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248
RealTime Motion Planning For Agile Autonomous Vehicles
 AIAA JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS
, 2000
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A SingleQuery BiDirectional Probabilistic Roadmap Planner with Lazy Collision Checking
, 2001
"... This paper describes a nev probabilistic roadmap (PRM) path planner that is: (1) singlequery instead of precomputing a roadmap covering the entire free space, it uses the tvo input query configurations as seeds to explore as little space as possible; (2) hidirectional it explores the robotis free ..."
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Cited by 115 (4 self)
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This paper describes a nev probabilistic roadmap (PRM) path planner that is: (1) singlequery instead of precomputing a roadmap covering the entire free space, it uses the tvo input query configurations as seeds to explore as little space as possible; (2) hidirectional it explores the robotis free space by concur rently building a roadmap made of tvo trees rooted at the query configurations; (3) adaptive it makes longer steps in opened areas of the free space and shorter steps in cluttered areas; and (4) lazy in checking collision it delays collision tests along the edges of the roadmap until they are absolutely needed. Experimental results shov that this combination of techniques drastically reduces planning times, making it possible to handle difficult problems, including multirobot problems in geometrically complex environments.
Reciprocal Velocity Obstacles for RealTime MultiAgent Navigation
 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 2008
"... In this paper, we propose a new concept  the "Reciprocal Velocity Obstacle"  for realtime multiagent navigation. We consider the case in which each agent navigates independently without explicit communication with other agents. Our formulation is an extension of the Velocity Obstacle c ..."
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Cited by 85 (21 self)
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In this paper, we propose a new concept  the "Reciprocal Velocity Obstacle"  for realtime multiagent navigation. We consider the case in which each agent navigates independently without explicit communication with other agents. Our formulation is an extension of the Velocity Obstacle concept, which was introduced for navigation among (passively) moving obstacles. Our approach takes into account the reactive behavior of the other agents by implicitly assuming that the other agents make a similar collisionavoidance reasoning. We show that this method guarantees safe and oscillationfree motions for each of the agents. We apply our concept to navigation of hundreds of agents in densely populated environments containing both static and moving obstacles, and we show that realtime and scalable performance is achieved in such challenging scenarios.
Inevitable collision states  a step towards safer robots
 Advanced Robotics
, 2004
"... Abstract — 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 ..."
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Cited by 72 (14 self)
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Abstract — 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.
Safe Motion Planning in Dynamic Environments
 in Proceedings of the IEEE International Conference on Intelligent Robots and Systems (IROS
, 2005
"... This paper addresses the problem of motion planning (MP) in dynamic environments. It is first argued that dynamic environments impose a realtime 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 t ..."
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Cited by 66 (7 self)
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This paper addresses the problem of motion planning (MP) in dynamic environments. It is first argued that dynamic environments impose a realtime 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 ICSfree partial motion, the system safety can be guaranteed. Application of PMP to the case of a carlike system in a dynamic environment is presented.
Kinodynamic Motion Planning Amidst Moving Obstacles
, 2000
"... This paper presents a randomized motion planner for kinodynamic asteroid avoidanceproblems, in which a robot must avoid collision with moving obstacles under kinematic, dynamic constraints and reach a specified goal state. Inspired by probabilisticroadmap (PRM) techniques, the planner samples the s ..."
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Cited by 66 (6 self)
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This paper presents a randomized motion planner for kinodynamic asteroid avoidanceproblems, in which a robot must avoid collision with moving obstacles under kinematic, dynamic constraints and reach a specified goal state. Inspired by probabilisticroadmap (PRM) techniques, the planner samples the state\Thetatime space of a robot by picking control inputs at random in order to compute a roadmap that captures the connectivity of the space. However, the planner does not precompute a roadmap as most PRM planners do. Instead, for each planning query, it generates, on the fly, a small roadmap that connects the given initial and goal state. In contrast to PRM planners, the roadmapcomputed by our algorithm is a directed graph oriented along the time axis of the space. To verify the planner's effectiveness in practice, we tested it both in simulated environments containing many moving obstacles and on a real robot under strict dynamic constraints. The efficiency of the planner makes it possibl...
Incremental Samplingbased Algorithms for Optimal Motion Planning
, 2006
"... During the last decade, incremental samplingbased motion planning algorithms, such as the Rapidlyexploring Random Trees (RRTs), have been shown to work well in practice and to possess theoretical guarantees such as probabilistic completeness. However, no theoretical bounds on the quality of the s ..."
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Cited by 59 (3 self)
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During the last decade, incremental samplingbased motion planning algorithms, such as the Rapidlyexploring Random Trees (RRTs), have been shown to work well in practice and to possess theoretical guarantees such as probabilistic completeness. However, no theoretical bounds on the quality of the solution obtained by these algorithms, e.g., in terms of a given cost function, have been established so far. The purpose of this paper is to fill this gap, by designing efficient incremental samplingbased algorithms with provable optimality properties. The first contribution of this paper is a negative result: it is proven that, under mild technical conditions, the cost of the best path returned by RRT converges almost surely to a nonoptimal value, as the number of samples increases. Second, a new algorithm is considered, called the Rapidlyexploring Random Graph (RRG), and it is shown that the cost of the best path returned by RRG converges to the optimum almost surely. Third, a tree version of RRG is introduced, called RRT ∗ , which preserves the asymptotic optimality of RRG while maintaining a tree structure like RRT. The analysis of the new algorithms hinges on novel connections between samplingbased motion planning algorithms and the theory of random geometric graphs. In terms of computational complexity, it is shown that the number of simple operations required by both the RRG and RRT ∗ algorithms is asymptotically within a constant factor of that required by RRT.
Incremental search methods for reachability analysis of continuous and hybrid systems
 In Hybrid Systems: Computation and Control
, 2004
"... Abstract. In this paper we present algorithms and tools for fast and efficient reachability analysis, applicable to continuous and hybrid systems. Most of the work on reachability analysis and safety verification concentrates on conservative representations of the set of reachable states, and conseq ..."
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Cited by 58 (6 self)
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Abstract. In this paper we present algorithms and tools for fast and efficient reachability analysis, applicable to continuous and hybrid systems. Most of the work on reachability analysis and safety verification concentrates on conservative representations of the set of reachable states, and consequently on the generation of safety certificates; however, inability to prove safety with these tools does not necessarily result in a proof of unsafety. In this paper, we propose an alternative approach, which aims at the fast falsification of safety properties; this approach provides the designer with a complementary set of tools to the ones based on conservative analysis, providing additional insight into the characteristics of the system under analysis. Our algorithms are based on algorithms originally proposed for robotic motion planning; the key idea is to incrementally grow a set of feasible trajectories by exploring the state space in an efficient way. The ability of the proposed algorithms to analyze the reachability and safety properties of general continuous and hybrid systems is demonstrated on examples from the literature. 1
Coordinating Multiple Robots with Kinodynamic Constraints along Specified Paths
, 2005
"... This paper focuses on the collisionfree coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize t ..."
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Cited by 58 (8 self)
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This paper focuses on the collisionfree coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize the completion time. The approach, which combines techniques from optimal control and mathematical programming, consists of identifying collision segments along each robot's path, and then optimizing the robots' velocities along the collision and collisionfree segments. First, for each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding twopoint boundary value problems. The collision avoidance constraints for pairs of robots can then be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations, which provide schedules that give lower and upper bounds on the optimum; the upper bound schedule is designed to provide continuous velocity trajectories that are feasible. The approach is illustrated with coordination of multiple robots, modeled as double integrators subject to velocity and acceleration constraints. An application to coordination of nonholonomic carlike robots is described, along with implementation results for 12 robots.