A Family of Robot Control Strategies for Intermittent Dynamical Environments

This article develops a formalism for describing and analyzing a very simple representative class of robotic tasks that require dynamical dexterity - among them, the task of juggling. The authors review their empirical success, to date, with a new class of control algorithms for this task domain, called mirror algorithms. The formalism for representing the task domain and encoding within it the desired robot behavior enables them to prove that a suitable mirror algorithm is correct with respect to a specified task

From stable to chaotic juggling: theory, simulation, and experiments

Recent results of dynamical systems theory are used to derive strong predictions concerning the global properties of a simplified model of a planar juggling robot. In particular, it is found that certain lower-order local (linearized) stability properties determine the essential global (nonlinear) stability properties, and that successive increments in the controller gain settings give rise to a cascade of stable period-doubling bifurcations that comprise a universal route to chaos. The theoretical predictions are verified by simulation and corroborated by experimental data from the juggling robot

Toward the Regulation and Composition of Cyclic Behaviors

Many tasks in robotics and automation require a cyclic exchange of energy between a machine and its environment. Since most environments are under actuated —that is, there are more objects to be manipulated than actuated degrees of freedom with which to manipulate them—the exchange must be punctuated by intermittent repeated contacts. In this paper, we develop the appropriate theoretical setting for framing these problems and propose a general method for regulating coupled cyclic systems. We prove for the first time the local stability of a (slight variant on a) phase regulation strategy that we have been using with empirical success in the lab for more than a decade. We apply these methods to three examples: juggling two balls, two legged synchronized hopping and two legged running—considering for the first time the analogies between juggling and running formally

Sequential Composition of Dynamically Dexterous Robot Behaviors

We report on our efforts to develop a sequential robot controller-composition technique in the context of dexterous “batting” maneuvers. A robot with a flat paddle is required to strike repeatedly at a thrown ball until the ball is brought to rest on the paddle at a specified location. The robot’s reachable workspace is blocked by an obstacle that disconnects the free space formed when the ball and paddle remain in contact, forcing the machine to “let go” for a time to bring the ball to the desired state. The controller compositions we create guarantee that a ball introduced in the “safe workspace” remains there and is ultimately brought to the goal. We report on experimental results from an implementation of these formal composition methods, and present descriptive statistics characterizing the experiments.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67990/2/10.1177_02783649922066385.pd

Globally stable closed loops imply autonomous behavior

A program of research in robotics that seeks to encode abstract tasks in a form that simultaneously affords a control scheme for the torque-actuated dynamical systems, as well as a proof that the resulting closed-loop behavior will correctly achieve the desired goals, is reviewed. Two different behaviors that require dexterity and might plausibly connote \u27intelligence\u27 - navigating in a cluttered environment and juggling a number of otherwise freely falling objects - are examined with regard to similarities in problem representation, method of solution, and causes of success. The central theme concerns the virtue of global stability mechanisms. At the planning level they lend autonomy, that is, freedom from dependence upon some \u27higher\u27 intelligence. They encourage the design of canonical procedures for model problems, which may then be instantiated in particular settings by a change of coordinates. The procedures developed result in provably autonomous behavior. Simulation results and physical experimental studies suggest the practicability of these methods

Robotics and neuroscience: A rhythmic interaction

At the crossing between motor control neuroscience and robotics system theory, the paper presents a rhythmic experiment that is amenable both to handy laboratory implementation and simple mathematical modeling. The experiment is based on an impact juggling task, requiring the coordination of two upper-limb effectors and some phase-locking with the trajectories of one or several juggled objects. We describe the experiment, its implementation and the mathematical model used for the analysis. Our underlying research focuses on the role of sensory feedback in rhythmic tasks. In a robotic implementation of our experiment, we study the minimum feedback that is required to achieve robust control. A limited source of feedback, measuring only the impact times, is shown to give promising results. A second field of investigation concerns the human behavior in the same impact juggling task. We study how a variation of the tempo induces a transition between two distinct control strategies with different sensory feedback requirements. Analogies and differences between the robotic and human behaviors are obviously of high relevance in such a flexible setup

Modular Hopping and Running via Parallel Composition

Though multi-functional robot hardware has been created, the complexity in its functionality has been constrained by a lack of algorithms that appropriately manage flexible and autonomous reconfiguration of interconnections to physical and behavioral components. Raibert pioneered a paradigm for the synthesis of planar hopping using a composition of ``parts\u27\u27: controlled vertical hopping, controlled forward speed, and controlled body attitude. Such reduced degree-of-freedom compositions also seem to appear in running animals across several orders of magnitude of scale. Dynamical systems theory can offer a formal representation of such reductions in terms of ``anchored templates,\u27\u27 respecting which Raibert\u27s empirical synthesis (and the animals\u27 empirical performance) can be posed as a parallel composition. However, the orthodox notion (attracting invariant submanifold with restriction dynamics conjugate to a template system) has only been formally synthesized in a few isolated instances in engineering (juggling, brachiating, hexapedal running robots, etc.) and formally observed in biology only in similarly limited contexts. In order to bring Raibert\u27s 1980\u27s work into the 21st century and out of the laboratory, we design a new family of one-, two-, and four-legged robots with high power density, transparency, and control bandwidth. On these platforms, we demonstrate a growing collection of $\{$body, behavior$\}$ pairs that successfully embody dynamical running / hopping ``gaits\u27\u27 specified using compositions of a few templates, with few parameters and a great deal of empirical robustness. We aim for and report substantial advances toward a formal notion of parallel composition---embodied behaviors that are correct by design even in the presence of nefarious coupling and perturbation---using a new analytical tool (hybrid dynamical averaging). With ideas of verifiable behavioral modularity and a firm understanding of the hardware tools required to implement them, we are closer to identifying the components required to flexibly program the exchange of work between machines and their environment. Knowing how to combine and sequence stable basins to solve arbitrarily complex tasks will result in improved foundations for robotics as it goes from ad-hoc practice to science (with predictive theories) in the next few decades

An Active Visual Estimator for Dexterous Manipulation

We present a working implementation of a dynamics based architecture for visual sensing. This architecture provides field rate estimates of the positions and velocities of two independent falling balls in the face of repeated visual occlusions and departures from the field of view. The practical success of this system can be attributed to the interconnection of two strongly nonlinear dynamical systems: a novel triangulating state estimator; and an image plane window controller. We detail the architecture of this active sensor, provide data documenting its performance, and offer an analysis of its soundness in the form of a convergence proof for the estimator and a boundedness proof for the manager

On the Control of a One Degree-of-Freedom Juggling Robot

International audienceThis paper is devoted to the feedback control of a one degree-of-freedom (dof) juggling robot, considered as a subclass of mechanical systems subject to a unilateral constraint. The proposed approach takes into account the whole dynamics of the system, and focuses on the design of a force input. It consists of a family of hybrid feedback control laws, that allow to stabilize the object around some desired (periodic or not) trajectory. The closed-loop behavior in presence of various disturbances is studied. Despite good robustness properties, the importance of good knowledge of the system parameters, like the restitution coefficient, is highlighted. Besides its theoretical interest concerning the control of a class of mechanical systems subject to unilateral constraints, this study has potential applications in non-prehensile manipulation, extending pushing robotic tasks to striking-and-pushing tasks