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 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

The open motion planning library (OMPL) is a new library for sampling-based motion planning, which contains implementations of many state-of-the-art planning algorithms. The library is designed in a way that it allows the user to easily solve a variety of complex motion planning problems with minimal input. OMPL facilitates the addition of new motion planning algorithms, and it can be conveniently interfaced with other software components. A simple graphical user interface (GUI) built on top of the library, a number of tutorials, demos, and programming assignments are designed to teach students about sampling-based motion planning. The library is also available for use through Robot Operating System (ROS).

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The Open Motion Planning Library

Describes an approach to probabilistic roadmap planners (PRMs). The overall theme of the algorithm, called Lazy PRM, is to minimize the number of collision checks performed during planning and hence minimize the running time of the planner. Our algorithm builds a roadmap in the configuration space, whose nodes are the user-defined initial and goal configurations and a number of randomly generated nodes. Neighboring nodes are connected by edges representing paths between the nodes. In contrast with PRMs, our planner initially assumes that all nodes and edges in the roadmap are collision-free, and searches the roadmap at hand for a shortest path between the initial and the goal node. The nodes and edges along the path are then checked for collision. If a collision with the obstacles occurs, the corresponding nodes and edges are removed from the roadmap. Our planner either finds a new shortest path, or first updates the roadmap with new nodes and edges, and then searches for a shortest path. The above process is repeated until a collision-free path is returned. Lazy PRM is tailored to efficiently answer single planning queries, but can also be used for multiple queries. Experimental results presented in the paper show that our lazy method is very efficient in practice.

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Path planning using lazy PRM

This paper presents a novel randomized motion planner for robots that must achieve a specified goal under kinematic and/or dynamic motion constraints while avoiding collision with moving obstacles with known trajectories. The planner encodes the motion constraints on the robot with a control system and samples the robot's state × time space by picking control inputs at random and integrating its equations of motion. The result is a probabilistic roadmap of sampled state ×time points, called milestones, connected by short admissible trajectories. The planner does not precompute the roadmap; instead, for each planning query, it generates a new roadmap to connect an initial and a goal state×time point. The paper presents a detailed analysis of the planner's convergence rate. It shows that, if the state×time space satisfies a geometric property called expansiveness, then a slightly idealized version of our implemented planner is guaranteed to find a trajectory when one exists, with probability quickly converg...

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Randomized Kinodynamic Motion Planning with Moving Obstacles

Recently, a new class of randomized path planning methods, known as Probabilistic Roadmap Methods (prms) have shown great potential for solving complicated high-dimensional problems. prms use randomization (usually during preprocessing) to construct a graph of representative paths in C-space (a roadmap) whose vertices correspond to collision-free con gurations of the robot and in which two vertices are connected by an edge if a path between the two corresponding con gurations can be found by a local planning method.

OBPRM: an obstacle-based PRM for 3D workspaces

This paper presents a comparative evaluation of different distance metrics and local planners within the context of probabilistic roadmap methods for planning the motion of rigid objects in three-dimensional workspaces. The study concentrates on cluttered three-dimensional workspaces typical of, for example, virtual prototyping applications such as maintainability studies in mechanical CAD designs. Our results include recommendations for selecting appropriate combinations of distance metrics and local planners for such applications. Our study of distance metrics shows that the importance of the translational distance increases relative to the rotational distance as the environment becomes more crowded. We find that each local planner makes some connections that none of the others does-indicating that better connected roadmaps will be constructed using multiple local planners. We propose a new local planning method we call rotate-at-s that often outperforms the common straight-line in C-space method in crowded environments.

Choosing good distance metrics and local planners for probabilistic roadmap methods

This paper proposes an adaptive framework for single shot motion planning, i.e., planning without preprocessing. This framework can be used in any situation, and in particular, is suitable for crowded environments in which the robot's free C-space has narrow corridors such as maintainability studies in complex 3D CAD models. Our iterative strategy adaptively selects a planner whose strengths match the current situation, and then, online, switches to a different planner when circumstances change. This requires techniques to evaluate the characteristics of the current query, and a set of planners which are characterized so that we can match the query with the best planner for it. Our experimental results in complex 3D CAD environments show that our strategy solves queries that none of the planners could solve on their own.

An adaptive framework for 'single shot' motion planning

This paperpresents a cumpurative evuluatiun uf different distance metrics and local planners within the context of probabilistic roadmap methods fir motion planning. Both C-space and Workspace distance metrics and local planners are considered. The study concentrates on cluttered three-dimensional Workspaces typical, e.g., of mechanical designs. Our results include recommendations for selecting appropriate combinations of distance metrics and local planners for use in motion planning methods, particularly probabilistic roadmap methods. We find that each local planner makes some connections than none of the others do - indicating that better connected roadmaps will be constructed using multiple localplanners. We propose a new local planning method we cull rotate-at-s that outperforms the common straight-line in C-space method in crowded environments.

Christopher Jones

Papers

OBPRM: an obstacle-based PRM for 3D workspaces

Choosing good distance metrics and local planners for probabilistic roadmap methods

An adaptive framework for 'single shot' motion planning

Choosing Good Distance Metria and Local Planners for Probabilistic Roadmap Methods