Rimless Wheel Research Articles

Control of stance-leg motion and zero-moment point for achieving perfect upright stationary state of rimless wheel type walker with parallel linkage legs

Abstract The authors have studied models and control methods for legged robots without having active ankle joints that can not only walk efficiently but also stop and developed a method for generating a gait that starts from an upright stationary state and returns to the same state in one step for a simple walker with one control input. It was clarified, however, that achieving a perfect upright stationary state including zero dynamics is impossible. Based on the observation, in this paper we propose a novel robotic walker with parallel linkage legs that can return to a perfect stationary standing posture in one step while simultaneously controlling the stance-leg motion and zero-moment point (ZMP) using two control inputs. First, we introduce a model of a planar walker that consists of two eight-legged rimless wheels, a body frame, a reaction wheel, and massless rods and describe the system dynamics. Second, we consider two target control conditions; one is control of the stance-leg motion, and the other is control of the ZMP to stabilize zero dynamics. We then determine the control input based on the two conditions with the target control period derived from the linearized model and consider adding a sinusoidal control input with an offset to correct the resultant terminal state of the reaction wheel. The validity of the proposed method is investigated through numerical simulations.

Development of a rimless wheel robot with telescopic legs for step adaptability

AbstractIn this study, we developed a rimless wheel robot with elastic telescopic legs that can overcome steps. Numerical studies have shown that a rimless wheel robot with elastic telescopic legs has high adaptability to steps. However, rimless wheel robots that can walk in environments with steps have not yet been developed. To develop a rimless wheel robot that could overcome the steps, we initially developed a three-dimensional model of the robot through Unity software and simulated its walking on level ground and surfaces with steps. Then, we determined the optimal elasticity of the elastic telescopic legs through numerical simulation and constructed a model with optimized parameters. Finally, we conducted the walking experiments employing the developed robot. The robot can walk on level ground and surfaces with steps.

Low-speed Passive Dynamic Walking of Rimless Wheel Based on Antigravity Effect of Semicircular Feet

Low-speed Passive Dynamic Walking of Rimless Wheel Based on Antigravity Effect of Semicircular Feet

Predicting impact scenarios of a rimless wheel: a geometrical approach

The 2D motion of a rigid rimless wheel on an inclined plane has been widely studied as a first simple case of passive walker. Usually, it is modelled as a hybrid dynamical system alternating continuous smooth phases and discrete impact ones. As in other bipedal walkers, the related research is often devoted to the analysis of cyclic motions and assumes that the spoke-ground collision is a single-point one. This work focuses exclusively on the impact problem and explores the possibility of different transitions within the impact interval (single-point to double-point collisions, dynamic jamb, stick-slide transitions and sliding reversal) as a function of the spokes angular aperture, the wheel inertia, the wheel-ground friction coefficient, and the initial conditions. This analysis is done through an innovative geometrical approach based on the Percussion Centre.

Walking experiments of small and lightweight rimless wheel robot

Walking experiments of small and lightweight rimless wheel robot

The split-belt rimless wheel

Split-belt treadmill walking, in which the two belts move at different speeds, reveals a mechanism through which energy can be extracted from the environment. When a person walks with positive step length asymmetry on a split-belt treadmill, the treadmill can perform net positive work on the person. Here we use a split-belt rimless wheel model to explore how people could take advantage of the treadmill. We show that a split-belt rimless wheel can passively walk steadily by capturing energy from the treadmill to overcome collision losses, whereas it loses energy on each step with no way to recover the losses when walking on tied belts. Our simulated split-belt rimless wheel can walk steadily for a variety of leg angle and belt speed combinations, tolerating both speed disturbances and ground height variability. The wheel can even capture enough energy to walk uphill. We also built a physical split-belt rimless wheel robot and demonstrated that it can walk continuously without additional energy input. In comparing the wheel solutions to human split-belt gait, we found that humans do not maximize positive work performed by the treadmill. Other aspects of walking, such as costs associated with swing, balance, and free vertical moments, likely limit people’s ability to benefit from the treadmill. This study uses a simple walking model to characterize the mechanics and energetics of split-belt walking, demonstrating that energy capture through intermittent contact with two belts is possible and providing a simple model framework for understanding human adaptation during split-belt walking.

Steady locomotion in torso-actuated rimless wheel robots

Steady locomotion in torso-actuated rimless wheel robots

Investigation of the relationship between steps required to stop and propulsive force using simple walking models

To prevent falls in the elderly, it is essential to evaluate their gait stability and identify factors that negatively affect it. Although one of the probable factors is a decrease in propulsive force of walking, the relationship between the force and the gait stability has not been fully clarified. To this end, two simple walking models were used to investigate the relationship between the propulsive force and the number of steps required to stop, denoted N. N was calculated as the number of steps required for the rimless wheel to stop and was treated as a variable which is an indirect indicator of stability. A lower N corresponds to the gait being closer to a stopped state. The propulsive force was calculated using the push-off impulse applied to the simplest walking model during the step-to-step transition. To account for the effects of the double support phase in human walking, the gravitational impulse, which is the integral of the body weight (gravitational force) over the double support time, was applied to the step-to-step transition equation of the models. The models revealed that the propulsive force is reduced by two factors: the reduction in step length and the reduction in walking speed. In the former, N increases; in the latter, N decreases. The former is consistent with previous experimental results on human gait, whereas the latter has not been experimentally investigated. These results may provide important insights in clarifying the relationship between the stability and the propulsive force in human gait.

Dynamics of rimless wheel robots during collision

Dynamics of rimless wheel robots during collision

Passive Dynamic Walking of Rimless Wheel Formed by Four Rigid Frames and Eight Springs

This paper proposes a novel rimless-wheel type legged robot that can be made by adding the constraint of the rotation axis to the tensegrity structure formed by four rigid frames and eight springs. First, we introduce a planar 12-DOF robot model for passive-dynamic walking on a gentle downhill, and develop the equations of motion, constraint conditions and inelastic collision. Second, we numerically show that the generated passive-dynamic gait is not always asymptotically stable due to the variable impact posture, and that it is possible to generate a passive-dynamic gait that is faster than a normal rimless wheel by appropriately setting the spring coefficient.

Passive Dynamic Walking of Combined Rimless Wheels Formed by Two Cross-shaped Frames and Eight Viscoelastic Elements

Passive Dynamic Walking of Combined Rimless Wheels Formed by Two Cross-shaped Frames and Eight Viscoelastic Elements

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The paper hypothesizes that bipedal walking is a process of self-oscillations in terms of variables. The simplest model of bipedal walking – the movement of a rimless wheel (a wheel with legs) is considered. In a nonlinear formulation, the dynamics of its plane motion down an inclined plane is analyzed analytically. It is shown that various modes of movement of a rimless wheel are possible. The most interesting of which is the existence of a stable periodic solution (self-oscillations).

Design, Modeling, and Control of a Differential Drive Rimless Wheel That Can Move Straight and Turn

A rimless wheel or a wheel without a rim, is the simplest example of a legged robot and is an ideal testbed to understand the mechanics of locomotion. This paper presents the design, modeling, and control of a differential drive rimless wheel robot that achieves straight-line movement and turning. The robot design comprises a central axis with two 10-spoked springy rimless wheels on either side and a central body that houses the electronics, motors, transmission, computers, and batteries. To move straight, both motors are commanded to constant pitch control of the central body. To turn while maintaining constant pitch, a differential current is added and subtracted from currents on either motor. In separate tests, the robot achieved the maximum speed of 4.3 m per sec (9.66 miles per hour), the lowest total cost of transport (power per unit weight per unit velocity) of 0.13, and a smallest turning radius of 0.5 m. A kinematics-based model for steering and a dynamics-based sagittal (fore-aft) plane model for forward movement is presented. Finally, parameters studies that influence the speed, torque, power, and energetics of locomotion are performed. A rimless wheel that can move straight and turn can potentially be used to navigate in constrained spaces such as homes and offices.

Evaluation of climbing performance of rimless wheel with springs

Evaluation of climbing performance of rimless wheel with springs

Development of Vibratory Conveyor System Using Frequency Entrainment for Underactuated Walking of Rimless Wheel

In this paper, we propose a novel vibratory conveyor system based on frequency entrainment of limit cycle walking. The conveyor system transports a passive rimless wheel utilizing a vibratory plate which moves up and down by rolling and impact of an active rimless wheel. First, we introduce the mathematical model of the proposed conveyor system. Next, we investigate the influence for the passive rimless wheel gait by vibration of the conveyance plate via the numerical simulation using the mathematical model, and confirm the entrainment phenomenon between the passive rimless wheel and the vibratory plate. Futermore, we conduct experiments using the prototype vibratory conveyor system, and confirm that experimental results show similar trends to the numerical simulation.

Gait Generation of Combined Rimless Wheel That Consists of Two Different Wheels by Considering Viscoelasticity of Body-frame

Gait Generation of Combined Rimless Wheel That Consists of Two Different Wheels by Considering Viscoelasticity of Body-frame

Realization of Fast Level Running of Rimless Wheel with Springs by Towing Force

Realization of Fast Level Running of Rimless Wheel with Springs by Towing Force

Generation and Motion Analysis of Stealth Walking Gait for Asymmetric Rimless Wheel Using Elasticity

The authors have investigated the method of stealth walking for achieving stable legged locomotion on irregular terrain. In this paper, we discuss a method for generating an asymmetric stealth walking gait. First, we introduce a mathematical model of an asymmetric rimless wheel with an elastic element, and develop the control law for highly efficient walking using DODC (Discrete-time Output Deadbeat Control) based on vertical ground reaction force. Second, we derive an approximate analytical solution for an appropriate initial state of the robot based on the equation of motion of the linearized model. Third, we perform numerical simulations on the linearized model, and we extend the results to the nonlinear model. Furthermore, we perform experiments using our prototype experimental machine, and verify the validity of the proposed control law.

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.

Study for 2D Level Running of Rimless Wheel by Towing Force

Study for 2D Level Running of Rimless Wheel by Towing Force