Overcoming Kinematic Singularities with the Filtered Inverse Approach

Vargas, Lucas V.; Leite, Antonio C.; Costa, Ramon R.

doi:10.3182/20140824-6-za-1003.01841

Cited by 13 publications

(12 citation statements)

References 14 publications

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“…An alternative solution to overcome the performance degradation of the kinematic control in the vicinity of singular configurations is to employ the recently proposed Filtered Inverse (FI) method [16]. From the FI method, we consider that the control law u uses a dynamically updated matrix Θ(t) instead of its inverse computed instantaneously as (J B a ) −1 such thatJ B a Θ = I.…”

Section: Dealing With Singularitiesmentioning

confidence: 99%

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Analysis of a moving remote center of motion for robotics-assisted minimally invasive surgery

Pham

Coutinho

Leite

et al. 2015

2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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This paper presents a novel control architecture for controlling a moving remote center of motion in addition to the end-effector motion during robotic surgery. In minimally invasive surgery, it is common to require that the point at which the robot enters the body, called the incision point or the trocar, does not allow for any lateral motion. It is generally considered that no motion should be applied to this point in order to avoid inflicting damage to the patient's skin. However, in surgery, the patient's body may be moving, for example due to breathing or the beating of the heart. In order to compensate for this motion-or if we for some other reason want to leverage the possible motion of the incision point to improve performance in any other way-we derive a new framework which allows us to actively control the motion both at the incision point and the end effector. The novelty of the approach lies in the possibility of controlling both the incision point and the end effector to follow a trajectory, and that we find a Jacobian matrix that satisfies the velocity constraints in both the end-effector and the incision point frames. This allows us to formulate a framework that is not only suited for control, but also for analyzing the condition number of the Jacobian and avoid any singular configurations that may arise either as a result of the constrained motion or the manipulator geometry. The approach is verified experimentally on a redundant industrial manipulator.

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Section: Dealing With Singularitiesmentioning

confidence: 99%

“…Notice that, in the particular case where the matrix to be inverted is constant, Θ can be interpreted as the output of a linear filter where the input is the true inverse. Finally, resorting to the FI method [16], the velocity control signal u can be defined in terms of the filtered inverse matrix Θ as:…”

Section: Dealing With Singularitiesmentioning

confidence: 99%

Analysis of a moving remote center of motion for robotics-assisted minimally invasive surgery

Pham

Coutinho

Leite

et al. 2015

2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

Self Cite

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“…Notice that the failure of this last assumption is a relevant research topic, which still remains as a challenging and open problem. An alternative solution to overcome the invertibility problem of the Jacobian matrix in the vicinity of a singularity is to resort to the so-called damped least-squares inverse algorithm or the newly proposed filtered inverse method [39,40]. Now, to simplify the analysis, let us consider first the kinematic control case, where the robot motion can be described by P q WD u and u 2 R n is the velocity control signal applied to the motor drive of the robot joints [39].…”

Section: Cascade Control Strategymentioning

confidence: 99%

Passivity‐based adaptive 3D visual servoing without depth and image velocity measurements for uncertain robot manipulators

Leite

Lizarralde

2016

Adaptive Control & Signal

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In this work, we consider the 3D visual tracking problem for a robot manipulator with uncertainties in the kinematic and dynamic models. The visual feedback is provided by a fixed and uncalibrated camera located above the robot workspace. The Cartesian motion of the robot end effector can be separated into a 1D motion parallel to the optical axis of the camera and a 2D motion constrained on a plane orthogonal to this axis. Thus, the control design can be simplified, and the overall visual servoing system can be partitioned in two almost-independent subsystems. Adaptive visual servoing schemes, based on a kinematic approach, are developed for image-based look-and-move systems allowing for both depth and planar tracking of a reference trajectory, without using image velocity and depth measurements. In order to include the uncertain robot kinematics and dynamics in the presented solution, we develop a cascade control strategy based on an indirect/direct adaptive method. The stability and convergence properties are analyzed in terms of Lyapunovlike functions and the passivity-based formalism. Numerical simulations including hardware-in-the-loop results, obtained with a robot manipulator and a web camera, are presented to illustrate the performance and feasibility of the proposed control scheme. and, therefore, the control system could exhibit degraded performance particularly when the robot is driven by direct-drive actuators or it has to perform high-speed tasks. Some exceptions can be found in earlier published works [16][17][18]. However, the proposals are applied only to the planar visual servoing problem, and their robot motion controllers based on the dynamic model require the measurement of the image velocity and, thus, the need of using an extra sensor. In addition, the measurement of the velocity for a moving target object from a sequence of images is impaired by the noisy image data, affecting the accuracy of the result [19,20].In this context, adaptive schemes for camera calibration without using visual velocity were proposed for 2D image-based visual servoing systems, with global stability properties under the assumption of exact knowledge of the robot mechanical parameters [21,22]. Adaptive control strategies for 2D visual tracking with uncertain robot manipulators were also developed, where the estimated Jacobian matrix of the camera-robot systems parameters has been simultaneously updated in an indirect manner [23]. Likewise, the uncertain Jacobian matrices related to the robot kinematics and the camera calibration parameters could be independently updated by using an indirect/direct adaptive schemes, respectively [24].Conversely, the robot motion control problem in a 3D Cartesian coordinate system has been addressed from the development of a 2-1/2-D visual servoing approach by using different choices of camera architectures [25,26]. As a restriction, some of the proposed solutions require the direct estimate of the depth information with respect to the camera frame, resorting to an off-line learning p...

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“…Uma outra solução, recente e promissora, é o método da Inversa Filtrada que é baseado na equação de cinemática diferencial e consiste em um algoritmo que estima dinamicamente a inversa da matriz Jacobiana, ao invés de computar a inversa instantaneamente [69]. O algoritmo possui a característica notável de ser robusto a singularidades e possuir apenas um parâmetro (i.e., um ganho de atualização) a ser sintonizado.…”

Section: -Cinemáticaunclassified

“…O algoritmo DLS utiliza um fator de amortecimento para tornar a inversão melhor condicionada, estabelecendo um compromisso entre a viabilidade e a exatidão da solução [40,41]. e o algorítimo da inversa filtrada [69].…”

Section: Algorítimos De Controleunclassified

Metodologia De Controle Para Mecanismos Paralelos Na Presença De Singularidades Cinemáticas

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Overcoming Kinematic Singularities with the Filtered Inverse Approach

Cited by 13 publications

References 14 publications

Analysis of a moving remote center of motion for robotics-assisted minimally invasive surgery

Analysis of a moving remote center of motion for robotics-assisted minimally invasive surgery

Passivity‐based adaptive 3D visual servoing without depth and image velocity measurements for uncertain robot manipulators

Metodologia De Controle Para Mecanismos Paralelos Na Presença De Singularidades Cinemáticas

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