The use of free vibration in elastic structure can lead to energy efficient robot locomotion, since it significantly reduces the energy expenditure if properly designed and controlled. However, it is not well understood how to harness the dynamics of free vibration for the robot locomotion, because of the complex dynamics originated in discrete events and energy dissipation during locomotion. From this perspective, this paper explores three minimalistic models of free vibration that can characterize the basic principle of robot locomotion. Since the robot mainly exhibits vertical hopping, three one-dimensional models are examined that contain different configurations of simple spring-damper-mass components. The self-stability of these models are also investigated in simulation. The real-world and simulation experiments show that one of the models best characterizes the robot hopping, through analyzing the basic kinematics and negative works in actuation. Based on this model, the control parameters are analyzed for the energy efficient hopping.

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 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.

The biological hypothesis of spinal engine states that locomotion is mainly achieved by the spine, while the legs may serve as assistance. Inspired by this hypothesis, a compliant, multiple degree-of-freedom, biologically-inspired spine has been embedded into a quadruped robot, named Kitty, which has no actuation on the legs. In this paper, we demonstrate how versatile behaviors (bounding, trotting, and turning) can be generated exclusively by the spine's movements through dynamical interaction between the controller, the body, and the environment, known as embodiment. Moreover, we introduce information theoretic approach to quantitatively study the spine internal dynamics and its effect on the bounding gait based on three spinal morphologies. These three morphologies differ in the position of virtual spinal joint where the spine is easier to get bent. The experimental results reveal that locomotion can be enhanced by using the spine featuring a rear virtual spinal joint, which offers more freedom for the rear legs to move forward. In addition, the information theoretic analysis shows that, according to the morphological differences of the spine, the information structure changes. The relationship between the observed behavior of the robot and the corresponding information structure is discussed in detail.