A family of robot control strategies for intermittent dynamical environments

Abstract

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. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. NOTE: At the time of publication, the author Daniel Koditschek was affiliated with Yale University. Currently, he is a faculty member of the School of Engineering at the University of Pennsylvania. ABSTRACT: 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.

Robotics and neuroscience: A rhythmic interaction

“…This feedback control law then requires a continuous tracking of the ball (continuous sensing feedback) that ensures to impact the ball at a constant position (s = 0) and with a constant velocity in steady-state. The mirror law and several extensions proved to be very robust, and led to successful experimental validations with bouncing robots in 1D, 2D and 3D environments (Buehler et al, 1988(Buehler et al, , 1990(Buehler et al, , 1994. The mirror law is based on continuous tracking of the juggled objects which requires permanent sensory processing.…”

A self-exciting controller for high-speed vertical running

“…In this sense, our construction bears closest resemblance to the work-directed algorithms of Raibert's hoppers [18] or Buehler's Scout [19] that scheduled actuator energy expenditures as a function of limb state, using no additional clock state. Feedback-based excitation ("self-excitation") has also been explored outside the realm of legged robots in the context of dynamically dexterous manipulation [20], [21], [22]; this work is characterized, as are [18] and [19], by a scheduled and intermittent application of force. The central difference between these earlier work-directed locomotion schemes and ours is that our use of discrete event-triggered hybrid control is limited to the introduction of a smooth, piecewise analytic function applied to a very general actuator model rather than a more extensive (and generally non-smooth) "case-based" logic applied to a specific body model.…”

The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper

“…The general idea of task encoding through the enforcement of a lower-dimensional target dynamics, rather than through the prescription of a set of reference trajectories, has been employed in the control of dynamically dexterous machines, including juggling, brachiating and running robots, by Koditschek and his collaborators; see [9], [33] and [37]. The same general idea, albeit in a fully actuated setting, has been employed in [5] and [4], where the method of controlled symmetries introduced in [45] together with a generalization of Routhian reduction for hybrid systems were combined to extend passive dynamic walking gaits, such as those obtained by McGeer's passive walker [28], in three-dimensions.…”