On the existence and synthesis of curvature-bounded paths inside nonuniform rectangular channels
01 Jun 2010-pp 5382-5387
TL;DR: In this article, the authors present a numerical algorithm for determining the existence of a curvature-bounded path contained within a rectangular channel, where the rectangular cells comprising the channel are assumed to be of arbitrary, non-uniform dimensions and the bounds on curvature are allowed to be different for different cells.
Abstract: Motion planners for autonomous mobile vehicles that are based on rectangular cell decompositions are often required to construct kinematically feasible path - typically curvature-bounded paths - traversing rectangular channels. In this paper, we present a numerical algorithm for determining the existence of a curvature-bounded path contained within a rectangular channel. The rectangular cells comprising the channel are assumed to be of arbitrary, non-uniform dimensions and the bounds on curvature are allowed to be different for different cells. The proposed algorithm is based on the explicit construction of the cone of feasible directions for a bounded-curvature path at the cell exit edge, given the entry point for each cell in the channel. Based on this analysis, we devise a path construction scheme that retains the convenience of cell-by-cell path synthesis but eliminates the guesswork involved in choosing terminal conditions within each cell.
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TL;DR: The proposed iterative 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.
Abstract: Motion planning for mobile vehicles involves the solution of two disparate subproblems: the satisfaction of high-level logical task specifications and the design of low-level vehicle control laws. A hierarchical solution of these two subproblems is efficient, but it may not ensure compatibility between the high-level planner and the constraints that are imposed by the vehicle dynamics. To guarantee such compatibility, we propose a motion-planning framework that is based on a special interaction between these two levels of planning. In particular, we solve a special shortest path problem on a graph at a higher level of planning, and we use a lower level planner to determine the costs of the paths in that graph. The overall approach hinges on two novel ingredients: 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.
62 citations
TL;DR: A class of Hamilton–Jacobi equations is derived which models such motions of a vehicle which travels under certain curvature constraints; it unifies two well-known vehicular models, the Dubins’ and Reeds–Shepp’s cars, and gives further generalizations.
Abstract: We propose a PDE approach for computing time-optimal trajectories of a vehicle which travels under certain curvature constraints. We derive a class of Hamilton---Jacobi equations which models such motions; it unifies two well-known vehicular models, the Dubins' and Reeds---Shepp's cars, and gives further generalizations. Numerical methods (finite difference for the Reeds---Shepp's car and semi-Lagrangian for the Dubins' car) are investigated for two-dimensional domains and surfaces.
44 citations
Cites background from "On the existence and synthesis of c..."
...This is a problem posed in [42], where it was solved using purely geometrical arguments....
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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
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.
18 citations
Cites background or methods from "On the existence and synthesis of c..."
...This paper presents detailed algorithms for the solution of the CBTA problem, a complete proof of Theorem 1, and applications of the proposed technique, neither of which appeared in [16]....
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...Preliminary versions of the discussion and results presented in this paper were previously presented in [16]....
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Dissertation•
10 Nov 2011
17 citations
Cites methods from "On the existence and synthesis of c..."
...This can be achieved by appropriately concatenating different Dubins’ paths using geometric arguments [29, 8, 9, 64] or by employing a discrete path planner (high level planning) that yields a set of way-points to be locally connected by means of Dubins-like paths (low level planning) [25, 111, 28, 155, 65]....
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References
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29 Jul 2010
TL;DR: A general framework, based on rectangular cell decompositions, is proposed for incorporating information about the kinodynamic behavior of the vehicle in the geometric planning layer itself, to design a geometric path planning scheme which simultaneously finds an obstacle-free channel of cells from the initial point to the goal.
Abstract: The hierarchical decomposition of motion planning tasks into geometric path planning, followed by kinodynamic motion planning is useful for designing efficient algorithms, but it entails the possibility of inconsistency between the two layers of planning. In an earlier paper, we proposed a general framework, based on rectangular cell decompositions, for incorporating information about the kinodynamic behavior of the vehicle in the geometric planning layer itself. In this paper, we use this framework to design a geometric path planning scheme which simultaneously finds an obstacle-free channel of cells from the initial point to the goal, as well as a vehicle state trajectory lying within that channel.
7 citations
"On the existence and synthesis of c..." refers background in this paper
...The work presented in this paper is intended to bridge the gap between the (high-level) geometric path planning and the (low-level) trajectory generation layers in the motion planning and control hierarchy [1]....
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