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This paper introduces the use of vector fields to design, optimize, and implement reactive schedules for safe cooperative robot patterns on planar graphs. We consider automated guided vehicles (AGVs) operating upon a predefined network of pathways. In contrast to the case of locally Euclidean configuration spaces, regularization of collisions is no longer a local procedure, and issues concerning the global topology of configuration spaces must be addressed. The focus of the present inquiry is the definition, design, and algorithmic construction of controllers for achievement of safe, efficient, cooperative patterns in the simplest nontrivial example (a pair of robots on a Y-network) by means of a hierarchical event-driven state feedback law.

Animals execute locomotor behaviors and more with ease. They have evolved these breath-taking abilities over millions of years. Cheetahs can run, dolphins can swim and flies can fly like no artificial technology can. It is often argued that if human technology could mimic nature, then biological-like performance would follow. Unfortunately, the blind copying or mimicking of a part of nature [Ritzmann et al., 2000] does not often lead to the best design for a variety of reasons [Vogel, 1998]. Evolution works on the “just good enough” principle. Optimal designs are not the necessary end product of evolution. Multiple satisfactory solutions can result in similar performances. Animals do bring to our attention amazing designs, but these designs carry with them the baggage of their history. Moreover, natural design is constrained by factors that may have no relationship to human engineered designs. Animals must be able to grow over time, but still function along the way. Finally, animals are complex and their parts serve multiple functions, not simply the one we happen to examine. In short, in their daunting complexity and integrated function, understanding animal behaviors remains as intractable as their capabilities are tantalizing.

It is now well established that running animals’ mass centers exhibit the characteristics of a Spring Loaded Inverted Pendulum (SLIP) in the sagittal plane (Blickhan and Full, 1993). What control policy accomplishes this collapse of dimension by which animals solve the “degrees of freedom problem” (Bernstein, 1967)? How valuable might this policy be to gait control in legged robots?

EDAR (event-driven assembler robot) — a mobile robot capable of moving a collection of disk-shaped parts located on a two-dimensional workspace from an arbitrary initial configuration to a desired configuration while avoiding collisions in a purely reactive manner, is presented. Since EDAR uses a higher-level scheduler to switch among the subtasks of moving individual parts, it is viewed as mediating a noncooperative game played among the parts.

The dynamics of a Spring Loaded Inverted Pendulum (SLIP) \template” [1] approximate well the center of mass (COM) of running animals, humans, and of the robot RHex [2]. Running control can therefore be ierarchically structured as a high level SLIP control and the anchoring of SLIP in the complex morphology of the physical system. Analysis of the sagittal plane lossless SLIP model has shown that it includes parameter regions where its gait is passively stabilized, i.e. with the discrete control input | the leg touchdown angle | held constant. We present numerical evidence to suggest that an open loop \clock” excitation of a high degree of freedom hexapedal robot model can lead to asymptotically stable limit cycles that \anchor” [1] the SLIP model in its self stabilizing regime. This motivates the search for completely feedforward SLIP locomotion control strategies, which we now speculate may be successfully used to elicit a self-stabilizing running robot such as RHex.

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The flexibility of computer vision is attractive when designing manipulation systems which must interact with otherwise unsensed objects. However, occlusions introduce significant challenges to the construction of practical vision-based control systems. This paper provides empirical validation of a vision based control strategy that affords guaranteed convergence to a visible goal from essentially any “safe” initial position while maintaining full view of all the feature points along the way. The method applies to first (quasi-static, or “kinematic”) and second (Lagrangian or “mechanical”) order plants that incorporate an independent actuator for each degree of freedom.

In this paper, the authors describe the design and control of RHex, a power autonomous, untethered, compliant-legged hexapod robot. RHex has only six actuators—one motor located at each hip—achieving mechanical simplicity that promotes reliable and robust operation in real-world tasks. Empirically stable and highly maneuverable locomotion arises from a very simple clock-driven, openloop tripod gait. The legs rotate full circle, thereby preventing the common problem of toe stubbing in the protraction (swing) phase. An extensive suite of experimental results documents the robot’s significant “intrinsic mobility”—the traversal of rugged, broken, and obstacle-ridden ground without any terrain sensing or actively controlled adaptation. RHex achieves fast and robust forward locomotion traveling at speeds up to one body length per second and traversing height variations well exceeding its body clearance.

We report on our progress in extending the behavioral repertoire of RHex, a compliant leg hexapod robot. We introduce two new controllers, one for climbing constant slope inclinations and one for achieving higher speeds via pronking, a gait that incorporates a, substantial aerial phase. In both cases, we make use of an underlying open-loop control strategy, combined with low bandwidth feedback to modulate its parameters. The inclination behavior arises from our initial alternating tripod walking controller and adjusts the angle offsets of individual leg motion profiles based on inertial sensing of the average surface slope. Similarly, the pronking controller makes use of a “virtual” leg touchdown sensing mechanism to adjust the frequency of the open-loop pronking, effectively synchronizing the controller with the natural oscillations of the mechanical system. Experimental results demonstrate good performance on slopes inclined up to /spl sim/250 and pronking up to speeds approaching 2 body lengths per second (/spl sim/1.0 m/s).

We describe a method for the decentralized phase regulation of two coupled hybrid oscillators. In particular, we prove that the application of this synchronization method to two hopping robots, each of which individually achieves only asymptotically stable hopping, results in an asymptotically stable limit cycle for the coupled system exhibiting the desired phase difference. This extends our previous work wherein the application of the method to two individually deadbeat-stabilized oscillators (paddle juggling mechanisms) was shown to yield the desired result. Central to this method is the idea that cyclic systems may be composed into a larger, aggregate, cyclic system. Its application entails moving from physical coordinates (for example, the position and velocity of each constituent mechanism) to the coordinates of phase and phase velocity. Within this canonical coordinate system we construct a model dynamical system, called a reference field, which encodes the desired behavior of each cyclic system as well as the phase relationships between them. We then force the actual composite system to behave like the model.

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.