Trajectory planning for an articulated probe

Teo, Ka Yaw; Daescu, Ovidiu; Fox, Kyle

doi:10.1016/j.comgeo.2020.101655

Cited by 2 publications

(20 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Unlike polygonal linkages that can rotate freely at their joints while moving between a start and target configuration [6,14,16], our simple articulated probe is constrained to a fixed sequence of moves -a straight line insertion, possibly followed by a rotation of the end link. This type of linkage motion has not received attention until recently [23,8].…”

Section: Related Workmentioning

confidence: 99%

“…The two-dimensional articulated probe trajectory planning problem with a constant length r was introduced by Teo, Daescu, and Fox [23], who presented a geometric-combinatorial algorithm for computing so-called extremal feasible probe trajectories in O(n 2 log n) time using O(n log n) space. In an extremal probe trajectory, one or two obstacle endpoints always lie tangent to the probe.…”

Section: Related Workmentioning

confidence: 99%

“…We consider the articulated probe trajectory planning problem originally introduced by Teo, Daescu, and Fox [23] with the following setup. We are given a two-dimensional workspace containing a set P of simple polygonal obstacles with a total of n vertices, and a target point t in the free space, all enclosed by a circle S of radius R centered at t. An articulated probe is modeled in 2 as two line segments, ab and bc, connected at point b.…”

Section: Introductionmentioning

confidence: 99%

“…It has been previously argued by Teo, Daescu, and Fox [23] that the polygonal obstacles can be treated by considering only their bounding line segments. Thus, for simplicity, assume that P consists of n non-crossing line segment obstacles (Figure 1).…”

Section: Introductionmentioning

confidence: 99%

“…Thus, for simplicity, assume that P consists of n non-crossing line segment obstacles (Figure 1). We further assume that S is not visible from t, since otherwise the problem reduces to computing visibility from t to infinity, which takes O(n log n) time [23]. Thus, in order to reach t, the probe has to rotate bc around b.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Characterization and Computation of Feasible Trajectories for an Articulated Probe with a Variable-Length End Segment

Daescu¹,

Teo²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

An articulated probe is modeled in the plane as two line segments, ab and bc, joined at b, with ab being very long, and bc of some small length r. We investigate a trajectory planning problem involving the articulated twosegment probe where the length r of bc can be customized. Consider a set P of simple polygonal obstacles with a total of n vertices, a target point t located in the free space such that t cannot see to infinity, and a circle S centered at t enclosing P . The probe initially resides outside S, with ab and bc being collinear, and is restricted to the following sequence of moves: a straight line insertion of abc into S followed by a rotation of bc around b. The goal is to compute a feasible obstacle-avoiding trajectory for the probe so that, after the sequence of moves, c coincides with t.We prove that, for n line segment obstacles, the smallest length r for which there exists a feasible probe trajectory can be found in O(n 2+ ) time using O(n 2+ ) space, for any constant > 0. Furthermore, we prove that all values r for which a feasible probe trajectory exists form O(n 2 ) intervals, and can be computed in O(n 5/2 ) time using O(n 2+ ) space. We also show that, for a given r, the feasible trajectory space of the articulated probe can be characterized by a simple arrangement of complexity O(n 2 ), which can be constructed in O(n 2 ) time. To obtain our solutions, we design efficient data

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Characterization and Computation of Feasible Trajectories for an Articulated Probe with a Variable-Length End Segment

Daescu¹,

Teo²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Computing Feasible Trajectories for an Articulated Probe in Three Dimensions

Daescu,

Teo

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Consider an input consisting of a set of n disjoint triangular obstacles in R 3 and a target point t in the free space, all enclosed by a large sphere S of radius R centered at t. An articulated probe is modeled as two line segments ab and bc connected at point b. The length of ab can be equal to or greater than R, while bc is of a given length r ≤ R. The probe is initially located outside S, assuming an unarticulated configuration, in which ab and bc are collinear and b ∈ ac. The goal is to find a feasible (obstacle-avoiding) probe trajectory to reach t, with the condition that the probe is constrained by the following sequence of moves -a straight-line insertion of the unarticulated probe into S, possibly followed by a rotation of bc at b for at most π/2 radians, so that c coincides with t.We prove that if there exists a feasible probe trajectory, then a set of extremal feasible trajectories must be present. Through careful case analysis, we show that these extremal trajectories can be represented by O(n 4 ) combinatorial events. We present a solution approach that enumerates and verifies these combinatorial events for feasibility in overall O(n 4+ ) time using O(n 4+ ) space, for any constant > 0. The enumeration algorithm is highly parallel, considering that each combinatorial event can be generated and verified for feasibility independently of the others. In the process of deriving our solution, we design the first data structure for addressing a special instance of circular sector emptiness queries among polyhedral obstacles

show abstract

Trajectory planning for an articulated probe

Cited by 2 publications

References 22 publications

Characterization and Computation of Feasible Trajectories for an Articulated Probe with a Variable-Length End Segment

Characterization and Computation of Feasible Trajectories for an Articulated Probe with a Variable-Length End Segment

Computing Feasible Trajectories for an Articulated Probe in Three Dimensions

Contact Info

Product

Resources

About