This paper presents an equivalence between feasible kinodynamic planning and optimal kinodynamic planning, in that any optimal planning problem can be transformed into a series of feasible planning problems in a state-cost space whose solutions approach the optimum. This transformation gives rise to a meta-algorithm that produces an asymptotically optimal planner, given any feasible kinodynamic planner as a subroutine. The meta-algorithm is proven to be asymptotically optimal, and a formula is derived relating expected running time and solution suboptimality. It is directly applicable to a wide range of optimal planning problems because it does not resort to the use of steering functions or numerical boundary-value problem solvers. On a set of benchmark problems, it is demonstrated to perform, using the EST and RRT algorithms as subroutines, at a superior or comparable level to related planners.
Several authors have extended RRT* to dynamically-constrained systems. It is relatively easy to apply RRT* to dynamically-constrained systems if a steering function is available @cite_15 . Proving convergence is harder, requiring analysis of small-time controllability conditions @cite_11 . Other authors have extended RRT* to systems whose dynamics and costs are (or can be approximated) by linear and quadratic functions, respectively, by definition of a suitable steering function based on the LQR principle @cite_8 @cite_7 . When more complex differential constraints are involved, it may not be possible to devise a suitable steering functions. One method generated complex maneuvers using RRT* and performed each rewiring step by numerically solving a two-point boundary value problems @cite_21 . This adds greatly to computational expense. A similar method performed rewiring using a spline-based trajectory representation that is optimized via a nonlinear program solver @cite_19 .
@cite_7 @cite_8 @cite_21 @cite_19 @cite_15 @cite_11
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Sampling-based algorithms such as the Rapidly-exploring Random Tree (RRT) have been recently proposed as an effective approach to computationally hard motion planning problem. However, while the RRT algorithm is known to be able to find a feasible solution quickly, there are no guarantees on the quality of such solution, e.g., with respect to a given cost functional. To address this limitation, the authors recently proposed a new algorithm, called RRT*, which ensures asymptotic optimality, i.e., almost sure convergence of the solution returned by the algorithm to an optimal solution, while maintaining the same properties of the standard RRT algorithm, both in terms of computation of feasible solutions, and of computational complexity. In this paper, the RRT* algorithm is extended to deal with differential constraints. A sufficient condition for asymptotic optimality is provided. It is shown that the RRT* algorithm equipped with any local steering procedure that satisfies this condition converges to an optimal solution almost surely. In particular, simple local steering procedures are provided for a Dubins' vehicle as well as a double integrator. Simulation examples are also provided for these systems comparing the RRT and the RRT* algorithms. Incremental sampling-based motion planning algorithms such as the Rapidly-exploring Random Trees (RRTs) have been successful in efficiently solving computationally challenging motion planning problems involving complex dynamical systems. A recently proposed algorithm, called the RRT*, also provides asymptotic optimality guarantees, i.e., almost-sure convergence to optimal trajectories (which the RRT algorithm lacked) while maintaining the computational efficiency of the RRT algorithm. In this paper, time-optimal maneuvers for a high-speed off-road vehicle taking tight turns on a loose surface are studied using the RRT* algorithm. Our simulation results show that the aggressive skidding maneuver, usually called the trail-braking maneuver, naturally emerges from the RRT* algorithm as the minimum-time trajectory. Along the way, we extend the RRT* algorithm to handle complex dynamical systems, such as those that are described by nonlinear differential equations and involve high-dimensional state spaces, which may be of independent interest. We also exploit the RRT* as an anytime computation framework for nonlinear optimization problems. The RRT* algorithm has efficiently extended Rapidly-exploring Random Trees (RRTs) to endow it with asymptotic optimality. We propose Goal-Rooted Feedback Motion Trees (GR-FMTs) that honor state input constraints and generate collision-free feedback policies. Given analytic solutions for optimal local steering, GR-FMTs obtain and realize safe, dynamically feasible, and asymptotically optimal trajectories toward goals. Second, for controllable linear systems with linear state input constraints, we propose a fast method for local steering, based on polynomial basis functions and segmentation. GR-FMTs with the method obtain and realize trajectories that are collision-free, dynamically feasible under constraints, and asymptotically optimal within a set we define. The formulation includes linear or quadratic programming of small sizes, where constraints are identified by root-finding in low or medium order of polynomials and added progressively. The RRT* algorithm has recently been proposed as an optimal extension to the standard RRT algorithm [1]. However, like RRT, RRT* is difficult to apply in problems with complicated or underactuated dynamics because it requires the design of a two domain-specific extension heuristics: a distance metric and node extension method. We propose automatically deriving these two heuristics for RRT* by locally linearizing the domain dynamics and applying linear quadratic regulation (LQR). The resulting algorithm, LQR-RRT*, finds optimal plans in domains with complex or underactuated dynamics without requiring domain-specific design choices. We demonstrate its application in domains that are successively torque-limited, underactuated, and in belief space. Recent motion planners, such as RRT*, that achieve asymptotic optimality require a local planner, which connects two states with a trajectory. For systems with dynamics, the local planner corresponds to a two-point boundary value problem (BVP) solver, which is not always available. Furthermore, asymptotically optimal solutions tend to increase computational costs relative to alternatives, such as RRT, that focus on feasibility. This paper describes a sampling-based solution with the following desirable properties: a) it does not require a BVP solver but only uses a forward propagation model, b) it employs a single propagation per iteration similar to RRT, making it very efficient, c) it is asymptotically near-optimal, and d) provides a sparse data structure for answering path queries, which further improves computational performance. Simulations on prototypical dynamical systems show the method is able to improve the quality of feasible solutions over time and that it is computationally efficient. We present Kinodynamic RRT*, an incremental sampling-based approach for asymptotically optimal motion planning for robots with linear dynamics. Our approach extends RRT*, which was introduced for holonomic robots [10], by using a fixed-final-state-free-final-time controller that optimally connects any pair of states, where the cost function is expressed as a trade-off between the duration of a trajectory and the expended control effort. Our approach generalizes earlier work on RRT* for kinodynamic systems, as it guarantees asymptotic optimality for any system with controllable linear dynamics, in state spaces of any dimension. In addition, we show that for the rich subclass of systems with a nilpotent dynamics matrix, closed-form solutions for optimal trajectories can be derived, which keeps the computational overhead of our algorithm compared to traditional RRT* at a minimum. We demonstrate the potential of our approach by computing asymptotically optimal trajectories in three challenging motion planning scenarios: (i) a planar robot with a 4-D state space and double integrator dynamics, (ii) an aerial vehicle with a 10-D state space and linearized quadrotor dynamics, and (iii) a car-like robot with a 5-D state space and non-linear dynamics. We present an approach for asymptotically optimal motion planning for kinodynamic systems with arbitrary nonlinear dynamics amid obstacles. Optimal sampling-based planners like RRT*, FMT*, and BIT* when applied to kinodynamic systems require solving a two-point boundary value problem (BVP) to perform exact connections between nodes in the tree. Two-point BVPs are non-trivial to solve, hence the prevalence of alternative approaches that focus on specific instances of kinodynamic systems, use approximate solutions to the two-point BVP, or use random propagation of controls. In this work, we explore the feasibility of exploiting recent advances in numerical optimal control and optimization to solve these two-point BVPs for arbitrary kinodynamic systems and how they can be integrated with existing optimal planning algorithms. We combine BIT* with a two-point BVP solver that uses sequential quadratic programming (SQP). We consider the problem of computing minimum-time trajectories. Since the duration of trajectories is not known a-priori, we include the time-step as part of the optimization to allow SQP to optimize over the duration of the trajectory while keeping the number of discrete steps fixed for every connection attempted. Our experiments indicate that using a two-point BVP solver in the inner-loop of BIT* is competitive with the state-of-the-art in sampling-based optimal planning that explicitly avoids the use of two-point BVP solvers. Some of the latest developments in motion planning methods have addressed the merging of optimal control with sampling-based approaches, to handle the problem of optimal kinodynamic motion planning for complex robot systems in cluttered environments. These include embedding the Linear Quadratic Regulator method in an RRT* context, or solving the kinematic problem with an RRT algorithm first and then feeding the solution to an NLP solver. An alternative approach is presented here, in which NLP is embedded in an RRT* context from the start. The resulting methodological features are illustrated with numerical examples. These include problems in which differential constraints play a fundamental role. Kinodynamic planning algorithms like Rapidly-Exploring 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 distance 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. We show that an affine quadratic regulator (AQR) design can be used to approximate the exact minimum-time distance pseudometric at a reasonable computational cost. We demonstrate improved exploration of the state spaces of the double integrator and simple pendulum when using this pseudometric within the RRT framework, but this improvement drops off as systems' nonlinearity and complexity increase. Future work includes exploring methods for approximating the exact minimum-time distance pseudometric that can reason about dynamics with higher-order terms. Kinodynamic RRT planners are considered to be general tools for effectively finding feasible trajectories for high-dimensional dynamical systems. However, they struggle when holonomic constraints are present in the system, such as those arising in parallel manipulators, in robots that cooperate to fulfill a given task, or in situations involving contacts with the environment. In such cases, the state space becomes an implicitly-defined manifold, which makes the diffusion heuristic inefficient and leads to inaccurate dynamical simulations. To address these issues, this paper presents an extension of the kinodynamic RRT planner that constructs an atlas of the state-space manifold incrementally, and uses this atlas both to generate random states and to dynamically steer the system towards such states. To the best of our knowledge, this is the first randomized kinodynamic planner that explicitly takes holonomic constraints into account. We validate the approach in significantly-complex systems. Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... Sampling-based motion planning algorithms, such as the Probabilistic RoadMap (PRM) and the Rapidly-exploring Random Tree (RRT), have received a large and growing amount of attention during the past decade. Most recently, sampling-based algorithms, such as the PRM* and RRT*, that guarantee asymptotic optimality, i.e., almost-sure convergence towards optimal solutions, have been proposed. Despite the experimental success of asymptotically-optimal sampling-based algorithms, their extensions to handle complex non-holonomic dynamical systems remains largely an open problem. In this paper, with the help of results from differential geometry, we extend the RRT* algorithm to handle a large class of non-holonomic dynamical systems. We demonstrate the performance of the algorithm in computational experiments involving the Dubins' car dynamics. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] The problem of testing complex reactive control systems and validating the effectiveness of multi-agent controllers is addressed. Testing and validation involve searching for conditions that lead to system failure by exploring all adversarial inputs and disturbances for errant trajectories. This problem of testing is related to motion planning. In both cases, there is a goal or specification set consisting of a set of points in state space that is of interest, either for finding a plan, demonstrating failure or for validation. Unlike motion planning problems, the problem of testing generally involves systems that are not controllable with respect to disturbances or adversarial inputs and therefore, the reachable set of states is a small subset of the entire state space. In this work, sampling-based algorithms based on the Rapidly-exploring Random Trees (RRT) algorithm are applied to the testing and validation problem. First, some of the factors that govern the exploration rate of the RRT algorithm are analysed, this analysis serving to motivate some enhancements. Then, three modifications to the original RRT algorithm are proposed, suited for use on uncontrollable systems. First, a new distance function is introduced which incorporates information about the system's dynamics to select nodes for extension. Second, a weighting is introduced to penalize nodes which are repeatedly selected but fail to extend.Third, a scheme for adaptively modifying the sampling probability distribution is proposed, based on tree growth. Application of the algorithm is demonstrated using several examples, and computational statistics are provided to illustrate the effect of each modification. The final algorithm is demonstrated on a 25 state example and results in nearly an order of magnitude reduction in computation time when compared with the traditional RRT. The proposed algorithms are also applicable to motion planning for systems that are not small time locally controllable. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. Rapidly-exploring Random Trees (RRTs) are widely used to solve large planning problems where the scope prohibits the feasibility of deterministic solvers, but the efficiency of these algorithms can be severely compromised in the presence of certain kinodynamics constraints. Obstacle fields with tunnels, or tubes are notoriously difficult, as are systems with differential constraints, because the tree grows inefficiently at the boundaries. Here we present a new sampling strategy for the RRT algorithm, based on an estimated feasibility set, which affords a dramatic improvement in performance in these severely constrained systems. We demonstrate the algorithm with a detailed look at the expansion of an RRT in a swingup task, and on path planning for a nonholonomic car. between planner conservatism and the risk of infeasibility. This paper presents a novel real-time planning algorithm, chance constrained rapidly-exploring random trees (CC-RRT), which uses chance constraints to guarantee probabilistic feasibility for linear systems subject to process noise and or uncertain, possibly dynamic obstacles. By using RRT, the algorithm enjoys the computational benets of sampling-based algorithms, such as trajectory-wise constraint checking and incorporation of heuristics, while explicitly incorporating uncertainty within the formulation. Under the assumption of Gaussian noise, probabilistic feasibility at each time step can be established through simple simulation of the state conditional mean and the evaluation of linear constraints. Alternatively, a small amount of additional computation can be used to explicitly compute a less conservative probability bound at each time step. Simulation results show that this algorithm can be used for ecient identication and execution of probabilistically safe paths in real time. The RRT algorithm can deal with the motion planning problems in consideration of non-holonomic differential constraints, but it does not taken into consideration the optimal path problem in planning process. Random selection of nodes leads to every planning cost relatively different because of only use of metric function in new node selection. In this paper, an improved heuristic RRT-A* algorithm is proposed for robot motion planning with non-holonomic constraints. In this algorithm, the cost function of A-Star(A*) is introduced into the RRT algorithm to optimize the performance. Meanwhile, several metric functions are used as the heuristic information functions respectively to measure the performance of different metric function. The simulation results shown that the Manhattan heuristic information function based RRT-A* planning algorithm is better than the other improved RRT algorithms in optimization path and computational cost. We discuss an implementation of the RRT* optimal motion planning algorithm for the half-car dynamical model to enable autonomous high-speed driving. To develop fast solutions of the associated local steering problem, we observe that the motion of a special point (namely, the front center of oscillation) can be modeled as a double integrator augmented with fictitious inputs. We first map the constraints on tire friction forces to constraints on these augmented inputs, which provides instantaneous, state-dependent bounds on the curvature of geometric paths feasibly traversable by the front center of oscillation. Next, we map the vehicle's actual inputs to the augmented inputs. The local steering problem for the half-car dynamical model can then be transformed to a simpler steering problem for the front center of oscillation, which we solve efficiently by first constructing a curvature-bounded geometric path and then imposing a suitable speed profile on this geometric path. Finally, we demonstrate the efficacy of the proposed motion planner via numerical simulation results. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results.