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27
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 568 (35 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 310 (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.
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 20 (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
Discrete Approximations to Continuous ShortestPath: Application to MinimumRisk Path Planning for Groups of UAVs
 In Proc. of the 42nd Conf. on Decision and Contr
, 2003
"... Abstract — This paper addresses the weighted anisotropic shortestpath problem on a continuous domain, i.e., the computation of a path between two points that minimizes the line integral of a costweighting function along the path. The costweighting depends both on the instantaneous position and di ..."
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Cited by 17 (4 self)
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Abstract — This paper addresses the weighted anisotropic shortestpath problem on a continuous domain, i.e., the computation of a path between two points that minimizes the line integral of a costweighting function along the path. The costweighting depends both on the instantaneous position and direction of motion. We propose an algorithm for the computation of shortestpath that reduces the problem to an optimization over a finite graph. This algorithm restricts the search to paths formed by the concatenation of straightline segments between points, from a suitably chosen discretization of the continuous region. To maximize efficiency, the discretization of the continuous region should not be uniform. We propose a novel “honeycomb” sampling algorithm that minimizes the cost penalty introduced by discretization. The resulting path is not optimal but the cost penalty can be made arbitrarily small at the expense of increased computation. This methodology is applied to the computation of paths for groups of Unmanned Air Vehicles (UAVs) that minimize the risk of being destroyed by ground defenses. We show that this problem can be formulated as a weighted anisotropic shortestpath optimization and show that the algorithm proposed can efficiently produce lowrisk paths. I.
A framework for planning feedback motion strategies based on a random neighborhood graph
 In Proc. Intl. Conf. on Robotics and Automation
, 2000
"... Randomized techniques have led to the development of many successful algorithms for path planning in highdimensional configuration spaces. This paper presents a randomized framework for computing feedback motion strategies, by defining a global navigation function over a collection of spherical bal ..."
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Cited by 15 (3 self)
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Randomized techniques have led to the development of many successful algorithms for path planning in highdimensional configuration spaces. This paper presents a randomized framework for computing feedback motion strategies, by defining a global navigation function over a collection of spherical balls in the configuration space. If the goal is changed, an updated navigation function can be quickly computed, offering benefits similar to the fast multiple queries permitted by the probabilistic roadmap approach to path planning. Our choice of balls is motivated in part by recent tools from computational geometry which compute point locations and arrangements efficiently without significant dependence on dimension. We present a construction algorithm that includes a Bayesian termination condition based on the probability that a specified fraction of the free space is covered. A basic implementation illustrates the framework for rigid and articulated bodies with up to fivedimensional configuration spaces. 1
A Quadratic RegulatorBased Heuristic for Rapidly Exploring State Space
, 2010
"... Kinodynamic planning algorithms like RapidlyExploring Randomized Trees (RRTs) hold the promise of finding feasible trajectories for rich dynamical systems with complex, nonconvex constraints. In practice, these algorithms perform very well on configuration space planning, but struggle to grow effi ..."
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Cited by 14 (2 self)
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Kinodynamic planning algorithms like RapidlyExploring Randomized Trees (RRTs) hold the promise of finding feasible trajectories for rich dynamical systems with complex, nonconvex constraints. In practice, these algorithms perform very well on configuration space planning, but struggle to grow efficiently in systems with dynamics or differential constraints. This is due in part to the fact that the conventional proximity metric, Euclidean distance, does not take into account system dynamics and constraints when identifying which node in the existing tree is capable of producing children closest to a given point in state space. Here we argue that the RRTs ’ coverage of state space is maximized by using a proximity psuedometric proportional to the length, in time, of the quickest possible trajectory
The samplingbased neighborhood graph: An approach to computing and executing feedback motion strategies
 IEEE Trans. Robot. Automat
, 2004
"... Abstract—This paper presents a samplingbased approach to computing and executing feedbackmotion strategies by defining a global navigation function over a collection of neighborhoods in configuration space. The collection of neighborhoods and their underlying connectivity structure are captured b ..."
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Cited by 13 (0 self)
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Abstract—This paper presents a samplingbased approach to computing and executing feedbackmotion strategies by defining a global navigation function over a collection of neighborhoods in configuration space. The collection of neighborhoods and their underlying connectivity structure are captured by a samplingbased neighborhood graph (SNG), on which navigation functions are built. The SNG construction algorithm incrementally places new neighborhoods in the configuration space, using distance information provided by existing collisiondetection algorithms. A termination condition indicates the probability that a specified fraction of the space is covered. Our implementation illustrates the approach for rigid and articulated bodies with up to sixdimensional configuration spaces. Even over such spaces, rapid online responses to unpredictable configuration changes can be made in a few microseconds on standard PC hardware. Furthermore, if the goal is changed, an updated navigation function can be quickly computed without performing additional collision checking. Index Terms—Feedback control, motion planning, navigation functions, potential fields. I.
Learning to Search: Structured Prediction Techniques for Imitation Learning
, 2009
"... Modern robots successfully manipulate objects, navigate rugged terrain, drive in urban settings, and play worldclass chess. Unfortunately, programming these robots is challenging, timeconsuming and expensive; the parameters governing their behavior are often unintuitive, even when the desired behav ..."
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Cited by 10 (2 self)
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Modern robots successfully manipulate objects, navigate rugged terrain, drive in urban settings, and play worldclass chess. Unfortunately, programming these robots is challenging, timeconsuming and expensive; the parameters governing their behavior are often unintuitive, even when the desired behavior is clear and easily demonstrated. Inspired by successful endtoend learning systems such as neural network controlled driving platforms (Pomerleau, 1989), learningbased “programming by demonstration ” has gained currency as a method to achieve intelligent robot behavior. Unfortunately, with highly structured algorithms at their core, modern robotic systems are hard to train using classical learning techniques. Rather than redefining robot architectures to accommodate existing learning algorithms, this thesis develops learning techniques that leverage the performance of modern robotic components. We begin with a discussion of a novel imitation learning framework we call Maximum Margin Planning which automates finding a cost function for optimal planning and control algorithms such as A*. In the linear setting, this framework has firm theoretical backing in the form of strong generalization and regret bounds. Further, we have developed practical nonlinear generalizations that are effective and efficient for realworld problems. This framework reduces imitation learning
What shape is your conjugate? A survey of computational convex analysis and its applications
 SIAM Rev
, 2010
"... Abstract. Computational Convex Analysis algorithms have been rediscovered several times in the past by researchers from different fields. To further communications between practitioners, we review the field of Computational Convex Analysis, which focuses on the numerical computation of fundamental ..."
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Cited by 7 (3 self)
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Abstract. Computational Convex Analysis algorithms have been rediscovered several times in the past by researchers from different fields. To further communications between practitioners, we review the field of Computational Convex Analysis, which focuses on the numerical computation of fundamental transforms arising from convex analysis. Current models use symbolic, numeric, and hybrid symbolicnumeric algorithms. Our objective is to disseminate widely the most efficient numerical algorithms useful for applications in image processing (computing the distance transform, the generalized distance transform, and mathematical morphology operators), partial differential equations (solving HamiltonJacobi equations, and using differential equations numerical schemes to compute the convex envelope), maxplus algebra (computing the equivalent of the Fast Fourier Transform), multifractal analysis, etc. The fields of applications include, among others, computer vision, robot navigation, thermodynamics, electrical networks, medical imaging, and network communication.
Efficient computation of optimal navigation functions for nonholonomic planning
 In Proc. First IEEE Int’l Workshop on Robot Motion and Control
, 1999
"... We present a fast, numerical approach to computing optimal feedback motion strategies for a nonholonomic robot in a cluttered environment. Although many techniques exist to compute navigation functions that can incorporate feedback, none of these methods is directly able to determine optimal strateg ..."
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Cited by 7 (2 self)
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We present a fast, numerical approach to computing optimal feedback motion strategies for a nonholonomic robot in a cluttered environment. Although many techniques exist to compute navigation functions that can incorporate feedback, none of these methods is directly able to determine optimal strategies for general nonholonomic systems. Our approach builds on previous techniques in numerical optimal control, and on our previous efforts in developing algorithms that compute feedback strategies for problems that involve nondeterministic and stochastic uncertainties in prediction. The proposed approach efficiently computes an optimal navigation function for nonholonomic systems by exploiting two ideas: 1) the principle of Dijkstra's algorithm can be generalized to continuous configuration spaces and nonholonomic systems, and 2) a simplicial mesh representation can be used to reduce the complexity of numerical interpolation. 1