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29
Randomized kinodynamic planning
 THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH 2001; 20; 378
, 2001
"... This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an initial configuration and velocity to a goal configuration and velocity while obeying physically based ..."
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Cited by 621 (36 self)
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This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an initial configuration and velocity to a goal configuration and velocity while obeying physically based dynamical models and avoiding obstacles in the robot’s environment. The authors consider generic systems that express the nonlinear dynamics of a robot in terms of the robot’s highdimensional configuration space. Kinodynamic planning is treated as a motionplanning problem in a higher dimensional state space that has both firstorder differential constraints and obstaclebased global constraints. The state space serves the same role as the configuration space for basic path planning; however, standard randomized pathplanning techniques do not directly apply to planning trajectories in the state space. The authors have developed a randomized
RapidlyExploring Random Trees: Progress and Prospects
 Algorithmic and Computational Robotics: New Directions
, 2000
"... this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints. ..."
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Cited by 337 (21 self)
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this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints.
Combining SpeedUp Techniques for ShortestPath Computations
 In Proc. 3rd Workshop on Experimental and Efficient Algorithms. LNCS
, 2004
"... Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. ..."
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Cited by 29 (7 self)
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Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. In most studies, such techniques are considered individually.
From dynamic programming to RRTs: Algorithmic design of feasible trajectories
 Control Problems in Robotics
, 2002
"... Abstract. This paper summarizes our recent development of algorithms that construct feasible trajectories for problems that involve both differential constraints (typically in the form of an underactuated nonlinear system), and global constraints (typically arising from robot collisions). Dynamic pr ..."
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Cited by 21 (0 self)
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Abstract. This paper summarizes our recent development of algorithms that construct feasible trajectories for problems that involve both differential constraints (typically in the form of an underactuated nonlinear system), and global constraints (typically arising from robot collisions). Dynamic programming approaches are described that produce approximatelyoptimal solutions for lowdimensional problems. Rapidlyexploring Random Tree (RRT) approaches are described that can find feasible, nonoptimal solutions for higherdimensional problems. Several key issues for future research are discussed. 1
SpeedUp Techniques for ShortestPath Computations
 IN PROCEEDINGS OF THE 24TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS’07
, 2007
"... During the last years, several speedup techniques for Dijkstra’s algorithm have been published that maintain the correctness of the algorithm but reduce its running time for typical instances. They are usually based on a preprocessing that annotates the graph with additional information which can ..."
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Cited by 20 (6 self)
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During the last years, several speedup techniques for Dijkstra’s algorithm have been published that maintain the correctness of the algorithm but reduce its running time for typical instances. They are usually based on a preprocessing that annotates the graph with additional information which can be used to prune or guide the search. Timetable information in public transport is a traditional application domain for such techniques. In this paper, we provide a condensed overview of new developments and extensions of classic results. Furthermore, we discuss how combinations of speedup techniques can be realized to take advantage from different strategies.
Common Misconceptions Concerning Heuristic Search
"... This paper examines the following statements about heuristic search, which are commonly held to be true: More accurate heuristics result in fewer states being expanded by A * and IDA*. A * expands fewer states than any other equally informed algorithm that finds optimal solutions. Any admissible heu ..."
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Cited by 9 (2 self)
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This paper examines the following statements about heuristic search, which are commonly held to be true: More accurate heuristics result in fewer states being expanded by A * and IDA*. A * expands fewer states than any other equally informed algorithm that finds optimal solutions. Any admissible heuristic can be turned into a consistent heuristic by a simple technique called. In search spaces whose operators all have the same cost A * with the heuristic function for all states, , is the same as breadthfirst search. Bidirectional A * stops when the forward and backward search frontiers meet. The paper demonstrates that all these statements are false and provides alternative statements that are true.
Counting paths and packings in halves
 in ESA
, 1007
"... Abstract. It is shown that one can count kedge paths in an nvertex graph and mset kpackings on an nelement universe, respectively, in n and, up to a factor polynomial in n, k, and m; in time ` n k/2 mk/2 polynomial space, the bounds hold if multiplied by 3 k/2 or 5 mk/2, respectively. These are ..."
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Cited by 7 (2 self)
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Abstract. It is shown that one can count kedge paths in an nvertex graph and mset kpackings on an nelement universe, respectively, in n and, up to a factor polynomial in n, k, and m; in time ` n k/2 mk/2 polynomial space, the bounds hold if multiplied by 3 k/2 or 5 mk/2, respectively. These are implications of a more general result: given two set families on an nelement universe, one can count the disjoint pairs of sets in the Cartesian product of the two families with O(nℓ) basic operations, where ℓ is the number of members in the two families and their subsets. 1
Using Randomization to Find and Optimize Feasible Trajectories for Nonlinear Systems
 Proc. Annual Allerton Conference on Communications, Control, Computing
, 2000
"... Abstract We present our current progress on the design and experimentation with trajectory planning and optimization algorithms for nonlinear systems that have significant statespace constraints. An overview of our planning method based on Rapidlyexploring Random Trees (RRTs) is given. We show our ..."
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Cited by 6 (0 self)
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Abstract We present our current progress on the design and experimentation with trajectory planning and optimization algorithms for nonlinear systems that have significant statespace constraints. An overview of our planning method based on Rapidlyexploring Random Trees (RRTs) is given. We show our current planning results for two challenging sets of nonlinear systems: 1) the determination of automobile trajectories through obstacle courses; 2) the design of reentry trajectories for a reusable launch vehicle model based on the NASA X33 prototype. We also briefly describe some early results on using randomization to optimize trajectories in the presence of state space constraints. 1
Towards a better understanding of bidirectional search
 In Proc. of AAAI84,6872
, 1984
"... Three admissible bidirectional search algorithms have been described in the literature: A Cartesian product approach due to Doran, Pohl's BHPA, and Champeaux and Sint's BHFFA2. This paper describes an algorithm, GP, which contains the latter two and others. New admissibility results are ob ..."
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Cited by 5 (0 self)
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Three admissible bidirectional search algorithms have been described in the literature: A Cartesian product approach due to Doran, Pohl's BHPA, and Champeaux and Sint's BHFFA2. This paper describes an algorithm, GP, which contains the latter two and others. New admissibility results are obtained. A first order analysis is made comparing the run times of Cartesian produc$ search, two versions of GP, and unidirectional A. The goal is to gain insight on when bidirectional search is useful and direction for seeking better bidirectional search algorithms. 1.