Predicting impact scenarios of a rimless wheel: a geometrical approach

The version of record os available online at: http://dx.doi.org/10.1007/s11071-022-07807-7The 2D motion ofarigid rimless wheel on an inclined plane has been widely studied as a first simple case of passive walker. Usually, it is modelled as a hybrid dynamical system alternating continuous smooth phases and discrete impact ones. As in other bipedal walkers, the related research is often devoted to the analysis of cyclic motions and assumes that the spoke-ground collision is a single-point one. This work focuses exclusively on the impact problem and explores the possibility of different transitions within the impact interval (single-point to double-point collisions, dynamic jamb, stick-slide transitions and sliding reversal) as a function of the spokes angular aperture, the wheel inertia, the wheel-ground friction coefficient, and the initial conditions. This analysis is done through an innovative geometrical approach based on the Percussion Centre.Peer ReviewedPostprint (published version

The Spherical Inverted Pendulum with Pelvis Width in Polar Coordinates for Humanoid Walking Design

The present communication is a follow up and extension of the paper “The Spherical Inverted Pendulum: Exact Solutions of Gait and Foot Placement Estimation Based on Symbolic Computation” by the same author. The walk design is approached by a 3-D inverted pendulum in a polar coordinate system. The advantage of this model is to easily offer indications of the energy expenditure of an efficient walk. However, the disadvantages that were never recognized by authors previously using this model is that the COG trajectory has to pass through the supporting foot location. This causes an unnecessary and unrealistic waving in the frontal plane during gait. The problem is discussed here and solved by extending the model of the inverted pendulum by introducing the pelvis width and the distance between the hips of the two legs, without adding dynamical complexity

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

Applied optimal control for dynamically stable legged locomotion

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 79-84).Online learning and controller adaptation will be an essential component for legged robots in the next few years as they begin to leave the laboratory setting and join our world. I present the first example of a learning system which is able to quickly and reliably acquire a robust feedback control policy for 3D dynamic bipedal walking from a blank slate using only trials implemented on the physical robot. The robot begins walking within a minute and learning converges in approximately 20 minutes. The learning works quickly enough that the robot is able to continually adapt to the terrain as it walks. This success can be attributed in part to the mechanics of our robot, which is capable of stable walking down a small ramp even when the computer is turned off. In this thesis, I analyze the dynamics of passive dynamic walking, starting with reduced planar models and working up to experiments on our real robot. I describe, in detail, the actor-critic reinforcement learning algorithm that is implemented on the return map dynamics of the biped. Finally, I address issues of scaling and controller augmentation using tools from optimal control theory and a simulation of a planar one-leg hopping robot. These learning results provide a starting point for the production of robust and energy efficient walking and running robots that work well initially, and continue to improve with experience.by Russell L. Tedrake.Ph.D

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

SWheg: A Wheel-Leg Transformable Robot With Minimalist Actuator Realization

This article presents the design, implementation, and performance evaluation of SWheg, a novel modular wheel-leg transformable robot family with minimalist actuator realization. SWheg takes advantage of both wheeled and legged locomotion by seamlessly integrating them on a single platform. In contrast to other designs that use multiple actuators, SWheg uses only one actuator to drive the transformation of all the wheel-leg modules in sync. This means an N-legged SWheg robot requires only N+1 actuators, which can significantly reduce the cost and malfunction rate of the platform. The tendon-driven wheel-leg transformation mechanism based on a four-bar linkage can perform fast morphology transitions between wheels and legs. We validated the design principle with two SWheg robots with four and six wheel-leg modules separately, namely Quadrupedal SWheg and Hexapod SWheg. The design process, mechatronics infrastructure, and the gait behavioral development of both platforms were discussed. The performance of the robot was evaluated in various scenarios, including driving and turning in wheeled mode, step crossing, irregular terrain passing, and stair climbing in legged mode. The comparison between these two platforms was also discussed

Dynamic Balance and Gait Metrics for Robotic Bipeds

For legged robots to be useful in the real world, they must be able to balance and walk reliably. Both of these abilities improve when a system is more effective at moving itself around relative to its contacts (i.e., its feet). Achieving this type of movement depends both on the controller used to perform the motion and the physical properties of the system. Although much work has been done on the development of dynamic controllers for balance and gait, only limited research exists on how to quantify a system’s physical balance capabilities or how to modify the system to improve those capabilities. From the control perspective, there are three strategies for maintaining balance in bipeds: flexing, leaning, and stepping. Both stepping and leaning strategies typically depend on balance points (critical points used for maintaining or regaining balance) to determine whether or not a step is needed, and if so, where to step. Although several balance point estimators exist, the majority of these methods make undesirable assumptions (e.g., ignoring the impact dynamics, assuming massless legs, planar motion, etc.). From the physical design perspective, one promising approach for analyzing system performance is a set of dynamic ratios called velocity and momentum gains, which are dependent only on the (scale-invariant) dynamic parameters and instantaneous configuration of a system, enabling entire classes of mechanisms to be analyzed at the same time. This thesis makes four key contributions towards improving biped balancing capabilities. First, a dynamic bipedal controller is proposed which uses a 3D balance point estimator both to respond to disturbances and produce reliable stepping. Second, a novel balance point estimator is proposed that facilitates stepping while combining and expanding the features of existing 2D and 3D estimators to produce a generalized 3D formulation. Third, the momentum gain formulation is extended to general 2D and 3D systems, then both gains are compared to centroidal momentum via a spatial formulation and incorporated into a generalized gain definition. Finally, the gains are used as a metric in an optimization framework to design parameterized balancing mechanisms within a given configuration space. Effectively, this enables an optimization of how well a system could balance without the need to pre-specify or co-generate controllers and/or trajectories. To validate the control contributions, simulated bipeds are subjected to external disturbances while standing still and walking. For the gain contributions, the framework is used to compare gain-optimized mechanisms to those based on the cost of transport metric. Through the combination of gain-based physical design optimization and the use of predictive, real-time balance point estimators within dynamic controllers, bipeds and other legged systems will soon be able to achieve reliable balance and gait in the real world

屋外調査用自律移動型ロボットの不整地移動性能

早大学位記番号:新7829早稲田大

Engineering for a Changing World: 59th IWK, Ilmenau Scientific Colloquium, Technische Universität Ilmenau, September 11-15, 2017 : programme

In 2017, the Ilmenau Scientific Colloquium is again organised by the Department of Mechanical Engineering. The title of this year’s conference “Engineering for a Changing World” refers to limited natural resources of our planet, to massive changes in cooperation between continents, countries, institutions and people – enabled by the increased implementation of information technology as the probably most dominant driver in many fields. The Colloquium, complemented by workshops, is characterised by the following topics, but not limited to them: – Precision Engineering and Metrology – Industry 4.0 and Digitalisation in Mechanical Engineering – Mechatronics, Biomechatronics and Mechanism Technology – Systems Technology – Innovative Metallic Materials The topics are oriented on key strategic aspects of research and teaching in Mechanical Engineering at our university

Viability in State-Action Space: Connecting Morphology, Control, and Learning

Wie können wir Robotern ermöglichen, modellfrei und direkt auf der Hardware zu lernen? Das maschinelle Lernen nimmt als Standardwerkzeug im Arsenal des Robotikers seinen Platz ein. Es gibt jedoch einige offene Fragen, wie man die Kontrolle über physikalische Systeme lernen kann. Diese Arbeit gibt zwei Antworten auf diese motivierende Frage. Das erste ist ein formales Mittel, um die inhärente Robustheit eines gegebenen Systemdesigns zu quantifizieren, bevor der Controller oder das Lernverfahren entworfen wird. Dies unterstreicht die Notwendigkeit, sowohl das Hardals auch das Software-Design eines Roboters zu berücksichtigen, da beide Aspekte in der Systemdynamik untrennbar miteinander verbunden sind. Die zweite ist die Formalisierung einer Sicherheitsmass, die modellfrei erlernt werden kann. Intuitiv zeigt diese Mass an, wie leicht ein Roboter Fehlschläge vermeiden kann. Auf diese Weise können Roboter unbekannte Umgebungen erkunden und gleichzeitig Ausfälle vermeiden. Die wichtigsten Beiträge dieser Dissertation basieren sich auf der Viabilitätstheorie. Viabilität bietet eine alternative Sichtweise auf dynamische Systeme: Anstatt sich auf die Konvergenzeigenschaften eines Systems in Richtung Gleichgewichte zu konzentrieren, wird der Fokus auf Menge von Fehlerzuständen und die Fähigkeit des Systems, diese zu vermeiden, verlagert. Diese Sichtweise eignet sich besonders gut für das Studium der Lernkontrolle an Robotern, da Stabilität im Sinne einer Konvergenz während des Lernprozesses selten gewährleistet werden kann. Der Begriff der Viabilität wird formal auf den Zustand-Aktion-Raum erweitert, mit Viabilitätsmengen von Staat-Aktionspaaren. Eine über diese Mengen definierte Mass ermöglicht eine quantifizierte Bewertung der Robustheit, die für die Familie aller fehlervermeidenden Regler gilt, und ebnet den Weg für ein sicheres, modellfreies Lernen. Die Arbeit beinhaltet auch zwei kleinere Beiträge. Der erste kleine Beitrag ist eine empirische Demonstration der Shaping durch ausschliessliche Modifikation der Systemdynamik. Diese Demonstration verdeutlicht die Bedeutung der Robustheit gegenüber Fehlern für die Lernkontrolle: Ausfälle können nicht nur Schäden verursachen, sondern liefern in der Regel auch keine nützlichen Gradienteninformationen für den Lernprozess. Der zweite kleine Beitrag ist eine Studie über die Wahl der Zustandsinitialisierungen. Entgegen der Intuition und der üblichen Praxis zeigt diese Studie, dass es zuverlässiger sein kann, das System gelegentlich aus einem Zustand zu initialisieren, der bekanntermassen unkontrollierbar ist.How can we enable robots to learn control model-free and directly on hardware? Machine learning is taking its place as a standard tool in the roboticist’s arsenal. However, there are several open questions on how to learn control for physical systems. This thesis provides two answers to this motivating question. The first is a formal means to quantify the inherent robustness of a given system design, prior to designing the controller or learning agent. This emphasizes the need to consider both the hardware and software design of a robot, which are inseparably intertwined in the system dynamics. The second is the formalization of a safety-measure, which can be learned model-free. Intuitively, this measure indicates how easily a robot can avoid failure, and enables robots to explore unknown environments while avoiding failures. The main contributions of this dissertation are based on viability theory. Viability theory provides a slightly unconventional view of dynamical systems: instead of focusing on a system’s convergence properties towards equilibria, the focus is shifted towards sets of failure states and the system’s ability to avoid these sets. This view is particularly well suited to studying learning control in robots, since stability in the sense of convergence can rarely be guaranteed during the learning process. The notion of viability is formally extended to state-action space, with viable sets of state-action pairs. A measure defined over these sets allows a quantified evaluation of robustness valid for the family of all failure-avoiding control policies, and also paves the way for enabling safe model-free learning. The thesis also includes two minor contributions. The first minor contribution is an empirical demonstration of shaping by exclusively modifying the system dynamics. This demonstration highlights the importance of robustness to failures for learning control: not only can failures cause damage, but they typically do not provide useful gradient information for the learning process. The second minor contribution is a study on the choice of state initializations. Counter to intuition and common practice, this study shows it can be more reliable to occasionally initialize the system from a state that is known to be uncontrollable