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

A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collision-free configurations and whose edges correspond to feasible paths between these configurations. These paths are computed using a simple and fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the roadmap; the roadmap is then searched for a path joining these two nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out to be relatively easy to choose, Increased efficiency can also be achieved by tailoring some components of the method (e.g., the local planner) to the considered robots. In this paper the method is applied to planar articulated robots with many degrees of freedom. Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (/spl ap/150 MIPS), after learning for relatively short periods of time (a few dozen seconds).

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Probabilistic roadmaps for path planning in high-dimensional configuration spaces

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

A simple and efficient randomized algorithm is presented for solving single-query path planning problems in high-dimensional configuration spaces. The method works by incrementally building two rapidly-exploring random trees (RRTs) rooted at the start and the goal configurations. The trees each explore space around them and also advance towards each other through, the use of a simple greedy heuristic. Although originally designed to plan motions for a human arm (modeled as a 7-DOF kinematic chain) for the automatic graphic animation of collision-free grasping and manipulation tasks, the algorithm has been successfully applied to a variety of path planning problems. Computed examples include generating collision-free motions for rigid objects in 2D and 3D, and collision-free manipulation motions for a 6-DOF PUMA arm in a 3D workspace. Some basic theoretical analysis is also presented.

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RRT-connect: An efficient approach to single-query path planning

This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an ...

Randomized kinodynamic planning

We present a new approach to path planning, called the "Ariadne's clew algorithm". It is designed to find paths in high-dimensional continuous spaces and applies to robots with many degrees of freedom in static, as well as dynamic environments -- ones where obstacles may move. The Ariadne's clew algorithm comprises two sub-algorithms, called SEARCH and EXPLORE, applied in an interleaved manner. EXPLORE builds a representation of the accessible space while SEARCH looks for the target. Both are posed as optimization problems. We describe a real implementation of the algorithm to plan paths for a six degrees of freedom arm in a dynamic environment where another six degrees of freedom arm is used as a moving obstacle. Experimental results show that a path is found in about one second without any pre-processing.

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The Ariadne's clew algorithm

The goal of the work described is to build a path planner able to drive a robot in a dynamic environment where the obstacles are moving. In order to do so, the authors propose a method, called Ariadne's clew algorithm, to build a global path planner based on the combination of two local planning algorithms: an explore algorithm and a search algorithm. The purpose of the explore algorithm is to collect information about the environment with an increasingly fine resolution by placing landmarks in the searched space. The goal of the search algorithm is to opportunistically check if the target can be easily reached from any given placed landmark. The Ariadne's clew algorithm is shown to be very fast is most cases, allowing planning in dynamic environment. It is shown to be complete, which means that it is sure to find a path when one exists. A massively parallel implementation of this algorithm is described.

The “Ariadne's clew” algorithm: global planning with local methods

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The "Ariadne's clew" algorithm: global planning with local methods

This paper proposes a novel and global approach to solving the point-to-point inverse kinematics problem for highly redundant manipulators. Given an initial configuration of the robot, the problem is to find a reachable configuration that corresponds to a desired position and orientation of the end-effector. Central to our approach is the novel notion of kinematic roadmap for a manipulator. The kinematic roadmap captures the connectivity of the connected component of the free configuration space of the manipulator in a finite graph like structure. The point-to-point inverse kinematics problem is then solved using this roadmap. We provide completeness results for our algorithm. Our implementation of SEARCH is an efficient closed form solution, albeit local, to inverse kinematics that exploits the serial kinematic structure of serial manipulator arms. Initial experiments with a 7-DOF manipulator have been extremely successful.

The kinematic roadmap: a motion planning based global approach for inverse kinematics of redundant robots

We present an ongoing research work on robot motion planning using genetic algorithms. Our goal is to use this technique to build fast motion planners for robot with six or more degree of freedom. After a short review of the existing methods, we will introduce the genetic algorithms by showing how they can be used to solve the invers kinematic problem. In the second part of the paper, we show that the path planning problem can be expressed as an optimization problem and thus solved with a genetic algorithm. We illustrate the approach by building a path planner for a planar arm with two degree of freedom, then we demonstrate the validity of the method by planning paths for an holonomic mobile robot. Finally we describe an implementation of the selected genetic algorithm on a massively parallel machine and show that fast planning response is made possible by using this approach.

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Juan-Manuel Ahuactzin

Papers

The Ariadne's clew algorithm

The “Ariadne's clew” algorithm: global planning with local methods

The "Ariadne's clew" algorithm: global planning with local methods

The kinematic roadmap: a motion planning based global approach for inverse kinematics of redundant robots

Using genetic algorithms for robot motion planning