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1、Zero-moment point trajectory modelling of a biped walking robot using an adaptive neuro-fuzzy systemD. Kim, S.-J. Seo and G.-T. ParkAbstract: A bipedal architecture is highly suitable for a robot built to work in human e
2、nvironments since such a robot will find avoiding obstacles a relatively easy task. However, the complex dynamics involved in the walking mechanism make the control of such a robot a challenging task. The zero-moment poi
3、nt (ZMP) trajectory in the robot’s foot is a significant criterion for the robot’s stability during walking. If the ZMP could be measured on-line then it becomes possible to create stable walking conditions for the robot
4、 and here also stably control the robot by using the measured ZMP, values. ZMP data is measured in real-time situations using a biped walking robot and this ZMP data is then modelled using an adaptive neuro-fuzzy system
5、(ANFS). Natural walking motions on flat level surfaces and up and down a 10? slope are measured. The modelling performance of the ANFS is optimized by changing the membership functions and the consequent part of the fuzz
6、y rules. The excellent performance demonstrated by the ANFS means that it can not only be used to model robot movements but also to control actual robots.1 IntroductionThe bipedal structure is one of the most versatile s
7、etups for a walking robot. A biped, robot has almost the same movement mechanisms as a human and it able to operate in environments containing stairs, obstacles etc. However, the dynamics involved are highly nonlinear, c
8、omplex and unstable. Thus, it is difficult to generate a human-like walking motion. The realisation of human-like walking robots is an area of considerable activity [1–4]. In contrast to industrial robot manipulators, th
9、e interaction between a walking robot and the ground is complex. The concept of a zero-moment point (ZMP) [2] has been shown to be useful in the control of this interaction. The trajectory of the ZMP beneath the robot fo
10、ot during a walk is after taken to be an indication of the stability of the walk [1–6]. Using the ZMP we can synthesise the walking patterns of biped robots and demonstrate a walking motion with actual robots. Thus, the
11、ZMP criterion dictates the dynamic stability of a biped robot. The ZMP represents the point at which the ground reaction force is taken to occur. The location of the ZMP can be calculated using a model of the robot. Howe
12、ver, it is possible that there can be a large error between the actual ZMP value and the calculated value, due to deviations in the physical parameters between the mathematical model and the real machine. Thus, the actua
13、l ZMP should be measured especially if it is to be used in a to parameters a control method for stable walking.In this work actual ZMP data taken throughout the whole walking cycle are obtained from a practical biped wal
14、ing robot. The robot will be tested both on a flat floor and also on 10? slopes. An adaptive neuro-fuzzy system (ANFS) will be used to model the ZMP trajectory data thereby allowing its use to control a complex real bipe
15、d walking robot.2 Biped walking robot2.1 Design of the biped walking robotWe have designed and implemented the biped walking robot shown in Fig. 1. The robot has 19 joints. The key dimensions of the robot are also shown
16、in Fig. 1. The height and the total weight are about 380 mm and 1700 g including batteries, respectively. The weight of the robot is minimised by using aluminium in its construction. Each joint is driven by a RC servomot
17、or that consists of a DC motor, gears and a simple controller. Each of the RC servomotors is mounted in a linked structure. This structure ensures that the robot is stable (i.e. will not fall down easily) and gives the r
18、obot a human-like appearance. A block diagram of our robot system is shown in Fig. 2. Out robot is able to walk at a rate of one step (48 mm) every 1.4 s on a flat floor or an shallow slopes. The specifications of the ro
19、bot are listed in Table 1. The walking motions of the robot are shown in Figs. 3–6.-Figures 3 and 4 are show front and side views of the robot, respectively when the robot is on a flat surface. Figure 5 is a snapshot of
20、the robot walking down a slope whereas Fig. 6 is a snapshot of the robot walking up a slope. The locations of the joints during motion are shown inFig. 7. The measured ZMP trajectory is obtained from ten-degree-of-freedo
21、m (DOF) data as shown in Fig. 7. Two degrees of freedom are assigned to the hips and ankles and one DOF to each knee. Using these joint angles, a cyclic walking pattern has been realised. Our robot is able to walk contin
22、uously without falling down. The joint angles in the four-step motion of our robot are summarised in the Appendix.q IEE, 2005IEE Proceedings online no. 20045007doi: 10.1049/ip-cta:20045007D. Kim and G.-T. Park are with t
23、he Department of Electrical Engineering, Korea University, 1, 5-ka, Anam-dong, Seongbuk-ku, Seoul 136-701, Korea S.-J. Seo is with the Department of Electrical and Electronic Engineering, Anyang University, 708-113, Anya
24、ng dong, Manan-gu, Anyang-shi, Kyunggi-do, 430-714, KoreaE-mail: upground@korea.ac.krPaper received 20th April 2004. Originally published online 8th June 2005IEE Proc.-Control Theory Appl., Vol. 152, No. 4, July 2005 411
25、2.2 ZMP measurement systemThe ZMP trajectory in a robot foot is a significant criterion for the stability of the walk. In many studies, ZMP coordinates are computed using a model of the robotTable 1: Specifications of th
26、e robotInput Height: 300 mm, width: 225 mmWeight 1.7 kgCPU S3C3410X (ARM7 core, 16 bit, 40 MHz) embedded in robotActuator RC servo motors (torque: 11 kg cm at 4.8 V, gearsand motor controller are included in package)Degr
27、ees of freedom 19 F (two legs: 12þ upper body: seven)Power source AA size Ni-Cd battery (2100 mAh)Walking speed 48 mm=1.4 sFig. 3 Front view of the robot on a flat floorFig. 4 Side view of the robot corresponding to
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