Quadrupeds exhibit remarkable locomotion performance through the coordination between their limbs and torso. From past biological knowledge, it is understood that during walking, the forelimbs primarily contribute to braking, while the hindlimb are responsible for propulsion. However, in the field of quadruped robot dynamics, effectively leveraging this coordination remains a challenge. To investigate the torso-limb coordination, this study explores the walking performance of a quadruped walker with a compliant torso, driven by the forelimb or the hindlimb. Through numerical simulations, we analyze the walking behavior under different control drive methods. The findings provide insights into the design of compliant-bodied robots and the optimal distribution of propulsion forces between the forelimbs and hindlimbs.

Quadrupedal locomotion involves coordinated interaction between limbs and torso, enabling them to achieve remarkable movement performance and adapt effectively to various environments. In previous studies, mathematical dynamic models of quadrupeds have been established to investigate the mechanisms of limb-torso interaction during walking. However, due to the strong nonlinearity within the model, analyzing how the torso’s motion, especially vibrations, affects walking remains a significant challenge. In this study, the linearization and frequency analysis methods are applied to the quadruped walker to analyze its vibration characteristics, including natural frequency and vibration amplitude. Subsequently, numerical simulations are conducted to examine the relationship between torso vibration and walking performance. Furthermore, a comparison between the vibration characteristics and the simulation results reveals a potential resonance phenomenon. This finding not only validates the effectiveness of the linearization approach but also offers new insights into the interaction between the limbs and torso.

In the natural world, benefited from the advantages of the spine, quadrupeds exhibiting extraordinary flexibility which allowing them to move efficiently on variable terrains. The previous researches have indicated the legged robots which efficiently utilizing their spine can achieve rapid and stable locomotion. However, within the field of legged robot dynamics, the design of the spine and understanding how it positively influences locomotion is unclear, which is significant for quadruped robot to achieve efficient and stable walking. In this study, we proposed a model formed by tensegrity spine and rimless wheel to represent quadrupeds, using passive dynamic walking as a method, which has been well-demonstrated for observing the inherent characteristics, exhibited the locomotion characteristic of the model proposed. By numerical simulation, we observed change trend of locomotion performance with the configurations of spine’s shape, and found direction of spine design that have a positive impact on walking. These findings contribute to the design of spine structures in quadruped robots.

This paper introduces a novel X-shaped walker with telescopic legs and investigates its control method with the aim of generating a stable wheel gait on a horizontal plane without including zero dynamics which is essentially unstable and difficult to stabilize. First, we outline a planar 6-DOF robot model with three control inputs, and describe the equations of motion and inelastic collision. Second, we design an output-following control system that smoothly controls the extension/contraction lengths of the legs and relative hip-joint angle to their target terminal values, and creates an asymmetric impact posture in the anteroposterior direction so that the robot can easily overcome the next potential barrier. The coefficients of the desired-time trajectory for each control output are updated with the position and velocity values immediately after each impact as the target initial values, so the generated leg motion and control inputs exhibit smooth time variation. The validity of the proposed gait generation method and the change trend of fundamental motion characteristics with respect to control parameters are investigated through numerical simulations.

The quadrupeds have wider active territory than humans. Their bodies can adapt various environments through evolution, enabling the efficient, elegant gait for their legged locomotion. Previous researches have indicated lots of examples of utilizing the advantages of body to achieve environment adaptive and stable gait, and for legged locomotion, especially with quadruped robot determining how to generate environment-adaptive mobile locomotion remains a significant challenge. In this study, we discussed the adaptability to environments of quadruped robots, specific walking stability and gait convergence in low-friction environments with compliant torso. The numerically simulations are proposed for observing the trend of walking performance with various friction coefficient. By analyzing the typical walking gait, the adaptability of quadruped walkers with compliant torso are found. These conclusions contribute to the design and development of compliant torso for quadruped walkers.

The movement of the legs involves the interaction between the feet and the ground. Consequently, most animals possess a wide variety of foot morphologies and multifunctional capabilities. The selection and switching of these foot functions are passive and environment-dependent, ensuring environmental compliance. Despite this, current research on compliant feet lacks mathematical models that simultaneously encompass locomotion and foot compliance. Therefore, conducting in-depth studies on locomotion properties under current conditions is challenging. In this study, we present novel passive compliant feet applicable to the passive walking of a rimless wheel. We first introduce a dynamic model, achieve passive walking through numerical simulations, and subsequently analyze the gait patterns for compliance and multi-period gait. This study bridges a gap in understanding the interaction between motion and compliance in foot design, providing insights into the dynamics of compliant motion.

This paper presents a water walking robot with 6 feet which consists of a rimless wheel and a flywheel, and has a foot attached to the tip of each leg. First, in order to make the robot walk on water, we propose a foot control method by imitating the legs of some animals that can walk on water. Second, in order to increase the robot's forward speed, we improved the control method. In addition we have analysed the effect of some different physical parameters on the motion of the robot. This research is aimed at building a versatile water walking model for such applications as marine exploration.

Rescue robots require versatility and the capability to operate in various environments to carry out a diverse set of tasks effectively. The eccentric paddle (ePaddle) mechanism stands out for its high efficiency and adaptability. Generally, it is designed as a quadruped robot with a combined structure for fully-actuated control, this approach is often both inefficient and inflexible due to the requirement for repeated front-to-back paths. Unlike the fully-actuated controller that assume torso is fixed, this study proposes an under-actuated controller, consisting of a single ePaddle mechanism and a free torso for more efficient and flexible movement. Inspired by human gait, precision walking, and non-precision walking are introduced to discuss the stability of zero dynamics. Additionally, the stability condition is presented and demonstrated by numerical simulation. Since this control is based on robot dynamics, it has a high fault-tolerance and benefited from its dynamics attractor. The concept of under-actuated controller we proposed in this study is not only applicable to the ePaddle mechanism, but also to other under-actuated legged locomotion models.

This paper proposes novel passive-dynamic walk-ers formed by two cross-shaped frames and eight viscoelastic elements. Since it is a combination of two four-legged rimless wheels via viscoelastic elements, we call it viscoelastically-combined rimless wheel (VCRW). Two types of VCRWs consisting of different cross-shaped frames are introduced; one is formed by combining two Greek-cross-shaped frames (VCRW1), and the other is formed by combining two-link cross-shaped frames that can rotate freely around the central axis (VCRW2). First, we describe the model assumptions and equations of motion and collision. Second, we numerically analyze the basic gait properties of passive dynamic walking. Furthermore, we consider an activation of VCRW2 for gen-erating a stable level gait, and discuss the significance of the study as a novel walking support device.

This paper introduces a planar tensegrity robot that walks passively and cyclically on a gentle downhill, where its gait versatility can be strengthened by applying actuation forces on the connection cables. The novelty of this work is that we design the structure of this passive robot inspired by the rimless wheel, which naturally generates cyclic locomotion. Consequently, its mathematical model is analytically derived based on passive dynamic walking. Besides, the limb support conditions and dynamics effects induced by the collisions can be precisely determined accordingly. Moreover, numerical simulation is performed to show the typical gait pattern, and resonance phenomenon is observed. Finally, a preliminary experimental study is conducted to prove the validity of the mathematical model. The robot we developed and the mathematical model we derived enable further extensions on the gait analysis and model-based control by conveniently adopting efficient passivemimic walking techniques.

This paper proposes a novel method for generating an underactuated bipedal gait that completes in one step. First, we introduce an underactuated biped robot model that has a circular torso as a reaction wheel. Second, we consider an input-output linearization to formulate an output-following control law for achieving collisionless limit cycle walking. We then mathematically analyze the stability of the zero dynamics and investigate the fundamental gait properties through numerical simulations. Furthermore, we discuss an extension to generation of a few-steps walking motion aimed at safe and quick passage from a safety island to the next.