Singularity Analysis and Singularity Avoidance Trajectory Planning for Industrial Robots

Given m square matrices A/sub 1/, ..., A/sub m/, let A denote the set of all their convex combinations. Then the authors consider the problem of determining a member of A whose minimum singular value is the smallest. A related problem, known as robust nonsingularity problem, is to determine if every member of A is nonsingular. Clearly a solution to the authors' problem automatically solves the robust nonsingularity problem. Unfortunately, the robust nonsingularity problem has been demonstrated to be NP-hard which in turn makes the authors' problem NP-hard. To avoid this computational intractability, the authors provide an algorithm that computes a lower bound and an upper bound on the least minimum singular value within a prescribed tolerance. Of course, if the prescribed tolerance is set to zero then the authors' algorithm would compute the least minimum singular value. The authors' method makes use of the so-called simplicial algorithms. >

When the system reaches the static voltage stability limit point, Jacobian matrix is singular. By checking if minimum singular value is zero, its very easy to determine whether or not Jacobian matrix is singular. So the minimum singular value of Jacobian matrix can reflects the degree of system voltage stability effectively. Firstly this paper introduces singular value decomposition, analyses load characteristic and excitation limits involved in this method and examples on PSD-FDS are demonstrated. At last, suggestion on voltage stability monitoring by minimum singular value is proposed.

The use of the minimum singular value (MSV) of the load flow Jacobian has been proposed as a security index for monitoring how close the operating condition of a power system is to a voltage instability. However, direct computation of singular value decomposition (SVD) is a very time consuming task. P.A. Lof et al. (see IEEE Trans. on Power Systems, vol.7, no.1, p.54-64, 1992) report on an elegant and an efficient algorithm for the computation of the MSV of the load flow Jacobian matrix (LFJM). This algorithm greatly reduces the time required for the computation of the MSV. In this letter, a new starting condition that reduces the computation time for the iterative process described by Lof et al. is proposed.

Singularity analysis of the Canadarm2

Accurate Detection and Smoothness-Oriented Avoidance Method of Singularity in 5-Axis CNC Machining

In this paper the static voltage stability index has been identified by minimum singular value of the power flow jacobian matrix. The system security in power system models by the scalar magnitude of a voltage stability index may be a very difficult task. When we are taking account of reactive power generation limits it is very difficult to predict stability index at voltage collapse points. Here a quick method is used to calculate the minimum singular value and the corresponding left and right singular vectors are presented. This developed algorithm is very useful in online because it required small amount of computation time. For different patterns of load and generation are increases, to determine voltage collapse point. For solving the maximum loading problem an optimal power flow approach was used with these points the MSV is calculated and used for training and testing the Neural Network.

In this work we examine the behavior of the minimum singular value of random Vandermonde matrices. In particular, we prove that the minimum singular value s 1 (N) is at most N exp(−C√N) where N is the dimension of the matrix and C is a constant. Furthermore, the value of the constant C is determined explicitly. The main result is obtained in two different ways. One approach uses techniques from stochastic processes and in particular, a construction related to the Brownian bridge. The other one is a more direct analytical approach involving combinatorics and complex analysis. As a consequence, we obtain a lower bound on the maximum absolute value of a random polynomial on the unit circle, which may be of independent mathematical interest.

Singularity analysis is one of the basic problems for parallel manipulators. When a manipulator moves in a singular configuration, the motion and transmission performance are poor. In certain serious cases, the normal operation could be damaged. Based on the topology structure and kinematics analysis of a 2(3HUS+S) parallel manipulator, the Jacobian matrices were established. Then, the singular locus surface was obtained by numerical simulation. In addition, the relationship between the motion path curve and the singular locus surface was analyzed. In this study, α, β, and γ are the attitude angles that describe the motion of moving platforms. There is a nonsingular attitude space in singular locus surfaces, and the singular locus surface is a single surface in a small attitude angle range. The nonsingular attitude space increases as the absolute value of γ increases, and singularity could be avoided when γ is large. Furthermore, the motion path curve passes through the singular locus surface two times, and the two intersection points are consistent with the positions where the motion dexterity is equal to zero. This study provides new insights on the singularity analysis of parallel manipulators, particularly for the structure parameter optimization of the nonsingular attitude space.

To solve the safety problems caused by the restriction of interaction space and the singular configuration of rehabilitation robot in terminal traction upper limb rehabilitation training, a trajectory planning and tracking control scheme for rehabilitation training is proposed. The human-robot safe interaction space was obtained based on kinematics modeling and rehabilitation theory, and the training trajectory was planned based on the occupational therapy in rehabilitation medicine. The singular configuration of the rehabilitation robot in the interaction space was avoided by exponential adaptive damped least square method. Then, a nonlinear controller for the upper limb rehabilitation robot was designed based on the backstepping control method. Radial basis function neural network was used to approximate the robot model information online to achieve model-free control. The stability of the controller was proved by Lyapunov stability theory. Experimental results demonstrate the effectiveness and superiority of the proposed singular avoidance control scheme.

The paper describes the automation of the shoe grinding process using an industrial robot. One of the major problems of flexible automation using industrial robots is how to avoid joint limitations, singular configuration and obstacles. This problem can be solved using kinematically redundant robots. Due to the circular shape of the grinding disc, the robot becomes kinematically redundant. This task redundancy was efficiently handled using virtual mechanism approach, where the tool is described as a serial mechanism.

UPFC control parameter identification for effective power oscillation damping

A pole-free formulation of the modal field-matching technique (MFMT) as applied to eigenvalue problems in electromagnetics is presented in this paper. The poles in the determinantal equation are systematically eliminated, without requiring previous knowledge of their locations or nature, resulting in well-behaved determinants. The minimum singular value in a singular-value decomposition of the pole-free matrix exhibits much wider dips than that obtained from the standard MFMT. The pole-free formulation is applied to determine the cutoff wavenumbers of a ridged waveguide to demonstrate its validity and efficiency.

This paper proposes a method to select the supplementary input signal for systems equipped with static synchronous compensators (STATCOM) to damp inter-area mode(s). Input-output observability-controllability analysis, minimum singular value, right half plane zeros and relative gain array are used to assess the most appropriate supplementary input signal. The open-loop frequency of the system is shown to examine the sensitivity of the selected supplementary input signal to inter-area mode. The method is applied to select the input signal for a small power system equipped with a single STATCOM and for a large power system equipped with two STATCOMs.

The signal sample tool which is called measurement matrix or observation matrix is very important for the theory of compressive sensing. Decreasing the correlation between any two different columns of the information operator is the basis of the design and optimization of the measurement matrix. Based on it, the non-diagonal elements of the upper triangular matrix of the QR decomposition of information operator was set to zero to increase its minimum singular value and decrease the column correlation of information operator, and thus this method can enhance the performance of the measurement matrix. Experiments illustrate that when the algorithm of this paper is utilized, the recovery error of signals and images are both diminished.

In order to adjust telescope mirrors with high precision, a 3 cylindrical-prismatic-spherical (CPS) parallel micro-manipulator with 6 degrees-of-freedom (DOF) and partial decoupling is proposed. Structure characteristics of the micro-manipulator were analyzed and the kinematic equations were derived based on Euler method. To avoid tedious derivation, Jacobian matrix with screw theory representing the input and output relation of micro-manipulator is established by using velocity influence coefficient method. Combining topological structure characteristics of the 3-CPS parallel micro-manipulator, the solving procedures of workspace are obtained. Moreover, the position workspace with a given orientation and the orientation workspace with a given translation position are constructed by numerical simulations. The workspace range is chosen as the optimization goal of structure parameters, and the circumcircle radius ratio of base and moving platform and the lengths of each sub-link are optimized. The maximum condition number and the minimum singular value are chosen as the precision indexes to analyze the precision performance of the workspace. Then, the properties of the position workspaces with various orientations and the orientation workspaces with various positions are simulated numerically, and the simulation results prove that the 3-CPS parallel micro-manipulator has an ability to achieve high precision operations. This research provides a workspace modeling and optimization method for the practical application in telescope mirror adjustment or other fields requiring high precision.