This paper explores a design strategy of hopping robots, which makes use of free vibration of an elastic curved beam. In this strategy, the leg structure consists of a specifically shaped elastic curved beam and a small rotating mass that induces free vibration of the entire robot body. Although we expect to improve energy efficiency of locomotion by exploiting the mechanical dynamics, it is not trivial to take advantage of the coupled dynamics between actuation and mechanical structures for the purpose of locomotion. From this perspective, this paper explains the basic design principles through modeling, simulation, and experiments of a minimalistic hopping robot platform. More specifically, we show how to design elastic curved beams for stable hopping locomotion and the control method by using unconventional actuation. In addition, we also analyze the proposed design strategy in terms of energy efficiency and discuss how it can be applied to the other forms of legged robot locomotion.

In recent years, there has been increasing interest in the study of gait patterns in both animals and robots, because it allows us to systematically investigate the underlying mechanisms of energetics, dexterity, and autonomy of adaptive systems. In particular, for morphological computation research, the control of dynamic legged robots and their gait transitions provides additional insights into the guiding principles from a synthetic viewpoint for the emergence of sensible self-organizing behaviors in more-degrees-of-freedom systems. This article presents a novel approach to the study of gait patterns, which makes use of the intrinsic mechanical dynamics of robotic systems. Each of the robots consists of a U-shaped elastic beam and exploits free vibration to generate different locomotion patterns. We developed a simplified physics model of these robots, and through experiments in simulation and real-world robotic platforms, we show three distinctive mechanisms for generating different gait patterns in these robots.

In this research, an innovative robot is presented that can move both on land and water thanks to a vibration-based locomotion mechanism. The robot consists of a U-shaped beam made of spring steel, two low-density feet that allow it to stand on the water surface without sinking, and a micro-DC motor with eccentric mass, which excites vibrations. The robot exhibits stable terrestrial and aquatic locomotion based on the synchronization between body vibrations and the centrifugal force due to the eccentric mass. On the one hand, in aquatic locomotion, the robot advances thanks to floating oscillations and the asymmetric shape of the floating feet. On the other hand, the terrestrial locomotion, which has already been demonstrated for a similar robot, exploits the modes of vibration of the elastic beam. In this study, the effect of different excitation frequencies on the locomotion speed in water is examined by means of experimental tests and a numerical model. A good agreement between experimental and numerical results is found. The maximum locomotion speed takes place when the floating modes of vibration are excited.

This study is devoted to the investigation of the effects of inertial, centripetal, and Coriolis forces on the dynamic response of a simply supported beam with a single crack under moving mass load. As in the case of beams without a crack, it is shown that these forces must be considered in the analysis. The inertial, centripetal, and Coriolis forces are appreciably affected by the mass and the velocity of the moving load. The response of the system is obtained in terms of Duhamel integral. The differential equation that involves a nonlinearity on its right side is solved via an iterative procedure. The results are exemplified for various values of the variables.

This study presents a novel approach to the design of low-cost and energy-efficient hopping robots, which makes use of free vibration of an elastic curved beam. We found that a hopping robot could benefit from an elastic curved beam in many ways such as low manufacturing cost, light body weight and small energy dissipation in mechanical interactions. A challenging problem of this design strategy, however, lies in harnessing the mechanical dynamics of free vibration in the elastic curved beam: because the free vibration is the outcome of coupled mechanical dynamics between actuation and mechanical structures, it is not trivial to systematically design mechanical structures and control architectures for stable locomotion. From this perspective, this paper investigates a case study of simple hopping robot to identify the design principles of mechanics and control. We developed a hopping robot consisting of an elastic curved beam and a small rotating mass, which was then modeled and analyzed in simulation. The experimental results show that the robot is capable of exhibiting stable hopping gait patterns by using a small actuation with no sensory feedback owing to the intrinsic stability of coupled mechanical dynamics. Furthermore, an additional analysis shows that, by exploiting free vibration of the elastic curved beam, cost of transport of the proposed hopping locomotion can be in the same rage of animals' locomotion including human running.

In order to understand the underlying mechanisms of animals' agility, dexterity and efficiency in motor control, there has been an increasing interest in the study of gait patterns in biological and artificial legged systems. This paper presents a novel approach to the study of gait patterns which makes use of intrinsic mechanical dynamics of robotic systems. Each of these robots consists of a U-shape elastic beam and exploits free vibration to generate different gait patterns. We developed a conceptual model for these robots, and through simulation and real-world experiments, we show three distinct mechanisms for generating four different gait patterns in these robots.