VIBRATION ANALYSIS AND MOTION CONTROL
OF STAND-UP ROBOT CONSISTING OF BODY
LINK, ARM LINK AND LEG LINK
International Journal of Applied Electromagnetics &
Mechanics. 2010, Vol. 33 Issue 3/4, p1431-1439. 9p.
BY:Hiroyuki Kojima, Tomohisa Hayakawa, Takahiro Tanaka
and Ayano Kamiyama
2014/4/9
Professor: Ming-Shyan Wang
Student: YU-Chen Dai
OUTLINE
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1. Introduction
2. Theoretical analysis of forced vibration response
3. Numerical calculation results of forced vibration response
4. Standup motion control system
5. Experimental results of standup motion control
6. Conclusions
7. References
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ABSTRACT
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In this study, first, the forced vibration response of a three-link stand-up robot is
investigated theoretically. The stand-up robot consists of an arm link, a body
link and a leg link. Considering the vibration analysis results, the trajectory
planning algorithm for the stand-up motion control by using a touch sensor
attached to the body link is devised. In the stand-up motion control, initially, the
vibrational swing motion control of the arm link starts. Then, immediately after
the time when the touch sensor signal is on for the first time, the swing motion
control of the leg link starts, and after a brief interval, the vibrational swing
motion control of the arm link finishes. Furthermore, the stand-up motion
control system consisting of the trajectory planning and the joint angle tracking
controller is constructed. Moreover, the experiments of the stand-up motion
control have been carried out, and it is confirmed that the stand-up motion
control could be well executed.
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INTRODUCTION
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Using interaction forces between links, robots can perform a variety of motions.
For example, the study of a three-link Stand-up robot using forced vibration of
two links has been reported [1]. Then, the study of a humanlike robot that can
stand up when it falls down was developed [2], and the study of a stand-up
motion using leg swing movement was reported [3]. In addition, the studies of
the learning for the stand-up motion by using reinforcement learning method
were reported [4,5]. On the other hand, the study of a stand-up robot due to the
vibration analysis by using a touch sensor to efficiently execute the stand-up
motion control seems to be important. However, the studies of stand-up robots
like this have been little investigated. In this study, first, the forced vibration
response of a three-link stand-up robot is theoretically investigated, and the
trajectory planning algorithm for the stand-up motion control by considering the
vibration analysis results and using a touch sensor attached to the body link is
devised. Then, the stand-up motion control system consisting of the trajectory
planning and the joint angle tracking controller is constructed. Furthermore, it is
confirmed experimentally that the standup motion control can be well executed.
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THEORETICAL ANALYSIS OF FORCED
VIBRATION RESPONSE(1/3)
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Figure 1 shows the photograph of a prototype threelink stand-up
robot with a touch sensor. The states of the standup robot are
classified into a bodyrecumbent phase and a leg-grounding phase.
Fig. 1. Photograph of three-link standup robot.
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THEORETICAL ANALYSIS OF FORCED
VIBRATION RESPONSE(2/3)
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And Fig. 2 shows the coordinate system of the three-link stand-up
in the bodyrecumbent phase. The stand-up robot consists of an
arm link, a body link and a leg link, and it has two joints driven by
reduction gears and DC motors with optical encoders.
Fig. 2. Coordinate system of three-link
stand-up robot.
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THEORETICAL ANALYSIS OF FORCED
VIBRATION RESPONSE(3/3)
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Using the parameters in Fig. 2, the coordinates of center of gravity of the body
link, the arm link and the leg link in the bodyrecumbent phase are expressed as
follows:
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1. xB = RB − r sin B
2. yB = R − r cos B
3. xA = RB − r sin B −¯lB cos B + lAC cos(A − B)
4. yA = R − r cos B +¯lB sin B + lAC sin(A − B)
5. xL = RB − r sin B +¯lB cos B + lLC cos(A − B − )
6. yL = R − r cos B −¯lB sin B + lLC sin(A − B − )
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NUMERICAL CALCULATION RESULTS OF
FORCED VIBRATION RESPONSE
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Figure 3 shows the numerical calculation results of the forced vibration
response of the attitude angle of the body link in the bodyrecumbent phase.
In these numerical calculations, the damping coefficient cB = 0.0023
Nms/rad was used. From this figure, it is seen that the resonance frequencies
vary with changes of the center angle Ao of the vibrational swing wave of the
arm link, and the resonance amplitudes increase with an increase of the
vibrational amplitudes Ao of the arm joint angle.
Fig. 3. Numerical calculation results of forced vibration response of stand-up robot.
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STANDUP MOTION CONTROL SYSTEM (1/2)
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Figure 4 shows the desired trajectories of the arm and leg joints. In this
trajectory planning, at the first, the vibrational swing motion control of the arm
link starts, and the swing motion control of the leg link automatically starts
immediately after the time when the output signal of the touch sensor is on for
the first time. Then, after that the time, the vibrational swing motion control of
the arm link automatically stops in response to the output signal of the touch
sensor.
Fig. 4. Desired trajectories of joint angles
for stand-up motion control.
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STANDUP MOTION CONTROL SYSTEM (2/2)
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The swing motion control of the leg link starts at the time when the output
signal of the touch sensor is on for the first time. Using this swing motion
control of the leg link, the standup robot can stand up by changing the inertia of
the stand-up robot. The desired trajectory of the leg joint angle shown in Fig. 4
is expressed as follows:
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EXPERIMENTAL RESULTS OF STANDUP
MOTION CONTROL (1/4)
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The parameters used in the stand-up motion control experiments are as follows:
fA = 1.20 Hz, Ao = 120 Ao = 30, TL1 = 0.18 s, TL2 = 0.20 s, TL1 = 0.32 s. The
vibrational swing frequency fA = 1.20 Hz of the arm link is nearly equal to the
resonance frequency fr = 1.18 Hz obtained by the vibration analysis, and the
vibrational swing frequency fA of the arm link was tuned experimentally by
using the resonance frequency fr as an initial value. Therefore, the usefulness of
the vibration analysis of the stand-up robot in the bodyrecumbent phase is
ascertained. The trajectory parameters TL1, TL2, TL3 of the leg joint angle
were experimentally tuned to well execute the stand-up motion control.
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EXPERIMENTAL RESULTS OF STANDUP
MOTION CONTROL (2/4)
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The joint tracking controller was constructed by using the PD control, and the
feedback coefficients were experimentally tuned. Figure 5 shows the
experimental results of the stand-up motion control, and Fig. 6 shows the
sequential photographs of the standup robot obtained by the experiment. From
these figures, it is confirmed that the vibrational amplitudes of the attitude angle
of the body link rapidly increase by the vibrational swing motion control of the
arm link in the bodyrecumbent phase, and the stand-up motion control could be
well executed by the swing motion control of the leg link as well as the
vibrational swing motion control of the arm link. This swing motion control of
the leg link contributes to the inertia variation control of the standup robot for
the standup motion control. In addition, the arm joint angle A and the leg joint
angle L was well controlled for the desired signals Ad, Ld. Then, it is
ascertained that, by the output signal of the touch sensor attached to the body
link, the swing motion control of the leg link automatically started, and the
vibrational swing control of the arm link automatically stopped. The tBS was
2.44 s.
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EXPERIMENTAL RESULTS OF STANDUP
MOTION CONTROL (3/4)
Fig. 5. Experimental results
of stand-up motion control.
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EXPERIMENTAL RESULTS OF STANDUP
MOTION CONTROL (4/4)
Fig. 6. Sequential photographs of stand-up robot obtained by experiment.
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CONCLUSIONS
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In this study, the forced vibration response of a threelink stand-up robot is
investigated theoretically, and the trajectory planning algorithmfor the
standupmotion control is devised by considering the forced vibration analysis
results, and using a touch sensor attached to the body link. Initially, the
vibrational swing motion control of the arm link starts. Then, immediately after
the time when the touch sensor signal is on, the swing motion of the leg link
starts, and after a brief interval, the vibrational swing motion control of the arm
link finishes. Furthermore, the standup motion control system consisting of the
trajectory planning and the joint angle tracking controller is constructed.
Moreover, the experiments of the standup motion control have been carried out,
and it is confirmed that the standupmotion control could be well executed.
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REFERENCES
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K. Nakakuki et al., Motion control of a robot composed of three serial links with curved
contour (1st report, concept and dynamic control of the robot), Transactions of the Japan
Society of Mechanical Engineers, Series C 58(555) (1992), 3299–3306.
H. Kanehiro et al., The Humanlike robot that can stand up when it falls down,
Proceedings of 13th Annual Conference of the Robotics Society of Japan (1995), 195–
196.
S. Ito et al., On a stand up motion using leg swing movement, Proceedings of 20th
Annual Conference of the Robotics Society of Japan 1I34 (1995), 1–3.
J. Morimoto and K. Doya, Learning dynamic motor sequence in highdimensional state
space by reinforcement learning(learning to stand up), The Transactions of the Institute
of Electronics, Information and Communication Engineers J82D2(11) (1999), 2118–
2131.
J. Morimoto and K. Doya, Acquisition of standup behaviour by a read robot using
hierarchical reinforcement learning, Robotics and Autonomous Systems 36 (2001), 37–51.
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2014/4/9
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2014/4/9