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

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

This paper describes a real-time motion planning algorithm, based on the rapidly-exploring random tree (RRT) approach, applicable to autonomous vehicles operating in an urban environment. Extensions to the standard RRT are predominantly motivated by: 1) the need to generate dynamically feasible plans in real-time; 2) safety requirements; 3) the constraints dictated by the uncertain operating (urban) environment. The primary novelty is in the use of closed-loop prediction in the framework of RRT. The proposed algorithm was at the core of the planning and control software for Team MIT's entry for the 2007 DARPA Urban Challenge, where the vehicle demonstrated the ability to complete a 60 mile simulated military supply mission, while safely interacting with other autonomous and human driven vehicles.

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Real-Time Motion Planning With Applications to Autonomous Urban Driving

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

Automatic assembly path planning for wiring harness installations

We present a resolution complete path planner based on an implicit grid in the configuration space. The planner can be described as a two-level process in which a global planner restricts a local planner to certain subsets of the grid. The global planner starts by letting the local planner search in a coarse subset of the grid, and successively refines the grid until a solution is found. The local planner applies a scheme for lazy evaluation on each subgrid in order to minimize collision checking and thereby increase the performance. Experimental results in an industrial application show that lazy evaluation on a grid is very efficient in practice. The algorithm is particularly useful in high dimensional, relatively uncluttered configuration spaces, especially when collision checking is computationally expensive. Single queries are handled quickly since no preprocessing is required.

Path planning in practice; lazy evaluation on a multi-resolution grid

This work is inspired by the problem of planning sequences of operations, as welding, in car manufacturing stations where multiple industrial robots cooperate. The goal is to minimize the station cycle time, i.e., the time it takes for the last robot to finish its cycle. This is done by dispatching the tasks among the robots, and by routing and scheduling the robots in a collision-free way, such that they perform all predefined tasks. We propose an iterative and decoupled approach in order to cope with the high complexity of the problem. First, collisions among robots are neglected, leading to a min–max Multiple Generalized Traveling Salesman Problem (MGTSP). Then, when the sets of robot loads have been obtained and fixed, we sequence and schedule their tasks, with the aim to avoid conflicts. The first problem (min–max MGTSP) is solved by an exact branch and bound (B&B) method, where different lower bounds are presented by combining the solutions of a min–max set partitioning problem and of a Generalized Traveling Salesman Problem (GTSP). The second problem is approached by assuming that robots move synchronously: a novel transformation of this synchronous problem into a GTSP is presented. Eventually, in order to provide complete robot solutions, we include path planning functionalities, allowing the robots to avoid collisions with the static environment and among themselves. These steps are iterated until a satisfying solution is obtained. Experimental results are shown for both problems and for their combination. We even show the results of the iterative method, applied to an industrial test case adapted from a stud welding station in a car manufacturing line.

An Iterative Approach for Collision Free Routing and Scheduling in Multirobot Stations

https://cyberleninka.org/article/n/901479.pdf

Robert Bohlin

Papers

Path planning using lazy PRM

Automatic assembly path planning for wiring harness installations

Path planning in practice; lazy evaluation on a multi-resolution grid

An Iterative Approach for Collision Free Routing and Scheduling in Multirobot Stations

Optimal Robot Placement for Tasks Execution