Results

**1 - 6**of**6**### Sampling-Based Coverage . . . Structures

, 2012

"... Path planning is an essential capability for autonomous robots, and many applica-tions impose challenging constraints alongside the standard requirement of obsta-cle avoidance. Coverage planning is one such task, in which a single robot must sweep its end effector over the entirety of a known worksp ..."

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Path planning is an essential capability for autonomous robots, and many applica-tions impose challenging constraints alongside the standard requirement of obsta-cle avoidance. Coverage planning is one such task, in which a single robot must sweep its end effector over the entirety of a known workspace. For two-dimensional environments, optimal algorithms are documented and well-understood. For three-dimensional structures, however, few of the available heuristics succeed over occluded regions and low-clearance areas. This thesis makes several contributions to sampling-based coverage path planning, for use on complex three-dimensional structures. First, we introduce a new algorithm for planning feasible coverage paths. It is more computationally efficient in problems of complex geometry than the well-known dual sampling method, especially when high-quality solutions are desired. Second, we present an improvement procedure that iteratively shortens and smooths a feasible coverage path; robot configurations are adjusted without violating any coverage con-straints. Third, we propose a modular algorithm that allows the simple components

### Sampling-Based Coverage Path Planning for Complex 3D Structures

, 2012

"... Path planning is an essential capability for autonomous robots, and many applica-tions impose challenging constraints alongside the standard requirement of obsta-cle avoidance. Coverage planning is one such task, in which a single robot must sweep its end effector over the entirety of a known worksp ..."

Abstract
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Path planning is an essential capability for autonomous robots, and many applica-tions impose challenging constraints alongside the standard requirement of obsta-cle avoidance. Coverage planning is one such task, in which a single robot must sweep its end effector over the entirety of a known workspace. For two-dimensional environments, optimal algorithms are documented and well-understood. For three-dimensional structures, however, few of the available heuristics succeed over occluded regions and low-clearance areas. This thesis makes several contributions to sampling-based coverage path planning, for use on complex three-dimensional structures. First, we introduce a new algorithm for planning feasible coverage paths. It is more computationally efficient in problems of complex geometry than the well-known dual sampling method, especially when high-quality solutions are desired. Second, we present an improvement procedure that iteratively shortens and smooths a feasible coverage path; robot configurations are adjusted without violating any coverage con-straints. Third, we propose a modular algorithm that allows the simple components

### Directional Sensor Control for Maximizing Information Gain

"... We develop tractable solutions to the problem of controlling the directions of 2-D directional sensors for maximizing information gain corresponding to multiple targets in 2-D. The target locations are known with some uncertainty given by a joint prior distribution (Gaussian). A sensor generates a ( ..."

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We develop tractable solutions to the problem of controlling the directions of 2-D directional sensors for maximizing information gain corresponding to multiple targets in 2-D. The target locations are known with some uncertainty given by a joint prior distribution (Gaussian). A sensor generates a (noisy) measurement of a target only if the target lies within the field-of-view of the sensor, and the measurements from all the sensors are fused to form global estimates of target locations. This problem is hard to solve exactly—the computation time increases exponentially with the number of sensors. We develop heuristic methods to solve the problem approximately and provide lower and upper bounds on the optimal information gain. We improve the solutions from these heuristic approaches by formulating the problem as a dynamic programming problem and solving it using a rollout approach.

### Monitoring the Plane with Rotating Radars

"... Consider a set P of n points in the plane and n radars located at these points. The radars are rotating perpetually (around their centre) with identical constant speeds, continuously emitting pulses of radio waves (modelled as half-infinite rays). A radar can “locate ” (or detect) any object in the ..."

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Consider a set P of n points in the plane and n radars located at these points. The radars are rotating perpetually (around their centre) with identical constant speeds, continuously emitting pulses of radio waves (modelled as half-infinite rays). A radar can “locate ” (or detect) any object in the plane (e.g., using radio echo-location when its ray is incident to the object). We propose a model for monitoring the plane based on a system of radars. For any point p in the plane, we define the idle time of p, as the maximum time that p is “unattended ” by any of the radars. We study the following monitoring problem: What should the initial direction of the n radar rays be so as to minimize the maximum idle time of any point in the plane? We propose algorithms for specifying the initial directions of the radar rays and prove bounds on the idle time depending on the type of configuration of n points. For arbitrary sets P we give a O(n logn) time algorithm guaranteeing a O(1/ n) upper bound on the idle time, and a O(n6 / ln3 n) time algorithm with associated O(logn/n) upper bound on the idle time. For a convex set P, we show a O(n logn) time algorithm with associated O(1/n) upper bound on the idle time. Further, for any set P of points if the radar rays are assigned a direction independently at random with the uniform distribution then we can prove a tight Θ(lnn/n) upper and lower bound on the idle time with high probability.

### Continuous surveillance of points by rotating floodlights

"... Let P and F be sets of n ≥ 2 and m ≥ 2 points in a plane, respectively. We study the problem of finding the minimum angle α ∈ [2pi/m, 2pi] such that one can install at each point of F a stationary rotating floodlight with illumination angle α, initially oriented in a suitable direction, in such a wa ..."

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Let P and F be sets of n ≥ 2 and m ≥ 2 points in a plane, respectively. We study the problem of finding the minimum angle α ∈ [2pi/m, 2pi] such that one can install at each point of F a stationary rotating floodlight with illumination angle α, initially oriented in a suitable direction, in such a way that, at all times, every target point of P is illuminated by at least one floodlight. All floodlights rotate clockwise at unit speed. We provide bounds for the case in which the elements of P ∪ F are on a given line, and present exact results for the case in the plane in which we have two floodlights and many target points. We further consider the non-rotating version of the problem and look for the minimum angle α such that one can install a non-rotating floodlight with illumination angle α at each point of F, in such a way that every target point of P is illuminated by at least one floodlight. We show that this problem is NP-hard and hard to approximate.