Straight-Leg Walking Through Underconstrained Whole-Body Control

We present an approach for achieving a natural, efficient gait on bipedal robots using straightened legs and toe-off. Our algorithm avoids complex height planning by allowing a whole-body controller to determine the straightest possible leg configuration at run-time. The controller solutions are biased towards a straight leg configuration by projecting leg joint angle objectives into the null-space of the other quadratic program motion objectives. To allow the legs to remain straight throughout the gait, toe-off was utilized to increase the kinematic reachability of the legs. The toe-off motion is achieved through underconstraining the foot position, allowing it to emerge naturally. We applied this approach of under-specifying the motion objectives to the Atlas humanoid, allowing it to walk over a variety of terrain. We present both experimental and simulation results and discuss performance limitations and potential improvements.Comment: Submitted to 2018 IEEE International Conference on Robotics and Automatio

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

Push recovery with stepping strategy based on time-projection control

In this paper, we present a simple control framework for on-line push recovery with dynamic stepping properties. Due to relatively heavy legs in our robot, we need to take swing dynamics into account and thus use a linear model called 3LP which is composed of three pendulums to simulate swing and torso dynamics. Based on 3LP equations, we formulate discrete LQR controllers and use a particular time-projection method to adjust the next footstep location on-line during the motion continuously. This adjustment, which is found based on both pelvis and swing foot tracking errors, naturally takes the swing dynamics into account. Suggested adjustments are added to the Cartesian 3LP gaits and converted to joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies also ensure enough ground clearance in perturbed walking conditions. The proposed structure is robust, yet uses very simple state estimation and basic position tracking. We rely on the physical series elastic actuators to absorb impacts while introducing simple laws to compensate their tracking bias. Extensive experiments demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness due to relatively soft springs in the ankles and avoiding any Zero Moment Point (ZMP) control in our proposed architecture.Comment: 20 pages journal pape

Optimal Control of the Cheetah During Rapid Manoeuvres

Cheetahs are incredibly fast, manoeuvrable and highly dynamic, but relatively little is understood about how this is achieved. Thus, understanding their abilities is a subject of research for roboticists and biologists. Trajectory optimisation is a tool often used to increase our understanding of cheetahs, but current approaches which handle the full complexity of poorly understood manoeuvres are slow. The lack of data means that there are no simulated models of cheetahs known to be representative of dynamic movements such as acceleration and turning. In this project, a modelling change is investigated that decreases the time to find trajectories for models involving long serial chains of rigid bodies. Leveraging this development, a software library is created which facilitates the process of finding trajectories of models of legged robots and animals. Using this library, a complex model of a cheetah is developed, based on real data and some experimentation. Finally, the model is used to generate high speed dynamic manoeuvres which present progress towards understanding the incredible abilities of cheetahs

Control Systems Approach to Balance Stabilization during Human Standing and Walking.

Humans rely on cooperation from multiple sensorimotor processes to navigate a complex world. Poor function of one or more components can lead to reduced mobility or increased risk of falls, particularly with age. At present, quantification and characterization of poor postural control typically focus on single sensors rather than the ensemble and lack methods to consider the overall function of sensors, body dynamics, and actuators. To address this gap, I propose a controls framework based on simple mechanistic models to characterize and understand normative postural behavior. The models employ a minimal set of components that typify human behavior and make quantitative predictions to be tested against human data. This framework is applied to four topics relevant to daily living: sensory integration for standing balance, limb coordination for one-legged balance, momentum usage in sit-to-stand maneuvers, and the energetic trade-offs of foot-to-ground clearance while walking. First, I demonstrate that integration of information from multiple physiological sensors can be modeled by an optimal state estimator. I show how such a model can predict human responses to conflict between visual, vestibular, and other sensors and use visual perturbation experiments to test this model. Second, I demonstrate that feedback control can model multi-limb coordination strategies during one-legged balance. I empirically identify a control law from human subjects and investigate how reducing stance ankle function necessitates greater gains from other limbs. Third, I show the advantages of momentum usage in sit-to-stand maneuvers. Counter to many human movements, this strategy is not performed with energetic economy, requiring excess mechanical work. However, with optimization models, I demonstrate that momentum serves to balance effort between knee and hip. Fourth, I propose a cost model for preferred ground clearance during swing phase of walking. Walking with greater foot lift is costly, but inadvertent ground contact is also costly. Therefore the tradeoff between these costly measures, modulated by movement variability, can explain expected cost of ground clearance. These controls-based models demonstrate the mechanisms behind normative behavior and enables predictions under novel situations. Thus these models may serve as diagnostic tools to identify poor postural control or aid design of intervention procedures.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/116654/1/amyrwu_1.pd