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 presents Continuous Curvature (CC) Steer, a steering method for car-like vehicles, i.e., an algorithm planning paths in the absence of obstacles. CC Steer is the first to compute paths with: 1) continuous curvature; 2) upper-bounded curvature; and 3) upper-bounded curvature derivative. CC Steer also verifies a topological property that ensures that when it is used within a general motion-planning scheme, it yields a complete collision-free path planner. The coupling of CC Steer with a general planning scheme yields a path planner that computes collision-free paths verifying the properties mentioned above. Accordingly, a car-like vehicle can follow such paths without ever having to stop in order to reorient its front wheels. Besides, such paths can be followed with a nominal speed which is proportional to the curvature derivative limit. The paths computed by CC Steer are made up of line segments, circular arcs, and clothoid arcs. They are not optimal in length. However, it is shown that they converge toward the optimal "Reeds and Shepp" paths when the curvature derivative upper bound tends to infinity. The capabilities of CC Steer to serve as an efficient steering method within two general planning schemes are also demonstrated.

/pdf/from-reeds-and-shepp-s-to-continuous-curvature-paths-5vndvwmrl4.pdf

From Reeds and Shepp's to continuous-curvature paths

An inevitable collision state for a robotic system can be defined as a state for which, no matter what the future trajectory followed by the system is, a collision with an obstacle eventually occurs. An inevitable collision state takes into account the dynamics of both the system and the obstacles, fixed or moving. The main contribution of this paper is to lay down and explore this novel concept (and the companion concept of inevitable collision obstacle). Formal definitions of the inevitable collision states and obstacles are given. Properties fundamental for their characterization are established. This concept is very general, and can be useful both for navigation and motion planning purposes (for its own safety, a robotic system should never find itself in an inevitable collision state). To illustrate the interest of this concept, it is applied to a problem of safe motion planning for a robotic system subject to sensing constraints in a partially known environment (i.e. that may contain unexpected obst...

/pdf/inevitable-collision-states-a-step-towards-safer-robots-kar46pktnw.pdf

Inevitable collision states - a step towards safer robots?

This paper addresses the problem of motion planning (MP) in dynamic environments. It is first argued that dynamic environments impose a real-time constraint upon MP: it has a limited time only to compute a motion, the time available being a function of the dynamicity of the environment. Now, given the intrinsic complexity of MP, computing a complete motion to the goal within the time available is impossible to achieve in most real situations. Partial motion planning (PMP) is the answer to this problem proposed in this paper. PMP is a motion planning scheme with an anytime flavor: when the time available is over, PMP returns the best partial motion to the goal computed so far. Like reactive navigation scheme, PMP faces a safety issue: what guarantee is there that the system will never end up in a critical situation yielding an inevitable collision? The answer proposed in this paper to this safety issue relies upon the concept of inevitable collision states (ICS). ICS takes into account the dynamics of both the system and the moving obstacles. By computing ICS-free partial motion, the system safety can be guaranteed. Application of PMP to the case of a car-like system in a dynamic environment is presented.

/pdf/safe-motion-planning-in-dynamic-environments-2y7drwyla5.pdf

Safe motion planning in dynamic environments

Reliable and efficient perception and reasoning in dynamic and densely cluttered environments are still major challenges for driver assistance systems. Most of today's systems use target tracking algorithms based on object models. They work quite well in simple environments such as freeways, where few potential obstacles have to be considered. However, these approaches usually fail in more complex environments featuring a large variety of potential obstacles, as is usually the case in urban driving situations. In this paper, we propose a new approach for robust perception and risk assessment in highly dynamic environments. This approach is called Bayesian occupancy filtering; it basically combines a four-dimensional occupancy grid representation of the ecobstacle state space with Bayesian filtering techniques.

/pdf/bayesian-occupancy-filtering-for-multitarget-tracking-an-1yitq6xbpu.pdf

Bayesian Occupancy Filtering for Multitarget Tracking: An Automotive Application

An inevitable collision state for a robotic system can be defined as a state for which, no matter what the future trajectory followed by the system is, a collision with an obstacle eventually occurs. An inevitable collision state takes into account both the dynamics of the system and the obstacles, fixed or moving. The main contribution of this paper is to lay down and explore this novel concept (and the companion concept of inevitable collision obstacle). Formal definitions of the inevitable collision states and obstacles are given. Properties fundamental for their characterisation are established. This concept is very general and can be useful both for navigation and motion planning purposes (for its own safety, a robotic system should never find itself in an inevitable collision state). The interest of this concept is illustrated by a safe motion planning example.

/pdf/inevitable-collision-states-a-step-towards-safer-robots-3ms8pne8mn.pdf

Thierry Fraichard

Papers

From Reeds and Shepp's to continuous-curvature paths

Inevitable collision states - a step towards safer robots?

Safe motion planning in dynamic environments

Bayesian Occupancy Filtering for Multitarget Tracking: An Automotive Application

Inevitable collision states. A step towards safer robots