The Univariate Closure Conditions of All Fully Parallel Planar Robots Derived From a Single Polynomial

Rojas, Nicolás; Thomas, Federico

doi:10.1109/tro.2013.2242376

Cited by 9 publications

(6 citation statements)

References 11 publications

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“…Proposed. Recently many mathematical techniques are proposed for the purpose of monitoring the changing environment [17], multirobot navigation [18], motion tracking [19], self-collision avoidance [20], blind juggler control [21], precise positioning [22], distant control [23], and motion grammar description [24]. In most proposals, the algorithm is complex [17][18][19][20], and/or the time derivatives are applied to the parameter analysis [20,21].…”

Section: Advantage Of the Methodsmentioning

confidence: 99%

“…On the other hand, the use of many controllable degrees of freedom (DOF) [19,20,22] leads us to a large RMS of errors. Polynomial formalism for the position control [23] requests many topological definitions to realize reliable forward kinematics. Application of motion grammar to robots [24] also requests many possible logical patterns to avoid undesirable actions.…”

Section: Advantage Of the Methodsmentioning

confidence: 99%

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Feasibility Investigation of Obstacle-Avoiding Sensors Unit without Image Processing

Ōmura¹,

Masuda²,

Mimura

2013

Journal of Sensors

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Feasibility of a simple method to detect step height, slope angle, and trench width using four infrared-light-source PSD range sensors is examined, and the reproducibility and accuracy of characteristic parameter detection are also examined. Detection error of upward slope angle is within 2.5 degrees, while it is shown that the detection error of downward slope angle exceeding 20 degrees is very large. In order to reduce such errors, a method to improve range-voltage performance of a range sensor is proposed, and its availability is demonstrated. We also show that increase in trial frequency is a better way, although so as not to increase the detection delay. Step height is identified with an error of ±1.5 mm. It is shown that trench width cannot be reliably measured at this time. It is suggested that an additional method is needed if we have to advance the field of obstacle detection.

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Section: Advantage Of the Methodsmentioning

confidence: 99%

Section: Advantage Of the Methodsmentioning

confidence: 99%

Feasibility Investigation of Obstacle-Avoiding Sensors Unit without Image Processing

Ōmura¹,

Masuda²,

Mimura

2013

Journal of Sensors

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“…Distance constraints provide intuitive geometric insights on aspects of the motion analysis problem which are difficult to discern otherwise. Moreover, these geometric insights allow deriving solutions common to problems that otherwise have to be treated case-by-case [33,47,46].…”

Section: Introductionmentioning

confidence: 99%

Distance Geometry in Active Structures

Porta

Rojas

Thomas

2018

Intelligent Systems, Control and Automation: Science and Engineering

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Distance constraints are an emerging formulation that offers intuitive geometrical interpretation of otherwise complex problems. It has applications in problems such as position and singularity analysis and path planning of mechanisms and structures. This paper reviews the recent advances in Distance Geometry providing a unified view of these apparently disparate problems. This survey reviews algebraic and numerical techniques and up to our knowledge, it is the first attempt to summarize the different approaches relaying in distance-based formulations.

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“…It provides a formulation invariant to the reference frame and, therefore, it gives geometric insights on different problems that remain concealed when using Cartesian geometry. These insights allow deriving solutions common to problems that otherwise have to be treated on a case-by-case basis [ 6 ]. Due to its generality, Distance Geometry finds application in many fields, including biochemistry [ 7 ], nano-technology [ 8 ], inverse/direct kinematics of serial/parallel robots [ 9 ], singularity analysis [ 10 ], or fusion of sensor data [ 11 ].…”

Section: Introductionmentioning

confidence: 99%

Sensor Localization from Distance and Orientation Constraints

Porta¹,

Rull²,

Thomas³

2016

Sensors

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The sensor localization problem can be formalized using distance and orientation constraints, typically in 3D. Local methods can be used to refine an initial location estimation, but in many cases such estimation is not available and a method able to determine all the feasible solutions from scratch is necessary. Unfortunately, existing methods able to find all the solutions in distance space can not take into account orientations, or they can only deal with one- or two-dimensional problems and their extension to 3D is troublesome. This paper presents a method that addresses these issues. The proposed approach iteratively projects the problem to decrease its dimension, then reduces the ranges of the variable distances, and back-projects the result to the original dimension, to obtain a tighter approximation of the feasible sensor locations. This paper extends previous works introducing accurate range reduction procedures which effectively integrate the orientation constraints. The mutual localization of a fleet of robots carrying sensors and the position analysis of a sensor moved by a parallel manipulator are used to validate the approach.

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The Univariate Closure Conditions of All Fully Parallel Planar Robots Derived From a Single Polynomial

Cited by 9 publications

References 11 publications

Feasibility Investigation of Obstacle-Avoiding Sensors Unit without Image Processing

Feasibility Investigation of Obstacle-Avoiding Sensors Unit without Image Processing

Distance Geometry in Active Structures

Sensor Localization from Distance and Orientation Constraints

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