Combined Rimless Wheel Research Articles

Gait Generation of Combined Rimless Wheel that Consists of Two Different Wheels by Using Wobbling Effect

It was clarified that the walking speed of a combined rimless wheel can be indirectly controlled by using an active wobbling mass via entrainment effect in the previous studies. Analyses on nonlinear properties of it have been conducted based on the theory of phase oscillation. To further investigate the dominance relationship among multiple oscillators in the locomotion systems, different rimless wheels and an active wobbling mass are connected by a rigid beam in this study. First, we describe the mathematical model and control. Second, we discuss the change of dominance relationship between the front and rear legs according to high-frequency oscillation of wobbling mass through numerical simulations.

Nonlinear analysis of an indirectly controlled limit cycle walker

Towards controlling the frequency of limit cycle locomotion as well as adapting to rough terrain and performing specific tasks, a novel and indirect method has been recently introduced using an active wobbling mass attached to limit cycle walkers. One of the strongest advantages of the method is the easiness of its implementation, prompting its applicability to a wide variety of locomotion systems. To deeply understand the nonlinear dynamics for further enhancement of the methodology, we use a combined rimless wheel with an active wobbling mass as an example to perform nonlinear analysis in this paper. First, we introduce the simplified equation of motion and the gait frequency control method. Second, we obtain Arnold tongue, which represents region of entrained locomotion. In regions where the locomotion is not entrained, we explore chaotic and quasi-periodic gaits. To characterize bistability of two different locomotions that underlie hysteresis phenomena, basins of attraction for the two locomotions were computed. The present nonlinear analysis may help understanding the detailed mechanism of indirectly controlled limit cycle walkers.

Generating 1-DOF limit cycle walking at target walking speed by feed-forward and feedback limit cycle control

We propose the feed-forward and feedback (FaF) control systems for generating the limit cycle walking at a target walking speed by the combined rimless wheel (CRW) model. The proposed FaF control systems can calculate a control input constantly based on the mathematical analysis of the current and target walking states. As a result, first, the limit cycle walking at the target walking speed is generated by numerical simulations when the walker is driven by the constant FaF control system. Second, for controlling the convergence speed, we extend the FaF control to the two-period stepwise control systems. The limit cycle walking at the target walking speed is still generated, and the convergence speed is controlled by the settling time parameter. Finally, the real-time walking state updating is considered in the FaF control systems to handle the disturbances. In this case, we find that for generating a target walking speed, a precise mathematical model is not necessary for generating the target state, but can make the control input stable and efficient.

Analysis of steady and target walking speeds in limit cycle walking

This paper presents the mathematical analysis of steady walking speed and target walking speed generation in 1-DOF limit cycle walking driven by time-settling control inputs. An actuated combined rimless wheel (CRW) model is introduced to analyse the steady walking state when the CRW is walking on level ground. First the initial and terminal boundary conditions driven by discrete stepwise control systems are analysed. The steady step period can be calculated and the target walking period can be generated by the formulas. Second we extend the mathematical analysis to \((n+1)\)-period stepwise control system and derive the general formula of the steady step period. Finally, the continuous piecewise control systems are analysed mathematically by discretizing the control input, and thus the boundary conditions can be analysed by the formula of \((n+1)\)-period stepwise control system. As a result, if the generated walking gait is single-step-cycle, the steady step period can be calculated and target walking steady speeds can be generated by our general formulas in the time-settling control systems.

Indirectly controlled limit cycle walking of combined rimless wheel based on entrainment to active wobbling motion

It has been clarified that a passive combined rimless wheel (CRW) that consists of two identical eight-legged rimless wheels can increase the walking speed either by adjusting the phase difference between the fore and rear legs or by using a passive wobbling mass that vibrates up-and-down in the body frame. Toward a further speeding-up of the CRW, this paper investigates the effect of an active wobbling mass driven by an actuator and the effect of an indirect excitation control. First, we develop the mathematical model and numerically show that the CRW generates a walking motion, which is entrained to the up-and-down motion of the active wobbling mass at frequencies higher than the natural frequency of the CRW. We discuss the gait properties mainly from the viewpoints of frequency and phase relationships. Second, we conduct verification experiments using our prototype CRW machine and describe the results.

2P1-E03 前後に振動する能動的な揺動質量を持つ連結型リムレスホイールの歩行解析(受動歩行ロボット(2))

This paper investigates the gait properties of a passive combined rimless wheel with an active wobbling mass that vibrates backward and forward in the body frame. First, we develop the mathematical model and numerically analyze the change in walking speed with respect to the frequency of the wobbling mass. Second, we perform experimental case study and validate the results obtained.

1A1-P07 揺動質量を持つ連結型リムレスホイールの歩行解析と実験的検証(受動歩行ロボット(1))

This paper investigates the gait properties of passive dynamic walking of a combined rimless wheel (CRW) with a wobbling mass. We show that the walking speed increases by the effect of the wobbling mass and the gait efficiency changes with respect to the elasticity. We discuss the transition from inverse to normal phase synchronization from the frequency point of view. We then denote effect of initial angular velocity on the CRW gait and show a hysteresis phenomenon of in the walking speed. Furthermore, the validity of the simulation results is verified using an experimental CRW machine.

2A2-Q01 連結型リムレスホイールにおける位相差の調節による高速化の実験的検証(受動歩行ロボット)

This paper investigates efficiency of passive dynamic walking of a combined rimless wheel (CRW) that consists of two identical 8-legged rimless wheels. We derive the mathematical equations of the CRW and conduct numerical simulations to examine that a stable passive gait can be generated in the presence of the phase difference between fore and hind legs. We then numerically show that the phase difference improves the gait efficiency in terms of walking speed, and discuss the inherent speeding-up mechanism from the potential barrier point of view. Furthermore, the validity of the derived results is evaluated by using an experimental machine.