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

In France, about 33% of roads victims are VRU1. In its 3rdframework, the french PREDIT2includes VRU Safety. The PUVAME project was created to generate solutions to avoid collisions between VRU and Bus in urban traffic. An important part of these collisions take place at intersection or bus stop. In this paper, we detail the hardware and software architecture designed and developped in the project. This solution is based on offboard cameras observing particular places (intersection and bus stop in our case) to detect and track VRU present in the environment. The position of the bus is also computed and a risk of collision between each VRU and the bus is determined. In case of high risk of collision, the bus driver is warned. The HMI to warn the bus driver is also described. Finally, some experimental results are presented.

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PUVAME - New French Approach for Vulnerable Road Users Safety

This letter presents the result of a study aiming at investigating to what extent the results obtained in the Crowd Simulation domain could be used to control a mobile robot navigating among people. It turns out that Crowd Simulation relies on two assumptions that would not hold for a real mobile robot, a test protocol has therefore been designed in order to thoroughly evaluate how three representative Crowd Simulation techniques would perform when said assumptions are relaxed. The study shows that all those techniques entail safety problems, i.e. they would cause collisions in the real world. The study also highlights the most promising candidate for a transposition on a real mobile robot.

/pdf/from-crowd-simulation-to-robot-navigation-in-crowds-4y15f0sfma.pdf

From Crowd Simulation to Robot Navigation in Crowds

Motion prediction for objects which are able to decide their trajectory on the basis of a planning or decision process (e.g. humans and robots) is a challenging problem. Most existing approaches operate in two stages: a) learning, which consists in observing the environment in order to identify and model possible motion patterns or plans and b) prediction, which uses the learned plans in order to predict future motions. In existing techniques, learning is performed on-line, hence, it is impossible to rene the existing knowledge on the basis of the new observations obtained during the prediction phase. This paper proposes a novel learning approach which represents plans as Hidden Markov Models and is able to estimate the parameters and structure of those models in an incremental fashion by using the Growing Neural Gas algorithm. Our experiments demonstrate that the technique works in real-time, is able to operate concurrently with prediction and that the resulting model produces long-term predictions.

https://hal.inria.fr/inria-00182039/document

Intentional Motion Online Learning and Prediction.

In the near future, it is expected that robotic systems will share the human living and working spaces: service robots and cybernetic transport systems are examples of two primary application areas. The technology is now mature; we have already witnessed autonomous mobile robots guiding people in museums and automated cars driving on the road network. While moving (especially at high speed), automated vehicles, mobile manipulators and humanoid robots can be potentially dangerous should a collision occur. Before letting such robotic systems transport or share space with people in a truly autonomous way, it is critical to assert and characterize their motion safety, i.e. their ability to avoid collision. Demonstrating that a robotic system is working properly on a limited set of experiments is not enough. If autonomous robots are ever to be deployed among human beings on a large scale, there is a need to characterize the level of motion safety that can be achieved and/or to specify the conditions under which it can be guaranteed. Collisions happen for reasons that broadly fall into one of the following category:

https://hal.inria.fr/hal-00733712/document

Guaranteeing motion safety for robots

Path deformation is a technique that was introduced to generate robot motion wherein a nominal path, that has been computed beforehand, is continuously deformed on-line in response to unforeseen obstacles. In an effort to improve path deformation, this paper presents a trajectory deformation scheme. The main idea is that by incorporating the time dimension and hence information on the obstacles' future behaviour, quite a number of situations where path deformation would fail can be handled. The trajectory represented as a discrete space-time curve is subject to deformation forces both external (to avoid collision with the obstacles) and internal (to maintain trajectory feasibility and connectivity). The trajectory deformation scheme has been tested successfully on a planar robot with double integrator dynamics moving in dynamic environments.

/pdf/navigating-dynamic-environments-with-trajectory-deformation-4ie9ctx68g.pdf

Thierry Fraichard

Papers

PUVAME - New French Approach for Vulnerable Road Users Safety

From Crowd Simulation to Robot Navigation in Crowds

Intentional Motion Online Learning and Prediction.

Guaranteeing motion safety for robots

Navigating Dynamic Environments with Trajectory Deformation