Abstract
Purpose
This paper aims to present a step-exchange strategy for balance control of a walking biped robot when a lateral impact acts suddenly. A step-out strategy has been recently proposed for balance control when an unknown lateral force acts to a biped robot during walking. This step-out strategy causes a robot to absorb the impact kinetic energy and efficiently maintain balance without falling down. Nevertheless, it was found that the previous strategies have drawbacks that the two foots should always be on the ground (double-support mode) after being balanced and the authors think it is difficult to continue walking after being balanced. Unlike the existing balance strategies, the proposed step-exchange strategy is to not only maintain balance but also to lift one leg in the air (single-support mode) after being balanced so that it is easy for a biped robot to keep walking after being balanced.
Design/methodology/approach
In the proposed step-exchange strategy, forward Newton–Euler equation, angular momentum and energy conservation equation were derived. Hill-climbing algorithm is utilized for numerically finding a solution. To verify the proposed strategy, a biped robot by Open Dynamics Engine was stimulated, and experiments with a real biped robot (LRH-1) were also conducted.
Findings
The proposed step-exchange strategy enables a walking biped robot under a lateral impact to keep balance and to keep a single-support mode after exchanging a leg. It is helpful for a biped robot to continue walking without any stop. It is found that the proposed step-exchange strategy can be applicable for maintaining balance even if a biped robot is moving. Even though this proposal seems immature yet, it is the first attempt to exchange the supporting foot itself. This strategy is very straightforward and intuitive because humans are also likely to exchange their supporting foot onto the opposite side when an unexpected force is acting.
Research limitations/implications
The proposed step-exchange strategy described in this paper can be applicable in the situation when the external force is applied in the +Y direction, the left leg is the swing leg and the right leg is the stance leg, or it can also be applicable in the situation when the external force is applied in −Y direction, the right leg is the swing leg and the left leg is the stance leg (Figure 2 for ±Y force direction). If an impact force acts to the side of the swing leg, the other step-exchange strategy is needed. The authors are studying this issue as a future work.
Originality/value
The authors have originated the proposed step-exchange strategy for balance control of a walking biped robot under lateral impact. The strategy is genuine and superior in comparison with the state-of-the-art strategy because not only can a biped robot be balanced but it can also easily continue walking by using the step-exchange strategy.
Keywords
Citation
Kim, Y.-J., Lee, J.-Y. and Lee, J.-J. (2014), "Step-exchange strategy for balance control of a walking biped under a lateral impact", Industrial Robot, Vol. 41 No. 5, pp. 456-464. https://doi.org/10.1108/IR-03-2014-0311
Publisher
:Emerald Group Publishing Limited
Copyright © 2014, Emerald Group Publishing Limited
1. Introduction
Studies of humanoid (biped) robots have been enriched as much as other robot studies by the belief that functionally human-like robots will make human life more comfortable. Hence, there are many studies concerning humanoid robots that replicate functions such as vision, intelligence and movability. Among these research subjects, locomotion of a humanoid robot has been one of the most active research subjects during the past decade because it is the most basic functionality of a humanoid robot and represents quite a complex dynamical behavior. Petman of Boston Dynamics, Asimo of Honda (Hirai et al., 1998) and Hubo in KAIST (Oh et al., 2006) report just a few state-of-the-art humanoid robots that can walk, run and even dance, and other state-of-the-art humanoid robots are found in Defense Advanced Research Projects Agency robotics challenge 2013 (Ackerman, 2013).
Recently, during research on the locomotion of a humanoid robot, some questions arose about the dynamic stability of a humanoid robot under an external force. This is an important topic because when the humanoid robot falls down due to an external force, it will be severely damaged, even though there is research related to the damage reduction (Fujiwara et al., 2002; Yun et al., 2009). Moreover, if the external force is exerted by a human being, the fall of the humanoid may also hurt the human being.
The dynamic stability of a humanoid robot subjected to an external force has been first addressed for the case when the humanoid robot is standing still. This is the so-called “push recovery” strategy. The push recovery strategy can be divided into three types. One is the ankle strategy, which can control the ankle torque so as to prevent falling down due to the external push (Hemani and Camana, 1976; Huang et al., 2000; Vadakkepat et al., 2008). The limitation of this strategy is that the amount of external force must be relatively small. Another strategy is the hip strategy, which controls the actuating motor attached to the hip of the biped robot. (Horak and Nashner, 1986; Nenchev and Nishio, 2008). This strategy can be applied when the external force is intermediate or a bit large. A combination of these two methods has also been studied. (Nenchev and Nishio, 2008; Asmar et al., 2012) The other method is called the step-out strategy, in which a robot steps out the swing leg when a large force is applied to the humanoid robot (Pratt et al., 2006). There is also a control strategy utilizing Central Pattern Generator–Zero Moment Point (ZMP) to maintain a limit-cycle motion while maintaining balance (Or, 2009).
The dynamic stability of a humanoid robot under an external force has also been treated in the case where the humanoid robot is walking (Harada et al., 2004; Komura et al., 2005; Motoi et al., 2007). Sustaining the dynamic stability during walking is more difficult than during standing because both the walking itself and the external force disturb the stability of the humanoid robot. In recent years, a step-out strategy has been published, which can absorb the impact energy by stepping out the swing leg (Li et al., 2012; Yasin et al., 2012). However, this method has the limitation that it is difficult to maintain walking after finishing the step-out movement because the two legs are on the ground due to the step-out strategy.
To overcome the limitation, in this paper, we present a noble step-exchange strategy for balance control of a walking biped robot under a lateral impact force. To verify the proposed strategy, we show experimental results. This strategy is based on the use of the rotating energy of the pushed biped robot. Because the biped robot has one leg on the ground and the other leg in the air, even though it is finishing the control strategy, it enables the robot to naturally continue walking after recovering. We are inspired by the fact that this type of behavior is also observed in a walking human being when recovering from a lateral push.
The subsequent sections are organized as follows. Section 2 provides an overview of the suggested control strategy. In Section 3, we explain the used of the biped robot model and the pre-defined walking pattern. In Section 4, we describe the suggested control strategy in detail. The experimental results are shown in Section 5. Conclusions are drawn in Section 6.
2. Overview of the suggested step-exchange strategy
In this section, we would like to present an overview of the suggested step-exchange strategy to provide a more concrete understanding before explaining in detail. The overall sequence is depicted in Figure 1. There are six subfigures in Figure 1. The subfigures are represented in time-ascending order. The biped robot, in the sagittal view, is presented in Figures 1(a-c), and that in a frontal view, is presented in Figures 1(d-f).
Let the biped robot be walking with a pre-defined walking gait as shown Figures 1(a-c). As shown in Figure 1(c), we assume that some lateral impact force, as directed to the y-axis, is applied to the torso of the biped robot. Here, the rotational velocity is Θ˙ 0 (Figure 1(d)) with respect to the inner side of the stance leg. Without a control strategy, the biped robot tends to fall down due to the rotational velocity Θ˙ 0. To avoid this, the proposed controller tries to spread the robot’s legs up to α. Spreading the legs causes the swing leg to hit the ground (Figure 1(e)), and eventually the biped robot reaches an instantaneous zero angular velocity (Figure 1(f), the dynamic balance). This sequence is depicted in Figures 1(d-f). After the dynamic balance, the proposed strategy controls the ankle angle of the stance leg in a feed-forward manner to further keep a balanced status. Finally, the proposed strategy activates a feedback controller for the ankle torque of the stance leg to provide fine-control of the balanced status. We provide the detailed explanations about how to determine α and about the feed-forward and feedback controllers in Section 4.
3. Biped robot and walking pattern
The biped robot used in this paper is LRH-1 with which we performed the experiment. LRH-1 has 12 degrees of freedom (DOF), 6 DOF in each leg. The joint motors of LRH-1 are position-controllable RX-24F motors (ROBOTIS e-Manual v1.1). The overall appearance of the robot is presented in Figure 2(1). Attitude and Heading Reference System (AHRS) is attached to the white upper body of LRH-1. The specification of the biped robot LRH-1 and the motor (RX-24F of Dynamics Inc.) is presented in Table I. LRH-1 and the controlling unit are connected via IEEE 485 protocol. The sampling rate of the controlling unit is 30 Hz.
The LRH-1 model is presented in Figure 2(b). The left picture represents the LRH-1 model which is a serial connection of 12 motors. Each motor has a local coordinate, and the inertial coordinate is represented by three red arrows attached to the tip of the right foot. The right picture is the sole of the LRH-1. All the data of LRH-1 are in Tables II and III.
As mentioned above, the step-exchange strategy might be triggered during walking. Therefore, we need some pre-defined walking patterns for the biped robot. For this purpose, we use energy-efficient walking patterns generated by the Tchebyshev method with the LRH-1 model (Kim et al., 2012). An energy-efficient walking pattern is generated by the parametric optimization method incorporated by the Tchebyshev method. The overall walking time is 9.75 s, and the walking stride is approximately 0.15 m. As shown in Figure 3, the left leg is the swing leg, and it is set backward in the initial position. The right leg is the stance leg.
4. Proposed step-exchange strategy for balance control
The details of the proposed step-exchange strategy are explained in this section. The strategy is composed of two parts. The first part is to determine α to spread the leg by the amount of α to achieve the dynamic balance (Figure 1(c-f)). The second part is the feed-forward and feedback control of the ankle torque of the stance leg that maintains the balanced status after dynamic balancing. We call the former “the dynamic balancer” and the latter “the balance maintainer”.
4.1 Dynamic balancer
The dynamic balancer aims to make an instantaneous zero angular velocity status after some lateral impact force is applied to the robot. The dynamic balancer accomplishes this by spreading the leg of the biped robot up to α, as depicted in Figure 1(c-f). The key point is how to determine α.
One way to determine α is to embed the foot placement estimator described in previous work (Wight et al., 2008) because the foot place estimator is proposed to make an active walking gait in a sagittal plane. However, this is based on the assumption that the biped robot has a torso with mass and mass-less legs. Because this assumption oversimplifies the actual biped robot, and if the biped robot has a relatively light torso, the assumption cannot be valid. Additionally, the foot placement estimator assumes that the lengths of the two legs should be equal. However, as shown in the situation in Figure 1(c), the lengths of the two legs are likely to be slightly different due to the fact that the configuration angles of the two legs are different when it walks, so applying the foot placement estimator could be error-prone.
To overcome these drawbacks of the foot placement estimator, we propose a different approach that considers the forward dynamics, angular momentum and energy equation in 13 mass models to calculate α.
Figure 4 depicts the control sequence of the dynamic balancer. There are four subfigures displayed in time-ascending order. The biped robot is viewed in front of it (laterally) in all four pictures. A red arrow located at the tip of the right foot shows the coordinate system. The actual biped robot has 13 masses and 12 motors, and the proposed strategy utilizes the 13-mass biped robot model. m i in Figure 4(a) represent the ith mass in a biped robot (i = 1-13). L 1i in Figure 4(b) represent the vector from the rotating point A to the ith mass. L 2i in angular momentum equation of Figure 5 represents the vector from the point B to the ith mass. L 3i is the same as L 2i , except that L 3i is defined when the dynamic balance is accomplished (in Figure 4(d)), whereas L 2i is defined in Figure 4(c). All the used parameters in equations (1–9) are in Table IV.
First, Figure 4(a) represents the situation in which the lateral impact is applied while the robot is walking and is at the brink of rotation with respect to the inner side of the stance foot. We assume that the initial angular velocity is measured, and its value is Θ˙ 0 (in an actual robot, this initial angular velocity must be measured by an Inertia Measuring Unit, and additional signal processing is necessary). Having determined the exact value of α, the dynamic balancer spreads the leg to the angle α with some joint motor velocity while rotating with respect to the inner side of the stance foot. The inner side of the left (swing) foot eventually collides with the ground. This situation is depicted in Figure 4(b). The angular velocity with respect to A (the inner side of the right foot) just before the collision is Θ˙ 1. After collision, the biped robot rotates with respect to the inner side of the left foot, and this situation is depicted inFigure 4(c). The value of this rotational velocity with respect to point B (the inner side of the left foot) is Θ˙ 2, and the angle between the sole of the left foot and the ground isβ. The biped robot rotates with respect to point B, and after rotation by the amount ofβ, the robot reaches status in Figure 4(d), which is the dynamic balance status.
The important point is that we assumed that the collision between the left foot and the ground is perfectly plastic with no bounce and no slip (this is an ideal condition, but the discrepancy between the ideal condition and the real condition will be compensated by the feed-forward and feedback controllers). Therefore, the angular momentum is conserved with respect to point A between in Figure 4(b and c). The detailed formula is represented below. Equation 1
Here, Inline Equation 1 represents the linear velocity of mass i just before the collision happens, and Ω 1 represents the angular momentum with respect to A just before the collision. Equation 2 Here, Inline Equation 2 represents the linear velocity of mass i just after the collision happens, and Ω 2 represents the angular momentum with respect to A just after the collision. Because the angular momentum with respect to A is conserved, we can equate Ω 1 and Ω 2, and eventually can calculate Θ˙ 2 with Θ˙ 1 as shown in equation (3). Equation 3 Another point to note is that when the dynamic balance state is reached in Figure 4(d), energy is conserved between a state in Figure 4(c) and a state in Figure 4(d). The energy of the state in Figure 4(c) is kinetic energy and potential energy (E 2 = K 2 + P 2), whereas the energy of the state in Figure 4(d) is potential energy because zero angular velocity is reached (E f = P f ). These energies are represented in Equation 4 and Equation 5. Because the energy is conserved, we can equate equations (4) and (5) as in equation (6) Equation 6. We first assumed that α is calculated properly such that the energy equation is conserved (dynamic balance is reached). Let us consider what would happen if we choose α to be smaller or larger than the exact value. When we choose smaller α, E 2 is larger than E f , and the biped robot keeps rotating without reaching the dynamic balance. Thus, it falls down. On the other hand, if we choose a larger α, E 2 is smaller than E f , so the biped robot rotates back and its right leg hits the ground.
The procedure for determining α is depicted in Figure 5. In Figure 5, we first determine the initial α t e m p . This value is just the initialization of a temporary α value. Then, with the biped robot posture, joint motor angular speed and measured initial angular speed Θ˙ 0, forward dynamics is used to determine Θ˙ 1 and β. The forward dynamics are used to solve discrete Newton–Euler equation of 13 mass biped robots. Because of the angular momentum conservation described in equation (3), Θ˙ 2 can be calculated. With these values and the energy equations (4) and (5), E 2 and E f can be calculated. If these two values are approximately equal, then α t e m p is α. If E 2 is less than or greater than E f , then α t e m p is determined by the steepest descent hill-climbing algorithm (Russell and Norvig, 2003).
The important thing to note is that the α determination algorithm will be activated just after the lateral impact is applied to the biped robot and the Θ˙ 0 value is measured. Thus, the algorithm must run fast enough (at approximately below 5 msec) to activate the step-exchange strategy of a real biped robot rapidly. The rule of thumb is to set the initial α t e m p to about 40 degrees and to set increment value to 0.5 degrees. With these settings, there are fewer than ten iterations required under our simulation conditions. The lower limit of Θ˙ 0 value at which the balance control is activated depends on the value of the joint motor velocity. The larger the joint motor velocity, the larger the lower limit of Θ˙ 0 because if the controller can control the joint motor fast enough, even the torso movement alone can balance the biped robot. Under our simulation conditions (joint motor velocity 1.047 rad/sec), the lower limit of Θ˙ 0 value is approximately 0.250 rad/sec. This value is determined by the joint motor velocity specifications and Open Dynamics Engine simulation results. If the Θ˙ 0 value is below the lower limit, the biped robot can restore its balance with just a slight torso movement.
4.2 Balance maintainer
After instantaneous zero angular velocity is achieved by the dynamic balancer, the balance maintainer controls the biped robot to keep it balanced after the dynamic balance (instantaneous zero angular velocity). As stated previously, the balance maintainer consists of two control algorithms. One uses feed-forward control and the other uses feedback control of the ankle of the stance leg.
4.2.1 Feed-forward control
The feed-forward controller calculates Δ Θ, which indicates the angle increment of the ankle of the stance leg and increases the angle of the ankle of the stance leg to the Δ Θ value. With this control, the biped robot can maintain some degree of balance before the fine feedback control. This is depicted in Figure 6. The equation to calculate Δ Θ is as follows: Equation 7
4.2.2 Feedback control.
After feed-forward control is achieved, feedback control of the ankle torque of the stance leg follows. This provides more robust balance control for the biped robot. The feed-forward controller controls the motor in the frontal plane only (12th motor in Figure 2(b)). The feedback controller, however, controls the motors in the lateral and sagittal planes (11th and 12th motors in Figure 2(b)). This feedback control uses a ZMP feedback control to shift the ZMPx and ZMPy to the center of the sole of the stance leg. The configuration of the biped robot under feedback control is depicted in Figure 7. The biped robot is viewed laterally in Figure 7(a), and it is viewed sagittally in Figure 7(b). The detailed equations are as follows: Equation 8 Equation 9 Equations (8) and (9) are for controlling ZMPy and ZMPx, respectively.
5. Experiment results
The proposed step-exchange strategy is verified by experiment with LRH-1. The experimental condition is in Table V. The impulsive force is applied to the torso of LRH-1 by a push gauge. The force-applying time is approximately half of the walking time. The angular velocity Θ 0 is measured by AHRS. The joint motor angular velocity is set to 10.681 rad/sec which is from the specification of RX-24F motor.
In Figure 8(a), the initial posture of walking is displayed. The left leg is set backward because it is the swing leg. During walking, at approximately 5.148 sec, the external impulsive force is applied to the torso of the robot as shown in Figure 8(b). The robot is rotated by the external impulsive force, then the angular velocity Θ 0 is measured by AHRS, and the controlling unit calculates α by the α determination algorithm. The calculated α is 16.24 degrees, and the robot spreads its leg with α exchanging its step [Figure 8(c)]. The feed-forward controller is activated almost simultaneously with the dynamic balancer. The feedback controller is activated last to maintain the balanced status (Figure 8(d)).
The ZMP results are in Figure 9. The upper picture represents ZMPx and the lower picture represents ZMPy. The coordinate system of ZMP is in the right picture of Figure 2(b). The sole size is 0.06 × 0.1 m2. So, the range of ZMPy is from −0.03 m to +0.03 m, and the range of ZMPx is from −0.1 to 0 m. There are three regions in the ZMP graph: normal walking region, step-exchange region and feedback control region. In normal walking, ZMPx and ZMPy is approximately −0.025 and +0.025 m, respectively. After step-exchange, ZMPx changes to −0.05 m and ZMPy changes to approximately −0.025 m and eventually converges to 0 with a minor fluctuation by the feedback controller. The video captures of the experiment are in Figure 10.
6. Conclusion
In this paper, a step-exchange strategy of a walking biped robot under a lateral impulsive impact is proposed. The step-exchange strategy consists of a dynamic balancer and a balance maintainer. The dynamic balancer spreads the leg of the biped robot in a frontal plane to reach an instantaneous zero angular velocity. It incorporates the forward dynamics, angular momentum conservation and energy equation to calculate the leg spreading angle α. After an instantaneous zero angular velocity is reached, the balance maintainer is activated to help the biped robot keep its balance. The balance maintainer is comprises a feed-forward and feedback controller. The experiment is performed to verify the proposed step-exchange strategy to indicate that the method can be applicable to a real biped robot. The future works are to make the step-exchange strategy more robust by incorporating the lateral impact classifier, which rejects the lateral impact that is not significant and trivial and to perform the experiments in different conditions.
Corresponding author
Joon-Yong Lee is the corresponding author and can be contacted at: [email protected]
References
Ackerman, E. (2013), “DARPA robotics challenge trials: final results”, available at: http://spectrum.ieee.org/automaton/robotics/humanoids/darpa-robotics-challenge-trials-results
Asmar, D.C. , Jalgah, B. and Fakih, A. (2012), “Humanoid fall avoidance using a mixture of strategies”, International Journal of Humanoid Robotics, Vol. 9 No. 1, p. - .
Fujiwara, K. , Kanehiro, F. , Kajita, S. , Kaneko, K. , Yokoi, K. and Hirukawa, H. (2002), “UKEMI: falling motion control to minimize damage to biped humanoid robot”, Proceedings of the 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, pp. 2521-2526.
Harada, K. , Kajita, S. , Kanehiro, F. and Fujiwara, K. (2004), “Walking motion for pushing manipulation by a humanoid robot”, Journal of Robotics Society Japan, Vol. 22 No. 3, pp. 392-399.
Hemani, H. and Camana, P. (1976), “Nonlinear feedback in simple locomotion systems”, IEEE Transaction on Automatic Control, Vol. 12 No. 6, pp. 855-860.
Hirai, K.H. , Haikawa, M. and Takenaka, T. (1998), “The development of Honda humanoid robot,” Proceedings of 1998 IEEE International Conference on Robotics and Automation, Leuven, pp. 1321-1326.
Horak, F. and Nashner, L. (1986), “Central programming of postural movement: adaptation to altered support-surface configurations”, Journal of Neurophysiology, Vol. 55 No. 6, pp. 1369-1381.
Huang, Q. , Kaneko, K. , Yokoi, K. , Kajita, S. , Kotoku, T. , Koyachi, N. , Arai, H. , Imamura, Nobuaki , Komoriya, K. and Tanie, K. (2000), “Balance control of a biped robot combining off-line pattern with real-time modification”, Proceeding of the 2000 IEEE International Conference on Robotics and Automation, San Francisco, CA, pp. 3346-3352.
Kim, Y.J. , Lee, J.Y. and Lee, J.J. (2012), “Bipedal walking Trajectory generation using Tchebyshev method,” International Conference on Mechatronics and Informatics, Shenyang, pp. 223-232.
Komura, T. , Leung, H. , Kudoh, S. and Kuffner, J. (2005), “A feedback controller for biped humanoids that can counteract large perturbation during gait”, Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain, pp. 1989-1995.
Li, T.S. , Su, Y.-T. , Liu, S.-H. , Hu, J.-J. and Chen, C.-C. (2012), “Dynamic balance control for biped robot walking using sensor fusion, kalman filter and fuzzy logic”, IEEE Transaction on Industrial Electronics, Vol. 59 No. 11, pp. 4394-4408.
Motoi, N. , Ikebe, M. and Onishi, K. (2007), “Real-time gait planning for pushing motion of humanoid robot”, IEEE Transaction on Industrial Informatics, Vol. 3 No. 2, pp. 154-163.
Nenchev, D.N. and Nishio, A. (2008), “Ankle and hip strategies for balance recovery of a biped subject to an impact”, Robotica, Vol. 26 No. 5, pp. 643-653.
Oh, J.H. , Hanson, D. , Kim, W.S. , Han, Y. , Kim, J.Y. and Park, I.W. (2006), “Design of android type humanoid Robert Albert HUBO,” 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, pp. 1428-1433.
Or, J. (2009), “A hybrid CPG–ZMP controller for the real-time balance of a simulated flexible spine humanoid Robot”, IEEE Transactions on Systems, Man, and Cybernetics – Part C: Application and Reviews, Vol. 39 No. 5, pp. 547-561.
Pratt, J.E. , Carff, J. , Drakunov, S. and Goswami, A. (2006), “Capture point: a step toward humanoid push recovery”, Proceeding of the 2006 IEEE-RAS International Conference on Humanoid Robots, Genova, pp. 200-207.
ROBOTIS e-Manual v-1.1, available at: http://support.robotis.com/en/product/dynamixel/rx_series/rx-24f.htm
Russell, S.J. and Norvig, P. (2003), Artificial Intelligence: A Modern Approach, 2nd ed., Prentice Hall, Englewood Cliffs, NJ, pp. 111-114.
Vadakkepat, P. , Goswami, D. and Hwee, C.M. (2008), “Disturbance rejection by online ZMP compensation”, Robotica, Vol. 26 No. 1, pp. 9-17.
Wight, D.L. , Kubica, E.G. and Wang, D.W.L. (2008), “Introduction of the foot placement estimator: a dynamic measure of balance for bipedal robotics”, Journal of Computational and Nonlinear Dynamics, Vol. 3 No. 1, pp. 1-9.
Yasin, A. , Huang, Q. , Xu, Q. and Ahang, W. (2012), “Biped robot push detection and recovery”, Proceedings of the 2012 IEEE International Conference on Information and Automation, Shenyang, pp. 993-998.
Yun, S.K. , Goswami, A. and Sakagami, Y. (2009), “Safe fall: humanoid robot fall direction change through intelligent stepping and inertia shaping”, IEEE International Conference on Robotics and Automation, Kobe, pp. 781-787.