Trajectory generation for continuous leg forces during double support and heel-to-toe shift based on divergent component of motion

This paper works with the concept of Divergent Component of Motion (DCM), also called ’(instantaneous) Capture Point’. We present two real-time DCM trajectory generators for uneven (three-dimensional) ground surfaces, which lead to continuous leg (and corresponding ground reaction) force profiles and facilitate the use of toe-off motion during double support. Thus, the resulting DCM trajectories are well suited for real-world robots and allow for increased step length and step height. The performance of the proposed methods was tested in numerous simulations and experiments on IHMC’s Atlas robot and DLR’s humanoid robot TORO

人間を模擬した知覚系を持つ2足ヒューマノイドロボットの自己位置推定機能に対する歩行動作の影響に関する研究

早大学位記番号:新8279早稲田大

Simulation and Framework for the Humanoid Robot TigerBot

Walking humanoid robotics is a developing field. Different humanoid robots allow for different kinds of testing. TigerBot is a new full-scale humanoid robot with seven degrees-of-freedom legs and with its specifications, it can serve as a platform for humanoid robotics research. Currently TigerBot has encoders set up on each joint, allowing for position control, and its sensors and joints connect to Teensy microcontrollers and the ODroid XU4 single-board computer central control unit. The components’ communication system used the Robot Operating System (ROS). This allows the user to control TigerBot with ROS. It’s important to have a simulation setup so a user can test TigerBot’s capabilities on a model before using the real robot. A working walking gait in the simulation serves as a test of the simulator, proves TigerBot’s capability to walk, and opens further development on other walking gaits. A model of TigerBot was set up using the simulator Gazebo, which allowed testing different walking gaits with TigerBot. The gaits were generated by following the linear inverse pendulum model and the basic zero-moment point (ZMP) concept. The gaits consisted of center of mass trajectories converted to joint angles through inverse kinematics. In simulation while the robot follows the predetermined joint angles, a proportional-integral controller keeps the model upright by modifying the flex joint angle of the ankles. The real robot can also run the gaits while suspended in the air. The model has shown the walking gait based off the ZMP concept to be stable, if slow, and the actual robot has been shown to air walk following the gait. The simulation and the framework on the robot can be used to continue work with this walking gait or they can be expanded on for different methods and applications such as navigation, computer vision, and walking on uneven terrain with disturbances

Pattern Generation for Walking on Slippery Terrains

In this paper, we extend state of the art Model Predictive Control (MPC) approaches to generate safe bipedal walking on slippery surfaces. In this setting, we formulate walking as a trade off between realizing a desired walking velocity and preserving robust foot-ground contact. Exploiting this formulation inside MPC, we show that safe walking on various flat terrains can be achieved by compromising three main attributes, i. e. walking velocity tracking, the Zero Moment Point (ZMP) modulation, and the Required Coefficient of Friction (RCoF) regulation. Simulation results show that increasing the walking velocity increases the possibility of slippage, while reducing the slippage possibility conflicts with reducing the tip-over possibility of the contact and vice versa.Comment: 6 pages, 7 figure

Development of a Hybrid Powered 2D Biped Walking Machine Designed for Rough Terrain Locomotion

Biped robots hold promise as terrestrial explorers because they require a single discrete foothold to place their next step. However, biped robots are multi-input multi-output dynamically unstable machines. This makes walking on rough terrain difficult at best. Progress has been made with non-periodic rough terrain like stairs or inclines with fully active walking machines. Terrain that requires the walker to change its gait pattern from a standard walk is still problematic. Most walking machines have difficulty detecting or responding to the small perturbations induced by this type of terrain. These small perturbations can lead to unstable gait cycles and possibly a fall. The Intelligent Systems and Automation Lab at the University of Kansas has built a three legged 2D biped walking machine to be used as a test stand for studying rough terrain walking. The specific aim of this research is to investigate how biped walkers can best maintain walking stability when acted upon by small perturbations caused by periodic rough terrain. The first walking machine prototype, referred to as Jaywalker has two main custom actuation systems. The first is the hip ratchet system. It allows the walker to have either a passive or active hip swing. The second is the hybrid parallel ankle actuator. This new actuator uses a pneumatic ram and stepper motor in parallel to produce an easily controlled high torque output. In open loop control it has less than a 1° tracking error and 0.065 RPM velocity error compared to a standard stepper motor. Step testing was conducted using the Jaywalker, with a passive hip, to determine if a walker with significant leg mass could walk without full body actuation. The results of testing show the Jaywalker is ultimately not capable of walking with a passive hip. However, the walking motion is fine until the terminal stance phase. At this point the legs fall quickly towards the ground as the knee extends the shank. This quick step phenomenon is caused by increased speeds and forces about the leg and hip caused by the extension of the shank. This issue can be overcome by fully actuating the hip, or by adding counterbalances to the legs about the hip

Augmented Linear Inverted Pendulum Model for Bipedal Gait Planning

Ph.DDOCTOR OF PHILOSOPH

Locomoção bípede adaptativa a partir de uma única demonstração usando primitivas de movimento

Doutoramento em Engenharia EletrotécnicaEste trabalho aborda o problema de capacidade de imitação da locomoção humana através da utilização de trajetórias de baixo nível codificadas com primitivas de movimento e utilizá-las para depois generalizar para novas situações, partindo apenas de uma demonstração única. Assim, nesta linha de pensamento, os principais objetivos deste trabalho são dois: o primeiro é analisar, extrair e codificar demonstrações efetuadas por um humano, obtidas por um sistema de captura de movimento de forma a modelar tarefas de locomoção bípede. Contudo, esta transferência não está limitada à simples reprodução desses movimentos, requerendo uma evolução das capacidades para adaptação a novas situações, assim como lidar com perturbações inesperadas. Assim, o segundo objetivo é o desenvolvimento e avaliação de uma estrutura de controlo com capacidade de modelação das ações, de tal forma que a demonstração única apreendida possa ser modificada para o robô se adaptar a diversas situações, tendo em conta a sua dinâmica e o ambiente onde está inserido. A ideia por detrás desta abordagem é resolver o problema da generalização a partir de uma demonstração única, combinando para isso duas estruturas básicas. A primeira consiste num sistema gerador de padrões baseado em primitivas de movimento utilizando sistemas dinâmicos (DS). Esta abordagem de codificação de movimentos possui propriedades desejáveis que a torna ideal para geração de trajetórias, tais como a possibilidade de modificar determinados parâmetros em tempo real, tais como a amplitude ou a frequência do ciclo do movimento e robustez a pequenas perturbações. A segunda estrutura, que está embebida na anterior, é composta por um conjunto de osciladores acoplados em fase que organizam as ações de unidades funcionais de forma coordenada. Mudanças em determinadas condições, como o instante de contacto ou impactos com o solo, levam a modelos com múltiplas fases. Assim, em vez de forçar o movimento do robô a situações pré-determinadas de forma temporal, o gerador de padrões de movimento proposto explora a transição entre diferentes fases que surgem da interação do robô com o ambiente, despoletadas por eventos sensoriais. A abordagem proposta é testada numa estrutura de simulação dinâmica, sendo que várias experiências são efetuadas para avaliar os métodos e o desempenho dos mesmos.This work addresses the problem of learning to imitate human locomotion actions through low-level trajectories encoded with motion primitives and generalizing them to new situations from a single demonstration. In this line of thought, the main objectives of this work are twofold: The first is to analyze, extract and encode human demonstrations taken from motion capture data in order to model biped locomotion tasks. However, transferring motion skills from humans to robots is not limited to the simple reproduction, but requires the evaluation of their ability to adapt to new situations, as well as to deal with unexpected disturbances. Therefore, the second objective is to develop and evaluate a control framework for action shaping such that the single-demonstration can be modulated to varying situations, taking into account the dynamics of the robot and its environment. The idea behind the approach is to address the problem of generalization from a single-demonstration by combining two basic structures. The first structure is a pattern generator system consisting of movement primitives learned and modelled by dynamical systems (DS). This encoding approach possesses desirable properties that make them well-suited for trajectory generation, namely the possibility to change parameters online such as the amplitude and the frequency of the limit cycle and the intrinsic robustness against small perturbations. The second structure, which is embedded in the previous one, consists of coupled phase oscillators that organize actions into functional coordinated units. The changing contact conditions plus the associated impacts with the ground lead to models with multiple phases. Instead of forcing the robot’s motion into a predefined fixed timing, the proposed pattern generator explores transition between phases that emerge from the interaction of the robot system with the environment, triggered by sensor-driven events. The proposed approach is tested in a dynamics simulation framework and several experiments are conducted to validate the methods and to assess the performance of a humanoid robot

사람 보행 분석 연구와 그 결과를 활용한 휴머노이드 로봇 보행 패턴 생성

학위논문 (박사) -- 서울대학교 대학원 : 융합과학기술대학원 융합과학부(지능형융합시스템전공), 2020. 8. 박재흥.발의 미끄러짐은 보행의 안정성을 떨어트리는 요인 중 하나이다. 보행 중 발에 발생하는 수평 전단력이 발과 지면 사이의 마찰력보다 커지면, 발은 접촉을 상실하고 미끄러지게 된다. 여기서, 발과 지면 사이의 마찰력은 발에 작용하는 수직력에 의해 결정되게 된다. 즉, 휴머노이드 로봇 보행 패턴 생성의 측면에서 보자면, 로봇 발에 발생하는 수평력과 수직력을 어떻게 설계하는지에 따라 보행 중 미끄러짐의 가능성이 바뀐다는 것이다. 선형 역진자 모델은 휴머노이드 로봇의 무게 중심 궤적 생성을 위해 자주 사용되어왔다. 선형 역진자 모델은 로봇의 무게 중심 높이를 일정하게 유지하도록 제한한다. 무게 중심의 높이 제한 때문에 로봇의 수직 방향의 가속도는 보행 속도와 관련 없이 항상 중력 가속도가 된다. 그러나 수평 방향의 가속도는 보행 속도가 증가하면 비례하여 증가한다. 따라서 빠른 보행 속도에서는 수직력에 비례하는 마찰력에 비해 수평 전단력이 커지면서 발의 미끄러짐이 발생할 수 있다. 선형 역진자 모델에 의한 일정한 수직 높이 구속 조건이 로봇 발의 미끄러짐을 유발할 수 있다는 것을 시사한다. 무게 중심의 적절한 수직 움직임을 생성함으로써 휴머노이드 로봇 보행 중 발의 미끄러짐을 줄일 수 있다. 인간공학 분야에서는 Available Coefficient of Friction(aCOF)과 Utilized Coefficient of Friction(uCOF)을 이용하여 사람 보행 중 발의 미끄러짐 가능성을 예측하는 연구들이 수행됐다. 여기서, aCOF는 두 물체의 재질이나 상태에 의해 결정되는 마찰 계수이다. 반면, uCOF는 보행 중 지지하는 발에 가해지는 수평 전단력과 수직력의 비이다. 인간공학 연구들에 따르면, uCOF가 aCOF를 초과할 때 발은 접촉을 상실하고 미끄러지게 된다. 로봇 발의 미끄러짐 감소를 위해서는 로봇 보행 중 발에 발생하는 uCOF가 로봇 발과 지면 사이의 aCOF 보다 작아지도록 적절한 수직 방향의 무게 중심 궤적을 생성하는 것이 필요하다. 다양한 형태의 수직 방향의 무게 중심 궤적 생성이 가능한데, 간단하면서도 효율적인 방법은 무게 중심의 에너지가 보존되도록 수직 방향의 무게 중심 궤적을 생성하는 것이다. 기존 선형 역진자 모델을 이용해 수평 방향의 무게 중심 궤적을 생성하고, 운동 에너지와 위치 에너지가 교환되면서 전체 에너지가 보존되는 수직 방향의 무게 중심 궤적을 추가하는 것이다. 무게 중심의 에너지 보존 원리를 이용하여 무게 중심의 양의 일(Mechanical Work) 생성을 최소화함으로써 관절의 양의 일 생성을 감소시키고, 이를 통해 보행 중 에너지 효율을 높이는 것이 가능하다. 이 논문은 발과 지면 사이의 aCOF 보다 작도록 보행 중 uCOF를 유지하면서 무게 중심의 양의 일을 최소화하는 적절한 수직 방향의 무게 중심 궤적을 생성하는 것을 목표로 한다. 발의 미끄러짐이 감소하면서 에너지 효율이 높은 휴머노이드 로봇 보행 패턴 생성을 위해, 먼저 사람 보행 중 uCOF에 관한 연구와 사람 보행 중 관절의 일에 관한 연구를 선행한다. 사람 보행에 관한 분석 연구와 사람 보행의 원리 이해를 통해 최적화 알고리즘 기반 수직 방향의 무게 중심 궤적 생성 방법이 제시된다. 제시된 알고리즘을 이용하여 구해진 수직 방향의 무게 중심 궤적을 휴머노이드 로봇 보행 실험에 적용한다. 궁극적으로 이 논문은, 수직 방향의 무게 중심 궤적을 추가함으로써 기존 선형 역진자 모델의 한계를 극복하여, 미끄러짐의 가능성이 감소하고 에너지 효율이 높은 휴머노이드 로봇 보행 패턴을 생성한다.Foot slippage is one of the factors responsible for the increasing instability during human walking. A slip occurs when the horizontal shear force acting on the foot becomes greater than the frictional force between the foot and the ground, which is proportional to the vertical force. For humanoid robot walking, the possibility of a slip depends upon how the horizontal shear force and vertical force both acting on the foot are designed. In the linear inverted pendulum model (LIPM), which is commonly used to generate the center of mass (COM) trajectory of humanoid robots, the vertical height of the COM is kept constant. The constant height of the COM restricts that the vertical force is always equal to the gravitational force at any walking speed. However, upon increasing the walking speed, the horizontal ground reaction force increases in proportion with the forward and lateral accelerations of the COM. This increase in the horizontal ground reaction force, while the vertical ground force is being constant, suggests that the robot-foot slippage can occur because of the restriction of the vertical motion by the LIPM constraint. By generating the appropriate vertical motion, the robot-foot slippage can be reduced during humanoid robot walking. Researchers in the field of ergonomics have been conducted studies on the relationship between the available coefficient of friction (aCOF) and the utilized coefficient of friction (uCOF) to predict the potential for a slip during human walking. The aCOF is both the static and dynamic coefficient of friction between two objects in contact, and it depends on the properties of the objects. The uCOF is the ratio of the horizontal shear force to the vertical force applied by the supporting foot. Foot slippage occurs when the uCOF exceeds the aCOF. Various types of vertical motion can set the maximum value of the uCOF to be less than the aCOF between the foot and floor for humanoid robot walking. One of the simple and energy-efficient methods is to minimize the mechanical work of the COM by introducing added vertical motion. Therefore, the COM pattern would become more energy efficient by exchanging kinetic energy and potential energy. This thesis aims to generate the appropriate vertical motion of the COM to maintain the utilized coefficient of friction (uCOF) less than the available coefficient of friction between the foot and the ground, and to minimize the mechanical work during humanoid robot walking. Before generating a slip-safe and energy-efficient COM trajectory for humanoid robot walking, studies on analyzing the COM patterns, mechanical work, and uCOF during human walking are conducted to understand the principle of walking. Vertical motions at various speeds are generated using an optimization method. Subsequently, the generated COM motion patterns are used as reference trajectories of the COM for humanoid robot walking. This thesis suggests a way to generate slip-safe and energy-efficient COM patterns, which, in turn, overcome the limitations of the LIPM by adding vertical COM motion.Chapter 1 Introduction 1 1.1 Research Background 1 1.2 Contributions of Thesis 3 1.3 Overviews of Thesis 4 Chapter 2 Dynamics of Walking 5 2.1 Walking Model 5 2.1.1 Linear Inverted Pendulum Model 5 2.1.2 Spring-Loaded Inverted Pendulum Model 6 2.1.3 Extrapolated Center of Mass Dynamics 9 2.2 Walking Theory 11 2.2.1 Step-to-Step Transition 11 Chapter 3 HumanWalking Analysis 13 3.1 Motion Capture for Walking 13 3.1.1 Motion Capture Technology 13 3.1.2 Joint Kinematics and Kinetics 15 3.2 Joint and COM During Human Walking 17 3.2.1 Introduction 17 3.2.2 Methods 19 3.2.3 Change of Joint Angle and the COM 20 3.2.4 Discussion 26 3.3 Slipping During Human Walking 27 3.3.1 Introduction 27 3.3.2 Methods 31 3.3.3 Change of uCOF and GRF 34 3.3.4 Interaction Effect Between Heel Area and Speed 36 3.3.5 Discussion 39 3.4 Mechanical Work During Human Walking 44 3.4.1 Introduction 44 3.4.2 Methods 46 3.4.3 Calculation for Joint Mechanical Work 48 3.4.4 Change of Joint Mechanical Work 51 3.4.5 Change of Stride Parameters 53 3.4.6 Discussion 54 Chapter 4 Robot Walking Pattern Generation 59 4.1 Introduction 59 4.2 Forward and Lateral COM 61 4.2.1 XcoM Method 61 4.2.2 Preview Control Method 63 4.3 Vertical COM 64 4.3.1 Calculation for uCOF 64 4.3.2 Calculation for ZMP 65 4.3.3 Calculation for COM Mechanical Work 66 4.3.4 Optimization for Vertical COM Generation 68 4.3.5 Results of Optimization for Vertical COM 73 4.4 Slipping During Robot Walking 75 4.4.1 Robot Simulation 75 4.4.2 Robot Experiments 77 4.5 Mechanical Work During Robot Walking 81 4.5.1 Robot Simulation 81 4.5.2 Robot Experiments 82 4.6 Discussion 87 4.6.1 Tracking Errors in Robot Experiments 87 4.6.2 Effect of Vertical Motions on Real Net Power 91 4.6.3 Trade-Off Between Efficiency and Stability 92 4.6.4 Difference Between Human and Robot 93 Chapter 5 Conclusions 95 Bibliography 97 Abstract (Korean) 111Docto

Postural stability during standing and walking and the effects of ageing

The postural stability during quiet stance and during walking was investigated in 22 elderly and 20 young subjects. A motion analysis system was used to simultaneously record movements of 14 markers on the body while a force plate recorded movement of the centre of pressure (COP) during stance (but not during walking). The movements of the body during stance could be well described (> 90 % of the variance explained) as a simple inverted pendulum moving about the ankles in the anterior-posterior and medial-lateral directions. This model was applicable to both young and elderly subjects and also predicted the records of COP movement well (r > 0.90). When account was taken of the ground reaction forces the prediction was further improved. The greater COP movements commonly observed in the elderly are shown to be due to increased pendulum sway in the medial-lateral direction, compared to young subjects. The inverted pendulum model also gave an adequate description of the deviations from the mean path ("sway") during walking which are larger than those during stance. The static measurement that best predicts sway during walking is medial-lateral movements of the COP when standing on a compliant surface with the eyes closed. The relationship between muscle strength and COP displacement was examined in a larger group of elderly subjects (N = 56). Maximum voluntary force per cross-sectional area was found not to be correlated with COP movements during quiet stance. This suggests that muscle weakness and increased sway in the elderly have separate physiological causes. A method was developed for inducing a trip-like perturbation of gait as subjects walked on a treadmill. Muscle activation patterns and body kinematics were recorded in 9 young subjects to establish the normative response to such a perturbation with a view to investigating these responses in the elderly