Session: Feedback Control I (Thursday morning, July 8)
Feedback Control of the Bipedal Robot MABEL
Abstract: MABEL is a bipedal testbed at the University of Michigan that was constructed in collaboration with Jonathan Hurst. The robot is planar, with a torso, two legs with revolute knees, and four actuators. Two of its actuators are in series with large springs for the purpose of enhancing both energy efficiency and agility of locomotion. The actuators are housed in the torso and the legs are light, placing the center of mass of the robot significantly above the hips. The presentation will focus on the development of a time-invariant feedback controller that respects the natural compliance of the open-loop system and realizes exponentially stable walking gaits. Experiments are presented that highlight different aspects of MABEL and the feedback design method, ranging from basic elements such as stable walking, to energy efficiency, fast walking, and walking over uneven terrain.
Sensitivity of Walking Gaits to Roughness of Terrain
Abstract: Stable gaits of passive walking mechanisms often have narrow and strangely shaped regions of attraction, which are difficult both to estimate analytically and to enlarge using feedback from just a few actuators. For instance, linearization of the first-return Poincaré map, being decisive for exponential orbital stability of a limit cycle, can be used for estimating neither its region of attraction nor possible deviations from a nominal trajectory in response to small parametric perturbations. In this talk, we reiterate and refine the arguments presented in 2008 and describe a procedure for constructing such estimates based on the notions of virtual holonomic constraints and transverse linearization. The method allows: (a) revealing mechanisms of instability of cycles when dynamics of an underactuated biped is perturbed by imperfections of a walking surface; (b) developing tools for planning gaits insensitive to certain perturbations; (c) designing robustly stabilizing feedback controllers. The results are presented on the examples of a compass-gait biped and a quadruped.
Energy-based Control Approaches to Efficient Dynamic Bipedal Walking
Abstract: We have proposed methods for generating energy-efficient dynamic bipedal gait based on passive dynamics. Parametrically excited dynamic bipedal walking is a novel approach to efficient level dynamic walking. In this method, the robot restores mechanical energy by pumping the telescopic legs without using any rotary actuators, and stable ZMP-free walking on level ground is then easily achieved. This method has also been extended to the cases of knee-joint actuation and ornithoid walking. In this presentation, we first outline the mathematical modeling, control laws, numerical simulations, and experimental results. Second, we introduce our method for generating an asymptotic stable gait based on the stability principle of a rimless wheel, and explain the importance of controlling mechanical energy in enhancing the asymptotic stability. We also analyzed the efficiency of asymmetric 2-period gait using an asymmetric rimless wheel model. Through the theoretical analysis, we found there is a possibility that asymmetric 2-period gait is less efficient than symmetric 1-period one in terms of the walking speed. We finally talk about our recent results on the effect of delayed feedback control (DFC) on the gait efficiency. We apply DFC to a parametrically excited walker with knees and examine how the walking speed and the stable domain change after the stabilization to 1-period gait. Based on the numerical results, we discuss about the role of period-doubling bifurcation in limit cycle walking.
Control and Planning with Asymptotically Stable Gait Primitives: 3D Dynamic Walking to Locomotor Rehabilitation
Abstract: This talk presents a hierarchical control framework that enables motion planning for fast and efficient 3D dynamic walkers in a similar manner to what is possible for bipeds using Center of Pressure (CoP) equilibrium constraints. Given any low-level controller that produces 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 switching rules by which the robot can follow a walking path that is a sequence of these gaits, so dynamically stable planning reduces to a simple tree search. Passivity-based controlled reduction is used to construct an example set of gait primitives for a 3D compass-gait biped, where each primitive corresponds to walking along a nominal arc of constant curvature for a fixed number of steps. We conclude with ongoing efforts at translating these ideas into systematic methods for designing and prescribing control strategies for personalized robot-assisted locomotor therapy.
Abstract:A robot or an animal with muscles can typically move in many more ways that the particular ways in which they usually move. So a frequent scientific or engineering question is: among all the essentially infinitely many different ways that the animal can accomplish a movement task, which is "best"? "Best" could mean "energy-optimal", "as fast as the animal can", etc. This tutorial is an introduction to some basic computational methods one might use to answer such questions. We will discuss the so-called shooting methods and the collocation methods in brief. We will set up and try to solve a "gait optimization" problem, involving an animal (walking biped or a swinging ape) that has two segments articulated by two muscles (motors). Example MATLAB codes (using a shooting-like method) that are almost complete will be provided and you will be asked to complete the solution of the gait optimization problem.
Software requirements: MATLAB + either MATLAB optimization toolbox (mainly fmincon) or student version of SNOPT (freely downloadable) or some other general nonlinear programming solver that interfaces with MATLAB.
Target audience: Some familiarity with MATLAB but no prior experience with trajectory optimization.
Session: Prosthetics, Orthotics, and Exoskeletons
Developing a Brain-Controlled Robotic Lower-Limb Exoskeleton
Abstract:Robotic technologies have greatly advanced in recent years, making robotic exoskeletons feasible as real devices instead of being limited to science fiction. However, prototype devices do not perform as well as expected, specifically in regard to reducing the metabolic cost of locomotion. To improve exoskeleton designs, we need to understand principles of neural adaptation to powered assistance so that future designs allow humans and machines to act as a coordinated system. The University of Michigan Human Neuromechanics Laboratory has designed robotic exoskeletons for assisting human locomotion with the primary intent of identifying principles of neuromechanical control and adaptation to powered assistance. Our most recent research is on developing mobile brain imaging techniques with the eventual goal of building a brain-controlled robotic lower limb exoskeleton.
Passive Elastic Running Prostheses; Very Good, But Not Yet Better
Abstract: Until recently, athletes using Passive Elastic Running Prostheses (PERPS) were clearly at a disadvantage compared to those with fully functional biological legs. The remarkable accomplishments of a few prominent athletes (e.g. Oscar Pistorius, Amy Palmierio-Winters) have raised the issue of advantage/disadvantage and stimulated a recent flurry of misinformation and scientific experiments. Although an initial measurement and suggested that PERPS enhance running economy, a growing body of evidence demonstrates equivalence. Yet, distance running performances are still much slower for athletes using PERPS. Athletes using PERPS cannot/do not apply ground reaction forces as great as those with biological legs. That limits maximum running speed and thus, sprint performance. The low mass and inertia of PERPS would seem to allow more rapid leg swing, but athletes using PERPS do not exhibit unnaturally fast swing times. Further, it is not clear that it would be advantageous if they did. Although we have learned a great deal about the science of PERPS in the last few years, the database, especially for runners using bilateral PERPS, is inadequate. I will outline the next most important experiments in this area of research.
Implicit Control of a Powered Knee and Ankle Prosthesis
Abstract: Lower limb prostheses have traditionally been passive devices that lack the ability to generate net power at the joints. This absence of net power generation impairs the ability of passive prosthesis to restore biomechanically healthy function to lower limb amputees. Recent advances in battery, motor, and microelectronics technologies have enabled the possibility of powered (i.e., active) lower limb prostheses. Instilling a lower limb prosthesis with power, however, changes greatly the nature and significance of the prosthesis control and interface problem (i.e., a passive prosthesis can fundamentally only react to the user's input, but a powered prosthesis can both act as well as react). This talk describes the development of a lower limb prosthesis with a powered knee and ankle joint, and describes the control methodology through which the prostheses interacts with the user. Results are presented that indicate the effectiveness of the prosthesis and control interface.
Grant Elliot and Alena Grabowski. Massachusetts Institute of Technology.
Can external springs augment human locomotion?
Abstract: During bouncing gaits such as human hopping and running, musculoskeletal mechanics are well characterized by a spring-mass model; whereby compliant structures of the leg reduce metabolic demand by facilitating elastic energy storage and return, and decreasing muscular work. We sought to determine if a springy leg exoskeleton placed in parallel to the human legs could reduce metabolic demand and muscle activity during bouncing gaits. We found that human hoppers retained linear spring-mass mechanics, required substantially less metabolic energy, and reduced triceps surae muscle activity while using an exoskeleton compared to normal hopping. Metabolic demand was 12-28% less when using an exoskeleton and 6-18% greater when hopping with the added weight of an exoskeleton across a wide range of hopping frequencies. Our exoskeleton likely decreases metabolic demand by transferring the weight of the body through the exoskeleton to the ground instead of this force being completely borne by the hopper's legs. In current and future work, we will analyze the effects of an exoskeleton during running.
Session: Feedback Control II
Cats, astronauts, trucks, bikes, arrows, and muscle-smarts: Stability, translation, and rotation
Ambarish Goswami. Honda Research Institute.
Reduced humanoid models possessing centroidal angular momentum
Abstract: Human and humanoid robots are often abstracted with various reduced models. These "inverted pendulum models" simplify the dynamics and enhance our understanding of the essentials of balance and gait. Most of these models contain a point mass and do not possess the body's centroidal dynamics. As a result important aspects of gait and balance are not captured by these models.
To remedy this, we are exploring reduced biped models that retain the body's centroidal dynamics through its instantaneous "locked inertia" or the composite rigid body (CCRB) inertia. The "Reaction Mass Pendulum" (RMP), which is an extension of the inverted pendulum, is one such model. Unlike point mass models, the RMP model can possess centroidal angular momentum, and the momentum equivalence with the biped allows one to compute the RMP parameters.
Models with centroidal dynamics also capture centroidal angular momentum, which, along with linear momentum, is naturally used to control balance, gait and a variety of movements.
Feedback Motion Planning via Sums-of-Squares Verification
Abstract: Designing controllers for legged locomotion requires dealing with complex nonlinear dynamics and non-trivial notions of stability including limit cycles and dynamically stable maneuvers. In this talk I will describe the LQR-Trees algorithm for designing feedback controllers for legged robots navigating on flat and rough terrain. The algorithm combines randomized motion planning and trajectory optimization algorithms, popular in robotics, with rigorous tools from control theory for verifying regional stability of nonlinear systems. The algorithm can efficiently handle limit cycles, impacts, trigonometric nonlinearities, and saturations. Under mild assumptions, it probabilistically converges to a feedback which stabilizes the entire controllable state space; guaranteeing that every initial condition which can be stabilized to the nominal limit cycle or goal will be stabilized to that goal.
Linearly-solvable optimal control: Theory and applications
Abstract: Optimal control has a lot of potential, however its applications to robotics have been limited, partly because the problem is very hard to solve even numerically. In this talk I will summarize a recently-developed formulation of stochastic optimal control which renders the problem linear (in the unknown value function). This makes it possible to use large numbers of basis functions for parameterizing the solution. Other advantages include a compositionality law for optimal controllers, as well as a duality with Bayesian inference. This duality yields an interesting relation between deterministic and stochastic optimization: the Hessian of the total cost around an optimal deterministic trajectory coincides with the Laplacian approximation to the density of stochastic trajectories generated by the optimal feedback controller. I will show how this relation can be exploited to optimize feedback controllers for periodic behaviors such as walking. The new formulation can also deal with contacts, because it relies on integral equations and does not need to assume smooth dynamics. This is in contrast with most prior application of optimal control to walking, where the contact states have usually been specified in advance.
Abstract:System identification the process of fitting a mathematical model to measurement records of inputs and outputs of a system. It is a large field with many different methods appropriate in different applications. The aim of this tutorial is to cover some basic ideas and methods, and to foster discussion amongst attendees about their experiences. We will discuss the relationship between model structure selection and parameter estimation, and computational methods such as basic least squares, nonlinear least squares, and if time permits more recent methods of robust nonlinear identification.
Software requirements: MATLAB/Simulink with the System Identification and Optimization Toolboxes.
Target audience: Some familiarity with MATLAB but no prior experience with system identification.
Session: Biomechanics/Neural Control I
Mechanics and control of a compliant muscle-tendon during cyclic contractions
Abstract:Compliant mechanical behavior of the lower-limb can capture the basic dynamics of stable walking and running across a range of speeds, but the neuromechanical mechanisms responsible for robust, spring-like limb dynamics are not entirely clear. In order for a compliant muscle-tendon unit to behave similar to an elastic spring, the mechanics of active (muscle fascicles) and passive (series-elastic tendon and aponeurosis) tissues must be appropriately coordinated (i.e. ‘tuned’) within the movement cycle. This ‘tuning’ involves adjusting the pattern of muscle activation to modulate muscle force/stiffness output (via intrinsic force-length and force velocity properties) in order to match the loading profile imposed by the environment through series elastic structures within the muscle-tendon unit.
Using bullfrog plantaris muscle-tendon, a servo-controlled muscle ergometer and sonomicrometry, we have developed a novel experimental framework to study the neuromechanics of a compliant muscle -tendon unit in vitro. In our initial experiments we employed classical work-loop techniques to understand how the feedforward (i.e. open-loop) muscle activation pattern (timing, magnitude and duration of stimulation) influences muscle-tendon unit net work output and internal energy exchange between muscle fascicles and series-elastic tissues. First I will present results demonstrating conditions that lead to ‘tuned’ elastic behavior of a compliant muscle-tendon unit. Then I will discuss plans to extend our framework and address the relative roles of neural feedback (length and/or force) and muscle-tendon architecture in stabilizing perturbations to steady-state, ‘tuned’ elastic cycles.
Tom Roberts. Brown University.
Fast, cheap and out of control: dynamic interactions of elastic structures and muscle motors
Abstract: It is now well established that the elastic function of tendons has a profound influence on the mechanics, energetics, and control of locomotion. A model of a simple Hookean spring in series with a muscle actuator reveals mechanisms that reduce the energy cost of locomotion, amplify muscle power output for ballistic movements, and provide passive dynamic responses to perturbations. Yet recent work suggests that this simple model fails to capture some important interactions between muscles and elastic structures. For example, we find that elastic structures influence muscle shape changes during contraction, and these shape changes in turn influence muscle force and velocity. Shape changes in muscle likewise result in tendon loading along more than one axis, resulting in an effective stiffness of tendons that varies dynamically. These observations have implications for motor control that are not yet fully explored. On the one hand, changes in muscle force and velocity mediated by muscle-spring interactions can provide rapid adjustments in mechanical output independent of neural control. On the other hand, motor commands for prescribed motions must account for these complex dynamics.
Diversity of bipedal locomotion among birds: Insights into the interplay of morphology, economy and stability.
Abstract: Birds are a diverse group of bipedal animals that span a range of body size, morphology and habitat use. This diversity can be exploited to reveal relationships between morphology, economy and stability of locomotion, providing a complementary perspective to studies of humans and robots. We are conducting comparative studies among birds to investigate the diversity of bipedal locomotion strategies. Our approach integrates terrain perturbation experiments, empirical measures of mechanics and energy cost and simple models. Recent experiments show that both pheasants and guinea fowl adjust stance leg posture, swing leg control and preferred speeds in terrain conditions with differing 'roughness', suggesting that they select among more stable or economic strategies depending on context. Differences in walking and running dynamics exist between these similarly sized birds that may relate to differences in morphology and habitat use. In continuing work we will compare locomotion strategies among ground birds ranging from quail to ostrich to investigate how morphology and body size influence the strategies used by bipedal animals to achieve both economy and robust stability of locomotion.
Optimal Workloop Energetics of Muscle-Actuated Systems: An Impedance Matching View
Abstract: Integrative approaches to studying the coupled dynamics of skeletal muscles with their loads while under neural control have focused largely on questions pertaining to the postural and dynamical stability of animals and humans. Prior studies have focused on how the central nervous system actively modulates muscle mechanical impedance to generate and stabilize motion and posture. However, the question of whether muscle impedance properties can be neurally modulated to create favorable mechanical energetics, particularly in the context of periodic tasks, remains open. Through muscle stiffness tuning, we hypothesize that a pair of antagonist muscles acting against a common load may produce significantly more power synergistically than individually when impedance matching conditions are met between muscle and load. Since neurally modulated muscle stiffness contributes to the coupled muscle-load stiffness, we further anticipate that power-optimal oscillation frequencies will occur at frequencies greater than the natural frequency of the load. These hypotheses were evaluated computationally by applying optimal control methods to a bilinear muscle model, and also evaluated through in vitro measurements on frog Plantaris longus muscles acting individually and in pairs upon a mass-spring-damper load. We find a 7-fold increase in mechanical power when antagonist muscles act synergistically compared to individually at a frequency higher than the load natural frequency. These observed behaviors are interpreted in the context of resonance tuning and the engineering notion of impedance matching. These findings suggest that the central nervous system can adopt strategies to harness inherent muscle impedance in relation to external loads to attain favorable mechanical energetics.
Session: Modeling, Dynamics, and Control
First steps toward closing the loop on walking: from human walking to hybrid systems to robotic walking and back
Abstract: This talk discusses the first steps toward closing the loop on walking: generating mathematical models for human walking, developing control laws that yield walking for 3D bipeds using these formal models, and comparing the resulting robotic walking to the human walking data from which the model was derived. I begin by considering human walking data which is used to construct a hybrid system. The discrete behavior, or phases, of the hybrid system are dictated by the discrete phases in the human walking data (heel lift, knee strike, heel strike, etc.), and the continuous behavior of the hybrid system on every phase are given by the equations of motion obtained by considering the human configuration through the discrete phase. I then consider a 3D bipedal robot which is modeled by this hybrid system; this model assumes a temporal ordering and structuring of discrete events that are anthropomorphic in nature. Control laws are constructed for this bipedal robot by combining human-inspired local control laws with techniques utilized in the dynamic walking community: passive walking inspired control, geometric reduction, and input/output linearization through the use of virtual constraints. The end result of combining all of these approaches in an integrative fashion is stable walking for the 3D bipedal robot. Given the anthropomorphic motivation for its model and controllers, the walking is remarkably human-like.
Katja Mombaur. LAAS-CNRS, Université de Toulouse.
Using optimal control and complex mechanical models to better understand dynamic walking
Abstract: The model-based investigation of human and human-like motions is an important interdisciplinary research topic which involves aspects of biomechanics, physiology, orthopedics, psychology, neurosciences, robotics, sport, computer graphics and applied mathematics. In this context, the detailed study on a joint level of basic locomotion forms such as walking and running is of particular interest due to the high demand on dynamic coordination, actuator efficiency and balance control. Mathematical models and numerical optimization techniques can help to better understand the basic underlying mechanisms of these motions and to improve them. In this talk, we present different studies of our research group on dynamic human motions which show how optimization can help to generate very natural looking motions. We use multibody dynamics models of the human body with ca. 30 degrees of freedom with realistic descriptions of ground impacts and state-of the art efficient optimization techniques. We not only study walking and running, but also some more artistic forms of locomotion. We show in particular how optimization can lead to improved stability properties of the dynamic systems. We also give a brief outlook on the inverse optimal control approach, which serves to identify objective functions of human motion from motion capture measurements.
Regions of Attraction to Limit Cycles of Nonlinear Hybrid Systems
Abstract: This talk will present a method for computing estimates of regions of attraction to limit cycles of quite a general class of nonlinear hybrid systems. Such limit cycles typically represent the "nominal" motion of a walking robot, with alternating phases of continuous motion and distinct impacts upon footfall. The problems of stabilizing such motions and characterizing the regions of stability are central in dynamic walking, and this talk will present contributions on both problems. It is well-known that limit cycles cannot be asymptotically stable in the standard sense, since perturbations in phase are persistent. The more relevant concept is orbital stability, which can be analyzed via a lower-dimensional coordinate system transversal to the target orbit. A new analytical construction is given which is applicable to general nonlinear systems with impacts. This coordinate system is then used for both control via transverse linearization, and computing estimates of regions of attraction via Lyapunov's direct method and the sum-of-squares relaxation of polynomial boundedness. Both impacts (switching surfaces) and the need for well-posedness of dynamics present interesting issues in the selection of transversal coordinate system, which will be discussed. The method will be illustrated with examples including the van der Pol oscillator, the rimless wheel, and the compass-gait walker.
Data Driven Floquet Analysis for Biomechanics and Robotics
Abstract: Floquet theory describes the linearization of an oscillator around its orbit. We convert this familiar classical result to an empirical form, allowing Floquet models to be constructed directly from experimentally obtained trajectories of periodic gaits. The Floquet model can be used to derive dimensionally reduced "templates" that predict responses to transient stimuli and be used as maneuvers through transient destabilization. The ability to express maneuvers in these reduced models holds promise for robot design and tuning, and for biomechanical research. We report on ongoing work applying our methods to human and cockroach data, and illustrate their use on some gaits of the Clock-Torqued Spring Loaded Inverted Pendulum (CT-SLIP) model.
Observations on the Structure of Optimal Gaits on Various Simple Bipedal Models
Abstract: It is thought that many aspects of steady human locomotion under normal conditions can be predicted by appealing to the hypothesis that healthy humans roughly move in a manner that minimizes the metabolic cost of locomotion. While energy optimization with sufficiently realistic and complex models might be required for detailed quantitative predictions, we might obtain a deeper understanding of the qualitative effects of various model features on energetic optimal gaits by considering relatively simple models. Here, we consider four simple bipedal models with different leg architectures, combined with many different metabolic cost functions and muscle properties. Performing careful gait optimization on these many model permutations reveals simple underlying gait structure and similarity between the optimal gaits for substantially different models. We are also able to make a number of observations about the structure of the optimal gaits of the various models, many of which have not been previously noted.
Exploitation of Natural Dynamics in Quadrupedal Locomotion
Abstract: Our research aims at the creation of fast and efficient running motions of four legged robotic systems. We design our robots to explicitly enable and exploit natural dynamic effects (such as the oscillation on springy legs) in their mechanical structure and their actuation with the goal of eliminating undesired negative work, minimizing the required actuator power, and alleviating shocks. For the variety of sub-problems that arise in this context (reaching from the proper hardware design to the efficient excitation and stabilization of the desired motion), we will present two complementary approaches: Firstly, by employing the concept of operational space control, we are able to project the dynamics of simple conceptual models onto an actual robotic system. This is shown for an extended SLIP-model, but the same technique can be employed to other models for which we developed efficient gaits and control strategies. By considering the obtained torques as a function of joint positions, we can then specifically design elastic elements that passively support the actuators. Secondly, we implemented a limit cycle based, optimal control approach using a Fourier series to efficiently excite the dynamics of a given robot or model – a method that was employed to identify different bounding gaits for a conceptual quadruped model, and to drive the most recent prototype of our robotic leg.
Session: Biomechanics and Neural Control II
Coordinated action of muscle-tendon systems in the avian hindlimb during walking, running, and jumping
Abstract: The extreme variation in hindlimb morphology that has occurred in the evolution of birds adapted to varying types of locomotion provides the opportunity to examine those features of muscle and limb architecture that appear to be associated with a particular locomotor habit, as well as features conserved across many avian taxa. Two examples of muscles systems are presented that provide insight into the coordinated actions across multiple joints and the potential for self-stabilizing behavior in birds adapted for terrestrial legged locomotion. First, the hamstring-like flexor cruris lateralis pars posterior (FCLP) has been found to act in concert with the intermediate head of the gastrocnemius (IG), and with an accessory head attached to the femur (FCLA). In vivo length and EMG measurements in these three muscles suggest the hypothesis that the FCLP acts through the tendon of insertion of the active IG in early stance to provide an extensor moment at the ankle, and switches to a pure hip extensor in late stance when EMG activity in the IG is reduced and FCLA becomes active. The FCLA system also provides the potential for automatic compensation of moments across three joints simultaneously in early stance. Second, the fibularis longus (FL) can alter its function across two joints due to the anatomy of its distal tendon. The FL tendon of insertion splits above the ankle, with one branch extending the ankle and the other branch producing digital flexion, particularly at the tarsometatarsal-phalangeal joint (TMP). Our data indicate that the effective moment arm of the FL at each joint is determined in large part by the angle of the second joint. Because of this interaction, the predicted function of the FL varies greatly between jumping and running. At the angles used in running the FL is predicted to act mostly as a toe flexor, but during jumping the FL switches almost completely from an ankle extensor early in the jump to a toe flexor just before takeoff. This interacting system also provides a potential compensatory mechanism for altering joint moments in both the ankle and TMP in response to variation in angles at these joints. Supported by NIH AR47337 and NSF IOB-0542795.
Pavitra Krishnaswamy. Massachusetts Institute of Technology. (work with Emery N. Brown and Hugh Herr)
Efficient Interplay between Human Leg Morphology and Control Resolves Ankle Actuation Redundancies in Walking
Abstract: A ubiquitous feature in biological neuromuscular systems is the redundancy in joint actuation. Understanding how these redundancies are resolved in typical joint movements has been a long-standing problem in biomechanics, neuroscience and prosthetics. A variety of empirical techniques have characterized how the human neuromuscular system resolves the many degrees of freedom in leg joint actuation. However, a unifying theoretical framework that consistently explains the several independent empirical observations is yet to be established.
We propose that the economical interplay between leg morphology and neural control is critical for explaining empirical observations about leg muscle-tendon operation in walking. Specifically, we hypothesize that leg muscles and tendons are designed holistically to enable metabolically optimal realization of human-like joint mechanics under the neural controls observed in normal walking. To test our hypothesis, we developed a musculoskeletal model-based method to investigate the leg muscle-tendon parameter space for correspondence to human gait data, EMG recordings, and empirically obtained efficiencies.
We find that there is a unique set of parameters fulfilling the above three criteria, and that this unique set corresponds to optimal metabolic economy. With the metabolically optimal leg parameters, we quantify the influence of leg muscle-tendon structure and neural drive to derive insights about roles, operation regimes and performance of different ankle muscle-tendon units. Results indicating the effectiveness of our approach in predicting independently obtained empirical results will be presented. Implications to understanding neuromuscular co-ordination and evaluating gait will be discussed.
Stable walking and running: how leg geometry and compliance shapes the way we move
Abstract: Leg function can be adapted to different gaits and environmental conditions. Here we investigate, to what extent the structure of the segmented leg and the upright posture of the trunk affects the dynamics and stability of legged locomotion. With the help of simple conceptual models we demonstrate how the control effort can be relaxed by relying on compliant leg function and by formulating generalized movement criteria.
Role of endurance running in human evolution, and how we ran without cushioned shoes
Abstract: Humans are mediocre sprinters at best. The top speed of Usain Bolt can be matched by a domestic cat. But when it comes to endurance running over many kilometers and long durations of time, very few animals measure up to humans. We present here evolutionary evidence for endurance running in the genus Homo and its impact on the evolution of our body. Given that humans may have run long distances well before the invention of the modern running shoe, we wondered how endurance runners without shoes cope with collisions of their foot with the ground during running. Each foot collides with the ground approximately 500 times per kilometer, with peak ground reaction forces of up to 3 body weights per collision. We present evidence that habitually barefoot runners often land on the fore-foot before bringing down the heel. In contrast, habitually shod runners mostly land on their heel first. We find that the running style of habitually barefoot runners leads to a much lower impulse, and present simple mechanical reasoning for this observation.
Session: Legged Robots
Development of Cybernetic Human HRP-4C - struggle to realize human walking
Abstract: Cybernetic human HRP-4C is a humanoid robot whose body dimensions were designed to match the average Japanese young female. I will explain the current status of HRP-4C and lessons we learned from the project.
Bio-inspired Robot Design for Hyper-Dynamic Locomotion
Abstract: Mobile robot designers are increasingly searching for inspirations and design cues from biological models. Biomechanics research of animals provides an invaluable source of ideas for legged robot design but the process of implementation involves great complexity. The direct implementation of biological features and morphology often becomes ineffective and misleads engineers due to various reasons. Firstly, engineers investigate animals to achieve a few particular functions whereas features of animals may serve for multiple functions or often remains unknown. Secondly, the difference between engineering manufacturing process and biological synthesis arouses the difficulties in direct replication.
The presentation introduces an abstract bio-inspired design process, which includes simplification of biological inspiration, abstraction of fundamental principles, engineering verification, and prototyping of bio-inspired robots. Introduction of bio-inspired robots exemplify the process: iSprawl, a cockroach-inspired hexapod with compliant, under-actuated legs, runs at 15 body-lengths per second. Spinybot, a hexapod that uses its toes with microspines to climb rough surfaces, including stucco, concrete and brick walls. Stickybot, a gecko-inspired quadruped that climbs smooth vertical surfaces using directional dry adhesion. At the smallest length scale, the undersides of the toes are covered with a unique material called directional polymeric stalks, inspired by the directional setae and lamellae of the gecko.
The future direction of the research includes the implementation of the design process to the hyper-dynamic robotics. Hyper-dynamic robotics entails the morphological design and the control architecture for the highly dynamic performance of legged systems. The development of a fast galloping quadruped will be the first challenge in this effort. The research field includes new actuation scheme, robust structure fabrication, and hierarchical control algorithms for complex systems. Extensive studies on biological runners such as dogs and cheetahs will be vital to the morphological design of the a galloping robot capable of the fast traverse on rough and unstructured terrains.
Humanoid Disturbance Recovery with Limited Available Footholds
Abstract: We present a method for controlling humanoid robots to recover from disturbances when available footholds are limited. This method involves determining the robot's Capture Region taking into consideration the available footholds, deciding where in the Capture Region to step to, and guiding the robot during stance so that the desired location to step to stays inside the Capture Region. We show how to estimate the Capture Region by using a Linear Inverted Pendulum model of walking. With this model, the dynamics of the Instantaneous Capture Point are first order and linear. Therefore, the Capture Region can be constructed using fairly simple and fast 2D overhead geometry constructions techniques. We demonstrate this technique for a simulated model of the robot M2V2 crossing stepping stones in the presence of pushes.
Port-Based Robotics and Variable Impedance Actuators
Abstract: In this talk a framework based on energetical reasoning for modeling and control purposes based on port-Hamiltonian theory will be briefly presented. Then this methodology will be used to analyse novel concepts of actuations called Variable Impedance Actuators. This is the main topic of a running European project called VIACTORS.
Dynamics Morphing Toward Globally Stable Bipedalism
Abstract: Beyond simple walking, bipedalism implies more generally a capability of manipulation with the feet (pedipulation), through discontinuous deformation of the standing region and continuous manipulation of the reaction forces within the standing region. In this talk, I will present "Dynamics Morphing", a control design paradigm which enables seamless transitions between regulatory and oscillatory behaviors. This paradigm can be used to design globally stable controllers by shaping the system dynamics, while considering both continuous and discontinuous dynamics. I will present various non-time-slaved bipedal motions generated by this approach in a computer simulation.
Marc Raibert and Gabe Nelson. Boston Dynamics.
Dynamic Legged Robots at Boston Dynamics
Abstract: Boston Dynamics strives to build robots with controls and mechanical design that make them naturally agile. BigDog is a quadruped robot that operates outdoors in rough terrain. PETMAN is an anthropomorphic robot that walks with a human-style dynamic gait. In this talk we will give a status report on these two robots and describe our plans for their next steps.