this paper is as follows: in Section 2, we collect some mathematical preliminaries from the literature on controllability of nonlinear systems and on classification of free Lie algebras. These are drawn from classical references in control theory [4, 17, 18, 36, 40] and Lie algebras [15, 43]. In Section 3, using some outstanding results of Brockett on optimal steering of certain classes of systems as motivation [5], we discuss the use of sinusoidal inputs for steering systems of first order, i.e., systems where controllability is achieved after just one level of Lie brackets of the input vector fields. Section 4 attempts to expand the domain of applicability of these results to more complex systems, where several orders of Lie brackets are needed to obtain the full Lie algebra associated with the input distribution. The 4 MURRAY AND SASTRY

Abstract—Weextend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline. I.

Programmable vector fields can be used to control a variety of flexible planar parts feeders. These devices can exploit exotic actuation technologies such as arrayed, massively-parallel microfabricated motion pixels or transversely vibrating (macroscopic) plates. These new automation designs promise great flexibility, speed, and dexterity---we believe they may be employed to orient, singulate, sort, feed, and assemble parts. However, since they have only recently been invented, programming and controlling them for manipulation tasks is challenging. When a part is placed on our devices, the programmed vector field induces a force and moment upon it. Over time, the part may come to rest in a dynamic equilibrium state. By chaining together sequences of vector fields, the equilibrium states of a part in the field may be cascaded to obtain a desired final state. The resulting strategies require no sensing and enjoy efficient planning algorithms. This paper begins by describing our experimen...

Configuration spaces of distinct labeled points on the plane are of practical relevance in designing safe control schemes for Automated Guided Vehicles (robots) in industrial settings. In this announcement, we consider the problem of the construction and classification of configuration spaces for graphs. Topological data associated to these spaces (e.g., dimension, braid groups) provide an effective measure of the complexity of the control problem. The spaces are themselves topologically interesting objects. We show that they are K(π1, 1) spaces whose homological dimension is bounded by the number of essential vertices. Hence, the braid groups are torsion-free. AMS classification: 57M15,57Q05,93C25,93C85.

Programmable force fields are an abstraction to represent a new class of devices for distributed, non-prehensile manipulation for applications in parts feeding, sorting, positioning, and assembly. Unlike robot grippers, conveyor belts, or vibratory bowl feeders, these devices generate force vector fields in which the parts move until they may reach a stable equilibrium pose.

the author and should not be interpreted as representing the o cial policies, either expressed or A good model of the mechanics of a task is a resource for a robot, just as actuators and sensors are resources. The e ective use of frictional, gravitational, and dynamic forces can substitute for extra actuators; the expectation derived from a good model can minimize sensing requirements. Despite this, most robot systems attempt to dominate or nullify task mechanics, rather than exploit them. There has been little e ort to understand the manipulation capabilities of even the simplest robots under more complete mechanics models. This thesis addresses that knowledge de cit by studying graspless or nonprehensile manipulation. Nonprehensile manipulation exploits task mechanics to achieve a goal state without grasping, allowing simple mechanisms to accomplish complex tasks. With nonprehensile manipulation, a robot can manipulate objects too large or heavy to be grasped and lifted, and a low-degree-of-freedom robot can control more degrees-of-freedom of an object by allowing relative motion between the object and the manipulator. Two key problems are determining controllability of and motion planning for

In this paper an on-line multi-robot navigation methodology is presented, extending the concept of navigation functions from the single robot to the multiple robot domain. An appropriate measure of the distance from bad sets, suitable for multirobot navigation is introduced.

It is perhaps not universally acknowledged that an outstanding place to find interesting topological objects is within the walls of an automated warehouse or factory. The examples of topological spaces that we construct in this exposition arose simultaneously from two seemingly disparate fields: the first author, in his thesis [1], discovered these spaces after working with H. Landau, Z. Landau, J. Pommersheim, and E. Zaslow on problems about random walks on graphs [2]. The second author discovered these same spaces while collaborating with D. Koditschek in the Artificial Intelligence Lab at the University of Michigan; see [7] and [8]. Sections 1 and 2 give some motivations arising from robotics, as well as a little background on configuration spaces. For the remainder of the paper we focus on a fascinating class of topological spaces related to motion-planning on graphs. 1. Robotics and topological motion planning Consider an automated factory equipped with a cadre of Automated Guided

We are developing paradigms and algorithms for browsing and editing families of animations using a haptic forcefeedback device called a Phantom. These techniques may be generalized to navigation of any high degree-offreedom system from a lower degree-of-freedom control space, with applications to telerobotics and simulation of virtual humans. We believe that modeling the animation configuration space coupled with the highly interactive nature of the haptic device provides us with useful and intuitive means of control. We have implemented our ideas in a system for the manipulation of animation motion capture data; in particular, anthropomorphic figures with 57 degrees of freedom are controlled by the user in real time. We treat trajectories, which encode animation, as first-class objects; haptic manipulation of these trajectories results in change to the animation. We have several haptic editing modes in which these trajectories are either haptically deformed or performed by the user w...

Assembly is a fundamental issue in the volume production of products that include microscopic (submillimeter) parts. These parts are often fabricated in parallel at high density but must then be assembled into patterns with lower spatial density. In this paper we propose a new approach to microassembly using 1) ultrasonic vibration to eliminate friction and adhesion, and 2) electrostatic forces to position and align parts in parallel. We describe experiments on the dynamic and frictional properties of collections of microscopic parts under these conditions. We first demonstrate that ultrasonic vibration can be used to overcome adhesive forces; we also compare part behavior in air and vacuum. Next, we demonstrate that parts can be positioned and aligned using a combination of vibration and electrostatic forces. Finally, we demonstrate part sorting by size. Motivated by these feasibility experiments, our goal is a systematic method for designing implementable planar force fields for mic...