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Nonsmooth Analysis, Convex Analysis, and their Applications to Motion Planning
, 1997
"... Nonsmooth analysis of a broad class of functions taking the form F (x) = min i f i (x), where each f i is a convex function. One element of this class of functions is the distance function, which measures the distance between a point and the nearest point on the nearest obstacle. Many motion plannin ..."
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Cited by 17 (6 self)
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Nonsmooth analysis of a broad class of functions taking the form F (x) = min i f i (x), where each f i is a convex function. One element of this class of functions is the distance function, which measures the distance between a point and the nearest point on the nearest obstacle. Many motion planning algorithms are based on the distance function, and thus rigorous analysis of the distance function can provide a better understanding of how to implement traditional motion planning algorithms. Finally, this paper enumerates some useful results in convex analysis. Keywords: Nonsmooth analysis, convex analysis, motion planning, roadmaps, Voronoi diagrams. 1. Introduction Robotic motion planning determines a path between two points q start and q goal , while avoiding obstacles fC i : i = 1; : : : ; ng. This one-dimensional path may exist in the robot's work space or in the robot's configuration space, the set of all robot locations and postures in a particular work space. Let W denote the ...
Pursuit-evasion in an unknown environment using gap navigation graphs
- In Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems
, 2004
"... In this paper we present an online algorithm for pursuitevasion in a unknown simply connected environment, for one pursuer that has minimal sensing and carries a set of stationary sentries that it can drop off and pick up during the pursuit. In our sensing model, the pursuer is only able to detect d ..."
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Cited by 17 (7 self)
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In this paper we present an online algorithm for pursuitevasion in a unknown simply connected environment, for one pursuer that has minimal sensing and carries a set of stationary sentries that it can drop off and pick up during the pursuit. In our sensing model, the pursuer is only able to detect discontinuities in depth information (gaps), and it is able to find all of the evaders without any explicit localization or geometric information, by using a Gap Navigation Tree. The strategy is based on growing an evader-free region, by reading “exploration” schedules from the Gap Navigation Tree, that is constructed online. We prove that a pursuer with k +1 sentries can clear any environment that could be cleared by k pursuers using the algorithm in [7], which required a complete map and perfect sensing. I.
The arctransversal median algorithm: an approach to increasing ultrasonic sensor accuracy
- In Proceedings of the IEEE International Conference on Robotics and Automation
, 1999
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A pursuit-evasion BUG algorithm
- In Proc. IEEE Int’l Conf. on Robotics and Automation
, 1954
"... We consider the problem of searching for an unpredictable moving target, using a robot that lacks a map of the environment, lacks the ability to construct a map, and has imperfect navigation ability. We present a complete algorithm, which yields a motion strategy for the robot that guarantees the el ..."
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Cited by 17 (10 self)
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We consider the problem of searching for an unpredictable moving target, using a robot that lacks a map of the environment, lacks the ability to construct a map, and has imperfect navigation ability. We present a complete algorithm, which yields a motion strategy for the robot that guarantees the elusive target will be detected, if such a strategy exists. It is assumed that the robot has an omnidirectional sensing device that is used to detect moving targets and also discontinuities in depth data in a 2D environment. We also show that the robot has the same problem-solving power as a robot that has a complete map and perfect navigation abilities. The algorithm has been implemented in simulation, and some examples are shown. 1
On comparing the power of robots
- International Journal of Robotics Research. Under review
"... Robots must complete their tasks in spite of unreliable actuators and limited, noisy sensing. In this paper, we consider the information requirements of such tasks. What sensing and actuation abilities are needed to complete a given task? Are some robot systems provably “more powerful, ” in terms of ..."
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Cited by 15 (7 self)
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Robots must complete their tasks in spite of unreliable actuators and limited, noisy sensing. In this paper, we consider the information requirements of such tasks. What sensing and actuation abilities are needed to complete a given task? Are some robot systems provably “more powerful, ” in terms of the tasks they can complete, than others? Can we find meaningful equivalence classes of robot systems? This line of research is inspired by the theory of computation, which has produced similar results for abstract computing machines. The basic idea is a dominance relation over robot systems that formalizes the idea that some robots are stronger than others. This comparison, which is based on the how the robots progress through their information spaces, induces a partial order over the set of robot systems. We prove some basic properties of this partial order and show that it is directly related to the robots’ ability to complete tasks. We give examples to demonstrate the theory, including a detailed analysis of a limited-sensing global localization problem. 1
Sensor Based Planning for a Planar Rod Robot
- In Proc. IEEE/SICE/RSJ Int. Conf. on Multisensor Fusion on Multisensor Fusion and Integration for Intelligent Systems
, 1996
"... Sensor based planning for rod-shaped robots is necessary for the realistic deployment of noncircular symmetric robots into unknown environments. To this end, the rod hierarchical generalized Voronoi graph (rod-HGVG), introduced in this paper, is a roadmap for rod-like robots. A key feature of this r ..."
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Cited by 14 (6 self)
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Sensor based planning for rod-shaped robots is necessary for the realistic deployment of noncircular symmetric robots into unknown environments. To this end, the rod hierarchical generalized Voronoi graph (rod-HGVG), introduced in this paper, is a roadmap for rod-like robots. A key feature of this roadmap is that it can be incrementally constructed using distance (range) information. This planning paradigm is an extension of previous work on sensor based planning for point robots.
Sensor Based Planning: Using a Honing Strategy and Local Map Method to Implement the Generalized Voronoi Graph
- In SPIE Conference on Systems and Manufacturing
, 1997
"... This work prescribes the procedures that are required to implement, on a conventional mobile robot, a sensor based motion planning algorithm based on the generalized Voronoi graph (GVG). The GVG isaroadmap of a static environment � recall that a roadmap is a one-dimensional representation of an envi ..."
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Cited by 11 (2 self)
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This work prescribes the procedures that are required to implement, on a conventional mobile robot, a sensor based motion planning algorithm based on the generalized Voronoi graph (GVG). The GVG isaroadmap of a static environment � recall that a roadmap is a one-dimensional representation of an environment which the robot can use to plan a path between any two points in that environment. Once the robot has constructed the roadmap, it has in essence explored the environment. This work describes some issues in incrementally constructing the GVG with a mobile robot with a ring of sonar sensors. Speci cally, we consider some issues in specularity and dead-reckoning error reduction.
Localization with limited sensing
- IEEE Transations on Robotics
, 2007
"... Abstract — Localization is a fundamental problem for many kinds of mobile robots. Sensor systems of varying ability have been proposed and successfully used to solve the problem. This paper probes the lower limits of this range by describing three extremely simple robot models and addressing the act ..."
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Cited by 10 (6 self)
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Abstract — Localization is a fundamental problem for many kinds of mobile robots. Sensor systems of varying ability have been proposed and successfully used to solve the problem. This paper probes the lower limits of this range by describing three extremely simple robot models and addressing the active localization problem for each. The robot, whose configuration is composed of its position and orientation, moves in a fully known simply connected polygonal environment. We pose the localization task as a planning problem in the robot’s information space, which encapsulates the uncertainty in the robot’s configuration. We consider robots equipped with (1) angular and linear odometers, (2) a compass and contact sensor, and (3) an angular odometer and contact sensor. We present localization algorithms for models 1 and 2 and show that no algorithm exists for model 3. An implementation with simulation examples is presented. Index Terms — information spaces, mobile robot localization, robots, robot sensing systems I.
Extending the path-planning horizon
, 2005
"... ii SINCE typical mobile robotic vehicles have mobility sensors (such as LADAR or stereo) that can only acquire data up to a few tens of meters, a navigation system has no knowledge about the world beyond this sensing horizon. As a result, path planners that rely only on this knowledge to compute pat ..."
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Cited by 10 (1 self)
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ii SINCE typical mobile robotic vehicles have mobility sensors (such as LADAR or stereo) that can only acquire data up to a few tens of meters, a navigation system has no knowledge about the world beyond this sensing horizon. As a result, path planners that rely only on this knowledge to compute paths are unable to anticipate obstacles sufficiently early and has no choice than to plan inefficient paths that trace obstacle boundaries. To alleviate this problem, We present an opportunistic navigation and view planning strategy that incorporates look-ahead sensing of possible obstacle configurations. This planning strategy is based on a “what-if ” analysis of hypothetical future configurations of the environment. Candidate vantage positions are evaluated based on their ability of observing anticipated obstacles. These vantage positions identified by this forward-simulation framework are used by the planner as intermediate waypoints. The validity of the strategy is supported by results from simulations as well as field experiments with a real robotic platform. These results also show that opportunistically significant reduction in path length can be achieved by using this framework.
Probabilistic localization with a blind robot. ICRA
, 2008
"... Abstract — Researchers have addressed the localization problem for mobile robots using many different kinds of sensors, including rangefinders, cameras, and odometers. In this paper, we consider localization using a robot that is virtually “blind”, having only a clock and contact sensor at its dispo ..."
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Cited by 10 (3 self)
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Abstract — Researchers have addressed the localization problem for mobile robots using many different kinds of sensors, including rangefinders, cameras, and odometers. In this paper, we consider localization using a robot that is virtually “blind”, having only a clock and contact sensor at its disposal. This represents a drastic reduction in sensing requirements, even in light of existing work that considers localization with limited sensing. We present probabilistic techniques that represent and update the robot’s position uncertainty and algorithms to reduce this uncertainty. We demonstrate the experimental effectiveness of these methods using a Roomba autonomous vacuum cleaner robot in laboratory environments. I.
