Modeling, analysis and control of robot-object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

International audienceSo-called robot-object Lagrangian systems consist of a class of nonsmooth underactuated complementarity Lagrangian systems, with a specific structure: an "object" and a "robot". Only the robot is actuated. The object dynamics can thus be controlled only through the action of the contact Lagrange multipliers, which represent the interaction forces between the robot and the object. Juggling, walking, running, hopping machines, robotic systems that manipulate objects, tapping, pushing systems, kinematic chains with joint clearance, crawling, climbing robots, some cable-driven manipulators, and some circuits with set-valued nonsmooth components, belong this class. This article aims at presenting their main features, then many application examples which belong to the robot-object class, then reviewing the main tools and control strategies which have been proposed in the Automatic Control and in the Robotics literature. Some comments and open issues conclude the article

Dynamics of the Inertia Coupled Rimless Wheel with Frictional Losses and Actuation

The Inertia Coupled Rimless (ICR) wheel is a mechanically simple walking device capable of energy efficient motion. Typically, walking robots that are capable of level ground transport are extremely energy inefficient. To address this performance issue, the ICR wheel was examined while considering real-world frictional losses. The ICR wheel has been previously shown to be capable of collisionless, periodic motion, but until now, the ICR wheel had only been examined as an ideal, theoretical model. The inertia device within the system was tested to determine both the magnitude of energy loss due to damping and a suitable model for its motion. Fitting friction models to the experimental results showed that the a visciously damped model most accurately represented the system\u27s motion. Simulations revealed that the ICR wheel with friction would be capable of walking passively on a ramp with half stable, periodic walking, but the collisionless motion was lost. An actuation scheme was designed in simulation to allow an ICR wheel with damping to achieve collisionless motion on level ground. Experimental testing of a passive ICR wheel on a $3^o$ ramp showed that a cost of transport of at least 0.052 is possible with this system. Simulations suggest that, with the inclusion of an actuation scheme, the cost of transport for the same system on level ground could be as low as 0.024. Understanding how to overcome frictional losses lays the foundation for the creation of a walking robot capable of level ground transport with significantly less energy use than current models are capable of achieving

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

A Hybrid Systems Model for Simple Manipulation and Self-Manipulation Systems

Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs individually. In concert, it is well known that the interaction of such idealized approximations can lead to conflicting and even paradoxical results. As robotics modeling moves from the consideration of isolated behaviors to the analysis of tasks requiring their composition, a mathematically tractable framework for building models that combine these simple approximations yet achieve reliable results is overdue. In this paper we present a formal hybrid dynamical system model that introduces suitably restricted compositions of these familiar abstractions with the guarantee of consistency analogous to global existence and uniqueness in classical dynamical systems. The hybrid system developed here provides a discontinuous but self-consistent approximation to the continuous (though possibly very stiff and fast) dynamics of a physical robot undergoing intermittent impacts. The modeling choices sacrifice some quantitative numerical efficiencies while maintaining qualitatively correct and analytically tractable results with consistency guarantees promoting their use in formal reasoning about mechanism, feedback control, and behavior design in robots that make and break contact with their environment. For more information: Kod*La

What is Robotics: Why Do We Need It and How Can We Get It?

Robotics is an emerging synthetic science concerned with programming work. Robot technologies are quickly advancing beyond the insights of the existing science. More secure intellectual foundations will be required to achieve better, more reliable and safer capabilities as their penetration into society deepens. Presently missing foundations include the identification of fundamental physical limits, the development of new dynamical systems theory and the invention of physically grounded programming languages. The new discipline needs a departmental home in the universities which it can justify both intellectually and by its capacity to attract new diverse populations inspired by the age old human fascination with robots. For more information: Kod*la