There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

This paper presents a method for robot motion planning in dynamic environments. It consists of selecting avoidance maneuvers to avoid static and moving obstacles in the velocity space, based on the cur rent positions and velocities of the robot and obstacles. It is a first- order method, since it does not integrate velocities to yield positions as functions of time.The avoidance maneuvers are generated by selecting robot ve locities outside of the velocity obstacles, which represent the set of robot velocities that would result in a collision with a given obstacle that moves at a given velocity, at some future time. To ensure that the avoidance maneuver is dynamically feasible, the set of avoidance velocities is intersected with the set of admissible velocities, defined by the robot's acceleration constraints. Computing new avoidance maneuvers at regular time intervals accounts for general obstacle trajectories.The trajectory from start to goal is computed by searching a tree of feasible avoidance maneuve...

Motion Planning in Dynamic Environments Using Velocity Obstacles

In this paper, we present a formal approach to reciprocal n-body collision avoidance, where multiple mobile robots need to avoid collisions with each other while moving in a common workspace In our formulation, each robot acts fully independently, and does not communicate with other robots Based on the definition of velocity obstacles [5], we derive sufficient conditions for collision-free motion by reducing the problem to solving a low-dimensional linear program We test our approach on several dense and complex simulation scenarios involving thousands of robots and compute collision-free actions for all of them in only a few milliseconds To the best of our knowledge, this method is the first that can guarantee local collision-free motion for a large number of robots in a cluttered workspace

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Reciprocal n-Body Collision Avoidance

This paper solves a motion planning problem from a motion safety perspective, where a variant of the classical Rapidly exploring Random Tree (RRT) approach [1] called p-safe RRT is proposed. The exploration of the search space is similar to RRT, however, the highlight of p-safe RRT is the integration of passive motion safety. The basic principle of this safety level is to guarantee that the system can brake down and stop before collision. P-safe RRT extends a tree through the state time space, where tree's nodes and primitives are checked for passive motion safety. The computed trajectory is passively safe and drives the robot from its initial state to the goal state. The developed algorithms have been tested in simulation scenarios; featuring both fixed and moving objects with unknown trajectories for a car-like robot with a limited field of view.

https://hal.inria.fr/hal-01400075/document

Real-time Safe Path Planning for Robot Navigation in Unknown Dynamic Environments

Despite their popularity, occupancy grids cannot be directly applied to problems where the identity of the objects populating an environment needs to be taken into account (e.g., object tracking, scene interpretation, etc.), in this cases it is necessary to postprocess the grid in order to extract object information. This paper approaches the problem by proposing a novel algorithm inspired on image segmentation techniques. The proposed approach works without prior knowledge about the number of objects to be detected and, at the same time, is very fast. This is possible thanks to the use of a novel self organizing network (SON) coupled with a dynamic threshold. Our experimental results on both real and simulated data show that our approach is robust and able to operate at normal camera frame rate

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Fast Object Extraction from Bayesian Occupancy Grids using Self Organizing Networks

Guaranteeing safe, i.e. collision-free, motion for robotic systems is usually tackled in the Inevitable Collision State (ICS) framework. This paper explores the use of the more general Viability theory as an alternative when safe motion involves multiple motion constraints and not just collision avoidance. Central to Viability is the so-called viability kernel, i.e. the set of states of the robotic system for which there is at least one trajectory that satisfies the motion constraints forever. The paper presents an algorithm that computes off-line an approximation of the viability kernel that is both conservative and able to handle time-varying constraints such as moving obstacles. Then it demonstrates, for different robotic scenarios involving multiple motion constraints (collision avoidance, visibility, velocity), how to use the viability kernel computed off-line within an on-line reactive navigation scheme that can drive the robotic system without ever violating the motion constraints at hand.

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Viability-Based Guaranteed Safe Robot Navigation

Mobile robot companions are service robots that are mobile and designed to share our living space For such robots, mobility is essential and their coexistence with humans adds new aspects to the mobility issue: the first one is to obtain appropriate motion and the second one is interaction through motion We encapsulate these two aspects in the term Human-Robot Motion (HRM) with reference to Human-Robot Interaction The long-term issue is to design robot companions whose motions, while remaining safe, are deemed appropriate from a human point of view This is the key to the acceptance of such systems in our daily lives The primary purpose of this paper is to explore how the psychological concept of attention can be taken into account in HRM To that end, we build upon an existing model of attention that computes an attention matrix that describes how the attention of each person is distributed among the different elements, persons and objects, of his/her environment Using the attention matrix, we propose the novel concept of attention field that can be viewed as an attention predictor Using different case studies, we show how the attention matrix and the attention field can be used in HRM

/pdf/human-robot-motion-an-attention-based-navigation-approach-1xhpmqvw7s.pdf

Human-Robot Motion: An attention-based navigation approach

A trajectory planning problem called the highway problem is discussed. It consists of planning a time-optimal trajectory for a mobile robot which is travelling in a structured workspace amidst moving obstacles and is subject to constraints on its velocity and acceleration. In a structured workspace there are lanes characterized by one-dimensional curves along which the mobile robot can move. The mobile robot has to follow a lane, but it may also shift from its lane to an adjacent one. An efficient method which determines an approximate time-optimal solution to the highway problem is presented. The approach consists of discretizing time and selecting the accelerations to be applied to the mobile robot among a discrete set. These hypotheses make it possible to define a grid in the mobile robot's time-state space, i.e. the state space augmented in the time dimension. This grid is then searched to find a solution. >

Thierry Fraichard

Papers

Real-time Safe Path Planning for Robot Navigation in Unknown Dynamic Environments

Fast Object Extraction from Bayesian Occupancy Grids using Self Organizing Networks

Viability-Based Guaranteed Safe Robot Navigation

Human-Robot Motion: An attention-based navigation approach

Kinodynamic planning in a structured and time-varying 2-D workspace