An Analytic Solution for Minimum-Norm Rate Coordination in Redundant Manipulators

1991 ◽  
Author(s):  
Hareendra Varma ◽  
Ming Z. Huang
Keyword(s):  
Solution Space ◽  
Geometric Interpretation ◽  
Alternative Formulation ◽  
Redundant Manipulators ◽  
Minimum Norm ◽  
Redundancy Resolution ◽  
Coordination Problem ◽  
Efficient Alternative ◽  
Novel Method ◽  
Pass Through

Abstract In this paper, we present a novel method which results in efficient minimum norm solution for the rate coordination problem in redundant manipulators. The theory is developed based on a geometric interpretation that, for minimum norm criterion, vectors orthogonal to constraint space should pass through the origin of the solution space. It is shown that for any spacial manipulator with 1, 2 or 3 degrees of redundancy, the minimum norm rate solution can be derived in analytic closed form. The method offers an equivalent but much more efficient alternative to using the pseudoinverse in redundancy resolution and, in fact, is applicable to any underdetermined linear system. An alternative formulation of pseudo-inverse arrived at in the course of the development is also presented.

A Note on Trajectory Planning for Conservative Motion of Redundant Manipulators

1998 ◽  
Author(s):  
Younker R. Chyu ◽  
Shin-Min Song
Keyword(s):  
Trajectory Planning ◽  
Time Domain ◽  
Closed Loop ◽  
Motion Trajectory ◽  
Redundant Manipulators ◽  
Minimum Norm ◽  
Redundant Manipulator ◽  
Tracking Errors ◽  
Pass Through ◽  
Arbitrary Trajectory

Abstract The conservative motion of a redundant manipulator has been a subject of research for many years. Up to the present time, a method which guarantees conservative motion for a redundant manipulator tracing an arbitrary trajectory has not been presented. Moreover, the implementation of any conservative motion trajectory planning in discrete time domain has not been adequately addressed. In this paper, a trajectory planning method which guarantees conservative motion and preserves minimum norm of joint rates for a redundant manipulator tracing a closed-loop trajectory is presented. This method includes two intermediate via points in each incremental movement so that the manipulator can precisely pass through, with constant joint accelerations, all incremental positions with minimum jerks. The tracking errors exist only at the via points but not at the incremental points. Thus, conservative motion is ensured. The overall tracking errors can be reduced by simply selecting a smaller increment. The presented method is simulated with a three-linked, planar redundant manipulator and the results are discussed.

GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-16
Author(s):  
Evgeniy Konopatskiy
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Analytical Description ◽  
Geometric Interpretation ◽  
Affine Geometry ◽  
Mathematical Apparatus ◽  
Multidimensional Interpolation ◽  
Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

Investigating the potential of redundant manipulators in narrow channels

2020 ◽  
pp. 095440622096451
Author(s):  
Ashish Singla ◽  
Jyotindra Narayan ◽  
Himanshu Arora
Keyword(s):  
Case Studies ◽  
Fuzzy Inference ◽  
Redundant Manipulators ◽  
Redundancy Resolution ◽  
Inference System ◽  
Narrow Channels ◽  
First Case ◽  
Task Priority ◽  
Patient Side

In this paper, an attempt has been made to investigate the potential of redundant manipulators, while tracking trajectories in narrow channels. The behavior of redundant manipulators is important in many challenging applications like under-water welding in narrow tanks, checking the blockage in sewerage pipes, performing a laparoscopy operation etc. To demonstrate this snake-like behavior, redundancy resolution scheme is utilized using two different approaches. The first approach is based on the concept of task priority, where a given task is split and prioritize into several subtasks like singularity avoidance, obstacle avoidance, torque minimization, and position preference over orientation etc. The second approach is based on Adaptive Neuro Fuzzy Inference System (ANFIS), where the training is provided through given datasets and the results are back-propagated using augmentation of neural networks with fuzzy logics. Three case studies are considered in this work to demonstrate the redundancy resolution of serial manipulators. The first case study of 3-link manipulator is attempted with both the approaches, where the objective is to track the desired trajectory while avoiding multiple obstacles. The second case study of 7-link manipulator, tracking trajectory in a narrow channel, is investigated using the concept of task priority. The realistic application of minimum-invasive surgery (MIS) based trajectory tracking is considered as the third case study, which is attempted using ANFIS approach. The 5-link spatial redundant manipulator, also known as a patient-side manipulator being developed at CSIR-CSIO, Chandigarh is used to track the desired surgical cuts. Through the three case studies, it is well demonstrated that both the approaches are giving satisfactory results.

scholarly journals Direct visualization of virus removal process in hollow fiber membrane using an optical microscope

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Miku Ayano ◽  
Yoshiyuki Sawamura ◽  
Tomoko Hongo-Hirasaki ◽  
Takayuki Nishizaka
Keyword(s):  
Hollow Fiber ◽  
Hollow Fiber Membrane ◽  
Imaging Techniques ◽  
Basic Research ◽  
Optical Microscope ◽  
Regenerated Cellulose ◽  
Fiber Membrane ◽  
Virus Removal ◽  
Novel Method ◽  
Pass Through

AbstractVirus removal filters developed for the decontamination of small viruses from biotherapeutic products are widely used in basic research and critical step for drug production due to their long-established quality and robust performance. A variety of imaging techniques have been employed to elucidate the mechanism(s) by which viruses are effectively captured by filter membranes, but they are limited to ‘static’ imaging. Here, we propose a novel method for detailed monitoring of ‘dynamic process’ of virus capture; specifically, direct examination of biomolecules during filtration under an ultra-stable optical microscope. Samples were fluorescently labeled and infused into a single hollow fiber membrane comprising cuprammonium regenerated-cellulose (Planova 20N). While proteins were able to pass through the membrane, virus-like particles (VLP) accumulated stably in a defined region of the membrane. After injecting the small amount of sample into the fiber membrane, the real-time process of trapping VLP in the membrane was quantified beyond the diffraction limit. The method presented here serves as a preliminary basis for determining optimum filtration conditions, and provides new insights into the structure of novel fiber membranes.

Local torque minimization for redundant manipulators: a correct formulation

Robotica ◽  
1996 ◽  
Vol 14 (2) ◽  
pp. 235-239 ◽  
Author(s):  
Shugen Ma ◽  
Dragomir N. Nenchev
Keyword(s):  
Redundant Manipulators ◽  
Redundancy Resolution ◽  
Instability Problem ◽  
Correct Formulation ◽  
Joint Velocity ◽  
Recent Formulation ◽  
Joint Acceleration ◽  
Stable Scheme

SUMMARYLocal torque minimization for redundant manipulators has been considered by using a redundancy resolution approach. Since its initial formulation, however, proposed solutions have been plagued by performance instabilities. Till now, the reason was not clear. In this paper it is shown that the instability problem occurred because of incorrect formulation. A correct formulation is proposed, which is used to analyze the reason for instability. Special attention is paid to joint acceleration terms at the selfmotion manifold. This helps explaining the recent formulation of a stable scheme based on local joint velocity minimization in terms of torque. The results obtained. are related to dynamic redundancy resolution in general.

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