A Si-ais Force Sensor with Parallel Support Mechanism to Measure the Ground Reaction Force of Humanoid Robot Koichi Nishiwaki Yoshifumi Murakami Satoshi Kagami Yasuo Kunioshi Masauki Inaba Hirochika Inoue Dept. of Mechano-Informatics, School of Information Digital Human Lab., National Institute of Science and Technolog, Univ. of Toko. Advanced Science and Technolog 7{3{1, Hongo, Bunko-ku, Toko, 113{8656, Japan. 2-41-6, Aomi, Kouto-ku, Toko, 135-64, Japan. fnishi,murakami,kuniosh,inaba,inoueg@jsk.t.u-toko.ac.jp s.kagami@aist.go.jp Abstract This paper describes a design of si-ais force sensor that mesures ground reaction force of human or humanoid robot. The ke concept is parallel support mechanisms that allow large torques and forces which are caused when foot is hitting to the environment. Basic concept and design of parallel support mechanisms are denoted. Finall ground reaction force measurement sstem for human walking, and application to humanoid robot walking are described. 1 Introduction Legged humanoid robots are epected to move and work in comple real world where human lives. ZMP(Zero Moment Point) [1] is often used to make robot balance on legs. Especiall in a horiontal plane walking scene, ZMP is useful and can be mesured b distributed force sensors each of which is mesuring a vertical force, so that three components of the force (vertical force F, roll moment M, pitch moment M ) can be obtained b those combination, then ZMP can be calculated (e. [2, 3]). However, si-ais force information (translational force F ;; and rotational force M ;; ) is useful for walking on rough terrain or stairs where both feet are not contacting in the same horiontal plane. It is also useful to measure aw moment and internal force caused b the closed loop that consists of two legs and the ground in order to achieve non-slipping walk. So far, there are man results with si-ais force sensors that is utilied for humanoid robot walking (e. [4,5]). Nevertheless it is dicult to select a si-ais force sensor that bears the landing impact and satises the sie and weight requirements from commercial products. In this paper, we propose a parallel support mechanism for si-ais force measurement. Each supporting point does not transfer rotational components of force. This mechanism realies high impact tolerance for desired components of force. It also can be designed to be thin and light so that it t into between sole and ankle joints. Distributed supporing points onl transfer translational components of force, and the are measured at each point. Then si-ais force is calculated from those values. The arrangement of supporting points can be changed according to the tolerance requirements for each component and the requirements of the shape. Basic principle and design are described in section 2. Developped si-ais ground reaction force mesurement sstem for human being and humanoid robot are described in section 3 and 4 respectivel. 2 Si-ais Force Sensor with Parallel Support Mechanisms 2.1 Problem of Traditional Si-ais Force Sensor Si-ais force sensor are widel used in robot manipulators in order to mesure the reaction force from the environment. In general, si-ais force sensor has several strain part which is sensitive for dierent input force direction. The arrangement of those strain part is usuall serial. In this arrangement, all force cause inuence to all strain part, so that each strain part must be strong enough for non-mesurement direction and interference of those strain sensors must be calibrated. Another problem of serial arrangement is its weakness for rotational force compared with translational force. Landing impact of humanoid robot ma be several times of its own weight, and it causes large rotational force at the measurement point. Therefore traditional design is not t for such application. 2277
Figure 1: Support Point. 2.2 Concept of Parallel Support Mechanism In order to overcome this problem, parallel support mechanism is proposed. Supporting points are distributed between two structures of which mutual si-ais force is measured. The concept is as follows, Support points each of which does not transfer rotational force are distributed, Each component of translational force is mesured b dierent strain part to avoid interference, Si-ais force is calculated from those combination. In this concept, ever strain part onl receives measuring component of force, therefore cancellation of interference is not required when calculating si ais force from the strain values. The arrangement of support point is decided accoding to the required tolerance for each component of force and shape. Eamples of arrangement are described in the following part of this section. 2.2.1 Design of Support Point At support points, rotational force should not be transfered. Therefore, mechanism with ball and mesurement beams is proposed(fig.1). Strain gauge sensor is attached to each mesurement beam and each beam mesures onl one component of translational force. 2.2.2 Arrangement of Support Points In order to calculate si-ais force, number of support point is at least three which is not on the same line. Fig.2 shows the smmetrical 8 ball arrangement eample. 8 balls are ed to structure A, and all the Figure 2: Si-ais Force Sensor that Measures between Structure A and B. (Solid balls are ed to A and beams are ed to B. 8 support points.) M Figure 3: Si-ais Force Sensor that Measures between Structure A and B. (Solid balls are ed to A and beams are ed to B. 4 support points.) strain measurement beams are ed to structure B. Structure A does not contact with structure B in other points, then all the mutual force between A and B is transferred through the support points. Therefore siais force can be calculated from the measured translational forces. Since the constraints of the ball b measurement beams are redundant, all the balls do not alwas transfer the translational force. The tolerance for three translational components and that for three rotational force are the same respectivel in this smmetrical arrangement Fig.3 shows the 4 ball arrangement eample. Tolerances for F, M, M will be high comparing with that of other components, and the shape will be thin in this design. Therefore this design is adopted for both human walking measurement sstem and humanoid foot sensor. 2278
P O A B R Q C D M A B Figure 5: Design of Si-ais Ground Reaction Force Sensor. A r B C D C D Figure 6: Design of a Beam that Measures Two Ais Forces. Figure 4: Calculation of Si-ais Force with 8 Support Points Arrangement. 2.2.3 Calculation of Si-ais Force Calculation method of si-ais force is denoted b using 8 support points eample. Let support point be distributed on vertices of a cube(fig.4 upper), and si-ais force calculation point be the center of the cube. Force for positive direction of F can be mesured as A + B + C + D, and negative direction as O + P + Q + R. Therefore, F can be calculated as follows; F = A + B + C + D O P Q R : (1) F ;F are also the same. Then let r be the distance between contacting points and the center of the cube (it is same for all the contacting points in this case), A be the angle of the line that connect the contacting point for A and the center of the cube from the -ais direction(fig.4 lower). Then rotational force M is calculated as follows; M = ra sin A ra sin A rb sin B rb sin B rc sin C rc sin C rd sin D rd sin D ro sin O ro sin O rp sin P rp sin P rq sin Q rq sin Q rr sin R rr sin R (2) M ;M are also the same. 3 Ground Reaction Force Sensor to Measure Human Motion Wearing tpe sensor that mesures si-ais ground reaction force was designed and developped in order to evaluate the mechanism before developping sensors for humanoid, and to measure human motion. In this paper, let forward, leftward, and upward direction be,,and direction respectivel. Also let rotational force around each ais be M ;M ;M. Large tolerance is required for M ;M ; andf,because of the impact when landing to the ground. 2279
Table 1: Specication of Strain Amplier. Number of Channel Sie Bridge Supp. Volt. Output Voltage Gain Bridge Balance 1 16 2 7 2 14mm 5V 1 1V 6 2 (set b trimmer) Set b trimer Figure 8: Applied Points and Directions of Translational Forces. 3.5-3 F F F M M M -.1* -.5* 3-25 2.5 Measured Torque [kgf m] Measured Force [kgf] -2-1 2 1.5 1.5 -.5-1 -2-1 -2-25 Figure 9: Output of the sensor (left: translational components, right: rotational components, cond. 1). Figure 7: Wearing tpe Si-ais Force Sensor. Therefore 4 supporting points are distributed as wide as possible in the sensor(fig.5). The advantage of this design is that si-ais force sensor can be thin enough to reduce the disturbance of human motion. 3.1 Development of Wearing Tpe Siais Force Sensor Fig.5 shows mechanical design of wearing tpe siais force sensor. In order to reduce the number of beams, hbrid mesurement beam is adopted for, and direction(fig.6). It also contributes to reduce the number of strain gauge and amplier circuit since direction forces of two support points are measured b one strain bridge, then total number of strain bridge is 1. In order to support more than 1[kgf], steel bearing ball (SUJ2 Hardened high carbon-chrome steel, surface hardness HR C 62 67 ) is adopted. For strain beam, hardened tool steel (SKD11 HR C65 ) is adopted. Strain amplier circuit is developed using single chip instrumentation IC (burr brown INA125). It is implemented inside the sensor. Specication of the circuit and pictures are shown in Table 1 and right 228 bottom of Fig.7. Fig.7 shows the wearing tpe si-ais force sensor. The shape of the sensor is similar to 'Geta' (clogs). In order to measure natural walking it allows bend of human sole using the toe joint. 3.2 3.2.1 Eperiments on Wearing Tpe Siais Force Sensor Liniarit and Non-Interferentialit Relationship between applied force and the output of the sensor is shown in Fig.9 and 1. Translational force is applied at a point b digital force gauge (Imada DPXT). The points are shown in Fig.8. As eperiment condition 1, direction translational force is applied. F output increases just the same as the input force while F; remains (Fig.9 left). M; also increase proportional to the input force while M remains (Fig.9 right). Average errors from desired outputs in this eperiment are.12[kgf](f ),.7[kgf](F ),.29[kgf](F ),.13[kgf m](m ),.19[kgf m](m ),.2[kgf m](m ). As eperiment condition 2, direction translational force is applied. F output increases just the same as the input force while F; remains (Fig.1 left). M; increase proportional to the input while M remains (Fig.1 left). Average errors in this condition are.21[kgf](f ),.26[kgf](F ),.37[kgf](F ),.14[kgf m](m ),.24[kgf m](m ), and.35[kgf m](m ).
3 25 F F F - 3 2.5 M M M -.1*.12* Measured Force [kgf] 2 15 1 Measured Torque [kgf m] 2 1.5 1 5.5-1 -2-25 -.5-1 -2 Figure 1: Output of the sensor (left: translational components, right: rotational components, cond. 2). 6 Figure 12: Displa Interface of Si-ais Sensor Output. 3 6 Force [kgf] -1-2 -3-4 F F F Torque [kgf m] 4 2 M M M Y -3-6 -2-4 -7 Z -6-14 -84-28 28 84 14 X Top View Figure 11: Measured ZMP when Force Applied on Grid-points. 3.2.2 ZMP mesurement eperiment Fig.11 shows calculated mp location when point forces are applied at 3 2 4 grid points. Average ZMP error from the grid points was 3.4[mm] when F 5:[kgf], and 2.9[mm] when F 1:[kgf]. Since ZMP calculation includes division b F, the error of ZMP becomes large when F is small. The displa output of mesurement sstem is shown in Fig.12, left side shows translational forces at each support point and total translational and rotational force vectors at the center of the sensor. 3.2.3 ZMP Mesuremnt in Walking Two graphs of Fig.13 show si-ais reaction force of human walking (around 7[kgf] of weight and about.8[s] per a step). The result shows that foot landing impact F is almost the same as the weight. Fig.14 shows the ZMP position is moving from back to front during one supporting phase. 4 Design and Development of Ground Reaction Force Sensor for Humanoid We developed humanoid \H7" (Height: 147[mm], Mass: 58[kg], Fig.15) for whole bod motion research in real world. Basicall the same mechanism (four support point tpe) is attached in between sole and 9 1 11 12 13 14 Time [sec] -6 9 1 11 12 13 14 Time [sec] Figure 13: Translational(left g.) and Rotaional(right g.) Reaction Forces of Human Walking. ankle joint of H7. Mass of si-ais sensor is about 7[g] and the height is about 35[mm], support points are distributed at the vertices of 14 2 94[mm] square (Fig.16). 4.1 Eperiments on Humanoid H7 Walking and stepping up trajecotries are designed to follow desired ZMP in dnamics simulation environment [6]. When the trajetories are eecuted on real robot, the are modied online using si-ais force sensor and gro sensor information to achieve stable motion. Measured ZMP trajector of left foot of forward walking is shown in Fig.17. Desired ZMP was designed to sta on a spot (about the center of the sole) while single leg support phase in this walking. 5 Conclusion This paper described a concept and development of si-ais force sensor with parallel support mechanism to mesure ground reaction force of human beings or humanoid robots. The ke ideas of this mechanism are, 1) distributed support points each of which does not transfer rotational force, 2) each ais force is mesured b dierent strain part to avoid interference, and 3) si-ais force of a point is calculated from the measured translational forces. This mechanism enables the sensor to be desined a) strong enough for landing impact, b) light and thin enough to attach on the feet. 2281
.2.15.1 ZMP [m].5 Figure 16: Si-ais Force Sensor Equipped in the Foot of Humanoid H7. -.5 -.1 -.15 5 -.2 8 9 1 11 Time [sec] 12 13 Figure 14: Transiton of ZMP while Human Walking. [mm] 5 1 Y-ais ZMP X-ais ZMP Left foot in contact Rigth foot in contact 15 2 8 9 1 11 12 13 [s] Figure 17: Mesured ZMP Position of Left Foot while H7 is Walking. Figure 15: H7 Walking Outdoors. According to this concept, we developed two sensors for di erent applications. One is wearing tpe si-ais ground reaction force mesurement sensor, and the other is si-ais force sensor for humanoid robot feet. The accurac of the sensors were evaluated. The result showed that caliblation matrices to cancel interferences are not required in this mechanism. Jumping and kicking motions were also carried out using the wearing tpe sensor. We could obtain si-ais force information in such high impact motion. We also succeeded to realie stable walking on humonoid H7 using the si-ais force sensor information. We believe that modeling human walking will greatl contribute to the research on humnaoid walk. Application. Springer{Verlag, Berlin, 199. [2] Y. Murase, K. Sakai, M. Inaba, and H. Inoue. Testbed hardware model of the hrp virtual platform. In Proc. of '98 Annual Smposium of Robotics-Mechatronics, pp. 2P2{89{91, 1998. [3] Koichi Nishiwaki, Satoshi Kagami, Yasuo Kunioshi, Masauki Inaba, and Hirochika Inoue. Toe joints that enhances bipedal and fullbod motion of humanoid tpe robot. In Proceddings of the 22 IEEE International Conference on Robotics and Automation, 22. [4] Qinghua LI, Atsuo TAKANISHI, and Ichiro KATO. Development of ZMP Measurement Sstem for Biped Walking Robot Using Universal Force-Moment Sensors. Journal of the Robotics Societ of Japan, Vol. 1, No. 6, pp. 828{833, 1992. [5] Kauo HIRAI. Current and Future Perspective of Honda Humanoid Robot. In Proc. of 1997 IEEE Intl. Conf. on Intelligent Robots and Sstems (IROS'97), pp. 5{58, 1997. [6] S. KAGAMI, K. NISHIWAKI, T. KITAGAWA, T. SUGIHARA, M. INABA, and H. INOUE. A fast generation method of a dnamicall stable humanoid robot trajector with enhanced mp constraint. In Proc. of IEEE International Conference on Humanoid, 2. Robotics (Humanoid2) References [1] M. Vukobratovi c, B. Borovac, D. Surla, and D. Stoki c. Biped Locomotion { Dnamics, Stabilit, Control and 2282