ZMP Analysis for Dynamic Walking of a Passivity-based Biped Robot with Flat Feet

Nima Fatehi,Adel Akbarimajd,Masoud Asadpour 제어로봇시스템학회 2010 제어로봇시스템학회 국제학술대회 논문집 Vol.2010 No.10

Zero moment point has been usually employed for balance keeping and walking analysis of active biped robots with bent knees, while balance and walking stability analysis of passive robots has been done using cyclic analysis approaches. While the problem in general is common, the two approaches have been separated in the literature for two different classes of passivity-based and ZMP-based robots. In this paper we have made a ZMP analysis for a passivity-based biped robot. The robot has been simulated using MSC Adams and Matlab/Simulink and a stable walking is achieved for a defined walking policy which is based on passivity-based walking with hips and ankles actuated and knee joints considered passive. The trajectory of ZMP is extracted and discussed during a stable walking. The role of Achill"s spring on ZMP is discussed and the overall profile of ZMP trajectory and its changes at specific crucial events, like knee strike and heel strike, is analyzed.

시간 이력 기반 ZMP–오일러 앵글 결합 수치해석 모델을 이용한 크롤러 크레인의 전도 안정성 평가

강범준,정진범,이호연 사단법인 유공압건설기계학회 2025 드라이브·컨트롤 Vol.22 No.4

This study examines the dynamic overturning stability of a 150-ton crawler crane using a ZMP–Euler coupled model. The algorithm combines Zero Moment Point (ZMP) theory with Euler angle transformations to assess stability during simultaneous luffing and slewing motions. Utilizing three-dimensional design data, a MATLAB-based numerical analysis was conducted to calculate time-varying ZMP trajectories and a normalized Stability Index (SI), which indicates the distance from the track boundary. The simulation results demonstrated that the crane maintained stable conditions under 60% and 80% of its rated load, while marginal stability was observed at the full-rated 150-ton capacity due to a forward shift in ZMP during slewing. Additionally, the developed approach effectively visualized the dynamic stability transition over time, providing valuable insights into how combined pitch and yaw motions affect the overall stability margin. This method quantitatively evaluates ZMP migration and offers practical guidance for ensuring safe operation and optimizing structural balance in large crawler cranes.

도립진자형 이족보행로봇의 유연한 궤적 생성

강찬수(Chan-Soo Kang),노경곤(Kyung-Kon Noh),공정식(Jung-Shik Kong),김진걸(Jin-Geol Kim) Korean Society for Precision Engineering 2005 한국정밀공학회지 Vol.22 No.7

This paper is concerned with smooth trajectory generation of biped robot which has inverted pendulum type balancing weight. Genetic algorithm is used to generate the trajectory of the leg and balancing weight. Balancing trajectory can be determined by solving the second order differential equation under the condition that the reference ZMP (Zero moment point) is settled. Reference ZMP effect on gait pattern absolutely but the problem is how to determine the reference ZMP. Genetic algorithm can find optimal solution under the high order nonlinear situation. Optimal trajectory is generated when use genetic algorithm which has some genes and a fitness function. In this paper, minimization of balancing joints motion is used for the fitness function and set the weight factor of the two balancing joints at the fitness function. Inverted pendulum type balancing weight is very similar with human and this model can be used for humanoid robot. Simulation results show ZMP trajectory and the walking experiment made on the real biped robot IWR-IV.

Zero Moment Point를 이용한 이족 보행 로봇의 경사로 걸음새 제어에 관한 연구

엄승현(Seung-hyun Um),임미섭(Mee-seub Lim),임준홍(Joon-hong Lim) 대한전기학회 2006 대한전기학회 학술대회 논문집 Vol.2006 No.10

In this paper, we propose stable walking algorithm using ZMP for the biped robot in the slope-way. At first, we define discrete state variables that classified stable area and unstable area by center of mass from ZMP during slope-way walking. For the stable walking gait, the discrete state controller for determining the high-level and low-level decision making are designed. The high-level decision making is composed of the discrete state variables; left foot support phase, right foot support phase, nat-way, and slope-way. Then the continuous state controller is implemented for the low-level decision making using ZMP.

인간의 COG 궤적의 분석을 통한 5-link 이족 로봇의 보행 패턴 생성

김병현(Byounghyun Kim),한영준(Youngjoon Han),한헌수(Hernsoo Hahn) 한국정보과학회 2009 정보과학회논문지 : 소프트웨어 및 응용 Vol.36 No.2

인간이 최소 에너지를 소비하면서 자연스럽고 안정된 상태로 보행한다는 것에 착안하여, 본 논문은 인간 보행의 COG 궤적을 분석함으로써 인간형 이족로봇의 자연스러운 보행에 관한 연구를 수행한다. 이를 위해서 본 논문은 sagittal plane과 frontal plane상의 보행 영상으로부터 계측된 COG 궤적을 고려함으로써 안정적이고 에너지를 최소화하는 자연스러운 이족로봇의 보행 패턴을 생성한다. 인간과 이족로봇은 기구학적인 형태는 유사하지만 자유도에 있어 많은 차이를 보이기 때문에 추출된 인간 관절의 회전력을 이족로봇에 바로 적용할 수 없다. 본 논문에서는 인간의 보행패턴으로부터 계측된 각 관절의 회전력과 인간의 COG 궤적으로부터 계산된 ZMP을 이용하는 적응적 보행 패턴 생성 GA 알고리즘을 통해 5-link 이족로봇 모델의 보행패턴을 생성한다. 제안된 알고리즘은 인간의 각 관절의 회전력과 ZMP 궤적을 고려하기 때문에 인간과 같이 유연하고 에너지 소비를 최소화하는 인간형 이족로봇의 보행패턴을 생성한다. 본 논문은 역기구학을 이용한 일반적인 방법과 제안하는 방법에 의해 생성된 보행 패턴을 각각 5-link 이족로봇 모델에 적용하여 시각적인 측면과 에너지 효율측면에서 평가함으로써 제안하는 알고리즘의 우수성을 입증하였다. Based on the fact that a human being walks naturally and stably with consuming a minimum energy, this paper proposes a new method of generating a natural gait of 5-link biped robot like human by analyzing a COG(Center Of Gravity) trajectory of human's gait. In order to generate a natural gait pattern for 5-link biped robot, it considers the COG trajectory measured from human's gait images on the sagittal and frontal plane. Although the human and 5-link biped robot are similar in the side of the kinematical structure, numbers of their DOFs(Degree Of Freedom) are different. Therefore, torques of the human's joints cannot are applied to robot's ones directly. In this paper, the proposed method generates the gait pattern of the 5-link biped robot from the GA algorithm which utilize human's ZMP trajectory and torques of all joints. Since the gait pattern of the 5-link biped robot model is generated from human's ones, the proposed method creates the natural gait pattern of the biped robot that minimizes an energy consumption like human. In the side of visuality and energy efficiency, the superiority of the proposed method have been improved by comparative experiments with a general method that uses a inverse kinematics.

ZMP를 이용한 굴삭기의 안정성에 관한 연구

최종환,엄혁,임태형,김승수,양순용,이병룡,안경관 한국공작기계학회 2003 한국공작기계학회 춘계학술대회논문집 Vol.2003 No.-

The hydraulic excavator has been a popular research object for automation because of its multi-workings and economic efficiency. When it works crane tasks, most of disasters happen. The stability of the excavator having crane function has a close relation with excavator's posture, motion and load. In this paper, the stability of tipping-over has been analysed using Zero Moment Point(ZMP),

푸리에 급수를 이용한 이족보행로봇의 보행 궤적 해석해 생성

박일우(Ill-Woo Park),백주훈(Juhoon Back) 제어로봇시스템학회 2009 제어·로봇·시스템학회 논문지 Vol.15 No.12

이족 보행로봇의 균형추 형태에 따른 안정성 해석

노경곤(Kyung-Kon Noh),김진걸(Jin-Geol Kim) Korean Society for Precision Engineering 2005 한국정밀공학회지 Vol.22 No.1

This paper is concerned with a balancing motion formulation and control of the ZMP (Zero Moment Point) for a biped-walking robot that has a prismatic balancing weight or a revolute balancing weight. The dynamic stability equation of a walking robot which have a prismatic balancing weight is conditionally linear but a walking robot's stability equation with a revolute balancing weight is nonlinear. For a stable gait, stabilization equations of a biped-walking robot are modeled as non-homogeneous second order differential equations for each balancing weight type, and a trajectory of balancing weight can be directly calculated with the FDM (Finite Difference Method) solution of the linearized differential equation. In this paper, the 3dimensional graphic simulator is developed to get and calculate the desired ZMP and the actual ZMP. The operating program is developed for a real biped-walking robot IWRIII. Walking of 4 steps will be simulated and experimented with a real biped-walking robot. This balancing system will be applied to a biped humanoid robot, which consist legs and upper body, as a future work.

Constant Pelvis Height ZMP-based Walking

Aliza Che Amran,Fariz Ali,Atsuo Kawamura 제어로봇시스템학회 2010 제어로봇시스템학회 국제학술대회 논문집 Vol.2010 No.10

Researchers introduced a constant center of mass walking, mainly to solve the ZMP equations analytically for center of mass trajectories in the x and y directions (case1). In this paper, case 2 proposes that if pelvis is made constant instead, energy usage could be reduced particularly at the leg joints. CoM-based kinematics methods are used to realize each case. Walking simulations of 0.22km/h are utilized for observations. In the simulation results, case 2 consumed almost 12% less in total energy consumption (electrical and mechanical) compared to case 1.

듀얼 암 로봇을 위한 제어 시스템 설계

고석조(Seok-Jo Go),이영진(Young-Jin Lee) 대한기계학회 2007 대한기계학회 춘추학술대회 Vol.2007 No.10

Robotic manipulators are increasingly deployed in complex environments or to perform complex tasks. Redundancy is necessary to cope with the increasing complexity. Redundancy is defined whenever a robot possesses more input degrees of freedom than required by the task at hand. Studies on dual arm robots have been continually carried out in robotics areas to provide robots in dangerous environments, similar to those which human beings would be normally in, without a special change to the working environment. In this study, a control system for a dual arm robot has been designed to provide a real-time connection between the controller and the robot by using a MEl's ZMP-SynqNet-PCI board. The dual arm robot consists of two arms with six degrees of freedom and a body with three degrees of freedom.