Tractable Quantification of Metastability for Robust Bipedal Locomotion

This work develops tools to quantify and optimize performance metrics for bipedal walking, toward enabling improved practical and autonomous operation of two-legged robots in real-world environments. While speed and energy efficiency of legged locomotion are both useful and straightforward to quantify, measuring robustness is arguably more challenging and at least as critical for obtaining practical autonomy in variable or otherwise uncertain environmental conditions, including rough terrain. The intuitive and meaningful robustness quantification adopted in this thesis begins by stochastic modeling of disturbances such as terrain variations, and conservatively defining what a failure is, for example falling down, slippage, scuffing, stance foot rotation, or a combination of such events. After discretizing the disturbance and state sets by meshing, step-to-step dynamics are studied to treat the system as a Markov chain. Then, failure rates can be easily quantified by calculating the expected number of steps before failure. Once robustness is measured, other performance metrics can also be easily incorporated into the cost function for optimization.For high performance and autonomous operation under variations, we adopt a capacious framework, exploiting a hierarchical control structure. The low-level controllers, which use only proprioceptive (internal state) information, are optimized by a derivative-free method without any constraints. For practicability of this process, developing an algorithm for fast and accurate computation of our robustness metric was a crucial and necessary step. While the outcome of optimization depends on capabilities of the controller scheme employed, the convenient and time-invariant parameterization presented in this thesis ensures accommodating large terrain variations. In addition, given environment estimation and state information, the high-level control is a behavioral policy to choose the right low-level controller at each step. In this thesis, optimal switching policies are determined by applying dynamic programming tools on Markov decision processes obtained through discretization. For desirable performance in practice from policies that are formed using meshing-based approximation to the true dynamics, robustness of high-level control to environment estimation and discretization errors are ensured by modeling stochastic noise in the terrain information and belief state while solving for behavioral policies

Metastable legged-robot locomotion

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 195-215).A variety of impressive approaches to legged locomotion exist; however, the science of legged robotics is still far from demonstrating a solution which performs with a level of flexibility, reliability and careful foot placement that would enable practical locomotion on the variety of rough and intermittent terrain humans negotiate with ease on a regular basis. In this thesis, we strive toward this particular goal by developing a methodology for designing control algorithms for moving a legged robot across such terrain in a qualitatively satisfying manner, without falling down very often. We feel the definition of a meaningful metric for legged locomotion is a useful goal in and of itself. Specifically, the mean first-passage time (MFPT), also called the mean time to failure (MTTF), is an intuitively practical cost function to optimize for a legged robot, and we present the reader with a systematic, mathematical process for obtaining estimates of this MFPT metric. Of particular significance, our models of walking on stochastically rough terrain generally result in dynamics with a fast mixing time, where initial conditions are largely "forgotten" within 1 to 3 steps. Additionally, we can often find a near-optimal solution for motion planning using only a short time-horizon look-ahead. Although we openly recognize that there are important classes of optimization problems for which long-term planning is required to avoid "running into a dead end" (or off of a cliff!), we demonstrate that many classes of rough terrain can in fact be successfully negotiated with a surprisingly high level of long-term reliability by selecting the short-sighted motion with the greatest probability of success. The methods used throughout have direct relevance to machine learning, providing a physics-based approach to reduce state space dimensionality and mathematical tools to obtain a scalar metric quantifying performance of the resulting reduced-order system.by Katie Byl.Ph.D

Systematic Controller Design for Dynamic 3D Bipedal Robot Walking.

Virtual constraints and hybrid zero dynamics (HZD) have emerged as a powerful framework for controlling bipedal robot locomotion, as evidenced by the robust, energetically efficient, and natural-looking walking and running gaits achieved by planar robots such as Rabbit, ERNIE, and MABEL. However, the extension to 3D robots is more subtle, as the choice of virtual constraints has a deciding effect on the stability of a periodic orbit. Furthermore, previous methods did not provide a systematic means of designing virtual constraints to ensure stability. This thesis makes both experimental and theoretical contributions to the control of underactuated 3D bipedal robots. On the experimental side, we present the first realization of dynamic 3D walking using virtual constraints. The experimental success is achieved by augmenting a robust planar walking gait with a novel virtual constraint for the lateral swing hip angle. The resulting controller is tested in the laboratory on a human-scale bipedal robot (MARLO) and demonstrated to stabilize the lateral motion for unassisted 3D walking at approximately 1 m/s. MARLO is one of only two known robots to walk in 3D with stilt-like feet. On the theoretical side, we introduce a method to systematically tune a given choice of virtual constraints in order to stabilize a periodic orbit of a hybrid system. We demonstrate the method to stabilize a walking gait for MARLO, and show that the optimized controller leads to improved lateral control compared to the nominal virtual constraints. We also describe several extensions of the basic method, allowing the use of a restricted Poincaré map and the incorporation of disturbance rejection metrics in the optimization. Together, these methods comprise an important contribution to the theory of HZD.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113370/1/bgbuss_1.pd

Steering natural dynamics to yield energy efficient, stable, and agile legged locomotion

We investigate how natural dynamics can yield stable, agile, and energy efficient robotic systems. Firstly, we cover a design with a single passive rolling element to stabilize frontal plane dynamics for a 3D biped walking across a range of forward velocities and/or step lengths. We examine aspects of the non-linear dynamics that contribute to the energy efficiency and stability of the system through simulations. Secondly, we examine switching controllers that allow for agile foothold selection in 5-link walkers. We leverage dynamic programming and discretization of the reachable space to walk across intermittent footholds. We utilize our meshing techniques to quantify stability and agility of these switching controllers. Finally, we provide experimental data on the effect of extra mass and power on humans at a variety of locations and forward velocities. This allows robot and exoskeleton designers to optimize for energy performance by understanding mass placements and power densities required for high performing legged locomotion. Finally, we present experimental data for an exoskeleton capable of assisting across running and walking speed

Rapid acceleration of legged robots: a pneumatic approach

For robotics to be useful to the public in a multifaceted manner, they need to be both legged and agile. The legged constraint arises as many environments and systems in our world are tailored to ablebodied adults. Therefore, a practically useful robot would need to have the same morphology for maximum efficacy. For robots to be useful in these environments, they need to perform at least as well as humans, therefore presenting the agility constraint. These requirements have been out of reach of the field until recently. The aim of this thesis was to design a planar monopod robot for rapid acceleration manoeuvres, that could later be expanded to a planar quadruped robot. This was achieved through a hybrid electric and pneumatic actuation system. To this end, modelling schemes for the pneumatic cylinder were investigated and verified with physical experiments. This was done to develop accurate models of the pneumatic system that were later used in simulation to aid in the design of the platform. The design of the platform was aided through the use of Simulink to conduct iterative testing and multivariate evaluations using Monte Carlo simulation methods. Once the topology of the leg was set, the detail design was conducted in Solidworks and validated with its built in simulation functions. In addition to the mechanical design of the platform, a specialist boom was designed. The design needed to compensate for the forces the robot exerts on the boom as well as the material constraints on the boom. This resulted in the development of a cable-stayed, four bar mechanism boom system. An embedded operating system was created to control the robot and take in and fuse sensor inputs. This was run using multiple sensors, sub-controllers and microcontrollers. Sensor fusion for the system was done using a Kalman Filter to improve readings and estimate unmeasured states of the robot. This Kalman Filter took LiDAR and accelerometer readings as inputs to the system to produce a subcentimetre accurate position measure for the system. Finally, the completed platform was validated using fixed-body forward hopping tests. These tests showed a significant degree of similarity to the simulated results and therefore validated the design process

Robust and Economical Bipedal Locomotion

For bipedal robots to gain widespread use, significant improvements must be made in their energetic economy and robustness against falling. An increase in economy can increase their functional range, while a reduction in the rate of falling can reduce the need for human intervention. This dissertation explores novel concepts that improve these two goals in a fundamental manner. By centering on core ideas instead of direct application, these concepts are aimed at influencing a wide range of current and future legged robots. The presented work can be broken into five major contributions. The first extends our understanding of the energetic economy of series elastic walking robots. This investigation uses trajectory optimization to find energy-miminizing periodic motions for a realistic model of the walking robot RAMone. The energetically optimal motions for this model are shown to closely resemble human walking at low speeds, and as the speed increases, the motions switch abruptly to those resembling human running. The second contribution explores the energetic economy of the real robot RAMone. Here the model used in the previous investigation is shown to closely match reality. In addition, this investigation demonstrates a concrete example of a trade-off between energetic economy and robustness. The third contribution takes a step towards addressing this trade-off by deriving a robot constraint that guarantees safety against falling. Such a constraint can be used to remove considerations of robustness while conducting future investigations into economical robot motions. The approach is demonstrated using a simple compass-gait style walking model. The fourth contribution extends this safety constraint towards higher-dimensional walking models, using a combination of hybrid zero dynamics and sums-of-squares analysis. This is demonstrated by safely modifying the pitch of a 10 dimensional Rabbit model walking over flat terrain. The final contribution pushes the safety guarantee towards a broader set of walking behaviours, including rough terrain walking. Throughout this work, a range of models are used to reason about the economy and robustness of walking robots. These model-based methods allow control designers to move away from heuristics and tuning, and towards generalizable and reliable controllers. This is vital for walking robots to push further into the wild.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/153459/1/nilssmit_1.pd

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

Bio-Inspired Robotics

Modern robotic technologies have enabled robots to operate in a variety of unstructured and dynamically-changing environments, in addition to traditional structured environments. Robots have, thus, become an important element in our everyday lives. One key approach to develop such intelligent and autonomous robots is to draw inspiration from biological systems. Biological structure, mechanisms, and underlying principles have the potential to provide new ideas to support the improvement of conventional robotic designs and control. Such biological principles usually originate from animal or even plant models, for robots, which can sense, think, walk, swim, crawl, jump or even fly. Thus, it is believed that these bio-inspired methods are becoming increasingly important in the face of complex applications. Bio-inspired robotics is leading to the study of innovative structures and computing with sensory–motor coordination and learning to achieve intelligence, flexibility, stability, and adaptation for emergent robotic applications, such as manipulation, learning, and control. This Special Issue invites original papers of innovative ideas and concepts, new discoveries and improvements, and novel applications and business models relevant to the selected topics of ``Bio-Inspired Robotics''. Bio-Inspired Robotics is a broad topic and an ongoing expanding field. This Special Issue collates 30 papers that address some of the important challenges and opportunities in this broad and expanding field