A text that makes the mathematical underpinnings of robot motion accessible and relates low-level details of implementation to high-level algorithmic concepts. Robot motion planning has become a major focus of robotics. Research findings can be applied not only to robotics but to planning routes on circuit boards, directing digital actors in computer graphics, robot-assisted surgery and medicine, and in novel areas such as drug design and protein folding. This text reflects the great advances that have taken place in the last ten years, including sensor-based planning, probabalistic planning, localization and mapping, and motion planning for dynamic and nonholonomic systems. Its presentation makes the mathematical underpinnings of robot motion accessible to students of computer science and engineering, rleating low-level implementation details to high-level algorithmic concepts.

Principles of Robot Motion: Theory, Algorithms, and Implementations

Motion planning is a fundamental research area in robotics. Sampling-based methods offer an efficient solution for what is otherwise a rather challenging dilemma of path planning. Consequently, these methods have been extended further away from basic robot planning into further difficult scenarios and diverse applications. A comprehensive survey of the growing body of work in sampling-based planning is given here. Simulations are executed to evaluate some of the proposed planners and highlight some of the implementation details that are often left unspecified. An emphasis is placed on contemporary research directions in this field. We address planners that tackle current issues in robotics. For instance, real-life kinodynamic planning, optimal planning, replanning in dynamic environments, and planning under uncertainty are discussed. The aim of this paper is to survey the state of the art in motion planning and to assess selected planners, examine implementation details and above all shed a light on the current challenges in motion planning and the promising approaches that will potentially overcome those problems.

Sampling-Based Robot Motion Planning: A Review

We present, implement, and analyze a spectrum of closely-related planners, designed to gain insight into the relationship between classical grid search and probabilistic roadmaps (PRMs). Building on quasi-Monte Carlo sampling literature, we have developed deterministic variants of the PRM that use low-discrepancy and low-dispersion samples, including lattices. Classical grid search is extended using subsampling for collision detection and also the optimal-dispersion Sukharev grid, which can be considered as a kind of lattice-based roadmap to complete the spectrum. Our experimental results show that the deterministic variants of the PRM offer performance advantages in comparison to the original PRM and the recent Lazy PRM. This even includes searching using a grid with subsampled collision checking. Our theoretical analysis shows that all of our deterministic PRM variants are resolution complete and achieve the best possible asymptotic convergence rate, which is shown superior to that obtained by random sampling. Thus, in surprising contrast to recent trends, there is both experimental and theoretical evidence that some forms of grid search are superior to the original PRM.

On the Relationship between Classical Grid Search and Probabilistic Roadmaps

We present an efficient, anytime method for path planning in dynamic environments. Current approaches to planning in such domains either assume that the environment is static and replan when changes are observed, or assume that the dynamics of the environment are perfectly known a priori. Our approach takes into account all prior information about both the static and dynamic elements of the environment, and efficiently updates the solution when changes to either are observed. As a result, it is well suited to robotic path planning in known or unknown environments in which there are mobile objects, agents or adversaries

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Anytime path planning and replanning in dynamic environments

Why is probabilistic roadmap (PRM) planning probabilistic? How does the probability measure used for sampling a robot's configuration space affect the performance of a PRM planner? These questions have received little attention to date. This paper tries to fill this gap and identify promising directions to improve future planners. It introduces the probabilistic foundations of PRM planning and examines previous work in this context. It shows that the success of PRM planning depends mainly and critically on favorable "visibility" properties of a robot's configuration space. A promising direction for speeding up PRM planners is to infer partial knowledge of such properties from both workspace geometry and information gathered during roadmap construction, and to use this knowledge to adapt the probability measure for sampling. This paper also shows that the choice of the sampling source--pseudo-random or deterministic--has small impact on a PRM planner's performance, compared with that of the sampling measure. These conclusions are supported by both theoretical and empirical results.

On the Probabilistic Foundations of Probabilistic Roadmap Planning.

We present a new method for generating collision-free paths for robots operating in changing environments. Our approach is closely related to recent probabilistic roadmap approaches. These planners use preprocessing and query stages, and are aimed at planning many times in the same environment. In contrast, our preprocessing stage creates a representation of the configuration space that can be easily modified in real time to account for changes in the environment. As with previous approaches, we begin by constructing a graph that represents a roadmap in the configuration space, but we do not construct this graph for a specific workspace. Instead, we construct the graph for an obstacle-free workspace, and encode the mapping from workspace cells to nodes and arcs in the graph. When the environment changes, this mapping is used to make the appropriate modifications to the graph, and plans can be generated by searching the modified graph. 
As part of our presentation, we discuss the construction of the roadmap, including how samples of the configuration space may be generated and how to connect the samples to form the roadmap. We then discuss the mapping from the workspace to the roadmap, explaining efficient techniques for its generation and representation. We continue with some robustness measures and how these may be used to enhance the robustness of the roadmap. We then present an extension of our method for mobile robots. Finally, we evaluate an implementation of our approach for serial-link manipulators with up to 20 joints.

A framework for real-time path planning in changing environments

Probabilistic roadmaps (PRMs) are a popular representation used by many current path planners. Construction of a PRM requires the ability to generate a set of random samples from the robot's configuration space, and much recent research has concentrated on new methods to do this. In this paper, we present a sampling scheme that is based on the manipulability measure associated with a robot arm. Intuitively, manipulability characterizes the arm's freedom of motion for a given configuration. Thus, our approach is to sample densely those regions of the configuration space in which manipulability is low (and therefore the robot has less dexterity), while sampling more sparsely those regions in which the manipulability is high. We have implemented our approach, and performed extensive evaluations using prototypical problems from the path planning literature. Our results show this new sampling scheme to be quite effective in generating PRMs that can solve a large range of path planning problems.

Using manipulability to bias sampling during the construction of probabilistic roadmaps

This paper proposes an approach for motion planning in indoor environments based on incomplete and uncertain information from a line-based binocular stereo system. The primary goal of the planning process is to plan an optimal path through an unknown or partially known environment, depending on the information gained from exploration and the current mission goal. This paper presents an adaptable motion planner that supports sensor-based map construction, object recognition and navigation in an unknown environment while carrying out a mission. Also presented are some preliminary experimental results that demonstrate the utility of the approach.

Perception-based motion planning for indoor exploration

We have previously (2000) developed a new method for generating collision-free paths for robots operating in changing environments. Our approach relies on creating a representation of the configuration space that can be easily modified in real time to account for changes in the environment. In this paper we address the issues of efficiency and robustness. First, we develop a novel, efficient encoding scheme that exploits the redundancy in the map from robot's Euclidean workspace to its configuration space. Then, we introduce the concept of /spl epsi/-robustness, and show how it can be used to enhance the representations that are used by the planner. Along the way, we present quantitative results that illustrate the efficiency and robustness of our approach.

P. Leven

Papers

A framework for real-time path planning in changing environments

Using manipulability to bias sampling during the construction of probabilistic roadmaps

Perception-based motion planning for indoor exploration

Robust, compact representations for real-time path planning in changing environments

Planning Collision-Free Paths Using Probabilistic Roadmaps