Energetic Efficiency And Stability In Bipedal Locomotion

In the second part, we discuss dynamics and optimality in perturbation rejection using simple mathematical models of human walking and running. We show that energy optimal perturbation recovery predicts features of the control seen previously in human locomotion -- for instance, using appropriate foot placement to redirect the leg force to correct for center of mass state deviations from the nominal. Leg force during stance phase is modulated more in walking than running perturbation recovery. Further, we find that the optimal feedback control is remarkably linear in many variables, suggesting that it may be possible to obtain effective control, large basins of attraction, and near-energy-optimality with relatively simple control architectures. Finally, in the third part, we elaborate on two mechanisms for responding to persistent and periodic perturbations during walking, such as those arising from an assistive device, exoskeleton, or prosthesis. First, we discuss entrainment to perturbations due to the intrinsic stable dynamics of the biped, providing a mathematical framework based on phase response curves. Next, we discuss entrainment to perturbations due to energy optimization, showing how entrainment to some kinds of repeated perturbations can reduce the energy cost of walking. The models, methods, and results in this thesis shed light on how walking and running could be controlled in humans and robots, and has future applications to the design of devices such as exoskeletons and prosthesis.

Human walking is dynamic, stable, and energy efficient. To achieve such remarkable legged locomotion in robots, engineers have explored bipedal robots developed based on two paradigms: trajectory-controlled and passive-based walking. Trajectory-controlled bipeds often deliver energy-inefficient gaits. The reason is that these bipeds are controlled via high-impedance geared electrical motors to accurately follow predesigned trajectories. Such trajectories are designed to keep a biped locally balanced continually while walking. On the other hand, passive-based bipeds provide energy-efficient gaits. The reason is that these bipeds adapt to their natural dynamics. Such gaits are stable limit-cycles through entire walking motion, and do not require being locally balanced at every instant during walking. However, passive-based bipeds are often of round/point foot bipeds that are not capable of achieving and experiencing standing, stopping, and some important bipedal gait phases and events, such as the double support phase. Therefore, the goals of this thesis are established such that the aforementioned limitations on trajectory-controlled and passive-based bipeds are resolved. Toward the above goal, comprehensive simulation and experimental explorations into bipedal walking have been carried out. Firstly, a novel systematic trajectory-controlled gait-planning framework has been developed to provide mechanical insights into bipedal walking in terms of gait characteristics and energy efficiency. For the same purpose, a novel mathematical model of passive-based bipedal walking with compliant hip-actuation and compliant-ankle flat-foot has been developed. Finally, based on mechanical insights that have been achieved by the aforementioned passive-based model, a physical prototype of a passive-based bipedal robot has been designed and fabricated. The prototype experimentally validates the importance of compliant hip-actuation in achieving a highly dynamic and energy efficient gait.

Here for the first time in one book is a comprehensive and systematic approach to the dynamic modeling and control of biped locomotion robots. A survey is included of various approaches to the control of biped robots, and a new approach to the control of biped systems based on a complete dynamic model is presented in detail. The stability of complete biped system is presented for the first time as a highly nonlinear dynamic system. Also included is new software for the synthesis of a dynamically stable walk for arbitrary biped systems, presented here for the first time. A survey of various realizations of biped systems and numerous numerical examples are given. The reader is given a deep insight into the entire area of biped locomotion. The book covers all relevant approaches to the subject and gives the most complete account to date of dynamic modeling, control and realizations of biped systems.

Bipedal locomotion is among the most difficult challenges in control engineering. Most books treat the subject from a quasi-static perspective, overlooking the hybrid nature of bipedal mechanics. Feedback Control of Dynamic Bipedal Robot Locomotion is the first book to present a comprehensive and mathematically sound treatment of feedback design for achieving stable, agile, and efficient locomotion in bipedal robots. In this unique and groundbreaking treatise, expert authors lead you systematically through every step of the process, including: Mathematical modeling of walking and running gaits in planar robots Analysis of periodic orbits in hybrid systems Design and analysis of feedback systems for achieving stable periodic motions Algorithms for synthesizing feedback controllers Detailed simulation examples Experimental implementations on two bipedal test beds The elegance of the authors' approach is evident in the marriage of control theory and mechanics, uniting control-based presentation and mathematical custom with a mechanics-based approach to the problem and computational rendering. Concrete examples and numerous illustrations complement and clarify the mathematical discussion. A supporting Web site offers links to videos of several experiments along with MATLAB® code for several of the models. This one-of-a-kind book builds a solid understanding of the theoretical and practical aspects of truly dynamic locomotion in planar bipedal robots.

Abstract: In this dissertation, two problems related to bipedal robot walking are presented. The first problem is the influence of parallel knee joint compliance on the average power cost of walking in an underactuated planar bipedal robot, ERNIE. The second problem is the design of walking controllers that induce aperiodic bipedal robot walking. It has been found that compliance plays important roles in walking and running in animals. Compliance has been used in robotic bipedal machines to improve energetic efficiency or reduce the peak power demand on the robot's actuators. This dissertation presents numerical and experimental studies of the influence of parallel knee joint compliance on the average power cost of walking in an underactuated planar bipedal robot, ERNIE. Four scenarios were studied: one without springs and three with springs of different stiffnesses and preloads. Optimal gaits in terms of average power cost for various speeds were designed for each scenario. It was found that for low-speed walking, soft springs are helpful to reduce power cost, while stiffer springs increase power cost. For high-speed walking, it was found that both soft and stiff springs reduce the average power cost of walking, but stiffer springs reduce the cost more than do softer springs. The second problem addressed in this dissertation is aperiodic walking controller design. The ability to walk stably in varying environments or with different tasks, such as stepping over stones, is of great interest in bipedal walking. In these scenarios, the walking is not periodic. This dissertation presents a new definition of stable walking that is not necessarily periodic for a class of biped robots. The inspiration for the definition is the commonly-held notion of stable walking: the biped does not fall. To make the definition useful, an algorithm is given to verify if a given controller induces stable walking. Also given is a framework to synthesize controllers that induce stable walking. The results are illustrated with numerical simulation and experiments. This dissertation also presents details of a modeling procedure for the experimental bipedal robot, ERNIE, and explores the possibility to apply iterative learning control to bipedal walking.

In the past decades, much progress has been made in the field of walking robots. The current state of technology makes it possible to create humanoid robots that nearly walk like a human being, climb stairs, or avoid small - stacles. However, the dream of a robot running as fast and as elegantly as a human is still far from becoming reality. Control of such fast motions is still a big technological issue in robotics, and the maximum running speed of contemporary robots is still much smaller than that of human track runners. The conventional control approach that most of these robots are based on does not seem to be suitable to increase the running speeds up to a biological level. In order to address this challenge, we invited an interdisciplinary community of researchers from robotics, biomechanics, control engineering and applied mathematics to come together in Heidelberg at the Symposium “Fast Motions in Biomechanics and Robotics – Optimization & Feedback Control” which was held at the International Science Forum (IWH) on September 7–9, 2005. The number of participants in this symposium was kept small in order to promote discussions and enable a fruitful exchange of ideas.

Balance control is important for biped standing. Due to the time-varying control bounds induced by the foot constraints, and the lack of tools for analyzing stability of highly nonlinear systems, it is extremely difficult to design balance control strategies for a standing biped with a rigorous stability analysis in spite of large efforts. In this thesis, three important issues are fully considered for a standing biped: maintaining the postural stability, minimizing the energy consumption and satisfying the constraints between the biped feet and the ground. Both the theoretical and the experimental studies on the constrained and energy-efficient control are carried out systematically using the genetic algorithm (GA). The stability for the proposed balancing system is thoroughly investigated using the concept of Lyapunov exponents. On the other hand, the controlled standing biped is characterized by high nonlinearity and great complexity. For systems with such features, in general the Lyapunov exponents are hard to be estimated using the model-based method. Meanwhile the biped is supposed to be stabilized at the upright posture, indicating that the system should possess negative Lyapunov exponents only. However the accuracy of negative exponents is usually poor if following the traditional time-series-based methods. As it is nontrivial to examine the system stability for bipedal robots, the numerical accuracy of the estimated Lyapunov exponents is extremely demanding. In this research, two novel approaches are proposed based upon system approximation using different types of Radial-Basis-Function (RBF) networks. Both the proposed methods can estimate the exponents reliably with straightforward algorithms, yet no mathematical model is required in any newly developed method. The efficacies of both methods are demonstrated through a linear quadratic regulator (LQR) balancing system for a standing biped, as well as several other dynamical systems. The thesis as a whole, has set up a framework for developing more sophisticated controllers in more complex movement for robot models with less conservative assumptions. The systematic stability analysis shown in this thesis has a great potential for many other engineering systems.

This thesis presents a hierarchical geometric control approach for fast and energetically efficient bipedal dynamic walking in three-dimensional (3-D) space to enable motion planning applications that have previously been limited to inefficient quasi-static walkers. In order to produce exponentially stable hybrid limit cycles, we exploit system energetics, symmetry, and passivity through the energy-shaping method of controlled geometric reduction. This decouples a subsystem corresponding to a lower-dimensional robot through a passivity-based feedback transformation of the system Lagrangian into a special form of controlled Lagrangian with broken symmetry, which corresponds to an equivalent closed-loop Hamiltonian system with upper-triangular form. The first control term reduces to mechanically-realizable passive feedback that establishes a functional momentum conservation law that controls the "divided" cyclic variables to set-points or periodic orbits. We then prove extensive symmetries in the class of open kinematic chains to present the multistage application of controlled reduction. A reduction-based control law is derived to construct straight-ahead and turning gaits for a 4-DOF and 5-DOF hipped biped in 3-D space, based on the existence of stable hybrid limit cycles in the sagittal plane-of-motion. Given such a set of asymptotically stable gait primitives, a dynamic walker can be controlled as a discrete-time switched system that sequentially composes gait primitives from step to step. We derive "funneling" rules by which a walking path that is a sequence of these gaits may be stably followed by the robot. The primitive set generates a tree exploring the action space for feasible walking paths, where each primitive corresponds to walking along a nominal arc of constant curvature. Therefore, dynamically stable motion planning for dynamic walkers reduces to a discrete search problem, which we demonstrate for 3-D compass-gait bipeds. After reflecting on several connections to human biomechanics, we propose extensions of this energy-shaping control paradigm to robot-assisted locomotor rehabilitation. This work aims to offer a systematic design methodology for assistive control strategies that are amenable to sequential composition for novel progressive training therapies.

This 3-volume handbook brings together contributions by the world ́s leading specialists that reflect the broad spectrum of modern palaeoanthropology, thus presenting an indispensable resource for professionals and students alike. Vol. 1 reviews principles, methods, and approaches, recounting recent advances and state-of-the-art knowledge in phylogenetic analysis, palaeoecology and evolutionary theory and philosophy. Vol. 2 examines primate origins, evolution, behaviour, and adaptive variety, emphasizing integration of fossil data with contemporary knowledge of the behaviour and ecology of living primates in natural environments. Vol. 3 deals with fossil and molecular evidence for the evolution of Homo sapiens and its fossil relatives.

Bioinspired Legged Locomotion: Models, Concepts, Control and Applications explores the universe of legged robots, bringing in perspectives from engineering, biology, motion science, and medicine to provide a comprehensive overview of the field. With comprehensive coverage, each chapter brings outlines, and an abstract, introduction, new developments, and a summary. Beginning with bio-inspired locomotion concepts, the book's editors present a thorough review of current literature that is followed by a more detailed view of bouncing, swinging, and balancing, the three fundamental sub functions of locomotion. This part is closed with a presentation of conceptual models for locomotion. Next, the book explores bio-inspired body design, discussing the concepts of motion control, stability, efficiency, and robustness. The morphology of legged robots follows this discussion, including biped and quadruped designs. Finally, a section on high-level control and applications discusses neuromuscular models, closing the book with examples of applications and discussions of performance, efficiency, and robustness. At the end, the editors share their perspective on the future directions of each area, presenting state-of-the-art knowledge on the subject using a structured and consistent approach that will help researchers in both academia and industry formulate a better understanding of bioinspired legged robotic locomotion and quickly apply the concepts in research or products. Presents state-of-the-art control approaches with biological relevance Provides a thorough understanding of the principles of organization of biological locomotion Teaches the organization of complex systems based on low-dimensional motion concepts/control Acts as a guideline reference for future robots/assistive devices with legged architecture Includes a selective bibliography on the most relevant published articles