama National University 79-5 Tokiwaai, Hoogaya-ku Yokohama JAPAN tel: ; fax: ; Abstract: We have evelope the bipe walking robot MARI-1. The robot has the light weight an joints on each leg an all control calculation is one with a DSP. The walking pattern is mae from the tip position an irection references in -Y- omain an those references are transforme into joint angle references by the inverse kinematics calculation. The position control of each joint is one with the high gain P control. In this paper, we trie an open-loop type walking. As a result, the quasi-ynamic walking was confirme by checking the position of the center of the mass(com). The smooth walking an fast walking are also achieve with the propose walking pattern. The frame of the robot is mae of the mono cast nylon. The ensity of mono cast nylon is little heavy compare with water. An it has tough mechanical strength an enurance. MARI-1 is very light weight ue to this material. The height of the robot is 1.21[m], the weight is 25[kg]. The appearance of the robot is shown in Fig.1. The controllers are locate outsie of the robot, thus many wires are connecte. 1 Introuction It is thought that the humanoi type robot is the best form to work in the human living environment. In the future, it is expecte to apply it in various inustrial area for a substitute of a part of human work. Thus in many palces, the bipe walking robot is stuie[1]. Hona has evelope the P2 on 199, an the P3 on 1997[2]. The height of P2 is 1.82[m] an the weight is 21[kg]. The height of P3 is 1.[m] an the weight is 13[kg]. An Wasea Univercity has evelope WABIAN on 1998[3]. The height of WABIAN is 1.[m] an the weight is 17[kg]. Both robot is mae of aluminum or magnesium. The weight of the robot is very heavy. MARI-1 has been evelope in our laboratory[4][1]. MARI-1 is mae of mono cast nylon. Thus the weight is very light, which is 25[kg] an the hight is 1.21[m]. The weight is very light compare with the height, thus the less power is neee to make the robot walk an this robot seems safe even if it is in the human living environment. 2 Harware Design an Control System 2.1 Frame Design The robot has joints on each leg, an each feet can take any position an posture in the 3-imentional space. Fig.1: Bipe Walking Robot MARI-1 An the emension of the robot is shown in Fig.2. The thickness of the frame is 2[mm]. The foot size is 25[mm] 12[mm] for a stable walking.

2 Boy 388 #14 # No.2 No.3 No Giro Scope #7 #1 #9 8 8 #3 #4 # #3 #2 No. No.5 No.4 Fig.3: Joints of the foot #11 F/T Sensor 5 # # Table 3: New selection of motors Joint No Power(before)[W] Power(after)[W] Fig.2: Dimension of the Robot 2.2 Motors An Gears At the initial esign DC servo motors with 5:1 harmonic gears were use as the actuators, which have rotary encoers. The rate power an torque of the motors were estimate by the simulator(rocos) an the results in Table2 was obtaine[4] [5]. Joint numbers are shown in Fig.3. The otte lines enote the irections of the rotation axes of the joint motors. Here the rate value means the average value. Then DC motors were selecte as shown in Table Control System All calculation of the control is one by one DSP boar with the TMS32C32-5MHz. The walking programs are evelope on the host computer by the C language. The control system is shown in Fig.4. In this experiments, we only use the function of the otte line section. Host Computer PC-AT 12bit D/A converter DSP TMS32C32 1bit Counter DSP TMS32C32 12bit A/D Converter Digital Output Table 1: Selecte motors Joint No. 1 2, 4 3, 5 Rate Power[W] Rate Torque[N m] Peak Torque [N m] Moter Driver with Current Controller DC servo Motor Joint Actuator Rotary Encoer Giro Scope Sensor Controller Giro Scope on Boy Force/Torque Sensor Controller Force / Torque Sensor on Foot Bipe Walking Robot The robot was mae with these motors. However in the experiments, it was foun the motor power an the torque was not large enough. Thus ankle motors were chanege for bigger power ones. Exchanege motors are shown in Table3. Also all harmonic gears were exchange to 1:1. Table 2: Estimate rate power an torque Joint No Rate Power[W] Rate Torque[N m] Fig.4: Control system 3.1 Inverse Kinematics 3 Walking Pattern When we make the robot walk, we must think the tip position an irection references of the both feet in the -Y- omain. Joint angle references can be obtaine to transform the tip position an irection references by the inverse

3 kinematics calculation. In this experiments, the inverse kinematics calculation is mae by the Newton-Raphson metho. The coorinates about the kinematics of the robot is shown in Fig.5. This figure shows only a right foot case. x Y 3.2 Generation of the Walking Pattern When the walking pattern is generate, position references x ref = {x, y, z} in the -Y- omain are ecie first. Position references are given with respect to the boy-fixe coorinate shown in Fig.5. The orbits of the tip in, Y an irection are given as the function of the time. The orbit in the irection is shown in Fig.. The footstep slie s in the irection is ecie first an the orbit beteween each point is connecte through the sine curve. Y Fig.5: Kinematics of the robot There are coorinates on each foot. Each coorinate is place on each joint. The base coorinate is the boy-fixe one - Y -. The relationship from the boy-fixe coorinate to the tip fixe coorinate - Y - can be escribe by the calcuration of the coorinates transformation. Tip position refernces are given by the tip position vector x = {x, y, z}, an irection references by the posture matrix A A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 (1) The first row vector a x = {a 11,a 21,a 31 } T is the unit vector which enotes where the axis points with respect to the boy-fixe cooinate. Similarly, the secon row vector a y an the thir row vector a z enotes the irection of Y an axes. Tip position an irection references are transforme into joint angle references by the inverse kinematics calculation as follows. Suppose the reference q ref = {x ref, A ref }. Then the position an the irection error vectors become e x = x ref x (2) e = 1 2 (a x a xref + a y a yref + a z a zref ) (3) Joint angle reference θ = {θ 1,θ 2,θ 3,θ 4,θ 5,θ } can be obtaine by the Newton-Raphson metho. θ n 1 = θ n + J 1 n e n (4) (n =1, 2, ) where ( ) ex e = e an J(θ) enotes the Jacobian matrix (5) J(θ) = e θ T () [m] s s right foot left foot Fig.: Orbit of irection The orbit in Y irection is shown in Fig.7. The istance of the motion in the Y irection is ecie first an the orbit is generate similarly. Y[m] Fig.7: Orbit of Y irection right foot left foot The orbit in the irection is shown in Fig.8. The height h to which the robot raises its foot is ecie first an the orbit is generate similarly. In this experiments, the feet of the robot were kept horizontal against the groun. Thus irection references A was given as follows: Y

4 z z h x y right foot left foot [m] h 74.3[cm] Fig.8: Orbit of irection Fig.9: Initial posture A = 1 1 (7) 1 The experiments was mae with various values of the parameters of the walking pattern. The values of the parameters were ecie through the experiments by trial an error. 3.3 Servo Control of Each Joint Before the remake of the robot, the PID control, the isturbance observer an the H control were use as the joint position control. But when the motors were overloae, joint angle errors were integrate an the tracking response to the position reference was not satisfactory. Thus the high gain P control is use. In this experiments, the same high gain P control is also use. 3.4 How to give the references Tip position an irection references are mae an transforme into joint angle references in abovementione metho. Those references are generate at every.1[s]. All joint angle refernces are sent to the walking program which is ownloae to the DSP. These calculations are one off-line. Before the walking, the robot has the initial posture first. The initial posture is shown in Fig.9. An the robot starts walking with given joint angle refernces. 4 Experimental Results In the present walking experiment system, the following ata can be measure. 1. joint angles 2. motor current references on each joint 3. position of COM(the centor of the mass) The following iscussion is one with these ata. 4.1 Quasi-Dynamic Walking It is well known that there are two kin of bipe walking. One is the static walking an the other is the quasi-ynamic walking. The quasi-ynamic walking has the faster walking spee an requires the less energy. If we can make the robot walk in the quasi-ynamic walking, it can be sai that the better walking is realize. We inspect if our bipe walking satisfies the conition of the quasi-ynamic walking. In the case of the static walking, COM is always in the range of the foot with of the support leg. If the robot can walk stably when the position of COM is not in the range of the foot, it can be sai that the robot makes the quasi-ynamic walking. Parameters of the walking pattern use in the experiment are shown in Table4. The range of the foot of support leg an the position of COM in the x irection is shown in Fig.1. Table 4: Parameters of the experiment Footstep slie s [cm] in x irection 7. Distance [cm] in y irection 7.8 Height h [cm]in z irection 3.2 Perio [s].8 The soli line enotes the position of COM. One otte line enotes the insie ege of the foot of the support leg, an another enotes the outsie ege. The painte area enotes the support polygon. In Fig.1, the position of COM is not always in the support polygon. Before an after of the change the support leg to the other free leg, the perio that the position of COM is out from the support polygon exists. The robot walke stably in all the moment of this walking pattern. Thus it is confirme that the robot i the quasi-ynamic walking. 4.2 Calculate MP from the axis position The position of COM in section 4.1 is not always locate in the support polygon. In this section, the MP is calculate from the mesure axis positions.

5 Position[m] COM Insie ege Outsie ege Fig.1: Range of the foot an the position of COM The two imensinal MP is given in [11]. MP = Y MP = k + g z )x k m k (x k + g x )z k k + g z ) (8) k + g z )y k m k (x k + g y )z k k + g z) (9) Where m k is the mass of kth link, x k,y k,z k is the (x, y, z) position mesure from the support leg tip. is the secon erivative, an g z is the gravity. When the coorinate is shifte to the center of the boy (COB),(8)(9) are moifie to the following. MP = [ Y MP = [ q + g z )x k m k (x k + x q + g x)(z k + z q )] (1) q + g z ) q + g z )y k m k (y k + y q + g y)(z k + z q )] (11) q + g z ) Where (x q,y q,z q ) is the position of COB mesure from the support leg tip.(x k, y k, z k ) is the position of the kth link mesure from the COB. Parameters for the walking patterns are the same as Table 4. The range of thefoot of support leg, the position of COM an the position of MP in x irection are shown in Fig11. The soli line enotes the position of MP.One ote line enotes the position of COM. Two ote line enotes the insie ege of the foot of the support leg, an another enotes the outsie ege. The shaowe area enotes the support polygon. In Fig11, the position of MP is not always in the support polygon. When the robot lifts the free leg, or just when the free leg touches own the floor, the MP approaches to the insie ege of the support leg. An for a short perio, the MP moves to outsie of the sole in Fig11.This is because the sole size is assume to be large enough in (1) an (11). The practical unerstaning is that for this short perio, the robot leans to the free leg irection, an the outsie ege of the support leg sole oes not fit to the floor. Authors are now investigating the better wallking pattern from the view point of MP. Position(m) MP COM Insie Ege Outsie ege Time(s) Fig.11: Range of the Foot an the position of MP 4.3 Effectiveness of the Servo Control The waveforms of a joint angle θ an a joint angle reference θ ref are shown in Fig.12. The high gain P control works without the error ivergence an joint angle errors were kept small. 4.4 Pattern For Better Walking We mae the experiments with various values of the parameters. When parameters are change, the state of the walking change. In this section, we make the two kin of estimation Smooth Walking If the require power for joints becomes large, the walking becomes unstable an the robot falls to the groun. To avoi the phenomena, we selecte the walking pattern so that the less power is consume. We select

6 Joint angle[ra] q q ref Energy[J] Perio[s] Fig.12: Joint angle references an joint angles at θ 4 Fig.14: Approximate power of joint No.2 the maximum current refernce of the motor as the one performance inex for the less power walking. The footstep slie s = 5.[cm], the istance = 7.[cm] an the height h =3.8[cm] are kept equal an the perio is only change. The change of the perio an the maximum current reference of the joint No.2 of the right leg is shown in Fig.13. An the approximate power of one perio of one step is shown in Fig.14. Aroun.8[s] of one step perio, both the maximum current an the power become the least. The robot has its own mechanical resonance frequency. It is thought that the frequency 1/.8[Hz] may be close to the mechanical resonance frequency. If the frequency of the walking pattern is near the mechanical resonance frequency, the robot coul walk with the less power. Current[A] Perio[s] Fig.13: Maximum current of joint No Fast Walking As another performance inex, the spee of the walking is selecte. The height h = 3.8[cm] an the perio T =.7[s] are kept equal an the footstep slie s is change. The istance is change accoring to the change of the footstep slie s. The change of the footstep slie an the maximum current reference of the joint No.2 of the right leg is shown in Fig.15. An the approximate power of one perio is shown in Fig.1. An the maximum current refernce an approximate power of the joint No.4 are shown in Fig.17, an Fig.18. The rotation axis of the joint No.2 is the roll axis. Thus it is thought that the variation of the current oes not have so many relationship with the variation of the footstep slie. On the other han, the rotation axis of the joint No.4 is the pitch axis. Thus the current increses as the footstep slie become large. Since the current limit of the motor on the joint No.4 is 1[A], the maximum current refernce must be kept less than 1[A]. 5 Conclusion We evelope the bipe walking robot MARI-1 an remae the frame of the robot an the motors with harmonic gears. An we mae the bipe walking experiments. We suceee in making the robot o the quasiynamic walking. An also we investigate the smooth walking an the fast walking. In future, we plan to make the robot walk faster an we will consier the walking pattern which has the minimum power for joint motors. An we plan to put the sensors on the robot an o the feeback control from the information of the acceleration, gyro, an force sensors. References [1] Special Issue: Walking Robot, Jarnal of the Robotics Society Japan, Vol.11, No.3, pp , [2] M. HIROSE, T. TAKENAKA, H. GOMI an N. OAWA, Humanoi Robot, Jarnal of the Robotics Society Japan, Vol.15, No.7, pp , [3] J. YAMAGUCHI, S. INOUE, D. NISINO, S. GEN, A. ISHII, S. MATSUO, Y. YAMAMOTO, H. OAWA, A. TAKANISHI, Development of the Wasea Bipe Humanoi Robot WABIAN -Design metho of the total system-, Proceeings of the 15th Annual Conference of

7 the Robotics Society of Japan, vol.3, pp , September [4] Y. FUJIMOTO, Stuy on Bipe Walking Robot with Environmental Force Interaction Doctoral Thesis, pp.5-24, 49-52, March [5] Y. FUJIMOTO, A. KAWAMURA, Autonomous Control of 3D Dynamics Simulations of Bipe Walking Robot, IEEE Robotics an Automation Magazine, Vol.5, No.2, pp.33-42, [] Robotics Society Japan, Robotics Hanbook, CORONA PUBLISHING CO., LTD., pp , 199. [7] J.J. Craig, Introuction to Robotics, Aison-Wesley Publishing Company, [8] S. KAJITA, A. KOBAYASHI, Dynamic Walk Control of a Bipe Robot with Potential Energy Conserving Orbit, SICE, Vol.23, No.3, pp , March [9] Y. FUJIMOTO, A. KAWAMURA, Robust Bipe Walking Active Interaction Control between Foot an Groun, ICRA, pp , [1] A.YONEMURA, Y.NAKAJIMA, A.HIRAKAWA, A. KAWAMURA, Experimental Approach for the Bipe Walking Robot MARI-1, AMC, pp , 2. [11] A.TAKANISHI, Bipe Walking Robot Compensating Moment by Trunk Motion, Journal of RSJ, pp , Vol.11, No.3, pp , Current[A] Energy[J] Fig.15: Maximum current of joint No Current[A] Fig.1: Approximate power of joint No Fig.17: Maximum current of joint No Energy[J] Fig.18: Approximate power of joint No.4