We present a novel approach for collision-free global navigation for continuous-time multi-agent systems with general linear dynamics. Our approach is general and can be used to perform collision-free navigation in 2D and 3D workspaces with narrow passages and crowded regions. As part of pre-computation, we compute multiple bridges in the narrow or tight regions in the workspace using kinodynamic RRT algorithms. Our bridge has certain geometric characteristics, that en- able us to calculate a collision-free trajectory for each agent using simple interpolation at runtime. Moreover, we combine interpolated bridge trajectories with local multi-agent navigation algorithms to compute global collision-free paths for each agent. The overall approach combines the performance benefits of coupled multi-agent algorithms with the pre- computed trajectories of the bridges to handle challenging scenarios. In practice, our approach can handle tens to hundreds of agents in real-time on a single CPU core in 2D and 3D workspaces.
 We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time @math , where @math is the number of robots and @math is the total complexity of the workspace. Moreover, the total length of the returned solution is at most @math , where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency. We present a decentralized algorithm for group-based coherent and reciprocal multi-agent navigation. In addition to generating collision-free trajectories for each agent, our approach is able to simulate macroscopic group movements and proxemic behaviors that result in coherent navigation. Our approach is general, makes no assumptions about the size or shape of the group, and can generate smooth trajectories for the agents. Furthermore, it can dynamically adapt to obstacles or the behavior of other agents. The additional overhead of generating proxemic group behaviors is relatively small and our approach can simulate hundreds of agents in real-time. We highlight its benefits on different benchmarks. We introduce a new concept; meso-scale planning in real-time multi-agent navigation. Whereas many traditional approaches to multi-agent navigation typically consist of two-levels - a macro-scale level providing agents with a global direction of motion around (large) static obstacles, and a micro-scale level in which agents seek to avoid collision with other agents - our approach adds a meso-scale level to give agents realistic behavior in scenarios where groups of other agents (e.g. families or crowds in a virtual world) form coherent entities. Rather than moving straight through such groups, our approach lets agents move around them. Our formulation considers each agent as an individual that may perceive sets of other agents as a group, and plans its motion accordingly. We base our approach on the velocity obstacle concept, and we show using simulation results that our method dramatically improves the quality of the trajectories computed for the agents. 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. 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. Motion safety for robotic systems operating in the real world is critical (especially when their size and dynamics make them potentially harmful for themselves or their environment). Motion safety is a taken-for-granted and ill-defined notion in the Robotics literature and the primary contribution of this paper is to propose three safety criteria that helps in understanding a number of key aspects related to the motion safety issue. A number of navigation schemes used by robotic systems operating in the real-world are then evaluated with respect to these safety criteria. It is established that, in all cases, they violate one or several of them. Accordingly, motion safety, especially in the presence of moving objects, cannot be guaranteed (in the sense that these robotic systems may end up in a situation where a collision inevitably occurs later in the future). Finally, it is shown that the concept of inevitable collision states introduced by Fraichard and Asama (2004) does respect the three above-mentioned safety criteria and therefore offers a theoretical answer to the motion safety issue. In unlabeled multi-robot motion planning several interchangeable robots operate in a common workspace. The goal is to move the robots to a set of target positions such that each position will be occupied by some robot. In this paper, we study this problem for the specific case of unit-square robots moving amidst polygonal obstacles and show that it is PSPACE-hard. We also consider three additional variants of this problem and show that they are all PSPACE-hard as well. To the best of our knowledge, this is the first hardness proof for the unlabeled case. Furthermore, our proofs can be used to show that the labeled variant (where each robot is assigned with a specific target position), again, for unit-square robots, is PSPACE-hard as well, which sets another precedence, as previous hardness results require the robots to be of different shapes. This paper investigates the computational complexity of planning the motion of a body B in 2-D or 3-D space, so as to avoid collision with moving obstacles of known, easily computed, trajectories. Dynamic movement problems are of fundamental importance to robotics, but their computational complexity has not previously been investigated. We provide evidence that the 3-D dynamic movement problem is intractable even if B has only a constant number of degrees of freedom of movement. In particular, we prove the problem is PSPACE-hard if B is given a velocity modulus bound on its movements and is NP-hard even if B has no velocity modulus bound, where, in both cases, B has 6 degrees of freedom. To prove these results, we use a unique method of simulation of a Turing machine that uses time to encode configurations (whereas previous lower bound proofs in robotic motion planning used the system position to encode configurations and so required unbounded number of degrees of freedom). We also investigate a natural class of dynamic problems that we call asteroid avoidance problems : B, the object we wish to move, is a convex polyhedron that is free to move by translation with bounded velocity modulus, and the polyhedral obstacles have known translational trajectories but cannot rotate. This problem has many applications to robot, automobile, and aircraft collision avoidance. Our main positive results are polynomial time algorithms for the 2-D asteroid avoidance problem, where B is a moving polygon and we assume a constant number of obstacles, as well as single exponential time or polynomial space algorithms for the 3-D asteroid avoidance problem, where B is a convex polyhedron and there are arbitrarily many obstacles. Our techniques for solving these asteroid avoidance problems use “normal path” arguments, which are an intereting generalization of techniques previously used to solve static shortest path problems. We also give some additional positive results for various other dynamic movers problems, and in particular give polynomial time algorithms for the case in which B has no velocity bounds and the movements of obstacles are algebraic in space-time. 