Efficient and Stable Locomotion for Impulse-Actuated Robots Using Strictly Convex Foot Shapes

Impulsive actuation enables robots to perform agile manoeuvres and surpass difficult terrain, yet its capacity to induce continuous and stable locomotion have not been explored. We claim that strictly convex foot shapes can improve impulse effectiveness (impulse used per travelled distance) and locomotion speed by facilitating periodicity and stability. To test this premise, we introduce a theoretical two-dimensional model based on rigidbody mechanics to prove stability. We then implement a more elaborate model in simulation to study transient behaviour and impulse effectiveness. Finally, we test our findings on a robot platform to prove their physical validity. Our results prove, that continuous and stable locomotion can be achieved in the strictly convex case of a disc with off-centred mass. In keeping with our theory, stable limit cycles of the off-centred disc outperform the theoretical performance of a cube in simulation and experiment, using up to 10 times less impulse per distance to travel at the same locomotion speed

Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics

Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most studies of simple walking and running models have focused on the basins of attraction of passive limit-cycles and the notion of self-stability. We instead emphasize the importance of stepping beyond basins of attraction. We show an approach based on viability theory to quantify robust sets in state-action space. These sets are valid for the family of all robust control policies, which allows us to quantify the robustness inherent to the natural dynamics before designing the control policy or specifying a control objective. We illustrate our formulation using spring-mass models, simple low dimensional models of running systems. We then show an example application by optimizing robustness of a simulated planar monoped, using a gradient-free optimization scheme. Both case studies result in a nonlinear effective stiffness providing more robustness.Comment: 15 pages. This work has been accepted to IEEE Transactions on Robotics (2019

On the discretisation of actuation in locomotion: Impulse- and shape-based modelling for hopping robots

In an age where computers challenge the smartest human beings in cognitive tasks, the conspicuous discrepancy between robot and animal locomotion appears paradoxical. While animals can move around autonomously in complex environments, today’s robots struggle to independently operate in such surroundings. There are many reasons for robots’ inferior performance, but arguably the most important one is our missing understanding of complexity. This thesis introduces the notion of discrete actuation for the study of locomotion in robots and animals. The actuation of a system with discrete actuation is restricted to be applied at a finite number of instants in time and is impulsive. We find that, despite their simplicity, such systems can predict various experimental observations and inspire novel technologies for robot design and control. We further find that, through the study of discrete actuation, causal relationships between actuation and resulting behaviour are revealed and become quantifiable, which relates the findings presented in this thesis to the broader concepts of complexity, self-organisation, and self-stability. We present four case studies in Chapters 3-6 which demonstrate how the concept of discrete actuation can be employed to understand the physics of locomotion and to facilitate novel robot technologies. We first introduce the impulsive eccentric wheel model which is a discretely actuated system for the study of hopping locomotion. We find that the model predicts robot hopping trajectories and animal related hopping characteristics by reducing the dynamics of hopping–usually described by hybrid differential equations–to analytic maps. The reduction of complexity of the model equations reveals the underlying physics of the locomotion process, and we identify the importance of robot shape and mass distribution for the locomotion performance. As a concrete application of the model, we compare the energetics of hopping and rolling locomotion in environments with obstacles and find when it is better to hop than to roll, based on the fundamental physical principles we discover in the model analysis. The theoretical insights of this modelling approach enable new actuation techniques and design for robots which we display in Robbit; a robot that uses strictly convex foot shapes and rotational impulses to induce hopping locomotion. We show that such systems outperform hopping with non-strictly convex shapes in terms of energy effective and robust locomotion. A system with discrete actuation motivates the exploitation of shape and the environment to improve locomotion dynamics, which reveals advantageous effect of inelastic impacts between the robot foot and the environment. We support this idea with experimental results from the robot CaneBot which can change its foot shape to induce timed impacts with the environment. Even though inelastic impacts are commonly considered detrimental for locomotion dynamics, we show that their appropriate control improves the locomotion speed considerably. The findings presented in this thesis show that discrete actuation for locomotion inspires novel ways to appreciate locomotion dynamics and facilitates unique control and design technologies for robots. Furthermore, discrete actuation emphasises the definition of causality in complex systems which we believe will bring robots closer to the locomotion behaviour of animals, enabling more agile and energy effective robots

Mechanism and Behaviour Co-optimisation of High Performance Mobile Robots

Mobile robots do not display the level of physical performance one would expect, given the specifications of their hardware. This research is based on the idea that their poor performance is at least partly due to their design, and proposes an optimisation approach for the design of high-performance mobile robots. The aim is to facilitate the design process, and produce versatile and robust robots that can exploit the maximum potential of today's technology. This can be achieved by a systematic optimisation study that is based on careful modelling of the robot's dynamics and its limitations, and takes into consideration the performance requirements that the robot is designed to meet. The approach is divided into two parts: (1) an optimisation framework, and (2) an optimisation methodology. In the framework, designs that can perform a large set of tasks are sought, by simultaneously optimising the design and the behaviours to perform them. The optimisation methodology consists of several stages, where various techniques are used for determining the design's most important parameters, and for maximising the chances of finding the best possible design based on the designer's evaluation criteria. The effectiveness of the optimisation approach is proved via a specific case-study of a high-performance balancing and hopping monopedal robot. The outcome is a robot design and a set of optimal behaviours that can meet several performance requirements of conflicting nature, by pushing the hardware to its limits in a safe way. The findings of this research demonstrate the importance of using realistic models, and taking into consideration the tasks that the robot is meant to perform in the design process

In silico case studies of compliant robots: AMARSI deliverable 3.3

In the deliverable 3.2 we presented how the morphological computing ap- proach can significantly facilitate the control strategy in several scenarios, e.g. quadruped locomotion, bipedal locomotion and reaching. In particular, the Kitty experimental platform is an example of the use of morphological computation to allow quadruped locomotion. In this deliverable we continue with the simulation studies on the application of the different morphological computation strategies to control a robotic system

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

Dynamic Walking: Toward Agile and Efficient Bipedal Robots

Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review article outlines the end-to-end process of methods which have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced order models that capture essential walking behaviors to hybrid dynamical systems that encode the full order continuous dynamics along with discrete footstrike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiation on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is agile and efficient