A Survey of Applications of Interval Analysis to Robust Control

Vehı́, Josep; Ferrer, Inées; Saínz, Miguel

doi:10.3182/20020721-6-es-1901.00399

Cited by 4 publications

(2 citation statements)

References 64 publications

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“…IA has been used in a wide range of applications in robotics, e.g., mobile robot localization [30], trajectory planning [31], continuous solution of the inverse geometric model [32], robust control [33], [34], parameter estimation [35], [36], tolerance analysis and synthesis [37], [38], [39] or workspace computation [40], [41].…”

Section: A Background On Interval Analysismentioning

confidence: 99%

Dynamics-Based Algorithm for Reliable Assembly Mode Tracking in Parallel Robots

2020

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Finding the current pose of the end-effector of a parallel robot is a problem, since its forward geometric model generally has several solutions. Current methods to address this problem operate mainly under the assumption that the robot never changes its assembly mode nor gets close to Type 2 singularities.Nonetheless, recent works proved that a parallel robot can change its assembly mode thanks to dedicated trajectory generation and control. Such a feature allows increasing the operational workspace of such manipulators. Hence tracking correctly the end-effector pose while crossing Type 2 singularities, is mandatory for a practical usage of this workspace enhancement method. However, on Type 2 singularities several solutions of the forward geometric model merge, making current tracking methods ineffective.To fill this gap, we propose a two-step pose-tracking methodology: First, a differential inclusion based on kinematics and dynamics is solved. Second, joint measurements are used to tighten resulting enclosures. The effectiveness of this method is discussed thanks to experimental data gathered on a planar parallel robot.

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Section: A Background On Interval Analysismentioning

confidence: 99%

Dynamics-Based Algorithm for Reliable Assembly Mode Tracking in Parallel Robots

2020

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“…Thus, it can be very useful for reliable computations in boundederror context. Numerous applications of IA can be found in robotics [19] and control, such as mobile robot localization [20] [21], robot kinematic calibration [22], robust control [23], positioning precision analysis and synthesis [24] [25]. In parallel robotics in particular, methods to compute the aspects of the workspace have been discovered [26] [27].…”

Section: Introductionmentioning

confidence: 99%

Certified detection of parallel robot assembly mode under Type 2 singularity crossing trajectories

Koessler

Goldsztejn

Briot

2017

2017 IEEE International Conference on Robotics and Automation (ICRA)

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Increasing the size of operationnal workspace is one of the main problems parallel robots are faced with. Among all the proposed solutions to that, crossing Type 2 singularities using dedicated trajectory generation and multimodel controller has a great potential. Yet, this approach is not sufficient for the robot to operate autonomously, as assembly mode detection during the motion currently requires additional redundant information. To tackle this problem, we propose an algorithm based on Interval Analysis (IA) that is able to track the end-effector of the robot even under assembly mode change. IA-based solvers for the forward kinematic problem of parallel robots are well known, but they cannot be used under assembly mode change. Compared to those classical approaches, the major modification introduced is the tracking of end-effector velocity in addition to its pose. Using this new information of velocity, the algorithm is capable to monitor the assembly mode change of the robot happening when the singularities are crossed. The behavior and the reliability of this algorithm are analyzed experimentally on a five-bar planar parallel mechanism.

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Applications of Interval B&BT Methods

Kubica

2019

Interval Methods for Solving Nonlinear Constraint Satisfaction, Optimization and Similar Problems

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A Survey of Applications of Interval Analysis to Robust Control

Cited by 4 publications

References 64 publications

Dynamics-Based Algorithm for Reliable Assembly Mode Tracking in Parallel Robots

Dynamics-Based Algorithm for Reliable Assembly Mode Tracking in Parallel Robots

Certified detection of parallel robot assembly mode under Type 2 singularity crossing trajectories

Applications of Interval B&BT Methods

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