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

This paper describes the dynamic window approach to reactive collision avoidance for mobile robots equipped with synchro-drives. The approach is derived directly from the motion dynamics of the robot and is therefore particularly well-suited for robots operating at high speed. It differs from previous approaches in that the search for commands controlling the translational and rotational velocity of the robot is carried out directly in the space of velocities. The advantage of our approach is that it correctly and in an elegantway incorporates the dynamics of the robot. This is done by reducing the search space to the dynamic window, which consists of the velocities reachable within a short time interval. Within the dynamic window the approach only considers admissible velocities yielding a trajectory on which the robot is able to stop safely. Among these velocities the combination of translational and rotational velocity is chosen by maximizing an objective function. The objective function includes a measure of progress towards a goal location, the forward velocity of the robot, and the distance to the next obstacle on the trajectory. In extensive experiments the approach presented here has been found to safely control our mobile robot RHINO with speeds of up to 95 cm/sec, in populated and dynamic environments.

This article describes the software architecture of an autonomous, interactive tour-guide robot. It presents a modular and distributed software architecture, which integrates localization, mapping, collision avoidance, planning, and various modules concerned with user interaction and Web-based telepresence. At its heart, the software approach relies on probabilistic computation, on-line learning, and any-time algorithms. It enables robots to operate safely, reliably, and at high speeds in highly dynamic environments, and does not require any modifications of the environment to aid the robot's operation. Special emphasis is placed on the design of interactive capabilities that appeal to people's intuition. The interface provides new means for human-robot interaction with crowds of people in public places, and it also provides people all around the world with the ability to establish a "virtual telepresence" using the Web. To illustrate our approach, results are reported obtained in mid-...

This article describes a methodology for programming robots known as probabilistic robotics. The probabilistic paradigm pays tribute to the inherent uncertainty in robot perception, relying on explicit representations of uncertainty when determining what to do. This article surveys some of the progress in the field, using in-depth examples to illustrate some of the nuts and bolts of the basic approach. Our central conjecture is that the probabilistic approach to robotics scales better to complex real-world applications than approaches that ignore a robot's uncertainty.

This paper describes Minerva, an interactive tour-guide robot that was successfully deployed in a Smithsonian museum. Minerva's software is pervasively probabilistic, relying on explicit representations of uncertainty in perception and control. This article describes

Autonomous robots must be able to learn and maintain models of their environments. Research on mobile robot navigation has produced two major paradigms for mapping indoor environments: grid-based and topological. While grid-based methods produce accurate metric maps, their complexity often prohibits efficient planning and problem solving in large-scale indoor environments. Topological maps, on the other hand, can be used much more efficiently, yet accurate and consistent topological maps are often difficult to learn and maintain in large-scale environments, particularly if momentary sensor data is highly ambiguous. This paper describes an approach that integrates both paradigms: grid-based and topological. Grid-based maps are learned using artificial neural networks and naive Bayesian integration. Topological maps are generated on top of the grid-based maps, by partitioning the latter into coherent regions. By combining both paradigms, the approach presented here gains advantages from both worlds: accuracy/consistency and efficiency. The paper gives results for autonomous exploration, mapping and operation of a mobile robot in populated multi-room environments.

The motion planning problem asks for determining a collision-free path for a robot amidst a set of obstacles. In this paper we present a new approach for solving this problem, based on the construction of a random network of possible motions, connecting the source and goal configuration of the robot.

. Learning provides a useful tool for the automatic design of autonomous robots. Recent research on learning robot control has predominantly focussed on learning single tasks that were studied in isolation. If robots encounter a multitude of control learning tasks over their entire lifetime, however, there is an opportunity to transfer knowledge between them. In order to do so, robots may learn the invariants of the individual tasks and environments. This task-independent knowledge can be employed to bias generalization when learning control, which reduces the need for real-world experimentation. We argue that knowledge transfer is essential if robots are to learn control with moderate learning times in complex scenarios. Two approaches to lifelong robot learning which both capture invariant knowledge about the robot and its environments are presented. Both approaches have been evaluated using a HERO2000 mobile robot. Learning tasks included navigation in unknown indoor environments an...

We study the path planning problem, without obstacles, for closed kinematic chains with n links connected by spherical joints in space or revolute joints in the plane. The configuration space of such systems is a real algebraic variety whose structure is fully determined using techniques from algebraic geometry and differential topology. This structure is then exploited to design a complete path planning algorithm that produces a sequence of compliant moves, each of which monotonically increases the number of links in their goal configurations. The average running time of this algorithm is proportional to n³. While less efficient than the O(n) algorithm of Lenhart and Whitesides, our algorithm produces paths that are considerably smoother. More importantly, our analysis serves as a demonstration of how to apply advanced mathematical techniques to path planning problems. Theoretically,

This paper describes an approach to learning a simple indoor robot navigation task through trial-and-error. A mobile robot, equipped with visual, ultrasonic and laser sensors, learns to servo to a designated target object. In less than ten minutes of operation time, the robot is able to navigate to a marked target object in an office environment. The central learning mechanism is the explanationbased neural network learning algorithm (EBNN). EBNN initially learns function purely inductively using neural network representations. With increasing experience, EBNN employs domain knowledge to explain and to analyze training data in order to generalize in a more knowledgeable way. Here EBNN is applied in the context of reinforcement learning, which allows the robot to learn control using dynamic programming. Keywords: explanation-based learning, mobile robots, machine learning, navigation, neural networks, perception 1 Introduction Throughout the last decades, the field of robotics has prod...