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A dish-spinning robot using a neural oscillator
International Congress Series 1301 (2007) 218 – 221
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A dish-spinning robot using a neural oscillator K. Matsuoka ⁎, M. Ooshima Department of Brain Science and Engineering, Kyushu Institute of Technology, Japan
Abstract. Recently, models of neural oscillators have been applied to many robots that perform various rhythmic movements. This paper describes a robot that performs a dish-spinning trick using a neural oscillator model. Two oscillators actuate a two-link manipulator to whirl a vertical rod on top of which a dish is hanged, while the angular position of the dish is fed back to the oscillators as input. Essentially, the controlled system has two different dynamic modes, i.e., a low-speed, largeradius whirl and a high-speed, small-radius one. A main difficulty in the control is that the oscillators must adapt to both the modes and change its mode from one to the other. Though there exists no direct interaction between the oscillators, the robot achieves the dish-spinning trick by making use of indirect interaction by way of the mechanical system. © 2007 Elsevier B.V. All rights reserved. Keywords: Neural oscillator; Central pattern generator; Dish-spinning; Natural frequency
1. Introduction Rhythmic movements such as locomotion of animals are known to be generated by certain neural oscillators called central pattern generators. Although many mathematical models have been proposed for the neural oscillators, the one proposed by one of the authors might be the most well-known [1,2]. Recently the model has been applied to many robots that perform various rhythmic movements. For example, Taga [3] and Kimura [4] used the model to realize locomotion of bipedal and quadruped robots, respectively. Williamson [5] applied the same model to a humanoid robot that performs cranking, sawing, and other functions. The control schemes in these robots are similar: some neural oscillators actuate the links of a robot while the joint angles and other state variables are fed back as the oscillators' inputs. A remarkable aspect of this scheme is that the oscillator is tuned to the natural dynamics of the controlled object and tends to ⁎ Corresponding author. Tel./fax: +81 93 695 6107. E-mail address: [email protected] (K. Matsuoka). 0531-5131/ © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2006.12.036
K. Matsuoka, M. Ooshima / International Congress Series 1301 (2007) 218–221
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oscillate at a natural frequency of the object. The neural-oscillator control does not only enable energy-efficient actuation, but also is quite robust. Ferris et al. [6] used the neural oscillator to produce swing motion in single, double, and triple pendulums and showed that the tuning to the pendulum dynamics occurred for a considerably wide range of the control parameters. The general aim of this study is to establish a method of the neural-oscillator control for the mechanical system that essentially has two dynamic modes and is required to automatically change the mode from one to the other. As an example, we recently demonstrated the control of a high-bar robot [7]. The key point was that the controlled system had two completely different modes, i.e., small swing and giant swing (rotation), and the neural oscillator had to adapt to both modes. This paper describes the control of a more complex system: a robot that performs the dishspinning trick. It has more degrees of freedom than the high-bar robot. While the high-bar robot was controlled by one neural oscillator, this robot is controlled by two oscillators. Though there exist no direct interactions between the oscillators, the robot achieves the dishspinning trick by making use of an indirect interaction by way of the mechanical system. An attempt to realize a dish-spinning trick was reported by Kajiwara et al. [8]. They analyzed some conditions to achieve the dish-spinning and applied them to an open-loop control for a robot; any feedback of the dish's state was not considered. The approach taken in this paper is quite different: it utilizes the feedback signal from the dish and utilizes the tuning capability of the neural oscillator to the controlled object. 2. Neural oscillator The neural oscillator used here is the one proposed by Matsuoka [1,2] and Taga [3]. It is composed of two neurons, each of which has a self-inhibitory property. The dynamics are given by sdx1 ¼ c−x1 −bm1 −ay2 −gðuÞ; T dm1 ¼ y1 −m1 ; sdx2 ¼ c−x2 −bm2 −ay1 −gð−uÞ; T dm2 ¼ y2 −m2 ; yi ¼ gðxi ÞJmaxð0; xi Þði ¼ 1; 2Þ; yout ¼ y1 −y2 : Variables xi, νi, and yi (i = 1, 2) are the membrane potential, the self-inhibition, and the output of each neuron. Each neuron i receives an inhibitory input − g(± u) from the outside, a mutual inhibition − ayj ( j ≠ i), and an excitatory tonic input c. The input and output of the whole oscillator are represented by u and yout, respectively. The mutual and self-inhibitions of the neurons induce a kind of relaxation oscillation even in the absence of the external input u; the nonlinear function in yi = g(xi) is introduced
Fig. 1. The dish-spinning robot.
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K. Matsuoka, M. Ooshima / International Congress Series 1301 (2007) 218–221
Fig. 2. Two modes of spinning.
to make a stable sustained oscillation. The oscillation frequency in that case is determined by the parameters of the oscillator. On the other hand, if a periodic signal is given to the neural oscillator as a sensory feedback signal u, then the oscillator comes to lock itself with the input. Due to the nonlinearity in − g(± u), the oscillator always receives negative inputs and therefore its state xi never diverges to infinity. 3. Dish-spinning robot A rod, on top of which a dish is hanged, is whirled by a two-link arm (see Fig. 1). Each link is actuated by a neural oscillator, producing a circular motion. The tip of the rod is inserted into a small pit on the back of the dish. Two small markers are attached on the upper surface of the dish to measure the dish position relative to the rod tip, with two cameras placed above it. Inherently the dish-spinning system has two dynamic modes. When the rod is whirled at a rotational speed under the natural frequency of the system, the plate takes a position as shown in Fig. 2(a). On the other hand, when the rod is whirled at a higher speed than the natural frequency, the plate rotates at an opposite position shown in Fig. 2(b). A difficulty in the dishspinning is that the robot has to shift the state from the first mode to the second one quickly. 4. Control system Fig. 3 shows the whole control system of the robot. Variable (X, Y ) stands for the relative position of the two marks on the plate; it is rotated by angle θ at the next block, giving (X′,Y′). Signals X′ and Y′ are each sent to two neural oscillators, through high-pass filters. The neural oscillators' outputs, yout1 and yout2, are normalized so as 2 2 to satisfy y′out1 + y′out2 = const. The normalized signals are low-pass filtered and are sent to the servomotors to move the links. The transition from the first mode to the second
Fig. 3. The control system of the dish-spinning robot.
K. Matsuoka, M. Ooshima / International Congress Series 1301 (2007) 218–221
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Fig. 4. Transition from the first mode to the second mode.
one is made by gradually changing two parameters as θ = π / 6 → − π[rad] and τ = 0.06 → 0.033[s]. The system has some tricks to achieve the dish-spinning. The nonlinear element just after the neural oscillators produces an exact circular motion. Introducing this element enables the two oscillators to synchronize with each other with a phase difference angle of 90°. In addition, the angular position of the plate is inputted to the oscillators with a shift of phase angle, θ : the left part in Fig. 3. The change of θ and τ works to increase the oscillation frequency. Fig. 4 shows the time course of the inputs to the two oscillators. For about 5 s in the beginning the frequency of the oscillation is low, which corresponds to the first-mode motion. Then, a high-frequency oscillation appears suddenly, implying that the state has been shifted to the second mode. 5. Conclusion In this paper we have described the control scheme for a dish-spinning robot. It utilizes an adaptive ability of the Matsuoka oscillator. The important point is that the system inherently has two modes of motion: slow-speed whirling and high-speed whirling. The oscillators persist in adapting to the natural dynamics of the system and this enables a quick shift from one mode to the other. References [1] K. Matsuoka, Sustained oscillations generated by mutually inhibiting neurons with adaptation, Biological Cybernetics 52 (1985) 367–376. [2] K. Matsuoka, Mechanisms of frequency and pattern control in the neural rhythm generators, Biological Cybernetics 56 (1987) 345–353. [3] G. Taga, A model of the neuro-musculo-skeletal system for human locomotion, I. Emergence of basic gait, Biological Cybernetics 73 (1995) 97–111. [4] H. Kimura, K. Sakurama, S. Akiyama, Dynamic walking and running of the quadruped using neural oscillators, Proceedings of IROS '98 1 (1998) 50–57. [5] M. M. Williamson, Robot Arm Control Exploiting Natural Dynamics, PhD thesis, Massachusetts Institute of Technology (1999). [6] D.P. Ferris, T.L. Viant, R.J. Campbell, Artificial neural oscillators as controllers for locomotion simulation and robotic exoskeletons, Fourth World Congress of Biomechanics (2002). [7] K. Matsuoka, et al., Control of a giant swing robot using a neural oscillator, Advances in Natural Computation (Proc. ICNC 2005, Part II), 2005, pp. 274–282. [8] H. Kajiwara, et al., Dynamics of a dish-spinning trick and its realization by robot, Journal of the Robotics Society of Japan 16 (1998) 483–490.
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A dish-spinning robot using a neural oscillator K. Matsuoka ⁎, M. Ooshima Department of Brain Science and Engineering, Kyushu Institute of Technology, Japan
Abstract. Recently, models of neural oscillators have been applied to many robots that perform various rhythmic movements. This paper describes a robot that performs a dish-spinning trick using a neural oscillator model. Two oscillators actuate a two-link manipulator to whirl a vertical rod on top of which a dish is hanged, while the angular position of the dish is fed back to the oscillators as input. Essentially, the controlled system has two different dynamic modes, i.e., a low-speed, largeradius whirl and a high-speed, small-radius one. A main difficulty in the control is that the oscillators must adapt to both the modes and change its mode from one to the other. Though there exists no direct interaction between the oscillators, the robot achieves the dish-spinning trick by making use of indirect interaction by way of the mechanical system. © 2007 Elsevier B.V. All rights reserved. Keywords: Neural oscillator; Central pattern generator; Dish-spinning; Natural frequency
1. Introduction Rhythmic movements such as locomotion of animals are known to be generated by certain neural oscillators called central pattern generators. Although many mathematical models have been proposed for the neural oscillators, the one proposed by one of the authors might be the most well-known [1,2]. Recently the model has been applied to many robots that perform various rhythmic movements. For example, Taga [3] and Kimura [4] used the model to realize locomotion of bipedal and quadruped robots, respectively. Williamson [5] applied the same model to a humanoid robot that performs cranking, sawing, and other functions. The control schemes in these robots are similar: some neural oscillators actuate the links of a robot while the joint angles and other state variables are fed back as the oscillators' inputs. A remarkable aspect of this scheme is that the oscillator is tuned to the natural dynamics of the controlled object and tends to ⁎ Corresponding author. Tel./fax: +81 93 695 6107. E-mail address: [email protected] (K. Matsuoka). 0531-5131/ © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2006.12.036
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oscillate at a natural frequency of the object. The neural-oscillator control does not only enable energy-efficient actuation, but also is quite robust. Ferris et al. [6] used the neural oscillator to produce swing motion in single, double, and triple pendulums and showed that the tuning to the pendulum dynamics occurred for a considerably wide range of the control parameters. The general aim of this study is to establish a method of the neural-oscillator control for the mechanical system that essentially has two dynamic modes and is required to automatically change the mode from one to the other. As an example, we recently demonstrated the control of a high-bar robot [7]. The key point was that the controlled system had two completely different modes, i.e., small swing and giant swing (rotation), and the neural oscillator had to adapt to both modes. This paper describes the control of a more complex system: a robot that performs the dishspinning trick. It has more degrees of freedom than the high-bar robot. While the high-bar robot was controlled by one neural oscillator, this robot is controlled by two oscillators. Though there exist no direct interactions between the oscillators, the robot achieves the dishspinning trick by making use of an indirect interaction by way of the mechanical system. An attempt to realize a dish-spinning trick was reported by Kajiwara et al. [8]. They analyzed some conditions to achieve the dish-spinning and applied them to an open-loop control for a robot; any feedback of the dish's state was not considered. The approach taken in this paper is quite different: it utilizes the feedback signal from the dish and utilizes the tuning capability of the neural oscillator to the controlled object. 2. Neural oscillator The neural oscillator used here is the one proposed by Matsuoka [1,2] and Taga [3]. It is composed of two neurons, each of which has a self-inhibitory property. The dynamics are given by sdx1 ¼ c−x1 −bm1 −ay2 −gðuÞ; T dm1 ¼ y1 −m1 ; sdx2 ¼ c−x2 −bm2 −ay1 −gð−uÞ; T dm2 ¼ y2 −m2 ; yi ¼ gðxi ÞJmaxð0; xi Þði ¼ 1; 2Þ; yout ¼ y1 −y2 : Variables xi, νi, and yi (i = 1, 2) are the membrane potential, the self-inhibition, and the output of each neuron. Each neuron i receives an inhibitory input − g(± u) from the outside, a mutual inhibition − ayj ( j ≠ i), and an excitatory tonic input c. The input and output of the whole oscillator are represented by u and yout, respectively. The mutual and self-inhibitions of the neurons induce a kind of relaxation oscillation even in the absence of the external input u; the nonlinear function in yi = g(xi) is introduced
Fig. 1. The dish-spinning robot.
220
K. Matsuoka, M. Ooshima / International Congress Series 1301 (2007) 218–221
Fig. 2. Two modes of spinning.
to make a stable sustained oscillation. The oscillation frequency in that case is determined by the parameters of the oscillator. On the other hand, if a periodic signal is given to the neural oscillator as a sensory feedback signal u, then the oscillator comes to lock itself with the input. Due to the nonlinearity in − g(± u), the oscillator always receives negative inputs and therefore its state xi never diverges to infinity. 3. Dish-spinning robot A rod, on top of which a dish is hanged, is whirled by a two-link arm (see Fig. 1). Each link is actuated by a neural oscillator, producing a circular motion. The tip of the rod is inserted into a small pit on the back of the dish. Two small markers are attached on the upper surface of the dish to measure the dish position relative to the rod tip, with two cameras placed above it. Inherently the dish-spinning system has two dynamic modes. When the rod is whirled at a rotational speed under the natural frequency of the system, the plate takes a position as shown in Fig. 2(a). On the other hand, when the rod is whirled at a higher speed than the natural frequency, the plate rotates at an opposite position shown in Fig. 2(b). A difficulty in the dishspinning is that the robot has to shift the state from the first mode to the second one quickly. 4. Control system Fig. 3 shows the whole control system of the robot. Variable (X, Y ) stands for the relative position of the two marks on the plate; it is rotated by angle θ at the next block, giving (X′,Y′). Signals X′ and Y′ are each sent to two neural oscillators, through high-pass filters. The neural oscillators' outputs, yout1 and yout2, are normalized so as 2 2 to satisfy y′out1 + y′out2 = const. The normalized signals are low-pass filtered and are sent to the servomotors to move the links. The transition from the first mode to the second
Fig. 3. The control system of the dish-spinning robot.
K. Matsuoka, M. Ooshima / International Congress Series 1301 (2007) 218–221
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Fig. 4. Transition from the first mode to the second mode.
one is made by gradually changing two parameters as θ = π / 6 → − π[rad] and τ = 0.06 → 0.033[s]. The system has some tricks to achieve the dish-spinning. The nonlinear element just after the neural oscillators produces an exact circular motion. Introducing this element enables the two oscillators to synchronize with each other with a phase difference angle of 90°. In addition, the angular position of the plate is inputted to the oscillators with a shift of phase angle, θ : the left part in Fig. 3. The change of θ and τ works to increase the oscillation frequency. Fig. 4 shows the time course of the inputs to the two oscillators. For about 5 s in the beginning the frequency of the oscillation is low, which corresponds to the first-mode motion. Then, a high-frequency oscillation appears suddenly, implying that the state has been shifted to the second mode. 5. Conclusion In this paper we have described the control scheme for a dish-spinning robot. It utilizes an adaptive ability of the Matsuoka oscillator. The important point is that the system inherently has two modes of motion: slow-speed whirling and high-speed whirling. The oscillators persist in adapting to the natural dynamics of the system and this enables a quick shift from one mode to the other. References [1] K. Matsuoka, Sustained oscillations generated by mutually inhibiting neurons with adaptation, Biological Cybernetics 52 (1985) 367–376. [2] K. Matsuoka, Mechanisms of frequency and pattern control in the neural rhythm generators, Biological Cybernetics 56 (1987) 345–353. [3] G. Taga, A model of the neuro-musculo-skeletal system for human locomotion, I. Emergence of basic gait, Biological Cybernetics 73 (1995) 97–111. [4] H. Kimura, K. Sakurama, S. Akiyama, Dynamic walking and running of the quadruped using neural oscillators, Proceedings of IROS '98 1 (1998) 50–57. [5] M. M. Williamson, Robot Arm Control Exploiting Natural Dynamics, PhD thesis, Massachusetts Institute of Technology (1999). [6] D.P. Ferris, T.L. Viant, R.J. Campbell, Artificial neural oscillators as controllers for locomotion simulation and robotic exoskeletons, Fourth World Congress of Biomechanics (2002). [7] K. Matsuoka, et al., Control of a giant swing robot using a neural oscillator, Advances in Natural Computation (Proc. ICNC 2005, Part II), 2005, pp. 274–282. [8] H. Kajiwara, et al., Dynamics of a dish-spinning trick and its realization by robot, Journal of the Robotics Society of Japan 16 (1998) 483–490.