M. Buhler

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.<<ETX>>

A Simple Juggling Robot: Theory and Experimentation

We have developed a formalism for describing and analyzing a very simple representative of a class of robotic tasks which involve repeated robot-environment interactions, among them the task of juggling. We review our empirical success to date with a new class of control algorithms for this task domain that we call “mirror algorithms.” These new nonlinear feedback algorithms were motivated strongly by experimental insights after the failure of local controllers based upon a linearized analysis. We offer here a proof that a suitable mirror algorithm is correct with respect to the local version of a specified task — the “vertical one-juggle” — but observe that the resulting ability to place poles of the local linearized system does not achieve noticeably superior transient performance in experiments. We discuss the further analysis and experimentation that should provide a theoretical basis for improving performance.

A family of robot control strategies for intermittent dynamical environments

A formalism is developed 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.<<ETX>>A formalism is developed for describing and analyzing a very simple representation of a class of robotic tasks which require dynamical dexterity, among them the task of juggling. Empirical success has been achieved with a class of control algorithms for this task domain, called mirror algorithms. Using the formalism for representing the task domain, and encoding within it the desired robot behavior, it can be proven that a suitable mirror algorithm is correct with respect to a special task. Although the generation of algorithm geometry is completely heuristic at present, the analytical tractability of the resulting robot-environment closed loop, which is demonstrated, raises the hope that sufficient understanding may soon be realized to afford automatic translation of suitably expressed task definitions into provable correct empirically valid robot controller designs.<<ETX>>

A new distributed real-time controller for robotics applications

A description is given of a dual-board real-time distributed control module based on the INMOS T414/T800 transputers. The CPU board provides fast external memory, support for the four 10-MHz serial transputer links including two fiber-optic links, and an I/O expansion connector. The boards backplane connector is pin-compatible with the INMOS ITEM development system. The plug-in I/O board provides a bidirectional latched 32-bit I/O bus with full handshaking support. Half of this board is allotted to a wire-wrap prototyping area allowing for customization to specific I/O needs. It is asserted that an easily configurable network built from this low-cost modular design should be able to tackle the most demanding real-time control applications, with respect to computation as well as I/O requirements. A description is given of two particular applications presently underway in the Yale Robotics Laboratory.<<ETX>>