Research on 3D Walking of Oscillator-Based Passive Biped Robot

Research on 3D Walking of Oscillator-Based Passive Biped Robot Xizhe Zang, Lin Wang, Yi-Xiang Liu, Sajid Iqbal 2015 International Conference on Mechanics and Control Engineering (MCE 2015) ISBN: 978-1-60595-219-2 2015 International Conference on Mechanics and Control Engineering (MCE 2015) ISBN: 978-1-60595-219-2 Research on 3D Walking of Oscillator-Based Passive Biped Robot Xi-Zhe ZANGa,*, Lin WANG, Yi-Xiang LIU, and Sajid IQBAL State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, China a zangxizhe@hit.edu.cn *Corresponding author Keywords: Passive Biped Robot, 3D Walking, Oscillator, Influencing Factors. Abstract. The passive biped robot has lots of advantages such as natural gait, high energy efficiency and simple control method, becoming one of hot contents in robotics research. Nowadays the researches of passive biped robot mainly focus on 2D walking in the sagittal plane and less attention is paid on 3D walking. To improve 3D walking stability of passive biped robots, a model of passive biped robot with oscillator was proposed to study the motion characteristics and influencing factors of the lateral swinging in the coronal plane. Finally, the comparative experiments of the prototype robot with the oscillator or not were conducted, which proved that the oscillator was useful in regulating the walking of the passive robot. Introduction Similar to human walking, 3D walking of the passive biped robot can be divided into the forward motion in the sagittal plane, the roll motion in the coronal plane and the yaw motion in the transversal plane [1]. The forward motion in the sagittal plane is the main motion of the biped robot; the roll motion in the coronal plane is mainly to increase the clearance between the foot of the swing leg and the ground; besides, the roll motion can also make the walking motion more natural; the yaw motion plays a small role in the walking motion so that the paper does not work on it. According to the existing research results [1, 2, 3], only when the forward and roll motion are compatible can the biped robot walk stably. Since the roll motion can not be maintained within a stable cycle, the passive biped robot can not walk stably. To study the movement mechanism and stability of 3D walking of the passive biped robots, a model of passive biped robot with oscillator in the robot hip was proposed. Under this circumstance, the roll motion in the coronal plane can be controlled through the dynamic adjustment of the oscillator to cooperate with the forward motion in the sagittal plane. Analysis of the Motion Characteristics in the Coronal Plane of the Robot with the Oscillator Similar to the humans, the walking of the passive biped robot comes in strict cycles. Since the coupling between the forward motion in the sagittal plane and the roll motion in the coronal plane is small, the motions in the sagittal and coronal plane can be studied individually. This paper focuses the roll motion in the coronal plane. Fig. 1 shows the coordinate system in the coronal plane. In this figure, the horizontal plane where the origin O lies in is treated as the zero potential energy surface, A is the center of the foot circle in the coronal plane, B is the center of mass of the robot, C is the center of mass of the oscillator, R is the radius of the robot foot, l is the length of the robot leg, a is the distance between the hip and the center of mass of the robot, b is the displacement of the oscillator relative to the hip, α is the angle of the lateral swinging, β is the angle among center of the foot circle, the inside edge of the foot and the center of mass of the robot, mB is the mass of the robot, mC is the mass of the oscillator, JR is the moment of inertia of the robot, JO is the moment of inertia of the oscillator about its center of mass and m1 is the mass of the robot leg. Besides, since there are so many relevant parameters of the robot and they have different orders of magnitude, this paper handles these parameters with dimensionless processing. Table 1 shows the procedure of dimensionless processing. According to the existing results [4-7], these parameters are set preliminarily as the basic model. The result is shown in Table 2. Figure 1. Coordinate system in the coronal plane. Table 1. The dimensionless processing of robot parameters. Original symbols Dimensionless processing Dimensionless symbols mB a b mC JR JO R t mB/ml a/l b/l mC/ml JR/(ml×l2) JO/(ml×l2) R/l t / l/g kmB ka kb kmC kJR mJO kR τ Table 2. The parameters of basic model in the coronal plane. Parameters Value kmB 2.8 kJR 0.6 ka 0.25 kR 1.4 β 0.02 kmC 0.6 mJO 0.01 The lateral swinging in the coronal plane of the passive robot is a typical inverted pendulum motion. The motion characteristics of the lateral swinging are relevant to the mass of robot, moment of inertia, the position of the center of mass, the radius of foot and so on. As the movement of the robot, the energy of the lateral swinging is lost through the friction and collision between the robot foot and the ground. Unlike the forward motion in the sagittal plane, the lost energy of the lateral swinging in the coronal plane can not be supplemented by the gravity potential energy so the lateral swinging can not stay at a fixed point naturally. As the previous discussion, only when the forward and roll motion are compatible can the biped robot walk stably so the oscillator is added to the hip of the robot to adjust the cycle of the roll motion and supplement the energy of the lateral swinging. When the oscillator is added to the robot, the robot has become the dynamic system of double rigid body in the coronal plane. The movement of the oscillator can be controlled while that of the robot can not so the movement of the robot is actually the forced vibration influenced by the movement of the oscillator. Since the sine movement is simple and easy to realize, the movement of the oscillator is set as sine movement. According to the relative calculation, the movement cycle of basic model of the robot in the sagittal plane TO is 5.655. Through the relative simulation, the amplitude of the movement AO is set as 0.25 so the equation of the movement of the oscillator is given by b=AO sin((2π/TO)τ) The movement state of the robot in the coronal plane can be described by α and α , namely (1) x  [ , ]T (2) The stable fixed point of the robot in the coronal plane can be obtained by continuous integration and the result is x*  [0,0.2457]T (3) The motion in the coronal plane can be solved through the fixed point and the max angle of swinging in the coronal plane Ψ is 0.2141 and the cycle T is 5.6550, which is consistent with the walking cycle in the sagittal plane. The change of the state variables is shown in Fig. 2. (a) Angle of swinging (b) Angular velocity of swinging (c) Phase diagram of swinging Figure 2. The motion curves of the lateral swinging of the basic model. These curves show that the curve of the angle of the lateral swinging is similar to sine curve and the curve of the angular velocity is similar to cosine wave. Besides, the phase trajectories converge to one-periodic limit cycle. Analysis of the Influencing Factors of Lateral Swinging in the Coronal Plane To study the influence of the characteristics of the robot on the lateral swinging, this paper set the max angle of swinging in the coronal plane Ψ and initial angular velocity of lateral swinging α as the movement state. In this paper, kR, kJR, ka, β, kmC, mJO, AO and TO are analyzed to study their influence on the lateral swinging. The related parameters are listed in Table 3 and the underlined variables are reduced by 15%. The parameters are analyzed through dynamic equations and the results are shown in Fig. 3. According to the figure, kR, TO and AO are the main influencing factors so the oscillator plays an important role in regulating the lateral swinging of the robot. Figure 3. The influence of the parameters on lateral swinging. Table 3. The related parameters combination. Parameters Basic model kR kJR ka β kmC mJO AO TO kR 1.4 1.19 1.4 1.4 1.4 1.4 1.4 1.4 1.4 kJR 0.6 0.6 0.51 0.6 0.6 0.6 0.6 0.6 0.6 ka 0.25 0.25 0.25 0.2125 0.25 0.25 0.25 0.25 0.25 β 0.02 0.02 0.02 0.02 0.017 0.02 0.02 0.02 0.02 kmC 0.6 0.6 0.6 0.6 0.6 0.51 0.6 0.6 0.6 mJO 0.01 0.01 0.01 0.01 0.01 0.01 0.0085 0.01 0.01 AO 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.2125 0.25 TO 5.6550 5.6550 5.6550 5.6550 5.6550 5.6550 5.6550 5.6550 4.8068 Design of the Prototype Robot and 3D Walking Experiment To study the influence of the oscillator on the walking of the robot, the prototype is designed and the structure is shown in Fig. 4. The external size of the robot is 0.556m×0.495m×0.2m and the whole mass is 4.04kg. The robot is composed of oscillator, hip, leg and foot. The oscillator is located in the hip. The experiment of the prototype walking is shown in Fig. 5. To study the influence of the oscillator on the walking of the robot, the experiment is divided into passive walking and oscillator-motivated walking and the result is shown in Table 4. These experiments are conducted in the slope, whose angles are 1.5°, 3° and 4.5°. These experiments are conducted for 300 times individually and the result is analyzed through statistics. According to the results, the robot can not walk stably in passive condition and it can only walk for 2 steps in most cases; when the robot is equipped with the oscillator, it can walk for more than 5 steps in nearly 60% of the cases and the weighted average step is 4.8 steps. Table 4. The result of comparative experiments. Times Steps 1 2 3 4 5 6 7 Passive walking 78 216 6 / / / / Oscillator-motivated walking 9 15 27 48 96 87 18 Experiment style Figure 4. Prototype Robot. Figure 5. The walking experiment of the prototype robot. Conclusion This paper puts forward to a model of passive robot with oscillator which can walk stably. The influence of the parameters on the lateral swinging is analyzed and it is verified that the foot radius, the cycle of the sinusoidal motion and amplitude play an important part in regulating the lateral swinging. Finally, the prototype is designed and it verifies that the adding of the oscillator is beneficial to the walking stability of the passive robot. Acknowledgement This work was supported by “Independent Research of State Key Laboratory of Robotics and System (HIT)” KLRS201304B) and National Magnetic Confinement Fusion Science Program “Multi-purpose Remote Handling System with Large-scale Heavy Load Arm)” (2012GB102004). References [1] Kuo A D, Stabilization of lateral motion in passive dynamic walking, J. The International Journal of Robotics Research. 18 (1999) 917-930. 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