LCP method for a planar passive dynamic walker based on an event-driven scheme

The main purpose of this paper is to present a linear complementarity problem （LCP） method for a planar passive dynamic walker with round feet based on an event-driven scheme. The passive dynamic walker is treated as a planar multi-rigid-body system. The dynamic equations of the passive dynamic walker are obtained by using Lagrange＇s equations of the second kind. The normal forces and frictional forces acting on the feet of the passive walker are described based on a modified Hertz contact model and Coulomb＇s law of dry friction. The state transition problem of stick-slip between feet and floor is formulated as an LCR which is solved with an event-driven scheme. Finally, to validate the methodology, four gaits of the walker are simulated： the stance leg neither slips nor bounces; the stance leg slips without bouncing; the stance leg bounces without slipping; the walker stands after walking several steps.

Modeling and analysis of passive dynamic bipedal walking with segmented feet and compliant joints

Passive dynamic walking has been developed as a possible explanation for the efficiency of the human gait. This paper presents a passive dynamic walking model with segmented feet, which makes the bipedal walking gait more close to natural human-like gait. The proposed model extends the simplest walking model with the addition of fiat feet and torsional spring based compliance on ankle joints and toe joints, to achieve stable walking on a slope driven by gravity. The push-off phase includes foot rotations around the toe joint and around the toe tip, which shows a great resemblance to human normal walking. This paper investigates the effects of the segmented foot structure on bipedal walking in simulations. The model achieves satisfactory walking results on even or uneven slopes.

Planning and Control for Passive Dynamics Based Walking of 3D Biped Robots

Efficient walking is one of the main goals of research on biped robots. Passive Dynamics Based Walking （PDBW） has been proven to be an efficient pattern in numerous previous approaches to 2D biped walking. The goal of this study is to develop feasible method for the application of PDBW to 3D robots. First a hybrid control method is presented, where a previously proposed two-point-foot walking pattern is employed to generate a PDBW gait in the sagittal plane and, in the frontal plane, a systematic balance control algorithm is applied including online planning of the landing point of the swing leg and feedback control of the stance foot. Then a multi-space planning structure is proposed to implement the proposed method on a 13-link 3D robot. Related kinematics and planning details of the robot are presented. Furthermore, a simulation of the 13-link biped robot verifies that stable and highly efficient walking can be achieved by the proposed control method. In addition, a number of features of the biped walking, including the transient powers and torques of the joints are explored.

Motion analysis of passive dynamic walking with a rigorously constraint model: A necessary condition for maintaining period-1 gait

The friction force is an important environmental factor that influences dynamic walking.While most of the related works simply assume static friction or Coulomb friction,we use the LuGre friction,which accounts for both static and dynamic effects,to model the horizontal ground reaction force of passive dynamic walking.We present a detailed mathematical modeling method and perform numerical simulations using it.Furthermore,we analyze the ground surface cases of the Coulomb friction condition and static friction condition to verify the model’s generalization.We discover the required condition for the existence of the period-1 gait through investigation.Our mathematical model and theoretical analysis add to our understanding of passive dynamic walking,which helps to positively utilize the natural dynamics of the legged locomotion system in control design.

Dynamics of a spacecraft with large flexible appendage constrained by multi-strut passive damper

This paper is concerned with the dynamics of a spacecraft with multi-strut passive damper for large flexible appendage.The damper platform is connected to the spacecraft by a spheric hinge,multiple damping struts and a rigid strut.The damping struts provide damping forces while the rigid strut produces a motion constraint of the multibody system.The exact nonlinear dynamical equations in reducedorder form are firstly derived by using Kane＇s equation in matrix form.Based on the assumptions of small velocity and small displacement,the nonlinear equations are reduced to a set of linear second-order differential equations in terms of independent generalized displacements with constant stiffness matrix and damping matrix related to the damping strut parameters.Numerical simulation results demonstrate the damping effectiveness of the damper for both the motion of the spacecraft and the vibration of the flexible appendage,and verify the accuracy of the linear equations against the exact nonlinear ones.

Preface

Micromechanics aims mainly at establishing the quantitative relation between the macroscopic mechanical behavior and the microstructure of heterogeneous materials.

Control of a Cheetah Robot in Passive Bounding Gait

Passive dynamics is always one of research emphases of the legged robots. Studies have proved that cheetah robot could achieve stably passive bounding motion under proper initial conditions in the ideal case. However, the actual robot must have energy dissipation because of friction and collision compared with the theoretical model. This paper aims to propose a control method that can drive the cheetah robot running in passive bounding gait. First, a sagittal-plane model with a rigid torso and two compliant legs is introduced to capture the dynamics of robot bounding. Numerical return map studies of the bounding model reveal that there exists a large variety of passively cyclic bounding motions （fixed points）. Based on the distribution law of fixed points, an open-loop control method including touchdown angle control strategy and leg length control strategy is put forward. At last, prototype of the cheetah robot is designed and manufactured, and locomotion experiment are carried out. The experiment results show that the cheetah robot can achieve a stable bounding motion at different speeds with the proposed control method.

Virtual Constraint Based Control of Bounding Gait of Quadruped Robots

This paper presents a control approach for bounding gait of quadruped robots by applying the concept of Virtual Constraints （VCs）. A VC is a relative motion relation between two related joints imposed to the robots in terms of a specified gait, which can drive the robot to run with desired gait. To determine VCs for highly dynamic bounding gait, the limit cycle motions of the passive dynamic model of bounding gait are analyzed. The leg length and hip/shoulder angle trajectories corresponding to the limit cycles are parameterized by leg angles using 4 th-order polynomials. In order to track the calculated periodic motions, the polynomials are imposed on the robot as virtual motion constraints by a high-level state machine controller. A bounding speed feedback strategy is introduced to stabilize the robot running speed and enhance the stability. The control approach was applied to a newly designed lightweight bioinspired quadruped robot, AgiDog. The experimental results demonstrate that the robot can bound at a frequency up to 5 Hz and bound at a maximum speed of 1.2 m·s^-1 in sagittal plane with a Froude number approximating to 1.