PERIOD ESTIMATION OF UNKNOWN PERIODIC PERTURBATION IN BIPED BALANCE CONTROL

This paper addresses a biped balancing task in which an unknown periodic external force is exerted. In the previous paper, we described a control and learning process using the ankle strategy model of the biped balance. However, the period estimation based on the filtering process did not so effectively work for the external force with two-frequency component. In this paper, we extend this control scheme by introducing the period estimation by local correlation. The effectiveness of period estimation as well as the torque pattern learning are confirmed by computer simulations and robot experiments. INTRODUCTION A biped balancing task in which an unknown periodic external force is exerted is observed on the boat, as shown in Fig. 1. On the periodically tilting floor of the boat, human can maintain upright posture by changing the joint angle of the ankle: Human firstly maintains this posture carefully depend on the sensory feedback. However, if boat motion that produces perturbation is periodic, the human learns its motion resulting in that the balance is maintained unconsciously. In other words, humans can learn the movement of the ankle as a periodic motion pattern. In our previous papers, we formulate such a balancing task by an ankle strategy model composing of two links, and then proposed a control and learning method for external force in known period condition [1], and extend it for unknown period condition with filter process to obtain its lower frequency (long-period) component from the ankle joint movements [2]. However, this method was difficult to apply to the case where the complex periodic external force such as that contains two frequency components, since the low frequency component is not so clearly filtered. In this paper, we extend it by introducing the period estimation based on the local autocorrelation. PROBLEM FORMULATION The control and learning problem in biped balance is treated here as the motion caused by so-called "ankle strategy" [3]. The link model of the biped balance in this paper is illustrated in Fig. 2: it is a two-link model in sagittal plane. The foot part contact the floor at only two points, where the vertical component of ground reaction forces T F and H F is detected. In addition, ankle joint angle θ and its velocity θ are obtained as sensory information. Ankle joint torque τ is actively outputted. Unknown external force denoted by x F and y F is exerted. The problem is: what control law can adaptively stabilize the upright posture, and what learning low can memorize a produced motion as a motion pattern. To describe the latter learning problem, it is here assumed that motion pattern is expressed as a torque pattern of, in this case, ankle joint. Therefore, the learning is a torque pattern memorization that is produced to cope with unknown periodic external forces. Regarding to the former control problem, we consider the sensory information of the ground reaction forces are important to stabilize the upright posture under unknown external forces. Then, the learning becomes a process that stabilizes it without crucial information on ground reaction forces. PERIOD ESTIMATION In the learning, the period estimation of the periodic motion caused by unknown periodic external force becomes a basic process. It is estimated from the ankle joint movements, because it usually shows the periodic motion with the same period as the external force. For the estimation, we utilize a local autocorrelation as follows: 1. The trajectory of the ankle joint angle is stored back in time to 0 ( , ) s t t θ during the interval s T from 0 t : 0 0 ( , ) ( ) s t t t t θ θ = + ( 0 s T t − ≤ ≤ ) 2. Using this 0 ( , ) s t t θ , the local autocorrelation is calculated by