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. Multiple cooperating robots are able to complete many tasks more quickly and reliably than one robot alone. Communication between the robots can multiply their capabilities and e ectiveness, but to what extent? In this research, the importance of communication in robotic societies is investigated through experiments on both simulated and real robots. Performance was measured for three di erent types of communication for three di erent tasks. The levels of communication are progressively more complex and potentially more expensive to implement. For some tasks, communication can signi cantly improve performance, but for others inter-agent communication is apparently unnecessary. In cases where communication helps, the lowest level of communication is almost as e ective as the more complex type. The bulk of these results are derived from thousands of simulations run with randomly generated initial conditions. The simulation results help determine appropriate parameters for the reactive control system which was ported for tests on Denning mobile robots.

This paper describes an efficient algorithm for computing the distance between non-convex objects. Objects are modeled as the union of a set of convex components. From this model we construct a hierarchical bounding representation based on spheres. The distance between objects is determined by computing the distance between pairs of convex components using preexisting techniques. The key to efficiency is a simple search routine that uses the bounding representation to ignore most of the possible pairs of components. The efficiency can further be improved by accepting a relative error in the returned result. Several empirical trials are presented to examine the performance of the algorithm. 1. Introduction Computing the distance between objects is a common problem in robotics. Using a mathematical model of two objects, we find a point on each object such that the distance between the points is minimized. If one object is a robot and the other object is the union of all the obstacles i...

This paper considers the problem of deploying a mobile sensor network in an unknown environment. A mobile sensor network is composed of a distributed collection of nodes, each of which has sensing, computation, communication and locomotion capabilities. Such networks are capable of self-deployment; i.e., starting from some compact initial configuration, the nodes in the network can spread out such that the area `covered' by the network is maximized. In this paper, we present a potential-field-based approach to deployment. The fields are constructed such that each node is repelled by both obstacles and by other nodes, thereby forcing the network to spread itself throughout the environment. The approach is both distributed and scalable.

We are concerned with the utility of social laws in a computational environment, laws which guarantee the successful coexistence of multiple programs and programmers. In this paper we are interested in the off line design of social laws, where we as designers must decide ahead of time on useful social laws. In the first part of this paper we suggest the use of social laws in the domain of mobile robots, and prove analytic results about the usefulness of this approach in that setting. In the second part of this paper we present a general model of social law in a computational system, and investigate some of its properties. This includes a definition of the basic computational problem involved with the design of multi-agent systems, and an investigation of the automatic synthesis of useful social laws in the framework of a model which refers explicitly to social laws. This work was supported in part by a grant from the US-Israel Binational Science Foundation. 1 Introduction This pa...

A new real-time obstacle avoidance approach for mobile robots has been developed and implemented. This approach permits the detection of unknown obstacles simultaneously with the steering of the mobile robot to avoid collisions and advancing toward the target. The novelty of this approach, entitled the Virtual Force Field, lies in the integration of two known concepts: Certainty Grids for obstacle representation, and Potential Fields for navigation. This combination is especially suitable for the accommodation of inaccurate sensor data (such as produced by ultrasonic sensors) as well as for sensor fusion, and enables continuous motion of the robot without stopping in front of obstacles. This navigation algorithm also takes into account the dynamic behavior of a fast mobile robot and solves the "local minimum trap" problem. Experimental results from a mobile robot running at a maximum speed of 0.78 m/sec demonstrate the power of the proposed algorithm. 2 1.

Potential field methods are rapidly gaining popularity in obstacle avoidance applications for mobile robots and manipulators. While the potential field principle is particularly attractive because of its elegance and simplicity, substantial shortcomings have been identified as problems that are inherent to this principle. Based upon mathematical analysis, this paper presents a systematic criticism of the inherent problems. The heart of this analysis is a differential equation that combines the robot and the environment into a unified system. The identified problems are discussed in qualitative and theoretical terms and documented with experimental results from actual mobile robot runs.

This paper reviews key concepts of the Autonomous Robot Architecture (AuRA). Its structure, strengths, and roots in biology are presented. AuRA is a hybrid deliberative/reactive robotic architecture that has been developed and refined over the past decade. In this article, particular focus is placed on the reactive behavioral component of this hybrid architecture. Various real world robots that have been implemented using this architectural paradigm are discussed, including a case study of a multiagent robotic team that competed and won the 1994 AAAI Mobile Robot Competition. 1 Introduction The Autonomous Robot Architecture (AuRA) was developed in the mid-1980's as a hybrid approach to robotic navigation [6]. Hybridization arises from the presence of two distinct components: a deliberative or hierarchical planner, based on traditional artificial intelligence techniques; and a reactive controller, based upon schema theory [2]. It was the first robot navigational system to be presented ...

Elastic bands are proposed as the basis for a new framework to close the gap between global path planning and real-time sensor-based robot control. An elastic band is a deformable collision-free path. The initial shape of the elastic is the free path generated by a planner. Subjected to artificial forces, the elastic band deforms in real time to a short and smooth path that maintains clearance from the obstacles. The elastic continues to deform as changes in the environment are detected by sensors, enabling the robot to accommodate uncertainties and react to unexpected and moving obstacles. While providing a tight connection between the robot and its environment, the elastic band preserves the global nature of the planned path. This paper outlines the framework and discusses an efficient implementation based on bubbles. 1. Introduction It is difficult to build a robot system that executes motion tasks autonomously. The problem has generally been approached from two directions: path p...

A Very Large Scale Robotic (VLSR) system may consist of from hundreds to perhaps tens of thousands or more autonomous robots. The costs of robots are going down, and the robots are getting more compact, more capable, and more flexible. Hence, in the near future, we expect to see many industrial and military applications of VLSR systems in tasks such as assembling, transporting, hazardous inspection, patrolling, guarding and attacking. In this paper, we propose a new approach for distributed autonomous control of VLSR systems. We define simple artificial force laws between pairs of robots or robot groups. The force laws are inverse-power force laws, incorporating both attraction and repulsion. The force laws can be distinct and to some degree they reflect the 'social relations' among robots. Therefore we call our method social potential fields. An individual robot's motion is controlled by the resultant artificial force imposed by other robots and other components of the system. The approach is distributed in that the force calculations and motion control can be done in an asynchronous and distributed manner. We also extend the social potential fields model to use spring laws as force laws. This paper presents the first and a preliminary study on applying potential fields to distributed autonomous multi-robot control. We describe the generic framework of our social potential fields method. We show with computer simulations that the method can yield interesting and useful behaviors among robots, and we give examples of possible industrial and military applications. We also identify theoretical problems for future studies. 1999 Published by Elsevier Science B.V. All rights reserved.