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450
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 620 (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
Optimal paths for a car that goes both forwards and backwards
 PACIFIC JOURNAL OF MATHEMATICS
, 1990
"... The path taken by a car with a given minimum turning radius has a lower bound on its radius of curvature at each point, but the path has cusps if the car shifts into or out of reverse gear. What is the shortest such path a car can travel between two points if its starting and ending directions are s ..."
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Cited by 270 (0 self)
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The path taken by a car with a given minimum turning radius has a lower bound on its radius of curvature at each point, but the path has cusps if the car shifts into or out of reverse gear. What is the shortest such path a car can travel between two points if its starting and ending directions are specified? One need consider only paths with at most 2 cusps or reversals. We give a set of paths which is sufficient in the sense that it always contains a shortest path and small in the sense that there are at most 68, but usually many fewer paths in the set for any pair of endpoints and directions. We give these paths by explicit formula. Calculating the length of each of these paths and selecting the (not necessarily unique) path with smallest length yields a simple algorithm for a shortest path in each case. These optimal paths or geodesies may be described as follows: If C is an arc of a circle of the minimal turning radius and S is a line segment, then it is sufficient to consider only certain paths of the form CCSCC where arcs and segments fit smoothly, one or more of the arcs or segments may vanish, and where reversals, or equivalently cusps, between arcs or segments are allowed. This contrasts with the case when cusps are not allowed, where Dubins (1957) has shown that paths of the form CCC and CSC suffice.
RealTime Motion Planning For Agile Autonomous Vehicles
 AIAA JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS
, 2000
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Geometric Shortest Paths and Network Optimization
 Handbook of Computational Geometry
, 1998
"... Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to ..."
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Cited by 194 (15 self)
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Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of the edges that comprise it. Efficient algorithms are well known for this problem, as briefly summarized below. The shortest path problem takes on a new dimension when considered in a geometric domain. In contrast to graphs, where the encoding of edges is explicit, a geometric instance of a shortest path problem is usually specified by giving geometric objects that implicitly encode the graph and its edge weights. Our goal in devising efficient geometric algorithms is generally to avoid explicit construction of the entire underlying graph, since the full induced graph may be very large (even exponential in the input size, or infinite). Computing an optimal
The Stochastic Motion Roadmap: A sampling framework for planning with Markov motion uncertainty
 in Robotics: Science and Systems III (Proc. RSS 2007
, 2008
"... Abstract — We present a new motion planning framework that explicitly considers uncertainty in robot motion to maximize the probability of avoiding collisions and successfully reaching a goal. In many motion planning applications ranging from maneuvering vehicles over unfamiliar terrain to steering ..."
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Cited by 95 (20 self)
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Abstract — We present a new motion planning framework that explicitly considers uncertainty in robot motion to maximize the probability of avoiding collisions and successfully reaching a goal. In many motion planning applications ranging from maneuvering vehicles over unfamiliar terrain to steering flexible medical needles through human tissue, the response of a robot to commanded actions cannot be precisely predicted. We propose to build a roadmap by sampling collisionfree states in the configuration space and then locally sampling motions at each state to estimate state transition probabilities for each possible action. Given a query specifying initial and goal configurations, we use the roadmap to formulate a Markov Decision Process (MDP), which we solve using Infinite Horizon Dynamic Programming in polynomial time to compute stochastically optimal plans. The Stochastic Motion Roadmap (SMR) thus combines a samplingbased roadmap representation of the configuration space, as in PRM’s, with the wellestablished theory of MDP’s. Generating both states and transition probabilities by sampling is far more flexible than previous Markov motion planning approaches based on problemspecific or gridbased discretizations. We demonstrate the SMR framework by applying it to nonholonomic steerable needles, a new class of medical needles that follow curved paths through soft tissue, and confirm that SMR’s generate motion plans with significantly higher probabilities of success compared to traditional shortestpath plans. I.
Guidelines in nonholonomic motion planning for mobile robots
 ROBOT MOTION PLANNNING AND CONTROL
, 1998
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Shortest Paths For The ReedsShepp Car: A Worked Out Example Of The Use Of Geometric Techniques In Nonlinear Optimal Control.
, 1991
"... We illustrate the use of the techniques of modern geometric optimal control theory by studying the shortest paths for a model of a car that can move forwards and backwards. This problem was discussed in recent work by Reeds and Shepp who showed, by special methods, (a) that shortest path motion coul ..."
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Cited by 77 (5 self)
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We illustrate the use of the techniques of modern geometric optimal control theory by studying the shortest paths for a model of a car that can move forwards and backwards. This problem was discussed in recent work by Reeds and Shepp who showed, by special methods, (a) that shortest path motion could always be achieved by means of trajectories of a special kind, namely, concatenations of at most five pieces, each of which is either a straight line or a circle, and (b) that these concatenations can be classified into 48 threeparameter families. We show how these results fit in a much more general framework, and can be discovered and proved by applying in a systematic way the techniques of Optimal Control Theory. It turns out that the "classical" optimal control tools developed in the 1960's, such as the Pontryagin Maximum Principle and theorems on the existence of optimal trajectories, are helpful to go part of the way and get some information on the shortest paths, but do not suffice ...
On Traveling Salesperson Problems for Dubins' vehicle: stochastic and dynamic environments
 CDC 2005, TO APPEAR
, 2005
"... In this paper we propose some novel planning and routing strategies for Dubins’ vehicle, i.e., for a nonholonomic vehicle moving along paths with bounded curvature, without reversing direction. First, we study a stochastic version of the Traveling Salesperson Problem (TSP): given n targets randomly ..."
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Cited by 73 (19 self)
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In this paper we propose some novel planning and routing strategies for Dubins’ vehicle, i.e., for a nonholonomic vehicle moving along paths with bounded curvature, without reversing direction. First, we study a stochastic version of the Traveling Salesperson Problem (TSP): given n targets randomly sampled from a uniform distribution in a rectangle, what is the shortest Dubins ’ tour through the targets and what is its length? We show that the expected length of such a tour is Ω(n 2/3) and we propose a novel algorithm that generates a tour of length O(n 2/3 log(n) 1/3) with high probability. Second, we study a dynamic version of the TSP (known as “Dynamic Traveling Repairperson Problem” in the Operations Research literature): given a stochastic process that generates targets, is there a policy that allows a Dubins vehicle to stabilize the system, in the sense that the number of unvisited targets does not diverge over time? If such policies exist, what is the minimum expected waiting period between the time a target is generated and the time it is visited? We propose a novel recedinghorizon algorithm whose performance is almost within a constant factor from the optimum.
Multiple UAV cooperative search under collision avoidance and limited range communication constraints
 In IEEE CDC
, 2003
"... This paper focuses on the problem of cooperatively searching, using a team of unmanned air vehicles (UAVs), an area of interest that contains regions of opportunity and regions of potential hazard. The objective of the UAV team is to visit as many opportunities as possible, while avoiding as many ha ..."
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Cited by 71 (5 self)
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This paper focuses on the problem of cooperatively searching, using a team of unmanned air vehicles (UAVs), an area of interest that contains regions of opportunity and regions of potential hazard. The objective of the UAV team is to visit as many opportunities as possible, while avoiding as many hazards as possible. To enable cooperation, the UAVs are constrained to stay within communication range of one another. Collision avoidance is also required. Algorithms for teamoptimal and individuallyoptimal/teamsuboptimal solutions are developed and their computational complexity compared. Simulation results demonstrating the feasibility of the cooperative search algorithms are presented. 1
Control of Mechanical Systems with Rolling Constraints: Application to the Dynamic Control of Mobile Robots”, Int
 Journal of Robotics Research
, 1994
"... There are many examples of mechanical systems that require rolling contacts between two or more rigid bodies. Rolling contacts engender nonholonomic constraints in an otherwise holonomic system. In this article, we develop a unified approach to the control of mechanical systems subject to both holo ..."
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Cited by 65 (3 self)
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There are many examples of mechanical systems that require rolling contacts between two or more rigid bodies. Rolling contacts engender nonholonomic constraints in an otherwise holonomic system. In this article, we develop a unified approach to the control of mechanical systems subject to both holonomic and nonholonomic constraints. We first present a state space realization of a constrained system. We then discuss the inputoutput linearization and zero dynamics of the system. This approach is applied to the dynamic control of mobile robots. Two types of control algorithms for mobile robots are investigated: trajectory tracking and path following. In each case, a smooth nonlinear feedback is obtained to achieve asymptotic inputoutput stability and Lagrange stability of the overall system. Simulation results are presented to demonstrate the effectiveness of the control algorithms and to compare the performance of trajectorytracking and pathfollowing algorithms. 1.