Curvature-Bounded Traversability Analysis in Motion Planning for Mobile Robots
TL;DR: A fast numerical algorithm is presented to determine whether a narrow planar passage can be traversed by a curve that satisfies prespecified upper bounds on its curvature, and it is demonstrated that the proposed algorithm can affirm traversability in cases where the most recent result in the literature fails.
Abstract: We consider the geometric problem of deciding whether a narrow planar passage can be traversed by a curve that satisfies prespecified upper bounds on its curvature. This problem is of importance for path- and motion-planning of autonomous mobile robots, particularly when vehicle dynamical constraints are considered during planning. For a special case of narrow passages, namely, rectangular channels, we present a fast numerical algorithm to determine if a given channel may be traversed via curvature- bounded paths. We demonstrate that the proposed algorithm can affirm traversability in cases where the most recent result in the literature fails.
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15 Jul 2015
TL;DR: A graph-search algorithm that operates on sequences of vertices and a lower level planner that ensures consistency between the two levels of hierarchy by providing meaningful costs for the edge transitions of a higher level planner using dynamically feasible, collision-free trajectories are proposed.
Abstract: New requirements of autonomous mobile vehicles necessitate hierarchical motion-planning techniques that not only find a plan to satisfy high-level specifications, but also guarantee that this plan is suitable for execution under vehicle dynamical constraints. In this context, the H-cost motion-planning technique has been reported in the recent literature. We propose an incremental motion-planning algorithm based on this technique. The proposed algorithm retains the benefits of the original technique, while significantly reducing the associated computational time. In particular, the proposed iterative algorithm presents during intermediate iterations feasible solutions, with the guarantee that the algorithm eventually converges to an optimal solution. The costs of solutions at intermediate iterations are almost always nonincreasing. Therefore, the proposed algorithm is suitable for real-time implementations, where hard bounds on the available computation time are imposed, and where the original H-cost optimization algorithm may not have sufficient time to converge to a solution at all. We illustrate the proposed algorithm with numerical simulation examples.
37 citations
Cites methods from "Curvature-Bounded Traversability An..."
...Algorithms for computing the sets S(·),Q(·) and R(·) for the Dubins car kinematic model (a model of a vehicle that moves forwards only at a constant speed with a fixed minimum turn radius) are provided in [19]....
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22 Jan 2016
TL;DR: The work highlights the use of logistic curves as a novel, analytically feasible, and applicable path planning methodology.
Abstract: Continuous-curvature path planning with obstacle avoidance is considered. Two path shapes, namely, S and half-S shapes derived from four parameter logistic curves are proposed as solution paths. Closed-form analytic conditions are derived for avoiding rectangular and circular obstacles. Using the zero end curvature property of the proposed paths, a complete path planner is presented joining the individual paths. An analytic bound on the maximum curvature of the paths is derived. A comparison is carried out with existing smooth path planning methodologies based on number of design parameters, complexity in obstacle avoidance, and nature of computations involved. The work highlights the use of logistic curves as a novel, analytically feasible, and applicable path planning methodology.
35 citations
Cites methods from "Curvature-Bounded Traversability An..."
...A typical path planning method generates a path between a given set of points with specific constraints on its heading and curvature [1]–[8]....
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TL;DR: A structured homotopy-based (SH-based) planner as an improvement of the conventional path elongation strategy, which has stronger flexibility and adaptability for different endpoint condition than simple elongation.
17 citations
TL;DR: A comprehensive and systematic framework to plan paths with target length, which is a generalization of the existing related studies and can produce the largest length coverage in different scenarios and under different conditions.
Abstract: In this paper, the traditional shortest path planning problem for vehicle is advanced to length-targeted path planning problem, i.e., to plan path with its length being as close to a specified value as possible. Lengthening and shortening of given initial paths are used to solve this problem. Based on an operation set consisting of three basic path homotopies, we build a comprehensive and systematic framework to plan paths with target length, which is a generalization of the existing related studies. Thereby, the expected paths can be independently searched through such deformation processes within topological classes. The proposed framework can produce the largest length coverage in different scenarios and under different conditions, and it can also generate expected paths with arbitrary topological classification in terms of the curvature constraint and the obstacle constraint. Examples show that our lengthening and shortening method can effectively solve the length-targeted path planning problem in environment without or with obstacles. Note to Practitioners —This paper presents a curvature-bounded lengthening and shortening approach for path planning of vehicles. The curvature and obstacle constraints in the path planning problem are handled using the topological technique. In addition, a rigorous classification system is presented to systematically categorize the potential paths. Within a path class, any path can be deformed to other paths while keeping the curvature bounded. Then, the path deformation process is conducted via a series of basic homotopy operations to approach the target length. The length coverage range of this process is reduced when some endpoint conditions are meet or the vehicle is trapped into a closed region.
12 citations
Cites background from "Curvature-Bounded Traversability An..."
...traversability analysis in some special application scenarios is addressed in [33]....
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06 Jul 2016
TL;DR: This work investigates motion-planning for a team of robotic vehicles assigned to a collaborative intelligent task in the form of global linear temporal logic (LTL) specifications, and applies the so-called method of lifted graphs to determine the feasibility of edge transitions in these graphs.
Abstract: We investigate motion-planning for a team of robotic vehicles assigned to a collaborative intelligent task in the form of global linear temporal logic (LTL) specifications. Specifically, we extend recent results from the literature to include nonholonomic kinematic constraints on the robotic vehicles. The problem formulation relies on workspace cell decompositions, where certain regions of interest in the robots' shared workspace are defined. The proposed algorithm involves two graphs: first, the topological graph arising from the workspace cell decomposition, and second, a graph arising from vertex aggregation on the previous graph. The main technical innovation is the application of the so-called method of lifted graphs to determine the feasibility of edge transitions in these graphs. We illustrate the proposed approach with numerical simulation examples.
10 citations
Cites methods from "Curvature-Bounded Traversability An..."
...Algorithms for computing the sets R(·),S(·), and Q(·) are described, based on geometric arguments, in [19]....
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References
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Book•
01 Dec 2001
TL;DR: A standard formulation of Predictive Control is presented, with examples of step response and transfer function formulations, and a case study of robust predictive control in the context of MATLAB.
Abstract: 1. Introduction to Predictive Control. 2. A Standard Formulation of Predictive Control. 3. Solving Predictive Control Problems. 4. Step Response and Transfer Function Formulations. 5. Tuning. 6. Stability. 7. Robust Predictive Control. 8. Perspectives. 9. Case Studies. 10. The Model Predictive Control Toolbox. References Appendices A. Some Commercial MPC Products B. MATLAB Program basicmpc C. The MPC Toolbox D. Solutions to Problems
5,468 citations
2,888 citations
"Curvature-Bounded Traversability An..." refers background in this paper
...In the absence of obstacles, the shortest curvature-bounded path between two prespecified configurations was shown to lie in a finite family of paths (henceforth referred to as Dubins paths), first via geometric arguments [5] and later via optimal control theory [6]....
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Posted Content•
TL;DR: The main contribution of the paper is the introduction of new algorithms, namely, PRM and RRT*, which are provably asymptotically optimal, i.e. such that the cost of the returned solution converges almost surely to the optimum.
Abstract: During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.
2,210 citations
Book•
20 May 2005
TL;DR: In this paper, the mathematical underpinnings of robot motion are discussed and a text that makes the low-level details of implementation to high-level algorithmic concepts is presented.
Abstract: A text that makes the mathematical underpinnings of robot motion accessible and relates low-level details of implementation to high-level algorithmic concepts. Robot motion planning has become a major focus of robotics. Research findings can be applied not only to robotics but to planning routes on circuit boards, directing digital actors in computer graphics, robot-assisted surgery and medicine, and in novel areas such as drug design and protein folding. This text reflects the great advances that have taken place in the last ten years, including sensor-based planning, probabalistic planning, localization and mapping, and motion planning for dynamic and nonholonomic systems. Its presentation makes the mathematical underpinnings of robot motion accessible to students of computer science and engineering, rleating low-level implementation details to high-level algorithmic concepts.
1,811 citations
10 May 1999
TL;DR: This paper presents a new, simple sampling strategy, which it is called the Gaussian sampler, that gives a much better coverage of the difficult parts of the free configuration space.
Abstract: Probabilistic roadmap planners (PRMs) form a relatively new technique for motion planning that has shown great potential. A critical aspect of PRM is the probabilistic strategy used to sample the free configuration space. In this paper we present a new, simple sampling strategy, which we call the Gaussian sampler, that gives a much better coverage of the difficult parts of the free configuration space. The approach uses only elementary operations which makes it suitable for many different planning problems. Experiments indicate that the technique is very efficient indeed.
578 citations