This paper investigates the mathematical modeling and basic motion properties of planar seven-link robots that forms passive closed and active open chains. The passive closed model is formed by connecting seven rigid frames via seven viscoelastic joints, and the active open model is formed by connecting them via actuated joints. The former is a convex heptagonal model and can exhibit passive-dynamic rolling on a gentle downhill, whereas the latter virtually forms a forward-leaning octagonal shape by controlling the six relative joint angles. In the first half of this paper, we describe the model assumptions and develop the mathematical equations of motion and collision of the passive closed model, and numerically analyze the motion characteristics by changing the slope angle while checking the conditions necessary for stable motion generation. In the second half, we outline the active open model, develop the PD control system, and numerically analyze the motion characteristics by changing the target angle parameter that controls the degree of forward lean of the virtual octagon.

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.

The authors have proposed a passive rotating locomotion robot that forms a convex heptagonal body by connecting seven identical linear rigid frames via viscoelastic rotational joints. In our previous study, it was confirmed through both numerical simulations and actual experiments that stable and passive rotating motion on a downhill could be generated. This paper proposes two new models in which the seven rigid frames are used as robust exoskeletons as they are, but the elastic elements attached to the rotating joints are removed and repositioned on the diagonals of the convex heptagon to reproduce the flexibility of the internal tissue. The elastic elements form a star-shaped polygon called a heptagram, which is formed by connecting seven vertices with a single stroke. The seven vertices can be connected in two different ways to form two different heptagram shapes. We report the basic numerical results of the change in the motion characteristics of the two models with respect to the slope angle and elastic modulus. An overview of the prototypes developed and the results of basic experiments are also reported.

This paper proposes a novel passive dynamic walker with a body shape similar to an eight-legged rimless wheel that performs a natural swinging motion of the swing leg through storage and release of elastic energy. The generated motion is period-1 and asymptotically stable, but the inherent limit cycle stability is nontrivial because it does not achieve constraint on impact posture. Since it has almost linear dynamics, however, its walkability can be instantaneously determined using a linearized model without numerical integration. With the equations of linearized motion and exact collision, the step period and the state at the next collision can be obtained numerically and instantaneously using a bisection method based on the geometric constraint condition at impact. Then, by updating the state for each collision and repeating the same calculation, it is possible to instantaneously determine whether or not the walking motion continues stably for a long period of time. By comparing the results of this calculation with those of the numerical integration of the nonlinear and linearized models, the effectiveness of the proposed method is confirmed. Furthermore, using the proposed method, we analyze the period-doubling bifurcation phenomenon and the change in the singular values of the Poincaré map that occurs with the change in the elastic modulus.

This paper addresses the problem of realizing a novel robotic bipedal locomotion called wheel gait, which is achieved by rotating the stance and swing legs in the same direction. First, a model of a planar 3-DOF X-shaped walker with a reaction wheel is introduced, and the mathematical equations are described. Second, the condition for stabilizing zero dynamics is formulated as the time integral value of control input to the reaction wheel for one step becomes zero, and the control system for achieving this is designed based on the method of continuous-time output deadbeat control. Third, a typical steady wheel gait of the linearized model is numerically generated, and its extension to the nonlinear model is discussed. Although the nonlinear model has only one nonlinear term in the gravity term, numerical simulations show that there is a big gap between this and the linearized model. Through analysis of the typical nonlinear wheel gaits, the difficulty of achieving the same walking speed as the linearized model is discussed.

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.