Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

Combinatorial Group Theory: COMBINATORIAL GROUP THEORY

One of the goals in the field of mobile robotics is the development of mobile platforms which operate in populated environments. For many tasks it is therefore highly desirable that a robot can track the positions of the humans in its surrounding. In this paper we introduce sample-based joint probabilistic data association filters as a new algorithm to track multiple moving objects. Our method applies Bayesian filtering to adapt the tracking process to the number of objects in the perceptual range of the robot. The approach has been implemented and tested on a real robot using laser-range data. We present experiments illustrating that our algorithm is able to robustly keep track of multiple people. The experiments furthermore show that the approach outperforms other techniques developed so far.

http://pages.iai.uni-bonn.de/schulz_dirk/articles/people-tracking-ijrr-03.pdf

People Tracking with Mobile Robots Using Sample-Based Joint Probabilistic Data Association Filters

Whenever people move through their environments they do not move randomly. Instead, they usually follow specific trajectories or motion patterns corresponding to their intentions. Knowledge about such patterns enables a mobile robot to robustly keep track of persons in its environment and to improve its behavior. In this paper we propose a technique for learning collections of trajectories that characterize typical motion patterns of persons. Data recorded with laser-range finders are clustered using the expectation maximization algorithm. Based on the result of the clustering process, we derive a hidden Markov model that is applied to estimate the current and future positions of persons based on sensory input. We also describe how to incorporate the probabilistic belief about the potential trajectories of persons into the path planning process of a mobile robot. We present several experiments carried out in different environments with a mobile robot equipped with a laser-range scanner and a camera system. The results demonstrate that our approach can reliably learn motion patterns of persons, can robustly estimate and predict positions of persons, and can be used to improve the navigation behavior of a mobile robot.

/pdf/learning-motion-patterns-of-people-for-compliant-robot-oi28akq38h.pdf

Learning Motion Patterns of People for Compliant Robot Motion

We review a range of techniques related to navigation of unmanned vehicles through unknown environments with obstacles, especially those that rigorously ensure collision avoidance (given certain assumptions about the system). This topic continues to be an active area of research, and we highlight some directions in which available approaches may be improved. The paper discusses models of the sensors and vehicle kinematics, assumptions about the environment, and performance criteria. Methods applicable to stationary obstacles, moving obstacles and multiple vehicles scenarios are all reviewed. In preference to global approaches based on full knowledge of the environment, particular attention is given to reactive methods based on local sensory data, with a special focus on recently proposed navigation laws based on model predictive and sliding mode control.

/pdf/algorithms-for-collision-free-navigation-of-mobile-robots-in-1s1ksc76if.pdf

Algorithms for collision-free navigation of mobile robots in complex cluttered environments: a survey

This paper considers what can be accomplished using a mobile robot that has limited sensing. For navigation and mapping, the robot has only one sensor, which tracks the directions of depth discontinuities. There are no coordinates, and the robot is given a motion primitive that allows it to move toward discontinuities. The robot is incapable of performing localization or measuring any distances or angles. Nevertheless, when dropped into an unknown planar environment, the robot builds a data structure, called the gap navigation tree, which enables it to navigate optimally in terms of Euclidean distance traveled. In a sense, the robot is able to learn the critical information contained in the classical shortest-path roadmap, although surprisingly it is unable to extract metric information. We prove these results for the case of a point robot placed into a simply connected, piecewise-analytic planar environment. The case of multiply connected environments is also addressed, in which it is shown that further sensing assumptions are needed. Due to the limited sensor given to the robot, globally optimal navigation is impossible; however, our approach achieves locally optimal (within a homotopy class) navigation, which is the best that is theoretically possible under this robot model.

/pdf/distance-optimal-navigation-in-an-unknown-environment-2u7y3gqp6i.pdf

Distance-Optimal Navigation in an Unknown Environment Without Sensing Distances

Planning exploration strategies for simultaneous localization and mapping

This paper presents an algorithm for a visibility-based pursuit-evasion problem in which bounds on the speeds of the pursuer and evader are given The pursuer tries to find the evader inside of a simply-connected polygonal environment, and the evader in turn tries actively to avoid detection The algorithm is at least as powerful as the complete algorithm for the unbounded speed case, and with the knowledge of speed bounds, generates solutions for environments that were previously unsolvable Furthermore, the paper develops a characterization of the set of possible evader positions as a function of time This characterization is more complex than in the unbound-speed case, because it no longer depends only on the combinatorial changes in the visibility region of the pursuer

http://msl.cs.uiuc.edu/~lavalle/papers/TovLav06.pdf

Visibility-based pursuit-evasion with bounded speed

In this paper we present our advances in a data structure, the Gap Navigation Tree (GNT), useful for solving different visibility-based robotic tasks in unknown planar environments. We present its use for optimal robot navigation in simply-connected environments, locally optimal navigation in multiply-connected environments, pursuit-evasion, and robot localization. The guiding philosophy of this work is to avoid traditional problems such as complete map building and exact localization by constructing a minimal representation based entirely on critical events in online sensor measurements made by the robot. The data structure is introduced from an information space perspective, in which the information used among the different visibility-based tasks is essentially the same, and it is up to the robot strategy to use it accordingly for the completion of the particular task. This is done through a simple sensor abstraction that reports the discontinuities in depth information of the environment from the robot’s perspective (gaps), and without any kind of geometric measurements. The GNT framework was successfully implemented on a real robot platform.

/pdf/gap-navigation-trees-minimal-representation-for-visibility-1o1vw2nqa2.pdf

Gap navigation trees: Minimal representation for visibility-based tasks

In this paper we develop a dynamite data structure, useful for robot navigation in an unknown, simply connected planar environment. The guiding philosophy in this work is to avoid traditional problems such as complete map building and localization by constructing a minimal representation based entirely on critical events in online sensor measurements made by the robot. Furthermore, this representation provides a sensor-feedback motion strategy that guides the robot along an optimal trajectory between any two environment locations, and allows the search of static targets, even though there is no geometric map of the environment. We present algorithms for building the data structure in an unknown environment, and for using it to perform optimal navigation. We implemented these algorithms on a real mobile robot. Results are presented in which the robot builds the data structure online, and is able to use it without needing a global reference frame. Simulation results are shown to demonstrate how the robot is able to find interesting objects in the environment.

Benjamín Tovar

Papers

Distance-Optimal Navigation in an Unknown Environment Without Sensing Distances

Planning exploration strategies for simultaneous localization and mapping

Visibility-based pursuit-evasion with bounded speed

Gap navigation trees: Minimal representation for visibility-based tasks

Optimal navigation and object finding without geometric maps or localization