Integrity-Driven Landmark Attention for GPS-Vision Navigation via Stochastic Reachability

Bhamidipati, Sriramya; Gao, Grace Xingxin

doi:10.33012/2020.17546

Cited by 7 publications

(9 citation statements)

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“…This enables robustness by ensuring that the set lies within, e.g., user-specified safety bounds. Recently, there has been growing interest in set-valued representations of receiver states and measurements for robust localization and motion planning in urban environments (Bhamidipati & Gao, 2020;Kousik et al, 2019;Shetty & Gao, 2020). Unfortunately, these methods typically require assuming a set-valued representation of uncertain measurements by, e.g., overapproximating a confidence level set of Gaussian distribution using a polytope (Bhamidipati & Gao, 2020;Shetty & Gao, 2020); in other words, one must make an assumption about the underlying distribution of measurements.…”

Section: Related Workmentioning

confidence: 99%

“…Recently, there has been growing interest in set-valued representations of receiver states and measurements for robust localization and motion planning in urban environments (Bhamidipati & Gao, 2020;Kousik et al, 2019;Shetty & Gao, 2020). Unfortunately, these methods typically require assuming a set-valued representation of uncertain measurements by, e.g., overapproximating a confidence level set of Gaussian distribution using a polytope (Bhamidipati & Gao, 2020;Shetty & Gao, 2020); in other words, one must make an assumption about the underlying distribution of measurements. Therefore, it remains an open challenge to generate set-valued receiver position estimates for the distributions that are common in urban environments (e.g., multi-modal with disconnected components).…”

Section: Related Workmentioning

confidence: 99%

“…Zonotopes are constructed as Minkowski sums (Althoff & Dolan, 2014) of line segments in an arbitrary-dimensional Euclidean space. These objects are well-known for representing reachable sets of dynamical systems (Althoff, 2015), which can enable formally-verified motion planning, fault detection, and navigation (Bhamidipati & Gao, 2020;Kousik et al, 2019;Shetty & Gao, 2020). These objects can also be extended to constrained zonotopes, which can represent arbitrary convex polytopes (Raghuraman & Koeln, 2020;Scott et al, 2016), avoiding the limitation of symmetry.…”

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Set-Valued Shadow Matching Using Zonotopes for 3-D Map-Aided GNSS Localization

Bhamidipati¹,

Kousik²,

Gao³

2022

Preprint

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Set-Valued Shadow Matching Using Zonotopes for 3-D Map-Aided GNSS Localization

Bhamidipati¹,

Kousik²,

Gao³

2022

Preprint

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“…In the controls, robotics, and navigation communities, it is often critical to place strict guarantees on the behavior of a dynamical system. Example applications of such guarantees include collision avoidance [1]- [4], fault detection [5], [6], and control invariance [4], [7], [8]. A common strategy for enforcing such guarantees, especially for uncertain dynamical systems, is to compute the system's reachable set of states, then guarantee that this set lies within certain bounds (e.g., for fault detection) or obeys non-intersection constraints (e.g., for collision avoidance).…”

Section: Introductionmentioning

confidence: 99%

Ellipsotopes: Combining Ellipsoids and Zonotopes for Reachability Analysis and Fault Detection

Kousik¹,

Dai²,

Gao

2021

Preprint

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Ellipsoids are a common representation for reachability analysis because they are closed under affine maps and allow conservative approximation of Minkowski sums; this enables one to incorporate uncertainty and linearization error in a dynamical system by exapnding the size of the reachable set. Zonotopes, a type of symmetric, convex polytope, are similarly frequently used due to efficient numerical implementation of affine maps and exact Minkowski sums. Both of these representations also enable efficient, convex collision detection for fault detection or formal verification tasks, wherein one checks if the reachable set of a system collides (i.e., intersects) with an unsafe set. However, both representations often result in conservative representations for reachable sets of arbitrary systems, and neither is closed under intersection. Recently, constrained zonotopes and constrained polynomial zonotopes have been shown to overcome some of these conservatism challenges, and are closed under intersection. However, constrained zonotopes can not represent shapes with smooth boundaries such as ellipsoids, and constrained polynomial zonotopes can require solving a non-convex program for collision checking (i.e., fault detection). This paper introduces ellipsotopes, a set representation that is closed under affine maps, Minkowski sums, and intersections. Ellipsotopes combine the advantages of ellipsoids and zonotopes, and enable convex collision checking at the expense of more conservative reachable sets than constrained polynomial zonotopes. The utility of this representation is demonstrated on several examples.

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“…To address the above challenges, we formulate the following objectives: (a) select a desirable subset of measurements from available GPS and vision that minimizes the position error bounds; (b) design a unified approach to address multiple faults in GPS and vision while ensuring computational tractability; and (c) predict integrity-driven measures of expected navigation performance for the measurement subset. This work is based on our recent ION GNSS+ 2020 conference paper [19].…”

Section: Introductionmentioning

confidence: 99%