Computing a Projection Operator onto the Null Space of a Linear Imaging Operator: Tutorial

2022 ◽  
Author(s):  
Joseph Kuo ◽  
Jason Granstedt ◽  
Umberto Villa ◽  
Mark anastasio
Keyword(s):  
Projection Operator ◽  
Null Space

Learning a projection operator onto the null space of a linear imaging operator

2021 ◽  
Author(s):  
Joseph Kuo ◽  
Jason L. Granstedt ◽  
Umberto Villa ◽  
Mark A. Anastasio
Keyword(s):  
Projection Operator ◽  
Null Space

Effective secondary task execution of redundant manipulators

Robotica ◽  
1998 ◽  
Vol 16 (4) ◽  
pp. 457-462 ◽  
Author(s):  
Jadran Lenarčič
Keyword(s):  
Projection Operator ◽  
Secondary Task ◽  
Numerical Experiments ◽  
Null Space ◽  
Numerical Procedure ◽  
Redundant Manipulators ◽  
Space Operator ◽  
Task Execution ◽  
Weighting Matrix ◽  
Space Projection

In standard pseudoinverse-based approaches to treat redundant manipulators, the vector of joint increments that corresponds to a desired motion in the space of the secondary task is projected in the Jacobian null space associated with the primary task. In general, this projection may distort the projected vector, so that the secondary task may not adequately be executed. A usual remedy is to rotate the null space projection operator by using a special-purpose weighting matrix. The problem, however, is that this rotation cannot be enforced arbitrarily since it influences the manipulator's performance. In our work we propose an algorithm that is independent on the chosen null space operator and always provides the best attainable motion in the space of the secondary task. Hence, the secondary task is executed more efficiently and the numerical procedure is more robust. A series of numerical experiments confirmed these results.

On the Representation of a Basis for the Null Space.

1983 ◽  
Author(s):  
P. E. Gill ◽  
W. Murray ◽  
M. A. Saunders ◽  
M. H. Wright
Keyword(s):  
Null Space

scholarly journals Interference Cancellation Based Spectrum Sharing for Massive MIMO Communication Systems

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3584
Author(s):  
Milembolo Miantezila Junior ◽  
Bin Guo ◽  
Chenjie Zhang ◽  
Xuemei Bai
Keyword(s):  
Interference Cancellation ◽  
Communication Systems ◽  
Spectrum Sharing ◽  
Null Space ◽  
Base Station ◽  
Base Stations ◽  
Small Cells ◽  
Data Traffic ◽  
New Approach ◽  
Lte Advanced

Cellular network operators are predicting an increase in space of more than 200 percent to carry the move and tremendous increase of total users in data traffic. The growing of investments in infrastructure such as a large number of small cells, particularly the technologies such as LTE-Advanced and 6G Technology, can assist in mitigating this challenge moderately. In this paper, we suggest a projection study in spectrum sharing of radar multi-input and multi-output, and mobile LTE multi-input multi-output communication systems near m base stations (BS). The radar multi-input multi-output and mobile LTE communication systems split different interference channels. The new approach based on radar projection signal detection has been proposed for free interference disturbance channel with radar multi-input multi-output and mobile LTE multi-input multi-output by using a new proposed interference cancellation algorithm. We chose the channel of interference with the best free channel, and the detected signal of radar was projected to null space. The goal is to remove all interferences from the radar multi-input multi-output and to cancel any disturbance sources from a chosen mobile Communication Base Station. The experimental results showed that the new approach performs very well and can optimize Spectrum Access.

Effects of Dynamic Model Errors in Task-Priority Operational Space Control

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Paolo Di Lillo ◽  
Gianluca Antonelli ◽  
Ciro Natale
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Null Space ◽  
Control Algorithms ◽  
Model Errors ◽  
Operational Space ◽  
Dynamic Level ◽  
Concurrent Tasks ◽  
Modeling Errors

SUMMARY Control algorithms of many Degrees-of-Freedom (DOFs) systems based on Inverse Kinematics (IK) or Inverse Dynamics (ID) approaches are two well-known topics of research in robotics. The large number of DOFs allows the design of many concurrent tasks arranged in priorities, that can be solved either at kinematic or dynamic level. This paper investigates the effects of modeling errors in operational space control algorithms with respect to uncertainties affecting knowledge of the dynamic parameters. The effects on the null-space projections and the sources of steady-state errors are investigated. Numerical simulations with on-purpose injected errors are used to validate the thoughts.

Manipulator system designs for drawing random objects through point cloud posture estimation

2021 ◽  
pp. 095440542097946
Author(s):  
Ching-Chang Wong ◽  
Hsuan Ming Feng ◽  
Yu-Cheng Lai ◽  
Hsiang-Yun Chen
Keyword(s):  
Point Cloud ◽  
Null Space ◽  
Robot Manipulator ◽  
Search Algorithm ◽  
Movement Control ◽  
Control Policy ◽  
Device Management ◽  
Redundant Robot ◽  
Better Regulation ◽  
The Right

This paper designed a 7-DOF redundant robot manipulator that can flexibly and efficiently pick-up random objects. The developed 7-DOF machine with an additional redundancy achieved great progress in terms of flexibility and efficiency in the operational space. A robot operating system (ROS) was used to configure the manipulator system’s software modules, supporting convenient system interface, appropriate movement control policy, and powerful hardware device management for better regulation of the manipulator’s motions. A 3D type Point Cloud Library (PCL) was utilized to perform a novel point cloud image pre-processing method that did not only reduce the point cloud number but also maintained the original quality. The results of the experiment showed that the estimation speed in object detection and recognition procedure improved significantly. The redundant robot manipulator architecture with the two-stage search algorithm was able to find the optimal null space. Suitable parameters in D-H transformation of forward kinematics were selected to efficiently control and position the manipulator in the right posture. Meanwhile, the reverse kinematics estimated all angles of the joints through the known manipulator position, orientation, and redundancy. Finally, motion panning implementation of manipulator rapidly and successfully reached the random object position and automatically drew it up to approximate the desired target.

scholarly journals An Enhanced Smoothed L0-Norm Direction of Arrival Estimation Method Using Covariance Matrix

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4403
Author(s):  
Ji Woong Paik ◽  
Joon-Ho Lee ◽  
Wooyoung Hong
Keyword(s):  
Covariance Matrix ◽  
Phased Array ◽  
Null Space ◽  
Estimation Method ◽  
Direction Of Arrival ◽  
Estimation Algorithm ◽  
Doa Estimation ◽  
Direction Of Arrival Estimation ◽  
Improve Performance ◽  
Space Projection

An enhanced smoothed l0-norm algorithm for the passive phased array system, which uses the covariance matrix of the received signal, is proposed in this paper. The SL0 (smoothed l0-norm) algorithm is a fast compressive-sensing-based DOA (direction-of-arrival) estimation algorithm that uses a single snapshot from the received signal. In the conventional SL0 algorithm, there are limitations in the resolution and the DOA estimation performance, since a single sample is used. If multiple snapshots are used, the conventional SL0 algorithm can improve performance in terms of the DOA estimation. In this paper, a covariance-fitting-based SL0 algorithm is proposed to further reduce the number of optimization variables when using multiple snapshots of the received signal. A cost function and a new null-space projection term of the sparse recovery for the proposed scheme are presented. In order to verify the performance of the proposed algorithm, we present the simulation results and the experimental results based on the measured data.

scholarly journals Computing the shape gradient of stellarator coil complexity with respect to the plasma boundary

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Arthur Carlton-Jones ◽  
Elizabeth J. Paul ◽  
William Dorland
Keyword(s):  
Null Space ◽  
Radial Distance ◽  
Plasma Boundary ◽  
Optimization Approach ◽  
Surface Parameters ◽  
Fixed Boundary ◽  
Plasma Surface ◽  
Shape Gradient ◽  
Derivative Free ◽  
Boundary Optimization

Coil complexity is a critical consideration in stellarator design. The traditional two-step optimization approach, in which the plasma boundary is optimized for physics properties and the coils are subsequently optimized to be consistent with this boundary, can result in plasma shapes which cannot be produced with sufficiently simple coils. To address this challenge, we propose a method to incorporate considerations of coil complexity in the optimization of the plasma boundary. Coil complexity metrics are computed from the current potential solution obtained with the REGCOIL code (Landreman, Nucl. Fusion, vol. 57, 2017, 046003). While such metrics have previously been included in derivative-free fixed-boundary optimization (Drevlak et al., Nucl. Fusion, vol. 59, 2018, 016010), we compute the local sensitivity of these metrics with respect to perturbations of the plasma boundary using the shape gradient (Landreman & Paul, Nucl. Fusion, vol. 58, 2018, 076023). We extend REGCOIL to compute derivatives of these metrics with respect to parameters describing the plasma boundary. In keeping with previous research on winding surface optimization (Paul et al., Nucl. Fusion, vol. 58, 2018, 076015), the shape derivatives are computed with a discrete adjoint method. In contrast with the previous work, derivatives are computed with respect to the plasma surface parameters rather than the winding surface parameters. To further reduce the resolution required to compute the shape gradient, we present a more efficient representation of the plasma surface which uses a single Fourier series to describe the radial distance from a coordinate axis and a spectrally condensed poloidal angle. This representation is advantageous over the standard cylindrical representation used in the VMEC code (Hirshman & Whitson, Phys. Fluids, vol. 26, 1983, pp. 3553–3568), as it provides a uniquely defined poloidal angle, eliminating a null space in the optimization of the plasma surface. In comparison with previous spectral condensation methods (Hirshman & Breslau, Phys. Plasmas, vol. 5, 1998, p. 2664), the modified poloidal angle is obtained algebraically rather than through the solution of a nonlinear optimization problem. The resulting shape gradient highlights features of the plasma boundary that are consistent with simple coils and can be used to couple coil and fixed-boundary optimization.

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