Proceedings of the 2002 IEEE International Conference on Robotics & Automation Washington, DC • May 2002
A Six-axis Force Sensor with Parallel Support Mechanism to Measure the Ground Reaction Force of Humanoid Robot
Koichi Nishiwakiy Yoshifumi Murakamiy Satoshi Kagamiz Yasuo Kuniyoshiy Masayuki Inabay Hirochika Inouey y
z
Dept. of Mechano-Informatics, School of Information Science and Technology, Univ. of Tokyo.
Advanced Science and Technology
7{3{1, Hongo, Bunkyo-ku, Tokyo, 113{8656, Japan.
fnishi,murakami,kuniyosh,inaba,
[email protected] Abstract
This paper describes a design of six-axis force sensor that mesures ground reaction force of human or humanoid robot.
The key 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.
Finally ground reaction force measure-
ment system for human walking, and application to humanoid robot walking are described.
1
Introduction
Legged humanoid robots are expected to move and work in complex real world where human lives. ZMP(Zero Moment Point) [1] is often used to make robot balance on legs. Especially in a horizontal plane walking scene, ZMP is useful and can be mesured by distributed force sensors each of which is mesuring a vertical force, so that three components of the force (vertical force Fz , roll moment Mx , pitch moment My ) can be obtained by those combination, then ZMP can be calculated (ex. [2, 3]). However, six-axis force information (translational force Fx;y;z and rotational force Mx;y;z ) is useful for walking on rough terrain or stairs where both feet are not contacting in the same horizontal plane. It is also useful to measure yaw moment and internal force caused by the closed loop that consists of two legs and the ground in order to achieve non-slipping walk. So far, there are many results with six-axis force sensors that is utilized for humanoid robot walking (ex. [4,5]). Nevertheless it is dicult to select a six-axis force sensor that bears the landing impact and satis es the size and weight requirements from commercial products. In this paper, we propose a parallel support mechanism for six-axis force measurement. Each supporting
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Digital Human Lab., National Institute of
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2-41-6, Aomi, Kouto-ku, Tokyo, 135-0064, Japan.
[email protected]
point does not transfer rotational components of force. This mechanism realizes 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 only transfer translational components of force, and they are measured at each point. Then six-axis 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 six-axis ground reaction force mesurement system for human being and humanoid robot are described in section 3 and 4 respectively. 2
Six-axis Force Sensor with Parallel Support Mechanisms
2.1
Problem of Traditional Six-axis Force Sensor
Six-axis force sensor are widely used in robot manipulators in order to mesure the reaction force from the environment. In general, six-axis force sensor has several strain part which is sensitive for di erent input force direction. The arrangement of those strain part is usually serial. In this arrangement, all force cause in uence 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 may 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.
Strain Mesurement Beam
Solid Ball Strain Mesurement Beam
Strain Mesurement Beam Solid Ball
Solid Ball
Figure 2: Six-axis Force Sensor that Measures between Structure A and B. (Solid balls are xed to A and beams are xed to B. 8 support points.)
Figure 1: Support Point. 2.2
Concept of Parallel Support Mechanism
z
In order to overcome this problem, parallel support mechanism is proposed. Supporting points are distributed between two structures of which mutual six-axis force is measured. The concept is as follows,
x
y
y x
Support points each of which does not transfer rotational force are distributed,
Mx
z
Each component of translational force is mesured
by di erent strain part to avoid interference, Six-axis force is calculated from those combination.
In this concept, every strain part only receives measuring component of force, therefore cancellation of interference is not required when calculating six axis force from the strain values. The arrangement of support point is decided accoding to the required tolerance for each component of force and shape. Examples 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 only one component of translational force. 2.2.2
Arrangement of Support Points
In order to calculate six-axis force, number of support point is at least three which is not on the same line. Fig.2 shows the symmetrical 8 ball arrangement example. 8 balls are xed to structure A, and all the
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Strain Mesurement Beam Solid Ball
Solid Ball Strain Mesurement Beam
Figure 3: Six-axis Force Sensor that Measures between Structure A and B. (Solid balls are xed to A and beams are xed to B. 4 support points.) strain measurement beams are xed 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 sixaxis force can be calculated from the measured translational forces. Since the constraints of the ball by measurement beams are redundant, all the balls do not always transfer the translational force. The tolerance for three translational components and that for three rotational force are the same respectively in this symmetrical arrangement Fig.3 shows the 4 ball arrangement example. Tolerances for Fz , Mx , My 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 system and humanoid foot sensor.
z 280
x
Px Ox Rx
Ax
120
y x
Qx 43
Bx Cx
x
Dx
z x
Figure 5: Design of Six-axis Ground Reaction Force Sensor.
Mx
y
Az
Ay
r
Bz By
Dy
Cy
Cz
Figure 6: Design of a Beam that Measures Two Axis Forces.
Dz
Figure 4: Calculation of Six-axis Force with 8 Support Points Arrangement.
lower). Then rotational force Mx is calculated as follows; sin Az 0 rAy sin Ay 0 rBz sin Bz sin By 0 rCz sin Cz 0 rCy sin Cy z sin Dz 0 rDy sin Dy 0 rOz sin Oz y sin Oy 0 rPz sin Pz 0 rPy sin Py z sin Qz 0 rQy sin Qy 0 rRz sin Rz y sin Ry (2) My ; Mz are also the same. Mx
=
0rA 0rB 0rD 0rO 0rQ 0rR
z
y
2.2.3
Calculation of Six-axis Force
Calculation method of six-axis force is denoted by using 8 support points example. Let support point be distributed on vertices of a cube(Fig.4 upper), and six-axis force calculation point be the center of the cube. Force for positive direction of Fx can be mesured as Ax + Bx + Cx + Dx , and negative direction as Ox + Px + Qx + Rx . Therefore, Fx can be calculated as follows; Fx
= Ax + Bx + Cx + Dx 0 Ox 0 Px 0 Qx 0 Rx : (1)
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), Az be the angle of the line that connect the contacting point for Az and the center of the cube from the z -axis direction(Fig.4
Fy ; Fz
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3
Ground Reaction Force Sensor to Measure Human Motion
Wearing type sensor that mesures six-axis 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 x, y ,and z direction respectively. Also let rotational force around each axis be Mx; My ; Mz . Large tolerance is required for Mx ; My ; andFz , because of the impact when landing to the ground.
Table 1: Speci cation of Strain Ampli er.
Number of Channel Size Bridge Supp. Volt. Output Voltage Gain Bridge Balance
10 160 2 70 2 14mm 5V 010 10V 600 2000 (set by trimmer) Set by trimer
Figure 8: Applied Points and Directions of Translational Forces. 3.5
-30
Fx Fy Fz x
Mx My Mz -0.1*x -0.05*x
3
-25
2.5 Measured Torque [kgf m]
Measured Force [kgf]
-20
-15
-10
2
1.5
1
0.5
-5
0 0
-0.5 0
-5
-10 Force Gauge [kgf]
-15
-20
0
-5
-10 Force Gauge [kgf]
-15
-20
-25
Figure 9: Output of the sensor (left: translational components, right: rotational components, cond. 1).
Figure 7: Wearing type Six-axis Force Sensor. Therefore 4 supporting points are distributed as wide as possible in the sensor(Fig.5). The advantage of this design is that six-axis force sensor can be thin enough to reduce the disturbance of human motion. 3.1
Development of Wearing Type Sixaxis Force Sensor
Fig.5 shows mechanical design of wearing type sixaxis force sensor. In order to reduce the number of beams, hybrid mesurement beam is adopted for y, and z direction(Fig.6). It also contributes to reduce the number of strain gauge and ampli er circuit since y direction forces of two support points are measured by one strain bridge, then total number of strain bridge is 10. In order to support more than 100[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 ampli er circuit is developed using single chip instrumentation IC (burr brown INA125). It is implemented inside the sensor. Speci cation of the circuit and pictures are shown in Table 1 and right
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bottom of Fig.7. Fig.7 shows the wearing type six-axis 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
Experiments on Wearing Type Sixaxis Force Sensor Liniarity and Non-Interferentiality
Relationship between applied force and the output of the sensor is shown in Fig.9 and 10. Translational force is applied at a point by digital force gauge (Imada DPX-50T). The points are shown in Fig.8. As experiment condition 1, z direction translational force is applied. Fz output increases just the same as the input force while Fx;y remains 0 (Fig.9 left). Mx;y also increase proportional to the input force while Mz remains 0 (Fig.9 right). Average errors from desired outputs in this experiment are 0.12[kgf](Fx ), 0.07[kgf](Fy ), 0.29[kgf](Fz ), 0.013[kgf m](Mx ), 0.019[kgf m](My ), 0.020[kgf m](Mz ). As experiment condition 2, y direction translational force is applied. Fy output increases just the same as the input force while Fx;z remains 0 (Fig.10 left). Mx;z increase proportional to the input while My remains 0 (Fig.10 left). Average errors in this condition are 0.21[kgf](Fx ), 0.26[kgf](Fy ), 0.37[kgf](Fz ), 0.014[kgf m](Mx ), 0.024[kgf m](My ), and 0.035[kgf m](Mz ).
3
30
Fx Fy Fz -x
Measured Torque [kgf m]
20 Measured Force [kgf]
Mx My Mz -0.1*x 0.012*x
2.5
25
2
1.5
15
10
1
0.5 5
0 0
0
-5
-10
-15
-20
-25
-0.5 0
-5
Force Gauge [kgf]
-10 Force Gauge [kgf]
-15
-20
Figure 10: Output of the sensor (left: translational components, right: rotational components, cond. 2). Figure 12: Display Interface of Six-axis Sensor Output.
60
30
6 0
-10
Torque [kgf m]
-20
Force [kgf]
0 -30
-40
2
0
-2
-50
Y
Mx My Mz
4
Fx Fy Fz
-30 -60
-4 -70 9
-60 -140
-84
-28
28
84
X
ZMP mesurement experiment
Fig.11 shows calculated zmp location when point forces are applied at 3 2 4 grid points. Average ZMP error from the grid points was 3.4[mm] when Fz 05:0[kgf], and 2.9[mm] when Fz 010:0[kgf]. Since ZMP calculation includes division by Fz , the error of ZMP becomes large when Fz is small. The display output of mesurement system 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. ZMP Mesuremnt in Walking
Two graphs of Fig.13 show six-axis reaction force of human walking (around 70[kgf] of weight and about 0.8[s] per a step). The result shows that foot landing impact Fz is almost the same as the weight. Fig.14 shows the ZMP position is moving from back to front during one supporting phase. 4
12
13
14
-6 9
10
11
12
13
14
Time [sec]
Figure 13: Translational(left g.) and Rotaional(right g.) Reaction Forces of Human Walking.
Top View
Figure 11: Measured ZMP when Force Applied on Grid-points.
3.2.3
11
Time [sec]
140
Z
3.2.2
10
Design and Development of Ground Reaction Force Sensor for Humanoid
We developed humanoid \H7" (Height: 1470[mm], Mass: 58[kg], Fig.15) for whole body motion research in real world. Basically the same mechanism (four support point type) is attached in between sole and
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ankle joint of H7. Mass of six-axis sensor is about 700[g] and the height is about 35[mm], support points are distributed at the vertices of 104 2 94[mm] square (Fig.16). 4.1
Experiments on Humanoid H7
Walking and stepping up trajecotries are designed to follow desired ZMP in dynamics simulation environment [6]. When the trajetories are executed on real robot, they are modi ed online using six-axis force sensor and gyro sensor information to achieve stable motion. Measured ZMP trajectory of left foot of forward walking is shown in Fig.17. Desired ZMP was designed to stay 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 six-axis force sensor with parallel support mechanism to mesure ground reaction force of human beings or humanoid robots. The key ideas of this mechanism are, 1) distributed support points each of which does not transfer rotational force, 2) each axis force is mesured by di erent strain part to avoid interference, and 3) six-axis 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.
0.2 x 0.15
y
0.1
ZMP [m]
0.05
0
Figure 16: Six-axis Force Sensor Equipped in the Foot of Humanoid H7.
-0.05
-0.1
-0.15
50 -0.2 8
9
10
11 Time [sec]
12
13
Figure 14: Transiton of ZMP while Human Walking.
0
[mm]
50
100
Y-axis ZMP X-axis ZMP Left foot in contact Rigth foot in contact
150
200
8
9
10
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 type six-axis ground reaction force mesurement sensor, and the other is six-axis force sensor for humanoid robot feet. The accuracy 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 type sensor. We could obtain six-axis force information in such high impact motion. We also succeeded to realize stable walking on humonoid H7 using the six-axis force sensor information. We believe that modeling human walking will greatly contribute to the research on humnaoid walk.
Application. Springer{Verlag, Berlin, 1990. [2] Y. Murase, K. Sakai, M. Inaba, and H. Inoue. Testbed hardware model of the hrp virtual platform. In Proc. of '98 Annual Symposium of Robotics-Mechatronics, pp. 2P2{89{091, 1998. [3] Koichi Nishiwaki, Satoshi Kagami, Yasuo Kuniyoshi, Masayuki Inaba, and Hirochika Inoue. Toe joints that enhances bipedal and fullbody motion of humanoid type robot. In Proceddings of the 2002 IEEE International Conference on Robotics and Automation, 2002. [4] Qinghua LI, Atsuo TAKANISHI, and Ichiro KATO. Development of ZMP Measurement System for Biped Walking Robot Using Universal Force-Moment Sensors. Journal of the Robotics Society of Japan, Vol. 10, No. 6, pp. 828{833, 1992. [5] Kazuo HIRAI. Current and Future Perspective of Honda Humanoid Robot. In Proc. of 1997 IEEE Intl. Conf. on Intelligent Robots and Systems (IROS'97), pp. 500{508, 1997. [6] S. KAGAMI, K. NISHIWAKI, T. KITAGAWA, T. SUGIHARA, M. INABA, and H. INOUE. A fast generation method of a dynamically stable humanoid robot trajectory with enhanced zmp constraint. In Proc. of IEEE International Conference on Humanoid
, 2000.
Robotics (Humanoid2000)
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