HUMANOID robots involve many technical issues to be

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1 IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 5, OCTOBER Sensory Reflex Control for Humanoid Walking Qiang Huang and Yoshihiko Nakamura, Member, IEEE Abstract Since a biped humanoid inherently suffers from instability and always risks tipping itself over, ensuring high stability and reliability of walk is one of the most important goals. This paper proposes a walk control consisting of a feedforward dynamic pattern and a feedback sensory reflex. The dynamic pattern is a rhythmic and periodic motion, which satisfies the constraints of dynamic stability and ground conditions, and is generated assuming that the models of the humanoid and the environment are known. The sensory reflex is a simple, but rapid motion programmed in respect to sensory information. The sensory reflex we propose in this paper consists of the zero moment point reflex, the landing-phase reflex, and the body-posture reflex. With the dynamic pattern and the sensory reflex, it is possible for the humanoid to walk rhythmically and to adapt itself to the environmental uncertainties. The effectiveness of our proposed method was confirmed by dynamic simulation and walk experiments on an actual 26-degree-of-freedom humanoid. Index Terms Biped walk, humanoid robot, pattern generation, sensory reflex. I. INTRODUCTION HUMANOID robots involve many technical issues to be solved, among which a stable and reliable biped walk is the most fundamental, and yet unsolved with a high degree of reliability. This subject has been studied mainly from the following two technical points of view. The first approach is to generate dynamically consistent walking patterns. Most of this approach is done offline, assuming the known models of the robot and the environment. Takanishi et al. [2], Hirai et al. [3], and Shin et al. [4] have proposed the methods of pattern synthesis based on the zero moment point (ZMP) offline. Recently, Kajita et al. [5], Lim et al. [6], and Nishiwaki et al. [7] discussed the methods of online pattern generation. The ZMP was originally defined for ground contacts of legs by Vukobratovic [1] as the point in the ground plane about which the total moments due to ground contacts become zero in the plane. It is important to recognize that the ZMP must always reside in the convex hull of the all contact points on the ground plane (see Appendix A), which is due to the fact that the normal forces at the contact points are always positive in the upper vertical direction. Therefore, only Manuscript received February 6, 2004; revised June 21, 2004 and November 24, This paper was recommended for publication by Associate Editor S. Ma and Editor I. Walker upon evaluation of the reviewers comments. This work was supported in part by the Robot Brain Project under the Core Research for Evolutional Science and Technology (CREST) Program of the Japan Science and Technology Agency. This paper was presented in part at the IEEE International Conference on Robotics and Automation, Seoul, Korea, May Q. Huang is with the Department of Mechatronic Engineering, Beijing Institute of Technology, Beijing , China ( qhuang@bit.edu.cn). Y. Nakamura is with the Department of Mechano-Informatics, University of Tokyo, Tokyo , Japan ( nakamura@ynl.t.u-tokyo.ac.jp). Digital Object Identifier /TRO if the ZMP stays in the convex hull of the ground contacts, the planned walk motion is dynamically possible for the humanoid. The above works first design a desired ZMP trajectory, then derive a hip or body motion that comprises with the desired ZMP trajectory. Since the body motion is limited, not every desired ZMP trajectory can be achieved [8]. In addition, to achieve the desired ZMP trajectory, the body acceleration may need to be large. Huang et al. [9] proposed a method to generate walk patterns with smooth body motion, simultaneously taking account of the ZMP constraints and the limitation of the body motion. The second approach is from the controller design point of view. Furusho et al. [10] and Fujimoto et al. [11] have discussed control methods based on the dynamical equations of motion. These methods demand high computation resources for realtime implementation. To ease real-time implementation, some researchers discussed the control methods based on simplified models [3], [12] [17]. For example, Hirai et al. [3] and Takenaka [17] proposed a stabilizing walk control using an inverted pendulum model, and its effectiveness has been confirmed by excellent demonstrations of Honda humanoid robots, such as P2, P3, and ASIMO. Yamaguchi et al. [18] developed a foot mechanism with a shock-absorbing material to adapt to uneven ground surfaces. Kun et al. [19] and Hu et al. [20] discussed adaptive control of biped robots using neural networks. Biological investigations suggest that a human s rhythmic walking is the consequence of combined inherent patterns and reflexive actions [22], [23]. The inherent patterns are rhythmic and periodic. They are considered as feedforward motion patterns acquired through the development in the typical walk environments. The reflexive actions are rapid local responses to sensory input. They are locally and distributively programmed in the human nerve system, and hierarchically organized to deal with sudden events, such as unexpected external disturbances and unknown ground irregularity. A biped humanoid requires not only a rhythmic walk in a known environment, but also adaptation to real-world uncertainties. It is, therefore, essential to design a human-like walk control taking account of inherent patterns and sensory reflexes. Although many papers have been published on the reflexive control in robotics, most of them were concerned with manipulators [24], [25] and mobile robots [26], [27]. Only a few researchers studied the reflexive control on legged robots; for example, Boone and Hodgins [28] have applied the reflexive control to overcome shipping and tripping for a hopping robot with a body and two telescoping legs, and Kimura et al. [29] have proposed a method combining a central pattern generator (CPG) and reflexes for quadruped locomotion. However, the biped-walk motion and the mechanism of the biped humanoid robot are different from those of the hopping robot and the /$ IEEE

2 978 IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 5, OCTOBER 2005 Fig. 2. Dual structure of walking control. Fig. 1. Biped humanoid with 26 DOFs. quadruped robot. The issue of improving the stability and reliability of the humanoid walk by exploiting reflexive actions has rarely been studied in previous literature. This paper explores designing the fundamental reflexive actions combining dynamic patterns for humanoid walking. The sensory reflex presented in this paper requires no explicit modeling, and has the advantage of quickly dealing with unexpected sudden events. The organization of this paper is as follows. In Section II, the scheme of walk control with a feedforward dynamic pattern and a feedback sensory reflex is presented, and the method of the dynamic pattern is outlined in Section III. In Section IV, we design a sensory reflex consisting of a ZMP reflex, a landing-phase reflex, and a bodyposture reflex based on sensory information. Experiments were conducted using a 26-degree-of-freedom (DOF) humanoid, and the results are provided in Section V, followed by the conclusions in Section VI. II. COORDINATION SCHEME OF DYNAMIC PATTERN AND SENSORY REFLEX The humanoid consists of a body, legs, and arms (Fig. 1). Each leg is composed of a thigh, shank, and foot, and of six DOFs in total, three of which are located in the hip joint, one in the knee joint, and two in the ankle joint. Each arm is composed of an upper arm, forearm, and hand of seven DOFs in total, three of which are located in the shoulder joint, one in the elbow joint, and three in the wrist joint. The human acquires the inherent walking patterns through development and repeated refinement by learning and practice. The humanoid robot without such a process has to make the best use of the knowledge of dynamics to generate a rhythmic and dynamic walk pattern. It is not straightforward to compute the dynamic walk pattern online, since its equations considering the dynamics of the whole body are nonlinear coupled differential equations [2]. Therefore, the dynamic walk-pattern generation generally requires an optimization process offline. The dynamic walk pattern can be considered as a feedforward motion in known typical environments. On the other hand, the sensory reflex is a quick response requiring little or no explicit modeling. It has the advantage of quickly dealing with unexpected sudden events. However, without taking account of the whole dynamics of the humanoid robot, the sensory reflex is a local feedback. It is, therefore, desirable to combine the sensory reflex only in the case when there are unexpected sudden events. The coordination of the dynamic pattern and the sensory reflex is concluded as keeping the dynamic pattern in known typical environments and stimulating the sensory reflex only when unexpected events occur. Fig. 2 shows the walk structure consisting of a feedforward dynamic pattern and a feedback sensory reflex. Let be the input command of one joint angle where is the value of the joint angle specified by the dynamic pattern, generated offline in this paper. is the value of the sensory reflex, and changes according to environmental conditions. For example, if the actual environmental conditions are the same as the assumed conditions when the dynamic pattern is generated offline, the sensory reflex is zero, and the humanoid walks in the dynamic pattern. If there are unexpected factors, such as an unexpected collision during walking, is not zero, and then the humanoid walks in a modified pattern. After the collision, becomes gradually zero, and the robot will return to the walk of the dynamic pattern. III. DYNAMIC WALKING PATTERN To ensure the reliability of a walk for a biped humanoid, the walking pattern must satisfy the constraints of dynamic stability. Some stability criteria, such as the foot rotation indicator (FRI) [30] and the generalized ZMP (GZMP) [31], were proposed for the walking stability of gait generation, and the concept of ZMP is used for the stability criterion in this paper. In addition, to be able to walk on various grounds such as level ground, rough terrain, and obstacle-filled environments, the ground constraints must be satisfied. We have already proposed a method for planning such walking patterns [9], and briefly outline here. (1)

3 HUANG AND NAKAMURA: SENSORY REFLEX CONTROL FOR HUMANOID WALKING 979 single-support phase, respectively (Fig. 3), the following equation can be obtained: (3) By using third-order spline interpolation, the trajectory of that satisfies the constraint (3) and the constraint of second derivative continuity can be obtained. Hence, a series of smooth are obtained by setting different values of and within fixed ranges, in particular,. Then, the smooth trajectory with the largest stability margin can be found by exhaustive search calculation. Fig. 3. Walking parameters. To simplify the analysis, only sagittal plane walking will be discussed in the following. For a sagittal plane, let vector denote each foot trajectory, and let vector denote the hip trajectory (Fig. 3). Supposing that the period necessary for one walking step is, the th walking step begins with the heel of the right foot leaving the ground at, and ends with the heel of the right foot touching the ground at. The characteristic constraints of the right foot slope are given by the following equations: where and be the designated slope angles of the right foot as it leaves and lands on the ground (Fig. 3), denotes the interval of the double-support phase, and and are the angles of the ground surface under the support foot. To generate a smooth trajectory, it is necessary that the second derivatives (accelerations) be continuous at all, including all breakpoints.to solve for the foot trajectory that satisfies constraint (2) and the constraints of second derivative continuity, third-order spline interpolation was used [32]. Similarly, and can be obtained. By setting the values of, and other parameters, such as clearance and stride length, different foot trajectories can be produced. To get high stability and smooth body motion along the axis, the following steps were considered: 1) generate a series of smooth ; 2) determine the final with a large stability margin. during a one-step cycle can be described by the doublesupport phase and the single-support phase functions. Letting and denote distances along the axis from the hip to the ankle of the support foot at the beginning and the end of the (2) IV. SENSORY REFLEX In general, if the ZMP of actual walking resides in the stable region, it is possible for the robot to walk. However, the robot may suddenly become unstable and begin to tip over when there are unexpected sudden events. In that case, the ZMP becomes uncontrollable, since the contact force between the ground and the feet cannot provide the necessary recovery moment to control the ZMP. For example, in the case when the actual ground surface is lower than the assumed surface for the planned dynamic pattern, the swing foot will land on the ground more slowly than the designed time of the planned dynamic pattern, which results in the humanoid tipping forward immediately. In addition, when the humanoid becomes unstable, the humanoid body slants from the desired body inclination. Thereafter, the body inclination is called the body posture. If the body posture is not recovered in time, the tipping moment becomes large and the body slanting increases continuously, which results in the humanoid tipping fast. To ensure the stability of actual walking, it is, therefore, desirable to control not only the ZMP, but also the parameters of the landing time and the body posture online. The sensory reflex presented in this section consists of a ZMP reflex, a landing-phase reflex, and a body-posture reflex. The three sensory reflexes are independent, and become active when their conditions are satisfied. The developed humanoid robot (Fig. 1) has sensory devices including a foot-force sensor, the body-inclination sensors, and joint encoders. The assumptions for the sensory reflex are given as follows: 1) the unexpected irregularities can be detected by the humanoid sensors; 2) the noise of sensors used for the sensory reflex can be filtered, and their responses are fast enough for the realtime control. A. ZMP Reflex The ZMP reflex is to control the ZMP of actual walking online. The actual ZMP is measured by a foot-force sensor. Generally, only one edge of the foot sole is in contact with the ground during humanoid tipping, for example, only the toe is in contact with the ground when the humanoid tips forward. Viewed from the concept of the ZMP, in those cases, the actual ZMP is on the toe, that is, the actual ZMP is on the boundary of the stable region. To avoid having only one edge of the foot sole contacting the ground, there should be some distance between the actual

4 980 IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 5, OCTOBER 2005 Fig. 4. Stable region and desired stable region. Fig. 6. Landing-phase reflex of foot position. (a) Landing on ground too fast. (b) Landing on ground too late. that is, the foot is in contact with the ground, the ankle joint of this foot is used to control the actual ZMP. If, the foot becomes the swing foot, and the ankle joint of this foot returns to the value of its dynamic pattern gradually. Fig. 5. ZMP reflex and body-posture reflex. ZMP and the boundary of the stable region. In the following, this distance during actual walking is called the actual stability margin. If the actual ZMP is always controlled in the center of the stable region, the actual stability margin is the largest. But in that case, the robot cannot move at high speed. In addition, if the actual stability margin is designated to be larger than the stability margin of the dynamic pattern, it is impossible for the humanoid to walk in the dynamic pattern. To keep walking in the dynamic pattern as possible, the actual stability margin is specified to be the same as the stability margin of the dynamic pattern. Thereafter, the region with such a stability margin is called the desired stable region (Fig. 4). One effective way to keep the actual ZMP within the desired stable region is to control the ankle joints of the support feet (Fig. 5). In the case when the actual ZMP is within the desired stable region, the ZMP reflex is not active. In the case when the actual ZMP is outside the desired stable region, the ZMP reflex is active, and the ankle joint realizing the ZMP reflex is calculated using the following equation: where is the sample period of the servo loop, and is the current time. is the distance between the actual ZMP and the boundary of the desired stable region (Fig. 4), and are coefficients. is the foot contact force with the ground, which is measured by a foot-force sensor. If, (4) (5) B. Landing-Phase Reflex The humanoid may suddenly become unstable if the swing foot cannot land on the ground in time for unexpected ground irregularities. For example, the ground surface is assumed to be level when the dynamic pattern is generated, but the actual ground surface is unknown rough terrain. In the case when the actual ground surface is higher than the assumed surface of the planned dynamic pattern [Fig. 6(a)], the swing foot lands on the ground faster than the designed time of the planned dynamic pattern, then the moment of tipping backward occurs, and the robot will tip backward. Conversely, the foot lands on the ground too slowly when the actual ground surface is lower than the assumed surface [Fig. 6(b)], the moment of tipping forward increases, and the robot will tip forward. The landing-phase reflex is to control the swing foot landing on the ground at a desired time online. In the case when the swing foot lands on the ground too fast, the robot lifts its foot. The increase of foot height to realize the landingphase reflex is given as follows: where are coefficients, and is an approximate value of the weight of the humanoid. If, the support foot nearly becomes the single-support foot, then the foot height returns to the value of the dynamic pattern. In the case when the swing foot lands on the ground too late, the robot lowers its foot to land on the ground. The increase of foot height to realize the landing-phase reflex is given as follows: where is a constant variable. The online change of foot height is achieved by controlling the hip and knee joints according to the kinematics. (6) (7) (8) (9)

5 HUANG AND NAKAMURA: SENSORY REFLEX CONTROL FOR HUMANOID WALKING 981 Fig. 7. Walking on a known level ground. (a) Virtual humanoid. (b) Actual humanoid. C. Body-Posture Reflex From the viewpoint of stability, it is desirable that the body posture is constant when there is no waist joint. The actual body posture is measured by inclination sensors, such as accelerometers and angular rate sensors. When the humanoid begins to tipping over, the actual body posture slants from its desired body posture. As the slanting increases, the tipping moment becomes larger. The body-posture reflex is to control the actual body posture to be the desired body posture online. Since the hip joints are near the body, the most effective way to keep the desired body posture is to control the hip joints (Fig. 5). The hip joint to realize the body-posture reflex is given as follows: (10) (11) where is the deflection between the actual body posture and the desired body posture, and is the coefficient. If, the foot is in contact with the ground, and the hip joint of this foot is used to control the body posture. On the other hand, if, the foot is the swing foot, and its hip joint does not affect the body posture. In this case, the hip joint of the swing foot returns to the value of the dynamic pattern. V. SIMULATION AND EXPERIMENT In this section, we provide the examples of simulation and experiment to test our proposed method. The humanoid may tip over during walking, so actual humanoid experiments carrying developing control algorithms are dangerous and costly. It is desirable and effective to verify various control algorithms using a software simulator before using an actual humanoid, especially for some dangerous experiments. Therefore, we have developed a dynamic simulator [33] including dynamics, geometry, actuators, controllers, and environmental factors using dynamic analysis and design systems (DADS). To evaluate the equivalence of our constructed simulator and the actual humanoid robot, we did some walking experiments by using the virtual humanoid robot and the actual humanoid robot. Parameters of the virtual humanoid robot are set as the same as the actual humanoid robot. The humanoid robot has 26 DOFs with a 0.5-m height and a 7.5-kg weight. The humanoid robot has sensory devices including force/torque sensors, accelerometers, and gyrosensors. The force/torque sensors are located on each foot to detect the contact force between the feet and the ground. The accelerometer and the gyrosensors are located on body to measure the body inclination relative to the gravitational direction. Figs. 7 and 8 show the walk on a known level ground with the step length 0.12 m/step and step period 1.8 s/step. Although the roll angle of the real humanoid body is larger than the virtual humanoid body [Fig. 8(a)], the change in both cases are positive and negative similarly at the same periods, that is, the real humanoid body and the virtual humanoid body slant right and left similarly during walking. The vibration of the pitch angle of the real humanoid is larger than the virtual humanoid [Fig. 8(b)], but the angles of both cases are almost positive, which means the real humanoid and the virtual humanoid slant backward during walking. Therefore, the biped walking of the virtual humanoid robot was similar to the biped walking of the actual humanoid robot. In addition, the main reason for the difference between the real humanoid and the virtual humanoid walking is that the exact model of the mechanical stiffness of the real humanoid is difficult to obtain. Fig. 9 shows the walk of the virtual humanoid in an environment with a disturbance. The disturbance is assumed to be the unexpected collision between a pendulum and the humanoid robot. Different collision forces add on the humanoid robot with different mass of the pendulum. The desired-body angle of the

6 982 IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 5, OCTOBER 2005 Fig. 8. Humanoid body angles during walking...: virtual humanoid; -: real humanoid. (a) Body roll angle. (b) Body pitch angle. planned dynamic pattern is zero, that is, the desired body posture is upright. In this simulation, there are three time collisions during walking, and the left foot is the support foot at collisions. From Fig. 9(b) and (c), it is known that the body posture and the hip joint change radically at collisions, and can be explained as follows. The robot body slants backward radically due to collisions [Fig. 9(b)], that is, the body posture (the pitch angle) becomes positive radically. According to the body-posture reflex, the hip joint of the support foot should be controlled to recover its desired body posture rapidly, so the hip joint of the left foot becomes positive radically [Fig. 9(c)]. Fig. 10 shows the experimental results on unknown rigid rough ground with a 0.01-m height obstacle. The humanoid robot can walk stably by using our proposed walking control. The foot-height increase to realize the landing-phase reflex [Fig. 10(b)] can be explained as follows. If the humanoid robot walks the same as the planned dynamic pattern, the depth of penetration between the landing foot and the ground is about 0.01 m when landing on the ground. If that were the case, and a very large foot contact force occurs, the humanoid robot will tip backward. Therefore, the humanoid robot must lift its foot higher than the planned walking pattern, that is, the foot-height increase becomes positive when landing. After the foot lands on the ground and becomes the single-support foot, the humanoid robot should return to its dynamic walking pattern gradually, and therefore, the becomes zero gradually. This also can be observed from the change of the knee joint. Fig. 9. Results of walking in an environment with a disturbance. (a) Hit by a pendulum during walking. (b) Body posture. (c) Hip 1 (t) of left foot. The solid curve of the modified pattern, with combining the dynamic pattern and the sensory reflex, becomes negative larger than the dotted curve of the dynamic pattern when starting in contact with the obstacle [Fig. 10(c)], which means the knee joint of modified motion bends more than the planned dynamic pattern, so as to lift the foot. VI. CONCLUSION In this paper, we focused on stable and reliable walking for a biped humanoid robot. The results of this paper are summarized as follows. 1) A walk control consisting of a feedforward dynamic pattern and a feedback sensory reflex was proposed.

7 HUANG AND NAKAMURA: SENSORY REFLEX CONTROL FOR HUMANOID WALKING 983 APPENDIX A ZMP CRITERION The ZMP can be computed using the following equations [9]: (12) (13) where is the mass of link and are the inertial components, and are the absolute angular velocity components around axis and axis at the center of gravity of link is the gravitational acceleration, is the coordinate of the ZMP, and is the coordinate of the mass center of link on an absolute Cartesian coordinate system. If the ZMP is within the convex hull of all contact points (the stable region), it is possible for the biped humanoid robot to walk. Fig. 10. Walking on unknown rough terrain. (a) Humanoid walking. (b) Foot height increase. (c) Dynamic pattern and modified motion of knee joint. The dynamic pattern is a rhythmic and periodic motion, considering the whole dynamics of the humanoid. The sensory reflex is a quick local feedback control to sensor input requiring no explicit modeling. 2) The sensory reflex consists of a ZMP reflex, a landingphase reflex, and a body-posture reflex. These reflexive actions are online hierarchically organized to satisfy the dynamic stability constraint, to guarantee to land on the ground in time, and to keep a stable body posture for humanoid walking. 3) The effectiveness of our proposed method was confirmed through walks on unknown rough terrain, and in an environment with disturbances by a dynamic simulator and an actual humanoid. REFERENCES [1] M. Vukobratovic and D. Juricic, Contribution to the synthesis of biped gait, IEEE Trans. Biomed. Eng., vol. BME-16, no. 1, pp. 1 6, [2] A. Takanishi, M. Ishida, Y. Yamazaki, and I. Kato, The realization of dynamic walking robot WL-10RD, in Proc. Int. Conf. Adv. Robot., 1985, pp [3] K. Hirai, M. Hirose, Y. Haikawa, and T. Takenaka, The development of Honda humanoid robot, in Proc. IEEE Int. Conf. Robot. Autom., 1998, pp [4] C. L. Shin, Y. Z. Li, S. Churng, T. T. Lee, and W. A. Cruver, Trajectory synthesis and physical admissibility for a biped robot during the single-support phase, in Proc. IEEE Int. Conf. Robot. Autom., 1990, pp [5] S. Kajita, O. Matsumoto, and M. Saigo, Real-time 3-D walking pattern generation for a biped robot with telescopic legs, in Proc. IEEE Int. Conf. Robot. Autom., 2001, pp [6] H. Lim, Y. Kaneshima, and A. Takanishi, On-line walking pattern generation for biped humanoid robot with trunk, in Proc. IEEE Int. Conf. Robot. Autom., 2002, pp [7] K. Nishiwaki, S. Kagami, Y. Kuniyoshi, M. Inaba, and H. Inoue, Online generation of humanoid walking motion based on fast generation method of motion pattern that follows desired ZMP, in Proc. IEEE Int. Conf. Intell. Robots Syst., 2002, pp [8] Q. Huang, S. Sugano, and K. Tanie, Stability compensation of a mobile manipulator by manipulator motion: Feasibility and planning, Adv. Robot., vol. 13, no. 1, pp , [9] Q. Huang, K. Yokoi, S. Kajita, K. Kaneko, N. Koyachi, H. Arai, and K. Tanie, Planning walking patterns for a biped robot, IEEE Trans. Robot. Autom., vol. 17, no. 3, pp , Jun [10] J. Furusho and A. Sano, Sensor-based control of a nine-link biped, Int. J. Robot. Res., vol. 9, no. 2, pp , [11] Y. Fujimoto, S. Obata, and A. Kawamura, Robust biped walking with active interaction control between foot and ground, in Proc. IEEE Int. Conf. Robot. Autom., 1998, pp [12] Y. F. Zheng and J. Shen, Gait synthesis for the SD-2 biped robot to climb sloping surface, IEEE Trans. Robot. Autom., vol. 6, no. 1, pp , Feb [13] A. Takanishi, T. Takeya, H. Karaki, and I. Kato, A control method for dynamic biped walking under unknown external force, in Proc. IEEE Int. Workshop Intell. Robots Syst., 1990, pp [14] S. Kajita and K. Tani, Adaptive gait control of a biped robot based on real-time sensing of the ground profile, in Proc. IEEE Int. Conf. Robot. Autom., 1996, pp [15] J. H. Park and H. C. Cho, An on-line trajectory modifier for base link of biped robots to enhance locomotion stability, in Proc. IEEE Int. Conf. Robot. Autom., 2000, pp

8 984 IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 5, OCTOBER 2005 [16] T. Sugihara, Y. Nakamura, and H. Inoue, Realtime humanoid motion generation through ZMP manipulation based on inverted pendulum control, in Proc. IEEE Int. Conf. Robot. Autom., 2000, pp [17] T. Takenaka, Attitude Stabilization Control System for a Legged Mobile Robot, U.S. Patent , Oct. 17, [18] J. Yamaguchi, N. Kinoshita, A. Takanishi, and I. Kato, Development of a dynamic biped walking system for humanoid Development of a biped walking robot adapting to the humans living floor, in Proc. IEEE Int. Conf. Robot. Autom., 1996, pp [19] A. Kun and W. Miller, Adaptive dynamic balance of a biped robot using neural networks, in Proc. IEEE Int. Conf. Robot. Autom., 1996, pp [20] J. Hu, J. Pratt, and G. Pratt, Adaptive dynamic control of a biped walking robot with radial basis function neural networks, in Proc. IEEE Int. Conf. Robot. Autom., 1998, pp [21] Q. Huang, Y. Nakamura, and T. Inamura, Humanoids walk with feedforward dynamic pattern and feedback sensory reflection, in Proc. IEEE Int. Conf. Robot. Autom., 2000, pp [22] L. M. Nashner, Balance adjustments of humans perturbed while walking, J. Neurophysiol., no. 44, pp , [23] V. T. Inman, H. J. Ralston, and F. Todd, Human Walking. Baltimore, MD: Willams & Wilkins, [24] C. Wu, K. S. Hwang, and S. L. Chang, Analysis and implementation of a neuromuscular-like control for robotic compliance, IEEE Trans. Control Syst. Technol., vol. 5, no. 6, pp , Nov [25] S. W. Weng and K. Y. Young, An impact control scheme inspired by human reflex, J. Robot. Syst., vol. 13, no. 12, pp , [26] W. S. Newman, Automatic obstacle avoidance at high speeds via reflex control, in Proc. IEEE Int. Conf. Robot. Autom., 1989, pp [27] H. C. Wong and D. E. Orin, Reflex control of the prototype leg during contact and slipping, in Proc. IEEE Int. Conf. Robot. Autom., 1988, pp [28] G. N. Boone and J. K. Hodgins, Slipping and tripping reflexes for bipedal robots, Auton. Robots, vol. 4, pp , [29] H. Kimura and Y. Fukuoka, Adaptive dynamic walking of a quadruped robot using neural system model, Adv. Robot., vol. 15, no. 8, pp , [30] A. Goswami, Foot rotation indicator (FRI) point: A new gait planning tool to evulaute postural stability of biped robots, in Proc. IEEE Int. Conf. Robot. Autom., 1999, pp [31] K. Harata, S. Kajita, K. Kaneko, and H. Hirukawa, Pushing manipulation by humanoid considering two kinds of ZMPs, in Proc. IEEE Int. Conf. Robot. Autom., Sep. 2003, pp [32] B. D. Bojanov, H. A. Hakopian, and A. A. Sahakian, Spline Function and Multivariate Interpolation. Norwell, MA: Kluwer, [33] Q. Huang, Y. Nakamura, H. Arai, and K. Tanie, Development of a biped humanoid simulator, in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst., 2000, pp Qiang Huang was born in Hubei, China, in He received the B.S. and M.S. degrees in electrical engineering from Harbin Institute of Technology, Harbin, China, and the Ph.D. degree in mechanical engineering from Waseda University, Tokyo, Japan, in 1986, 1989, and 1996, respectively. In 1996, he jointed the Mechanical Engineering Laboratory (MEL), Ministry of International Trade and Industry (AIST-MITI), Tsukuba, Japan, as a Research Fellow, and was a Researcher of Core Research for Evolutional Science and Technology (CREST) of the Japan Science and Technology Corporation (JST) at the University of Tokyo, Tokyo, Japan, from 1999 to Currently, he is a Professor with the Department of Mechatronics, Beijing Institute of Technology, Beijing, China. His research interests include biped walking robots, and humanoid and mobile manipulators. He has published about 100 refereed papers in several domestic and international academic journals and the proceedings of international conferences. Dr. Huang is a member of the IEEE Robotics and Automation Society. Yoshihiko Nakamura (M 87) was born in Osaka, Japan, in He received the B.S., M.S., and Ph.D. degrees from Kyoto University, Kyoto, Japan, in precision engineering in 1977, 1978, and 1985, respectively. He was an Assistant Professor at the Automation Research Laboratory, Kyoto University, from 1982 to He joined the Department of Mechanical and Environmental Engineering, University of California, Santa Barbara (UCSB), in 1987 as an Assistant Professor, and became an Associate Professor in He was also the Co-Director of the Center for Robotic Systems and Manufacturing at UCSB. Since 1991, he has been with Department of Mechano-Informatics, University of Tokyo, Tokyo, Japan, and is currently a Professor. His fields of research include redundancy in robotic mechanisms, nonholonomy of robotic mechanisms, kinematics and dynamics algorithms, computer graphics computation, nonlinear dynamics, brain-like information processing, and medical robotic systems. He served as the PI of Brain-like Information Processing for Humanoid Robots ( ) under the CREST project of the Japan Science and Technology Corporation. His book publications include Advanced Robotics: Redundancy and Optimization (Reading, MA: Addison-Wesley, 1991), Building the Robot Brain (Tokyo, Japan: Iwanami Shoten, 2003, in Japanese), and Robot Motion (Tokyo, Japan: Iwanami Shoten, 2004, in Japanese, with M. Uchiyama). Dr. Nakamura received the Excellent Paper Awards from the Society of Instrument and Control Engineers (SICE) in 1985, from the Artificial Intelligence Society of Japan in 2003, and from the Robotics Society of Japan in 1996, 2000, and He was a recipient of King-Sun Fu Memorial Best Transactions Paper Award, IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, in 2001 and Dr. Nakamura also received the International 3-D Award for Technological Innovation in He is a member of the IEEE Robotics and Automation Society, ASME, SICE, the Japan Robotic Society, the Japan Society of Mechanical Engineers, the Institute of Systems, Control, and Information Engineers, the Japan Society of Computer Aided Surgery, and Japan Council of IFToMM.