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

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During the last decade, sampling-based path planning algorithms, such as probabilistic roadmaps (PRM) and rapidly exploring random trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g. as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g. showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e. such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.

Sampling-based algorithms for optimal motion planning

During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.

Sampling-based Algorithms for Optimal Motion Planning

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

Robot navigation in the presence of humans raises new issues for motion planning and control when the humans must be taken explicitly into account. We claim that a human aware motion planner (HAMP) must not only provide safe robot paths, but also synthesize good, socially acceptable and legible paths. This paper focuses on a motion planner that takes explicitly into account its human partners by reasoning about their accessibility, their vision field and their preferences in terms of relative human-robot placement and motions in realistic environments. This planner is part of a human-aware motion and manipulation planning and control system that we aim to develop in order to achieve motion and manipulation tasks in the presence or in synergy with humans.

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A Human Aware Mobile Robot Motion Planner

This paper presents the combined results of two studies that investigated how a robot should best approach and place itself relative to a seated human subject. Two live Human Robot Interaction (HRI) trials were performed involving a robot fetching an object that the human had requested, using different approach directions. Results of the trials indicated that most subjects disliked a frontal approach, except for a small minority of females, and most subjects preferred to be approached from either the left or right side, with a small overall preference for a right approach by the robot. Handedness and occupation were not related to these preferences. We discuss the results of the user studies in the context of developing a path planning system for a mobile robot.

/pdf/how-may-i-serve-you-a-robot-companion-approaching-a-seated-31wq46462p.pdf

How may I serve you?: a robot companion approaching a seated person in a helping context

This paper presents a variant of probabilistic roadmap methods (PRM) that recently appeared as a promising approach to motion planning. We exploit a free-space structuring of the configuration space into visibility domains in order to produce small roadmaps, called visibility roadmaps. Our algorithm integrates an original termination condition related to the volume of the free space covered by the roadmap. The planner has been implemented within a software platform allowing us to address a large class of mechanical systems. Experiments show the efficiency of the approach, in particular for capturing narrow passages of collision-free configuration spaces.

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Visibility-based probabilistic roadmaps for motion planning

This paper addresses path planning to consider a cost function defined over the configuration space. The proposed planner computes low-cost paths that follow valleys and saddle points of the configuration-space costmap. It combines the exploratory strength of the Rapidly exploring Random Tree (RRT) algorithm with transition tests used in stochastic optimization methods to accept or to reject new potential states. The planner is analyzed and shown to compute low-cost solutions with respect to a path-quality criterion based on the notion of mechanical work. A large set of experimental results is provided to demonstrate the effectiveness of the method. Current limitations and possible extensions are also discussed.

/pdf/sampling-based-path-planning-on-configuration-space-costmaps-2yj1j7v2k0.pdf

Sampling-Based Path Planning on Configuration-Space Costmaps

This paper deals with motion planning for robots manipulating movable objects among obstacles. We propose a general manipulation planning approach capable of addressing continuous sets for modeling both the possible grasps and the stable placements of the movable object, rather than discrete sets generally assumed by the previous approaches. The proposed algorithm relies on a topological property that characterizes the existence of solutions in the subspace of configurations where the robot grasps the object placed at a stable position. It allows us to devise a manipulation planner that captures in a probabilistic roadmap the connectivity of sub-dimensional manifolds of the composite configuration space. Experiments conducted with the planner in simulated environments demonstrate its efficacy to solve complex manipulation problems.

/pdf/manipulation-planning-with-probabilistic-roadmaps-1nhiw0727i.pdf

Thierry Siméon

Papers

A Human Aware Mobile Robot Motion Planner

How may I serve you?: a robot companion approaching a seated person in a helping context

Visibility-based probabilistic roadmaps for motion planning

Sampling-Based Path Planning on Configuration-Space Costmaps

Manipulation Planning with Probabilistic Roadmaps