A Technique Based on Adaptive Extended Jacobians for Improving the Robustness of the Inverse Numerical Kinematics of Redundant Robots

Simas, Henrique; Gregorio, Raffaele Di

doi:10.1115/1.4042514

Cited by 13 publications

(4 citation statements)

References 35 publications

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“…Analysis has shown that use of the generalized inverse of Equation ( 8) leads to nonholonomic equations of redundancy resolution that create systematic noncyclicity of the manipulator [12,13], i.e., a periodic output trajectory maps into a nonperiodic input trajectory. While some effort has been devoted to creating generalized inverses that overcome these problems, e.g., [14,15] and references cited therein, no comprehensive result has been reported. A treatment based on concepts similar to those employed herein is shown to partially resolve the noncyclicity problem [16].…”

Section: Problems With Generalized-inverse-velocity-based Redundancy ...mentioning

confidence: 99%

Obstacle Avoidance in Operational Configuration Space Kinematic Control of Redundant Serial Manipulators

Peidro,

Haug

2023

Machines

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Kinematic control of redundant serial manipulators has been carried out for the past half century based primarily on a generalized inverse velocity formulation that is known to have mathematical deficiencies. A recently developed inverse kinematic configuration mapping is employed in an operational configuration space differentiable manifold formulation for redundant-manipulator kinematic control with obstacle avoidance. This formulation is shown to resolve deficiencies in the generalized inverse velocity formulation, especially for high-degree-of-redundancy manipulators. Tracking a specified output trajectory while avoiding obstacles for four- and twenty-degree-of-redundancy manipulators is carried out to demonstrate the effectiveness of the differentiable manifold approach for applications with a high degree of redundancy and to show that it indeed resolves deficiencies of the conventional generalized inverse velocity formulation in challenging applications.

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Section: Problems With Generalized-inverse-velocity-based Redundancy ...mentioning

confidence: 99%

Obstacle Avoidance in Operational Configuration Space Kinematic Control of Redundant Serial Manipulators

Peidro,

Haug

2023

Machines

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“…Using the Cholesky decomposition and the Ritz method, he proposed an optimal extended Jacobian IK algorithm. To keep robots far from singularities, Simas et al [13] proposed the algorithm of adaptive coefficients in constraint functions to obtain a good conditioning index of the extended Jacobian.…”

Section: A Related Workmentioning

confidence: 99%

A Novel Solution to the Inverse Kinematics Problem of General 7R Robots

et al. 2022

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Task and Motion Planning for a 7-DOF serial robot containing only revolute joints needs a fast and numerically stable inverse kinematics solution. The analytical methods are real-time, but they are robot dependent. Although the numerical methods based on inverse differential kinematics can solve the inverse kinematics problem (IKP) of 7R robots with arbitrary geometric parameters, their numerical stability is insufficient. Moreover, it is time-consuming for them to converge to a single solution that depends on the initial guess. The main innovation of this article is the development of a practical method for solving the IKP of general 7R robots. The proposed method can find multiple solutions and is also faster than the numerical method. It combines symbolic preprocessing, Sylvester dialytic elimination, and eigendecomposition. First, according to the Denavit-Hartenberg convention of geometric representation, a general kinematics model of a 7R manipulator is established. Secondly, the joint variables are separated by symbolic preprocessing, and then two symbolic matrices are obtained. After numerical substitution, a square matrix of polynomial coefficients is computed through Gaussian and Sylvester dialytic elimination. Finally, utilizing the eigendecomposition of the matrix restructured from the square matrix, the values of some variables are obtained, and then the remaining variables are solved by back-substitution. The simulation and experimental data are analyzed. The comparison results verify that the proposed method applies to solving the IKP of general 7R robots and is almost real-time, effective, and numerically stable.

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“…In particular, the Jacobian becomes singular even if the single task Jacobians are full rank [25]. Later, Simas et al proposed a method to adapt the coefficients describing the constraints included in the EJ in order to keep the robot far from singularities [26].…”

Section: Approaches Towards Robot Redundancymentioning

confidence: 99%

On the Modelling of Tethered Mobile Robots as Redundant Manipulators

2021

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Controlling a chain of tethered mobile robots (TMRs) can be a challenging task. This kind of system can be considered kinematically as an open-chain robotic arm where the mobile robots are considered as a revolute joint and the tether is considered as a variable length link, using a prismatic joint. Thus, the TMRs problem is decoupled into two parallel problems: the equivalent robotic manipulator control and the tether shape computation. Kinematic redundancy is exploited in order to coordinate the motion of all mobile robots forming the chain, expressing the constraints acting on the mobile robots as secondary tasks for the equivalent robotic arm. Implementation in the Gazebo simulation environment shows that the methodology is capable of controlling the chain of TMRs in cluttered environments.

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A Technique Based on Adaptive Extended Jacobians for Improving the Robustness of the Inverse Numerical Kinematics of Redundant Robots

Cited by 13 publications

References 35 publications

Obstacle Avoidance in Operational Configuration Space Kinematic Control of Redundant Serial Manipulators

Obstacle Avoidance in Operational Configuration Space Kinematic Control of Redundant Serial Manipulators

A Novel Solution to the Inverse Kinematics Problem of General 7R Robots

On the Modelling of Tethered Mobile Robots as Redundant Manipulators

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