Singularity Avoidance Research Articles

Quantum cosmology

AbstractWe give an introduction into quantum cosmology with emphasis on its conceptual parts. After a general motivation, we review the formalism of canonical quantum gravity on which discussions of quantum cosmology are usually based. We then present the minisuperspace Wheeler–DeWitt equation and elaborate on the problem of time, the imposition of boundary conditions, the semiclassical approximation, the origin of irreversibility, and singularity avoidance. Restriction is made to the framework of quantum geometrodynamics.

Singular Configuration Analysis and Singularity Avoidance with Application in an Intelligent Robotic Manipulator

Recently, robotic sensor systems have gained more attention annually in complex system sense strategies. The robotic sensors sense the information from itself and the environment, and fuse information for the use of perception, decision, planning, and control. As an important supplement to traditional industrial robots, co-bots (short for co-working robots) play an increasingly vital role in helping small and medium-sized enterprises realize intelligent manufacturing. They have high flexibility and safety so that they can assist humans to complete highly repetitive and high-precision work. In order to maintain robot safe operation in the increasing complex working environment and human–computer intelligent interactive control, this paper is concerned with the problem of applicant accuracy analysis and singularity avoidance for co-bots. Based on the dynamic model with load and torque sensors, which is used to detect the external force at the end of the robot, this paper systematically analyzes the causes of singularity phenomenon in the robot motion control. The inverse solution is obtained by analytical method and numerical method, respectively. In order to ensure the smooth and safe operation in the whole workspace, it is necessary for a robot to avoid singularity. Singularity avoidance schemes are utilized for different control tasks, including point-to-point control and continuous path control. Corresponding simulation experiments are designed to verify the effectiveness of different evasion schemes, in which the advantages and disadvantages are compared and analyzed.

Singularity avoidance adaptive output‐feedback fixed‐time consensus control for multiple autonomous underwater vehicles subject to nonlinearities

AbstractThis article investigates the singularity avoidance adaptive output‐feedback fixed‐time consensus control problem for multiple autonomous underwater vehicles (AUVs) subject to nonlinearities. A distributed state observer is designed to reconstruct the unmeasurable coupling states of each AUV system. In order to handle the unknown nonlinearities of the multi‐AUV systems, the fuzzy logic systems are adopted to approximate unknown hydrodynamic parameters. By combining adaptive fixed‐time control with backstepping technology, an adaptive singularity avoidance fixed‐time consensus control algorithm is developed, where a new error switching mechanism is designed for avoiding the singularity problem caused by the differentiation of the virtual control law. Subsequently, a singularity avoidance distributed adaptive output‐feedback fixed‐time fuzzy controller is presented, under which an auxiliary function is designed to handle the difficulty of the fixed‐time stability analysis under the output‐feedback control strategy, where two types of observer errors are needed in the designed Lyapunov function to achieve the fixed‐time stability. Then, based on the fixed‐time stability criterion, it is proved that both the consensus tracking performance and the closed‐loop stability can be guaranteed in fixed time. Finally, a simulation example verifies the effectiveness of the developed control strategy.

산업용 로봇암의 잔류진동 저감을 위한 포텐셜 필드 기반 충돌 회피 궤적 계획

In industrial robots, preventing collisions with obstacles and creating smooth trajectories are critical issues. In previous research, an S-curve profile has been studied to reduce jerk. Many potential field method approaches have been researched to avoid collisions with obstacles in mobile robots. Typical potential fields generate a repulsive force for a robot to avoid obstacles inside the assumed boundary near the obstacle, but this repulsive force can affect robot motion that is above the maximum velocity because the repulsive force adds to the attractive force after avoiding an obstacle if the attractive and repulsive forces are in the same direction. This paper presents an asymmetric S-curve profile with a modified potential field, which generates a smooth velocity trajectory while avoiding the static obstacle and being over maximum velocity, as well as reducing residual vibration. The 6-axis robot uses a damped least square for singularity avoidance, and an augmented Jacobian is used with wrist parts added to the end-effector for a fixed pose. Simulations were conducted on MATLAB. We applied the simulation results to the NEUROMEKA INDY7 (6-axis) robot. According to the results, the proposed method produces a smoother trajectory than existing methods.

A Note on Singularity Avoidance in Fourth-Order Gravity

We consider the fourth-order differential theory of gravitation to treat the problem of singularity avoidance: studying the short-distance behaviour in the case of black-holes and the big-bang we are going to see a way to attack the issue from a general perspective.

Three-Dimensional Biased Proportional Navigation Guidance Based on Spatial Rotation of Predicted Final Velocity

This study presents the design of three-dimensional biased proportional navigation guidance laws for arrival at a stationary target along a desired direction based on spatial rotation of predicted final velocity vector. The focus is on full constructive derivation using vector-form expressions without introducing local representation of rotation such as Euler angles or quaternions. The proposed approach synthesises the bias command in the form of an angular velocity vector through realisation of the predictive control design philosophy, the direction which has been unexplored in a three-dimensional setting. The proposed approach avoids heuristic choices and approximations in the design process and hence overcomes the limitation of earlier studies. The vector-form design approach provides theoretical and practical advantages including rigour in derivation, clear geometric understandings about the problem provided by identification of the most effective direction for rotation of final velocity, independence from selection of a fixed coordinate system, avoidance of singularities in local representations, more direct trajectory shaping, and simple implementation.

Distributed Path Planning Classification with Web-based 3D Visualization using Deep Neural Network for Internet of Robotic Things

Internet of Robotic Things (IoRT) distributes heterogeneous intelligences among devices and platforms. A distributed control of a three-degree-of-freedom (3-DOF) robot manipulator is integrated with web-based 3D visualization. An asynchronous protocol was utilized to broadcast kinematic data of a 3-DOF robot manipulator between platforms. However, kinematic data computed using inverse kinematic equations directly cannot identify the singularity issue of robot manipulator. Singularity avoidance required to prevent robot component or joint from damage. Therefore, this study proposed a deep neural network approach as a classification-based of manipulator robot path planning to avoid singularity issues. Deep neural network (DNN) was trained in 12 minutes, 52 seconds in 500 iterations. Training accuracy measured with value 96,23 percent, validation accuracy measured with value 96,13 percent, and testing accuracy measured with value 96,48 percent Additionally, 3 DOF manipulator robot web-based 3D visualization was made using Web Graphics Library (WebGL). The distributed platform was tested successfully and can distribute and classify 2352 motions per second.

Closeness to singularity based on kinematics and dynamics and singularity avoidance of a planar parallel robot with kinematic redundancy

Planar parallel robots are appealing due to their structural simplicity, high stiffness, and large payload capacity. One major problem is that workspace and singularity of non-redundant parallel robots are unchangeable. Hence, when the desired path crossed with singularity or exceeded the workspace’s boundary, the robot is incapable of finishing the task. Another one is closeness to singularity. If one can know the distance between the end manipulator and singularity or workspace’s boundary, the robot will avoid lose control or breakdown. Compared with the traditional planar parallel robot, the planar parallel robot with kinematic redundancy possesses the advantages of avoiding singularity, expanding workspace by adjusting kinematic redundancy parameter. Therefore, the objective of this article is to present an offline action-strategy of a planar robot with kinematic redundancy to measure the closeness to singularity and avoid singularity. It includes two main parts: First, before the robot moves along the desired paths, the closeness to singularity was measured based on the performance of the kinematics and dynamics so that one can know where to pause the robot. Second, an algorithm is designed to previously find the proper kinematic redundancy parameters for changing singularity and workspace. Hence, the robot can smoothly move far from the singularity to finish all paths. The results indicate that the robot can adjust its configuration to well realize the goal by the offline action-strategy.

Kinematics and Singularity Analysis of a 7-DOF Redundant Manipulator.

A new method of kinematic analysis and singularity analysis is proposed for a 7-DOF redundant manipulator with three consecutive parallel axes. First, the redundancy angle is described according to the self-motion characteristics of the manipulator, the position and orientation of the end-effector are separated, and the inverse kinematics of this manipulator is analyzed by geometric methods with the redundancy angle as a constraint. Then, the Jacobian matrix is established to derive the conditions for the kinematic singularities of the robotic arm by using the primitive matrix method and the block matrix method. Then, the kinematic singularities conditions in the joint space are mapped to the Cartesian space, and the singular configuration is described using the end poses and redundancy angles of the robotic arm, and a singularity avoidance method based on the redundancy angles and end pose is proposed. Finally, the correctness and feasibility of the inverse kinematics algorithm and the singularity avoidance method are verified by simulation examples.

A Gimballed Control Moment Gyroscope Cluster Design for Spacecraft Attitude Control

This paper addresses the problem of singularity avoidance in a cluster of four Single-Gimbal Control Moment Gyroscopes (SGCMGs) in a pyramid configuration when used for the attitude control of a satellite by introducing a new gimballed control moment gyroscope (GCMG) cluster scheme. Four SGCMGs were used in a pyramid configuration, along with an additional small and simple stepper motor that was used to gimbal the full cluster around its vertical (z) axis. Contrary to the use of four variable-speed control moment gyroscopes (VSCMGs), where eight degrees of freedom are available for singularity avoidance, the proposed GCMG design uses only five degrees of freedom (DoFs), and a modified steering law was designed for the new setup. The proposed design offers the advantages of SGCMGs, such as a low weight, size, and reduced complexity, with the additional benefit of overcoming the internal elliptic singularities, which create a minor attitude error. A comparison with the four-VSCMG cluster was conducted through numerical simulations, and the results indicated that the GCMG design was considerably more efficient in terms of power while achieving a better gimbal configuration at the end of the simulation, which is essential when it is desired for different manoeuvres to be consecutively executed. Additionally, for a nano-satellite of a few kilograms, the results prove that it is feasible to manufacture the GCMG concept by using affordable and lightweight commercial off-the-shelf (COTS) stepper motors.

A Riemannian metric for geometry-aware singularity avoidance by articulated robots

Articulated robots such as manipulators increasingly must operate in uncertain and dynamic environments where interaction (with human coworkers, for example) is necessary. In these situations, the capacity to quickly adapt to unexpected changes in operational space constraints is essential. At certain points in a manipulator’s configuration space, termed singularities, the robot loses one or more degrees of freedom (DoF) and is unable to move in specific operational space directions. The inability to move in arbitrary directions in operational space compromises adaptivity and, potentially, safety. We introduce a geometry-aware singularity index, defined using a Riemannian metric on the manifold of symmetric positive definite matrices, to provide a measure of proximity to singular configurations. We demonstrate that our index avoids some of the failure modes and difficulties inherent to other common indices. Further, we show that our index can be differentiated easily, making it compatible with local optimization approaches used for operational space control. Our experimental results establish that, for reaching and path following tasks, optimization based on our index outperforms a common manipulability maximization technique and ensures singularity-robust motions.

Infinite-time singularities models and possible avoidance

In this work, we explore two models of future Infinite time singularities in f(T) theory, where T is the torsion scalar. We consider the algebraic function g(T) as the teleparallel term T plus arbitrary function f(T). A suitable Hubble parameter expression is assumed to characterize both of the two singularities models and an expanding universe is provided from imposed constraints. We solve differential equations of g(T) and obtain the algebraic g(T) models of each type of future infinite singularity. In order to study the possible avoidance of singularities, we take into account the viscosity in the fluid and explore three interesting cases: constant viscosity δo, non-constant viscosity proportional to energy density δoρα with α a real parameter and the general case where the viscosity is proportional to (−T)n2, where n is a natural number. We notice that in the first case, the Little Rip singularity may be avoided but the Pseudo Rip is robust against the viscous fluid while for the non-constant viscosity and general case, both singularities cannot be avoided.

Serial-robot Wrist-singularity Mitigation Along Alternative Optimally Adjusted Paths

Abstract Adjusting the displacement path of a serial robot encountering the wrist singularity to pass either through the singularity or around it mitigates its adverse effects. Both such path adjustments are commonly called singularity avoidance and are applied here to either a spherical or an offset wrist. These adjustments avoid high joint rates that can occur at singularity encounter. A recent through-the singularity method limits joint rates and accelerations in the robot with either a spherical or offset wrist when conducting a constant rate of traversal of the tool manipulated by the robot. A kinematic model adding multiple virtual joints allows a modified high-order path-following algorithm to maintain accurate tool position while achieving an optimal level of tool deviation in orientation. Whereas a path reversal resulting from a turning-point type singularity had been revealed for an offset wrist over a finite range of close-approach, these conditions are met when connecting the isolated path segments. Procedures are developed here with this capability for an around-the-singularity path. Choosing between the through and around-singularity alternatives offers the overall optimum.

Observer-based robust platoon formation control of electrically driven car-like mobile robots under collision avoidance and connectivity maintenance with a prescribed performance

This study intends to address the platoon formation control problem of a team of N electrically driven underactuated autonomous car-like mobile robots. A platoon controller is proposed by using the relative distance and angle between each two successive robots in the platoon. A high-gain observer is also used to leave out velocity sensors to reduce the cost of the implementation/maintenance and the weight of the robots. Then, the dynamic surface control method is used to prevent complexity of the controller design. Next, by utilizing the prescribed performance bound method, predetermined desired transient and steady-state behavior of the tracking formation errors, robots connectivity preservation, and their collision avoidance are guaranteed as well as singularity avoidance. Adaptive neural networks and adaptive robust controllers are used to improve the tracking performance in the presence of parametric and nonparametric uncertainties, unmodeled dynamics, actuator saturation nonlinearity, and unwanted external disturbances including exogenous forces and torques, friction, and vibration. The Lyapunov direct method proves that all signals of the closed-loop control system are uniformly ultimately bounded. Finally, simulation results are demonstrated to show the superiority of the proposed convoy tracking system.

Singularity avoidance for manipulators with spherical wrists using the approximate damped reciprocal algorithm

Due to the loss of freedom, the stability and tracking ability of the manipulator around the singularity become worse. This article aims at improving the accuracy of the manipulator and ensuring the stability of the system with the damped reciprocal method. Firstly, the singularities are separated into forearm and wrist singularities to obtain the singular factors of the manipulator respectively. Secondly, a new mathematical function of the approximate damped reciprocal of the singular factor is proposed. Thirdly, the singularities are avoided by modifying the Jacobian matrixes of the manipulator with the approximate damped reciprocal algorithm. Finally, the effectiveness and the stability of the system are proved by the simulations on a manipulator with the spherical wrist. The simulation results prove that this method can largely improve the accuracy of the end-effector and can ensure the stability of the system around the singular region.

Singularity Avoidance Algorithm Based on Bounded Deviation Path Correction Method

Focused on the abnormal problems of path planning when a custom 6-DOF robot goes passed singular points, this paper makes descriptions based on kinematic analysis and dynamic analysis. It is pointed out that linear interpolation should not be simply abandoned but choose joint motion when singularity problems encounters. Instead, this paper suggests a singularity algorithm to modify the interpolated point sequence in the singular interval after a preliminary path planning of the interpolated point sequences, of which the modification method is called “Bounded Deviation Path Correction Method”(BDPC) in this paper. This algorithm can ensure both the accuracy of the end position and the attitude, and finally realizes the effective and reliable motion planning of the manipulator through the singular interval.

Hořava-Lifshitz Scalar Field Cosmology: Classical and Quantum Viewpoints

In this paper, we study a projectable Hořava-Lifshitz cosmology without the detailed balance condition minimally coupled to a nonlinear self-coupling scalar field. In the minisuperspace framework, the super-Hamiltonian of the presented model is constructed by means of which some classical solutions for the scale factor and scalar field are obtained. Since these solutions exhibit various types of singularities, we came up with the quantization of the model in the context of the Wheeler-DeWitt approach of quantum cosmology. The resulting quantum wave functions are then used to investigate the possibility of the avoidance of classical singularities due to quantum effects which show themselves important near these singularities.

Base position optimization of mobile manipulators for machining large complex components

• A BP optimization method for mobile manipulator considering both kinematics and stiffness performance is proposed. • A performance index MSPI is proposed to evaluate the robot's global stiffness performance. • A multi-constrained BP optimization model with maximum MSPI is established. • A sparse uniform grid decomposition + SQP solution method that can accurately obtain the optimal BP is designed. • Simulation and experiment verify the effectiveness of the BP optimization method. With good mobility and high flexibility, the mobile manipulator shows a broad application prospect in the machining of large complex components. In these applications, in order to fully utilize the capabilities of the robot, it is usually necessary to design a series of suitable working positions (i.e. robot's base position) for the mobile manipulator. However, the performance distribution of the robot in the task space is highly nonlinear, which makes it difficult to determine the optimal base positions. Therefore, this paper proposes a new base position optimization method, which can accurately find the optimal base position that takes into account both kinematics and stiffness performance. First, a task-oriented performance index MSPI (mean stiffness performance index) is proposed to evaluate the global stiffness performance of the robot. Based on MSPI, an optimization model considering multiple constraints such as joint range, joint speed, singular avoidance and collision avoidance is established. The optimization model is solved by sparse uniform grid decomposition and Sequential Quadratic Programming (SQP) method, the former is used to find a suitable initial value, the latter is used to determine the optimal base position. Finally, simulation analysis and experiments confirmed the effectiveness of the optimization method and the correctness of the performance index MSPI.

On Time-Synchronized Stability and Control

Previous research on finite-time control focuses on forcing a system state (vector) to converge within a certain time moment, regardless of how each state element converges. In the present work, we introduce a control problem with unique finite/fixed-time stability considerations, namely time-synchronized stability (TSS), where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">at the same time</i> , all the system state elements converge to the origin, and fixed-TSS, where the upper bound of the synchronized settling time is invariant with any initial state. Accordingly, sufficient conditions for (fixed-) TSS are presented. On the basis of these formulations of the time-synchronized convergence property, the classical sign function, and also a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">norm-normalized sign function</i> , are first revisited. Then in terms of this notion of TSS, we investigate their differences with applications in control system design for first-order systems (to illustrate the key concepts and outcomes), paying special attention to their convergence performance. It is found that while both these sign functions contribute to system stability, nevertheless an important result can be drawn that norm-normalized sign functions help a system to additionally achieve TSS. Furthermore, we propose a fixed-time-synchronized sliding-mode controller for second-order systems; and we also consider the important related matters of singularity avoidance there. Finally, numerical simulations are conducted to present the (fixed-) time-synchronized features attained; and further explorations of the merits of the proposed (fixed-) TSS are described.

Global Steering for Control Moment Gyroscope Clusters Using Heuristic Variable Search Techniques

This paper addresses the problem of singularity avoidance in a four-control-moment-gyroscope cluster as used for the attitude control of a satellite. A global search algorithm is developed that adjusts the null motion added upon the singularity robust inverse steering law. Its principal characteristic is that it uses global information gathered from the whole maneuver, compared to most conventional techniques that consider only some local information, near the current gimbal configuration for the optimization. The method is implemented using a ternary tree structure, and a heuristic algorithm optimizes a cost function that depends on the manipulability index, the time spent in the vicinity of singularity, the quaternion error, and the gimbal rates. Specific measures are taken to decrease the execution time of the algorithm, even for long maneuvers, without the need of a visit histogram. In addition, the tuning of only two variables can drastically change the execution time and the computational resources needed. The numerical simulation used to evaluate the algorithm indicates that the elliptic singularity can sufficiently be avoided and the algorithm drives the system fast away from the singularity with an overall performance improvement.