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Self-Excited Walking of a Biped Mechanism.

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The authors studied the self-excited walking of a four-link biped mechanism that possesses an actuated hip joint and passive knee joints with stoppers. They showed that the self-excitation control enables the three-degree-of-freedom planar biped model to walk on level ground by numerical simulation. From the parameter study, it was found that stable walking locomotion is possible over a wide range of feedback gain and link parameter values and that the walking period is almost independent of the feedback gain. Various characteristics of the self-excited walking of a biped mechanism were examined in relation to leg length, and length and mass ratios of the shank. Next, a biped mechanism was manufactured similar to the analytical model. After parameter modification, the authors demonstrated that the biped robot can perform natural dynamic walking on a plane with a 0.8 degree inclination. The simulated results also agree with the experimental walking locomotion.
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Walking direction
Support leg
θ
Stopper
Swing leg
3
T
2nd phase 1st phase
3rd phase
a
al
l
θ
Link 2
θ
1
3
3
Link 3
1
θ2
Link 1
T
3
1
Walking direction
−10 0 10 20
−200
−100
0
100
Angular Position [deg]
Angular Velocity [deg/s]
t=T4
t=T0
t=T1
t=T1
t=T2
t=T3
t=T3
t=T2
+
+
+
t=T4
+
θ1 , θ3
θ1−π, θ3
θ1−π
θ3
(Support leg phase)
(Swing leg phase)
567
0.2
0.3
0.4
0.5
0.6
1.15
1.2
1.25
Feedback gain k [Nm/rad]
Velocity [m/s]
4
6
Input energy [W]
Velocity
Input energy
2
Period
Period [s]
(a)
Motor
0.4 m0.4 m
0.4 m
04812
0
0.5 Experiment Simulation
Relative Angle [rad]
time [s]
α
... It may appear to be confused, but the authors considered this as an attempt by the biped to walk. There is a well-known method for a planar biped locomotion using cyclic oscillation [7,[20][21][22][23][24][25][26]. By providing sensory feedback using foot contact to the dynamics of the nonlinear oscillator, it will be possible for the locomotion to adapt to the environment. ...
... There is a method via forced oscillation of a joint by which a passive dynamic walking can be extended to the horizontal surface [7,[20][21][22][23][24][25][26]. The authors introduced a telescopic knee joint to RW03 to provide sinusoidal oscillation, and attempted to extend 3-D PDW to a 3-D active dynamic biped walking on a horizontal surface. ...
... The leg swung forward when it lifted off the ground, because of the inclination. Some studies had shown that the variation of a telescopic knee joint can realize a 2-D biped walking on a horizontal surface in a manner similar to the PDW as mentioned above [7,[20][21][22][23][24][25][26]. Hence, the same approach had been applied to RW04. ...
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The purpose of this study is to extend the three-dimensional (3-D) passive dynamic biped walker to a 3-D dynamic biped walker, i.e., a walker that can walk on a horizontal surface based on a passive dynamic walking. A new prototype of 3-D biped walker called RW04, which has telescopic knee joints, was developed and its ability for walking was validated through some experiments. A sinusoidal oscillation, which is regarded as a central pattern generator with no sensory feedback, was provided to the knee joints to achieve the biped walking. The results showed that the biped gait of RW04 was possible only via a sinusoidal oscillation of the knee joint. Moreover, the 3-D dynamic walking gait via frequency response and zero moment point (ZMP) trajectory was also analyzed. The biped locomotion had a resonance, i.e., the frequency matched the natural frequency of the locomotion in the gain property. An "8" shaped ZMP trajectory was observed, which was found to be similar to that of the human gait. However, the simple sinusoidal oscillation had limitations such as stride reduction or discontinuation by phase difference. Therefore, in future work, more adaptable control strategy such as a sensory feedback using ZMP should be provided.
... Recently, inclusion of joint self-impact phenomenon in system modeling has been studied by a number of researchers in the fields of dynamical systems and biomechanics. They have pointed out that this phenomenon should be considered as a constraint in the governing equations [6][7][8][9][10][11]. This is despite the fact that in most studies modeling has been carried out ignoring these constraints [12][13][14][15][16][17]. ...
... In these studies, the swing leg has been modelled as a simple double pendulum. On the other hand, there have been some studies in which a linear proportional controller for a robot walking on a smooth surface has been designed when taking into account the constraint as a stopper [4,[7][8][9][10][11]. ...
... One of these approaches is that the energy which is dissipated from the system during the constraint establishment must be compensated in each gait cycle. Ono and colleagues [7][8][9] obtained the dissipated energy due to joint self-impact stopper. In order to restore the dissipated energy per cycle, a torque was applied to the hip joint model; this torque was determined by a simple proportional controller. ...
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For human walking, the swing leg is usually modeled as a double pendulum. Considering a joint self-impact constraint at the knee joint of the double pendulum model is the main difference in this study. The primary objective of this research is to propose a nonlinear Adaptive Neural Network (ANN) for this system. By using Gaussian RBF networks, asymptotically stable tracking is attained. We will use the available data of normal human walking for the desired trajectories of the hip and knee joints. By simulation of the system, we perceive that the swing leg tracks the normal human gait with a negligible and tolerable error.
... Also, the biped robots or humanoids with the human-friendly appearance are suitable for care giving companions, navigation and assistance robots (Oda et al., 2012). The understanding and development of biped walking robots have been researched since the 1970s (Ono et al., 2001). During this period, biped walking robots have transformed into biped humanoid robots through the technological development (Kim et al., 2007). ...
... Considering joint self-impact phenomenon, as a natural property, in modeling of the body can exhibit a more realistic behavior of the system. One way to consider the self-impact constraint is to assume a "stopper" at the knee joint, which was proposed in some research studies (Ono et al., 2000;Ono et al., 2001;Ono et al., 2004;Sangwan et al., 2004;Mukherjee et al., 2007;Huang et al., 2007;Hoshino et al., 2011;Zhihuan, 2011). The other way is to assume a "brake" at the knee joint, which was suggested by some other researchers (Ono et al., 2002;Ono et al., 2006). ...
... In the second technique, there was a bending angle held at the knee of the support leg. As a result, the biped model could walk faster than the fully straight support leg (stopper) model (Ono et al., 2000;Ono et al., 2001;Ono et al., 2004;Sangwan et al., 2004;Mukherjee et al. 2007;Huang et al., 2007;Hoshino et al., 2011;Zhihuan, 2011). Despite this assumption, the model included only an almost straight knee state, which does not exactly reproduce natural walking characteristics. ...
Article
Full-text available
In order to achieve the practical characteristics of natural bipedal walking, a key feature is to realize "the straight knee state of walking" during stance and swing motions. Considering a straight knee necessitates that the shank link of each leg not to undergo the rotation angles which are greater than that of the thigh link. For this purpose, various methods have been proposed; the joint self-impact constraint has been suggested for energy-efficient (natural) bipedal walking while realizing the straight knee constraint. The prominent objective of this research is to present a model based control method for trajectory tracking of a normal humanlike bipedal walking, by considering the joint self-impact constraint. To achieve this objective, the dynamical equations of motion of an unconstrained biped are taken, developed and then modified to consider the joint self-impact constraint at the knee joint. To control this complicated dynamical system, the available anthropometric normal gait cycle data are taken to generate the desired trajectories of the thigh and knee joints of the self-impact biped. Due to the existence of complex nonlinear terms in the dynamical governing equations of self-impact biped, the authors propose to design a nonlinear intelligent controller by taking advantage of the adaptive neural network control method, which neither requires the evaluation of inverse dynamical model nor the time consuming training process. According to the simulation results, the tracking control of the biped robot is accomplished well and the biped walking seems naturally, despite of involving complex nonlinear terms in the dynamical governing equations of the self-impact biped.
... As a result, it was found that stable walking motion is possible over the wide range of feedback gain. The walking velocity and period were not so affected by feedback gain because this control strategy utilized the natural motion of the biped mechanism [2]. An efficient path planning algorithm is required for the robot to move in a complex known and unknown environment. ...
... The coordinates of the leg end (point P) will be 2 3 p p r r r = + + X = r 2 cosθ 2 + r 3 cosθ 3 + r p cosθp; Y = r 2 sinθ 2 + r 3 sinθ 3 + r p sinθp; ...
... In this study, the events are chosen from those that can be easily obtained in the system, such as detecting the landing impact of the swing leg by a switch under the feet and timing the actuation duration via the system clock. Considering the concrete approaches to realizing level-ground walking based on the passive dynamics of the bipedal robot, some previous researchers have introduced actuations and controls to replace the slope to supply energy to the system [29,30,[37][38][39][40][41]. Such methods effectively use the dynamics of the robot, resulting in an efficient and natural gait. ...
Article
Recent studies have shown that a bipedal robot with a torso supported by springs on the hip can have a stable passive gait on a slope, while such a robot walking on level ground is a new challenge and has rarely been studied. This research adds actuators in series with the springs to form series elastic actuators on the hip and applies a state machine as controller to achieve stable walking on level ground. During walking, hip series elastic actuators support the torso from the legs as well as complement the energy to the system via elastic potential energy. The state machine uses the landing impact of the swing leg and the actuation durations as events to make the robot switch between successive active and passive walking processes. Because this simple scheme makes full use of the dynamics of the robot, it can lead to an efficient and natural gait. By means of numerical simulation, in addition to the stable period-1 gait, we found a variety of gait bifurcation phenomena, including the period-doubling bifurcation, the Neimark-Sacker bifurcation, the Neimark-Sacker-2 bifurcation, the period-X bifurcation, and the Neimark-Sacker-X bifurcation, among which many types have never been reported in previous studies. We also show that the unstable period-1 gait embedded in the bifurcation gait can be stabilized by applying the Ott-Grebogi-Yorke method. Not only can the gait bifurcation be suppressed, but also higher gait performance can be achieved.
... According to the current research, foreign universities and institutes have made great efforts to establish humanoid robots. From the novelty search results, the leading international universities include UT, Carnegie Mellon University (CMU) and Delft University678910. Zhang, Hu: Multi-Model Stability Control Method of Underactuated Biped Robots Based … ...
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In this paper, a stability control strategy for underactuated biped robots is proposed based on imbalance degree. The dynamic models of single-leg support of underactuated biped robots are firstly illustrated. Based on the external disturbance force strength of the system, the motion process of an underactuated biped robot is partitioned into three stages according to the imbalance degree. In different stages, corresponding dynamic models, tracking, gesture and gait switching control are adopted. Analysis of simulation result shows that the proposed underactuated gait control method is stable, practicable in engineering, and satisfies the real-time requirement.
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The article proposes an acceleration feedback based technique for exciting modal self-oscillation in a class of multi degrees-of-freedom mechanical systems. The controller comprises a bank of second-order filters and the control law is formulated as the nonlinear function of the filter output. A design methodology is developed to excite self-oscillation in any desired mode or combination of modes (mixed-mode oscillation). The choice of control parameters takes into account the control cost and robustness of the controller. The effects of structural damping on the system performance are also studied. Analytical results are confirmed by numerical simulations. An adaptive control is proposed to maintain the oscillation amplitude at the desired level.
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In research of biped walking robot, energy-efficiency is an important issue. We have proposed an optimal trajectory planning method to obtain the energy-efficient walking gait for active biped model. In previous report, we conducted the walking performance analysis of a biped model with circular feet, and evaluated the effect of foot radius and foot position on walking velocity, consumed energy rate, specific cost, and showed the improvement of the walking performance. However, since the ankle joint was fixed in this model, we could not control the walking velocity and its stable walking area was narrow. In this report, we introduce the model with variable ankle joint, which can control ankle torque. With this model, we evaluate the effect of ankle joint torque on walking performance and apply walking velocity control. It is shown that the stable walking area is widen, and the walking performance is improved.
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In research of biped walking robot, energy-efficiency is an important issue. Full-actuated type robots using ZMP based control have high environmental adjustability and high robustness, but they consume much energy. On the other hand, passive dynamic walking type robots have high energy-efficiency, but they don't have high-environmental adjustability and robustness. Then, we have proposed an optimal trajectory planning method to obtain the energy-efficient walking under full-actuated model. In this paper, we conduct the walking performance analysis of the circular feet model, and evaluated the effect of foot radius and foot position for walking velocity, consumed energy rate, specific cost. Furthermore, the stable walking area for foot radius and foot position is evaluated, and specific cost in the stable walking area is discussed.
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Since the present passive walking robots can only achieve a single gait and tend to tumble easily, the stable walking control problem for a semi-passive biped robot is studied. A quasi open-loop walking control method is presented through combining the advantages of passive walking and active walking. By detecting the signal values of contact sensors installed under the foot and at the kneecap, an intermittent and small open-loop oscillatory torque is imposed on the hip joint to realize stable walking with high efficiency. The simulation results show that the biped robot can achieve stable walking within a relative large region of control parameters and the energy cost of walking is similar to human beings. By modifying the parameters of the oscillatory torque, the robot can achieve stable transition between walking patterns.
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We demonstrate that an irreducibly simple, uncontrolled, 2D, two-link model, vaguely resembling human legs, can walk down a shallow slope, powered only by gravity. This model is the simplest special case of the passive-dynamic models pioneered by McGeer (1990a). It has two rigid massless legs hinged at the hip, a point-mass at the hip, and infinitesimal point-masses at the feet. The feet have plastic (no-slip, no-bounce) collisions with the slope surface, except during forward swinging, when geometric interference (foot scuffing) is ignored. After nondimensionalizing the governing equations, the model has only one free parameter, the ramp slope γ. This model shows stable walking modes similar to more elaborate models, but allows some use of analytic methods to study its dynamics. The analytic calculations find initial conditions and stability estimates for period-one gait limit cycles. The model exhibits two period-one gait cycles, one of which is stable when 0 < γ < 0.015 rad. With increasing γ, stable cycles of higher periods appear, and the walking-like motions apparently become chaotic through a sequence of period doublings. Scaling laws for the model predict that walking speed is proportional to stance angle, stance angle is proportional to γ 1/3 , and that the gravitational power used is proportional to v 4 where v is the velocity along the slope.
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It is well-known that a suitably designed unpowered mechanical bipedrobot can “walk” down an inclined plane with a steady periodicgait. The energy required to maintain the motion comes from theconversion of the biped's gravitational potential energy as itdescends. Investigation of such passive natural motions maypotentially lead us to strategies useful for controlling activewalking machines as well as to understand human locomotion. In this paper we demonstrate the existence and the stability ofsymmetric and asymmetric passive gaits using a simple nonlinear bipedmodel. Kinematically the robot is identical to a double pendulum(similar to the Acrobot and the Pendubot) and is able to walk withthe so-called compass gait. Using the passivebehavior as a reference we also investigate the performance ofseveral active control schemes. Active control can enlarge the basinof attraction of passive limit cycles and can create new gaits.
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Full-text available
We demonstrate that an irreducibly simple, uncontrolled, two-dimensional, two-link model, vaguely resembling human legs, can walk down a shallow slope, powered only by gravity. This model is the simplest special case of the passive-dynamic models pioneered by McGeer (1990a). It has two rigid massless legs hinged at the hip, a point-mass at the hip, and infinitesimal point-masses at the feet. The feet have plastic (no-slip, no-bounce) collisions with the slope surface, except during forward swinging, when geometric interference (foot scuffing) is ignored. After nondimensionalizing the governing equations, the model has only one free parameter, the ramp slope gamma. This model shows stable walking modes similar to more elaborate models, but allows some use of analytic methods to study its dynamics. The analytic calculations find initial conditions and stability estimates for period-one gait limit cycles. The model exhibits two period-one gait cycles, one of which is stable when 0 < gamma < 0.015 rad. With increasing gamma, stable cycles of higher periods appear, and the walking-like motions apparently become chaotic through a sequence of period doublings. Scaling laws for the model predict that walking speed is proportional to stance angle, stance angle is proportional to gamma 1/3, and that the gravitational power used is proportional to v4 where v is the velocity along the slope.
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As a practical example of a self-excited actuator theoretically presented in the 1st report, we developed a biped walking mechanism driven by a self-excited actuator. Referring to a biped walking toy which walks on a slope with a self-excited mechanism using potential energy, we proposed a mechanism which walks on flat ground with two single-link legs. Biped walking motion is realized by the swing roll motion of the upper body driven by a two-degree-of-freedom self-excited vibration system with asymmetric stiffness matrices. The fundamental characteristics of the self-excited actuating system are analyzed theoretically, and its efficiency and robustness are discussed by comparing the equivalent forced excitation system. The theoretical results are verified from the experimental study of the prototype. It is also found that the self-excited system has a better robustness to disturbance and variation of system parameters caused by walking motion, and can realize stabler walking motion, compared to the forced excitation system.
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As a practical example of a self-excited actuator theoretically presented in the previous paper, we developed an extended theory of the two-degree-of-freedom swing wing vibratory mechanism and showed its experimental prototype as a model of insect wings. In order to realize a self-excited system, we proposed not only a positive velocity feedback with nonlinear damping similar to the Van der Pole system, but also a more efficient Coulomb friction-type positive feedback system. Since the first-mode swing motion tends to be drawn into the second-mode limit cycle, we proposed two methods to excite only the first mode : one of them is the suppression of the second mode by means of a low-pass filter and the other is a cross feedback capable of exciting either mode.
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The authors studied the self-excited walking of a four-link biped mechanism that possesses an actuated hip joint and passive knee joints with stoppers. They showed that the self-excitation control enables the three-degree-of-freedom planar biped model to walk on level ground by numerical simulation. From the parameter study, it was found that stable walking locomotion is possible over a wide range of feedback gain and link parameter values and that the walking period is almost independent of the feedback gain. Various characteristics of the self-excited walking of a biped mechanism were examined in relation to leg length, and length and mass ratios of the shank. Next, a biped mechanism was manufactured similar to the analytical model. After parameter modification, the authors demonstrated that the biped robot can perform natural dynamic walking on a plane with a 0.8 degree inclination. The simulated results also agree with the experimental walking locomotion.
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In order to develop a periodical motion mechanism with high robustness against the variation of system parameters and enviroments, we study a self-excited vibratory actuator theoretically. As a two-degree-of-freedom self-excited vibratory system, the Van der Pole (VDP)-type vibration system and self-excited vibration system related to asymmetry of the stiffness matrix (ASM) with a nonlinear damping term are studied. Their characteristics are analyzed in detail using an analytical approximation method and numerical method. In the VDP-type vibrating system, one of the natural modes of vibrations of the original passive system is self-excited. In the ASM-type vibrating system, on the other hand, the original passive system is self-excited near the antiresonance fruquency in the limit cycle, so that we can utilize a vibratory motion with a large amplitude of unforced mass and small amplitude of the forced one. The methods of actuating two-degree-of-freedom passive systems as self-excited vibratory actuators and the robustness and efficiency of the actuator are also discussed.
Conference Paper
It is shown that passive dynamic walking, a phenomenon originally described for bipeds having straight legs, also works with knees. Thus, giving only a downhill slope as a source of energy, a human-like pair of legs will settle into a natural gait generated by the passive interaction of gravity and inertia. No muscular input is required. The physics is much the same as in straight-legged walking, but the knee-jointed form has two advantages: it offers a simple solution to the problem of foot clearance during the recovery phase, and, in some cases, it is more stable
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In this paper, a control study on a three-degree-of-freedom kneeless biped locomotion system is performed. Based on the biped dynamics and joint trajectories of the walking gait, a robust adaptive control scheme consisting of a control law and an adaptation law was used. The control law has the structure of the inverse dynamics servo but uses estimates of the dynamics parameters in the computation of torques which propel the biped. The adaptation law uses the tracking error to compute the parameter estimates for the control law. To improve the convergence of the estimated parameters, we modify the timing of applying the adaptation by incorporating a dead-zone operation. Our simulation results show that the adaptive control technique can be effectively used for the biped locomotion control. The joint tracking errors can be made acceptably small and the performance is also robust despite relatively large deviations in the initial estimates of the system parameters.
Conference Paper
This paper presents the self-excited walking of a four-link biped walking mechanism which possesses an actuated hip joint, passive knee joints and a curved feet. Instead of gravity potential energy, the natural walking motion of the four-link biped mechanism is self-excited by the hip joint torque which is proportional to the angle of the swing shank. In this paper, we show that this self-excitation control enables the 3-DOF planar biped model to walk on level ground by numerical simulation. From the parameter study of the feedback gain, we found that stable walking motion was possible over the wide range of this parameters, and walking velocity and periods were not so much affected. It was confirmed that the properties of this self-exciting walking, such as walking velocity and duration, were changed by the structural parameters of the walking model