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262
Realtime motion planning for agile autonomous vehicles,
 AIAA Journal of Guidance and Control
, 2002
"... Planning the path of an autonomous,agile vehicle in a dynamicenvironment is a very complex problem, especially when the vehicle is required to use its full maneuvering capabilities. Recent efforts aimed at using randomized algorithms for planning the path of kinematic and dynamic vehicles have demo ..."
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Cited by 225 (16 self)
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Planning the path of an autonomous,agile vehicle in a dynamicenvironment is a very complex problem, especially when the vehicle is required to use its full maneuvering capabilities. Recent efforts aimed at using randomized algorithms for planning the path of kinematic and dynamic vehicles have demonstrated considerable potential for implementation on future autonomous platforms. This paper builds upon these efforts by proposing a randomized path planning architecture for dynamical systems in the presence of xed and moving obstacles. This architecture addresses the dynamic constraints on the vehicle's motion, and it provides at the same time a consistent decoupling between lowlevel control and motion planning. The path planning algorithm retains the convergence properties of its kinematic counterparts. System safety is also addressed in the face of nite computation times by analyzing the behavior of the algorithm when the available onboard computation resources are limited, and the planning must be performed in real time. The proposed algorithm can be applied to vehicles whose dynamics are described either by ordinary differential equations or by higherlevel, hybrid representations. Simulation examples involving a ground robot and a small autonomous helicopter are presented and discussed.
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 120 (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 104 (22 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 86 (15 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 77 (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.
Anytime path planning and replanning in dynamic environments,”
 in IEEE International Conference on Robotics and Automation,
, 2006
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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 69 (5 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...
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 68 (9 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.
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 66 (4 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.
Reciprocal nbody Collision Avoidance
 INTERNATIONAL SYMPOSIUM ON ROBOTICS RESEARCH
, 2009
"... In this paper, we present a formal approach to reciprocal nbody 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 o ..."
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Cited by 65 (22 self)
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In this paper, we present a formal approach to reciprocal nbody 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, we derive sufficient conditions for collisionfree motion by reducing the problem to solving a lowdimensional linear program. We test our approach on several dense and complex simulation scenarios involving thousands of robots and compute collisionfree 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 collisionfree motion for a large number of robots in a cluttered workspace.