# On the existence and synthesis of curvature-bounded paths inside nonuniform rectangular channels

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.

...read more

##### Citations

62 citations

39 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....

[...]

37 citations

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]....

[...]

15 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]....

[...]

...Preliminary versions of the discussion and results presented in this paper were previously presented in [16]....

[...]

##### References

2,613 citations

### Additional excerpts

...[10]–[12] is to appropriately choose a finite set of configurations (position and orientation) in the environment, and connecting these configurations by Dubins paths, and then perform a graph search using the length of the Dubins paths as edge costs....

[...]

...[7] presents a synthesis algorithm for the Dubins problem....

[...]

...Ref- erence [6] reproduces Dubins’ result using optimal control theory, while Ref....

[...]

...Curvature-bounded path planning has been studied extensively, starting with the seminal work of Dubins [5]....

[...]

...[14] for a survey of motion planning and control for nonholonomic vehicles (of which the Dubins car is a specific example)....

[...]

802 citations

### "On the existence and synthesis of c..." refers background in this paper

...[14] for a survey of motion planning and control for nonholonomic vehicles (of which the Dubins car is a specific example)....

[...]

359 citations

### "On the existence and synthesis of c..." refers background or methods in this paper

...[10]–[12] is to appropriately choose a finite set of configurations (position and orientation) in the environment, and connecting these configurations by Dubins paths, and then perform a graph search using the length of the Dubins paths as edge costs....

[...]

...References [10]–[12] present algorithms for efficiently finding approximations to shortest curvature-bounded paths in polygonal environments....

[...]

171 citations

### "On the existence and synthesis of c..." refers methods in this paper

...[7] presents a synthesis algorithm for the Dubins problem....

[...]

130 citations