Singularity Avoidance Research Articles

Singularity Avoidance for a Deployable Mechanism Using Elastic Joints

This paper aims at dealing with the deployment vibration problem of the rigid-links deployable mechanism caused by mobility bifurcation. A triangular prismoid deployable mechanism with mobility bifurcation is employed as an example to demonstrate the design and analysis process. First, the mobility of the triangular prismoid deployable mechanism is analyzed, which shows that there exists mobility bifurcation and the possibility of deployment vibration. Second, the revolute joints that introduce mobility bifurcation are analyzed, which shows that they can be replaced by the elastic joints without changing its mobility. Third, a detailed design procedure for this type of elastic joints is discussed; the main parameters of the elastic joints can then be determined based on the mobility and motion range of the deployable mechanism. Physical prototypes of both the rigid-links prismoid deployable mechanism and the corresponding improved mechanism with elastic joints are fabricated, and the deployment experiments of both mechanisms are conducted to show improvement in the latter mechanism.

A Gouge-Free Tool Axis Reorientation Method for Kinematics Compliant Avoidance of Singularity in 5-Axis Machining

Abstract When a cutter traverses a region local to the singularity in 5-axis machining, the stability of machine tool motion may be violated and inevitably lead to a reduction in machining quality and accuracy. In this paper, the underlying cause of the singular machine behaviors is first investigated by differentiating tool path motions, on the basis of the tool path motion expressions in part and machine coordinate systems. A further investigation indicates abrupt kinematic changes to be inevitable when the rotary axes approach a singularity. To eliminate such possible singular risks in 5-axis machining, a local tool path modification method is proposed by adjusting the two rotary axes out of a singular configuration. The critical kinematics smoothing and the consequent gouging concerns resulting from reorientation are comprehensively incorporated in the process of singularity avoidance, by means of a novel tool orientation optimization model. Specifically, the algorithm starts with the determination of an appropriate adjustment range in a simple yet effective manner, and then the primary rotary axis is adjusted in a constrained region away from zero, so as to avoid singularity. After that, the second rotary axis is accordingly adjusted, with no gouging requirements being violated. In this way, singularity problems in 5-axis machining are solved, and both the machine axes kinematics and surface gouging errors are under control. Machining simulation and laboratory experiments were conducted to validate the effectiveness of the proposed method.

Continuous Task Transition Approach for Robot Controller Based on Hierarchical Quadratic Programming

Robots with high degrees of freedom (DoFs), such as humanoids and mobile manipulators, are expected to perform multiple tasks simultaneously. Hierarchical quadratic programming (HQP) can effectively compute a solution for strictly prioritized tasks. However, the continuity of the control input is not guaranteed when the priorities of the tasks are modified during operation. In this letter, we propose a continuous task transition method for HQP-based controller to insert, remove, and swap arbitrary tasks without discontinuity. Smooth task transition is assured because our approach uses activation parameters of the new and existing tasks without modifying the control structure. The proposed approach is applied to various task transition scenarios including joint limit, singularity, and obstacle avoidance to guarantee stable execution of the robot. The proposed control scheme has been implemented on a 7-DoF robotic arm, and its performance is demonstrated by the continuity of the control input during various task transition scenarios.

Singularity Avoidance Control of a Non-Holonomic Mobile Manipulator for Intuitive Hand Guidance

Mobile manipulators are robot systems capable of combining logistics and manipulation tasks. They thus fulfill an important prerequisite for the integration into flexible manufacturing systems. Another essential feature required for modern production facilities is a user-friendly and intuitive human-machine interaction. In this work the goal of code-less programming is addressed and an intuitive and safe approach to physically interact with such robot systems is derived. We present a natural approach for hand guiding a sensitive mobile manipulator in task space using a force torque sensor that is mount close to the end effector. The proposed control structure is capable of handling the kinematic redundancies of the system and avoid singular arm configurations by means of haptic feedback to the user. A detailed analysis of all possible singularities of the UR robot family is given and the functionality of the controller design is shown with laboratory experiments on our mobile manipulator.

A convex programming approach to the base placement of a 6-DOF articulated robot with a spherical wrist

Robot manipulators are widely used in various areas of industrial factory automation. However, their base positioning is still achieved through trial-and-error methods based on the intuition and expertise of the engineer, even with the use of off-line programming software. Most previous studies do not provide on-line or on-site solutions suitable for practical applications because the nonlinearity and derivative complexity of the robot kinematics result in heavy computational burden and lengthy processing times. In this paper, we suggest a convex programming approach that uses time-efficient and reliable methods to solve the optimization problem in order to determine the base position of a six-degrees-of-freedom articulated robot with a spherical wrist. The proposed method uses convex optimization to accurately check the reachability of the given task without solving the inverse kinematics and to determine the feasible base position to satisfy singularity avoidance and spatial limitations. The feasibility of the proposed method is evaluated through various simulations, and the results show that not only the feasible base position but also the range of allowable base locations as an ellipsoidal volume can be provided within a few minutes without high computing performance or large resources.

Vector Control-Based Singularity Avoidance/Escape Steering Law for Single Gimbal Control Moment Gyros

The single-gimbal control moment gyros (SGCMGs) steering law has been a standing topic in the field of spacecraft attitude control for several decades. A practical steering law should meet the following requirements simultaneously: powerful singularity avoidance ability, high precision torque output ability and fast singularity escape ability. Moreover, the angular velocity commands generated by the steering law should not jitter sharply. In this paper, a vector control-based singularity avoidance and escape steering law for SGCMGs is proposed to satisfy these goals. In addition, a system angular momentum state evaluation function for command torque is defined for the first time, which can be used to effectively evaluate the remaining angular momentum resources for the command torque. We demonstrate the effectiveness and superiority of the proposed steering law with detailed comparisons to existing efforts.

Online Time-Optimal Trajectory Planning for Robotic Manipulators Using Adaptive Elite Genetic Algorithm With Singularity Avoidance

In this paper, a new method of online planning high smooth and time-optimal trajectory for robotic manipulators that applies an adaptive elite genetic algorithm with singularity avoidance (AEGA-SA) is presented. The strategy is designed as a combination of the time-optimal trajectory planning with quintic polynomial in Cartesian space. For improving optimization performance, elitist group and adaptive adjustment mechanisms are used based on genetic algorithm (GA) framework. In the meantime, GA is combined with singularity avoidance mechanism to avoid the singularities appearing in the trajectory, improves the recognition capability of optimum solution. Experimental results show that, the proposed approach is more effective and better performance than the original GA and its variants, with ensuring a both smooth and efficiency performance for the robotic manipulators.

Simultaneous Planning Method Considering Both Overall Configuration and End Pose for Hyper-Redundant Manipulators

Featured by extreme flexibility, hyper-redundant manipulators are gradually developed and applied to perform detection and maintenance tasks in confined on-orbit environments. However, its configuration planning is very challenging due to a large number of degrees of freedom. This paper proposes a simultaneous planning method considering both overall configuration and end pose for hyper-redundant manipulators. First, the end effector and intermediate universal joints of the hyper-redundant manipulator are selected as the follow-up controlled points. The corresponding active control points are freely set near the follow-up controlled points. Then, the Euclidean distance between the active control point and the follow-up controlled point is calculated. Combined with gradient projection method, the calculated Euclidean distance is taken as the objective function to be optimized. By adjusting the active control point and the scale factor of gradient projection method, the adjustment of follow-up controlled points (i.e. overall configuration and end pose) can be realized. What is more, this method can optimize its overall configuration to adjust the follow-up controlled points close to or far from the active control point to achieve other planning goals (i.e. obstacle avoidance, singularity avoidance and so on). Therefore, this method satisfies the requirements of simultaneous planning considering both overall configuration and end pose for hyper-redundant manipulators. Finally, the proposed simultaneous planning method is executed in physical experiment system. Results verify the effectiveness of the proposed method.

Safety-Enhanced Model-Free Visual Servoing for Continuum Tubular Robots Through Singularity Avoidance in Confined Environments

Minimally invasive procedures have gained ever-increasing popularity due to their advantages of smaller incisions, faster recoveries, fewer complications, and reduced scarring to name a few. With the force exertion and curvilinear flexibility at their distal end effectors, the continuum tubular robots have the potential to perform robot-assisted trans-orifice minimally invasive surgery, such as transnasal and transoral operations. During these procedures, it is important and challenging for the continuum tubular robot to automatically adjust its pose according to the target surgical sites and compensate for undesired disturbance, such as respiratory motions. In this paper, a singularity-avoidance visual servoing algorithm based on Jacobian Optimization has been proposed to improve safety and control continuum tubular robots based on intra-operative visual feedback in confined environments. Without the prior knowledge of robot kinematics or hand-eye calibration between the robot and the endoscope, the proposed model-free eye-in-hand visual servoing technique is capable of accomplishing the targeting tasks by adopting the safety-enhanced singularity avoidance mechanism and an efficient image-processing algorithm. The multiple experiments, including simulations, experiments conducted in a confined environment, and cadaveric studies, have been implemented and demonstrated to illustrate the superiority of the proposed singularity-avoidance visual servoing method.

Impedance Control Method with Capability of Singular Configuration Avoidance

Impedance Control Method with Capability of Singular Configuration Avoidance

Quantum cosmology of Eddington-Born–Infeld gravity fed by a scalar field: The big rip case

We study the quantum avoidance of the big rip singularity in the Eddington-inspired-Born-Infeld (EiBI) phantom model. Instead of considering a simple phantom dark energy component, which is described by a perfect fluid, we consider a more fundamental degree of freedom corresponding to a phantom scalar field with its corresponding potential, which would lead the classical universe to a big rip singularity. We apply a quantum geometrodynamical approach by performing an appropriate Hamiltonian study including an analysis of the constraints of the system. We then derive the Wheeler-DeWitt (WDW) equation and see whether the solutions to the WDW equation satisfy the DeWitt boundary condition. We find that by using a suitable Born-Oppenheimer (BO) approximation, whose validity is proven, the DeWitt condition is satisfied. Therefore, the big rip singularity is expected to be avoided in the quantum realm.

6 자유도 매니퓰레이터의 선형 운동에 대한 특이점 회피

There is growing interest in the application of robots within industry and agriculture. Kinematic singularities should be considered for stable motion of robotic manipulators for real-world applications which involve linear motion in various areas. In this study, a kinematic singularity avoidance algorithm is proposed for a general 6-DOF manipulator to improve its stability. The proposed method enables the robot to pass the point of singularity while maintaining the planned path. Parts of joint angles are interpolated within the region near the singularity for smooth joint motion. The partial inverse kinematics model is analyzed to derive unknown joint angles. The simulation results show that the robot can move on the planned linear path without position error through singularity configuration. Additionally, the orientation error is much smaller than that of a commercial robot.

A Novel Kinematically Redundant Planar Parallel Robot Manipulator With Full Rotatability

This paper presents a novel kinematically redundant planar parallel robot manipulator, which has full rotatability. The proposed robot manipulator has an architecture that corresponds to a fundamental truss, meaning that it does not contain internal rigid structures when the actuators are locked. This also implies that its rigidity is not inherited from more general architectures or resulting from the combination of other fundamental structures. The introduced topology is a departure from the standard 3-RPR (or 3-RRR) mechanism on which most kinematically redundant planar parallel robot manipulators are based. The robot manipulator consists of a moving platform that is connected to the base via two RRR legs and connected to a ternary link, which is joined to the base by a passive revolute joint, via two other RRR legs. The resulting robot mechanism is kinematically redundant, being able to avoid the production of singularities and having unlimited rotational capability. The inverse and forward kinematics analyses of this novel robot manipulator are derived using distance-based techniques, and the singularity analysis is performed using a geometric method based on the properties of instantaneous centers of rotation. An example robot mechanism is analyzed numerically and physically tested; and a test trajectory where the end effector completes a full cycle rotation is reported. A link to an online video recording of such a capability, along with the avoidance of singularities and a potential application, is also provided.

A Novel Approach for a Inverse Kinematics Solution of a Redundant Manipulator

Kinematically-redundant manipulators present considerable difficulties, especially from the view of control. A high number of degrees of freedom are used to control so-called secondary tasks in order to optimize manipulator motion. This paper introduces a new algorithm for the control of kinematically-redundant manipulator considering three secondary tasks, namely a joint limit avoidance task, a kinematic singularities avoidance task, and an obstacle avoidance task. For path planning of end-effector from start to goal point, the potential field method is used. The final inverse kinematic model is designed by a Jacobian-based method considering weight matrices in order to prioritize particular tasks. Our approach is based on the flexible behavior of priority value due to the acceleration of numerical simulation. The results of the simulations show the advantage of our approach, which results in a significant decrease of computing time.

Cosmological dynamics of brane gravity: A global dynamical system perspective

The braneworld model of gravity is well-known for several notable cosmological features such as self-acceleration originating from a geometric and not matter source, effective dark energy behavior with phantom characteristics but not leading to a Big-Rip singularity, rough resemblance to the $\Lambda$CDM evolution, etc. The dynamical system tools usually allow us to obtain generic conclusions on the global dynamics of a system over a wide range of initial conditions. With this motivation, in order to recover the important features of the braneworld model from a more global perspective, here, we investigate the global cosmological dynamics of the braneworld model using dynamical system techniques. We first analyze the case where there is just a normal matter on the brane and then extend the analysis to the case with an extra scalar field also trapped on the brane. In the presence of a scalar field, potentials belonging to different classes are considered. The stability behavior of critical points is examined using linear stability analysis and when necessary center manifold theory as well as numerical perturbation techniques are also used. To understand the global dynamics of a dynamical system, we utilized the Poincar\'e compactification method to capture the properties of all possible critical points. Applying dynamical system analysis, we found that brane gravity is consistent with observed actions of the Universe. In particular, our analysis shows that important cosmological behaviors like the long-lasting matter-dominated era, late time acceleration as well as the avoidance of Big-Rip singularity can be realized in brane gravity for a wide range of initial conditions.

Universe as an oscillator

We apply the idea of using a matter time gauge in quantum gravity to quantum cosmology. For the Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe with dust and cosmological constant $\Lambda$, we show that the dynamics maps exactly to the simple harmonic oscillator in the dust-time gauge. For $\Lambda >0$ the oscillator frequency is imaginary, for $\Lambda<0$ it is real, and for $\Lambda=0$ the Universe is a free particle. This result provides (i) a simple demonstration of non-perturbative singularity avoidance in quantum gravity for all $\Lambda$, (ii) an exact Lorentzian Hartle-Hawking wave function, and (iii) gives the present age of the Universe as the characteristic decay time of the propagator.

Deeply-learnt damped least-squares (DL-DLS) method for inverse kinematics of snake-like robots

Recently, snake-like robots are proposed to assist experts during medical procedures on internal organs via natural orifices. Despite their well-spelt advantages, applications in radiosurgery is still hindered by absence of suitable designs required for spatial navigations within clustered and confined parts of human body, and inexistence of precise and fast inverse kinematics (IK) models. In this study, a deeply-learnt damped least squares method is proposed for solving IK of spatial snake-like robot. The robot’s model consists of several modules, and each module has a pair of serial-links connected with orthogonal twists. For precise control of the robot’s end-effector, damped least-squares approach is used to minimize error magnitude in a function modeled over analytical Jacobian of the robot. This is iteratively done until an apt joint vector needed to converge the robot to desired positions is obtained. For fast control and singularity avoidance, a deep network is built for prediction of unique damping factor required for each target point in the robot’s workspace. The deep network consists of 11 x 15 array of neurons at the hidden layer, and deeply-learnt with a huge dataset of 877,500 data points generated from workspace of the snake robot. Implementation results for both simulated and actual prototype of an eight-link model of the robot show the effectiveness of the proposed IK method. With error tolerance of 0.01 mm, the proposed method has a very high reachability measure of 91.59% and faster mean execution time of 9.20 (±16.92) ms for convergence. In addition, the method requires an average of 33.02 (±39.60) iterations to solve the IK problem. Hence, approximately 3.6 iterations can be executed in 1 ms. Evaluation against popularly used IK methods shows that the proposed method has very good performance in terms of accuracy and speed, simultaneously.

A dual quaternion approach to efficient determination of the maximal singularity-free joint space and workspace of six-DOF parallel robots

The avoidance of singularities is critical to design and control of parallel robots. This paper aims at efficient determination of the maximal singularity-free joint space and workspace of a class of six-DOF parallel robots with six kinematic chains of same type. We represent the singularity-free joint space by a 6-cube and determine it firstly. The singularity-free workspace is generated by continuous motion of all active joints in the singularity-free joint space. As a result, the boundary of the workspace can be obtained with simultaneous consideration of position and orientation of the mobile platform. The size relation between the maximal singularity-free joint space and workspace is discussed. To efficiently determine the singularity-free joint space and workspace, we propose dual quaternion-based Jacobian matrices and construct an efficient algorithm. The algorithm detects singularities in a given joint space and simultaneously calculates its corresponding workspace. The computational costs of the proposed algorithm and the traditional one are compared using a 6-UPS parallel robot, leading to 9 seconds and 458 seconds respectively. Finally, both the maximal singularity-free joint space and workspace of a 6-PUS parallel robot are determined to further demonstrate the effectiveness of the new approach.

Singularity-Free Trajectory Planning of a 3-RPRR Planar Kinematically Redundant Parallel Mechanism for Minimum Actuating Effort

Kinematic redundancy is a way to enlarge the workspace and to eliminate the singularities of parallel mechanisms. The objective of the present research is to introduce a new motion planning strategy for singularity avoidance and reducing the actuator forces, especially in the vicinity of singular configurations. The method is implemented to a planar kinematically redundant mechanism categorized as 3-RPRR type. Dynamic equations of motion are derived using the principle of virtual work, and the optimum inverse dynamics is obtained. Some numerical examples are solved, and the results are compared with those obtained in the counterpart non-redundant mechanisms. It is illustrated that the redundant mechanism can avoid singular configurations and track the given trajectory with feasible generalized forces.

Robust Attitude Control Using a Double-Gimbal Variable-Speed Control Moment Gyroscope

This paper derives a linear parameter-varying (LPV) model for three-axis attitude control of a spacecraft with a single double-gimbal variable-speed control moment gyroscope (DGVSCMG) and magnetic torquers (MTQs) and develops a singularity avoidance steering law. The LPV control theory provides an optimal gain-scheduled (GS) controller while considering both control performance and robustness. However, in the spacecraft attitude control problem, it is impossible to design a GS controller due to excesses of the number of parameters in most mission scenarios. To avoid this difficulty, this paper designs two types of easy-to-use LPV models for adapting an LPV control theory. The first model is developed by linearization of the kinematics around the equilibrium point of the target attitude. The second one is developed by introducing a virtual state variable together with a parameter-dependent coordinate transformation. Next, a GS controller is designed by using linear matrix inequalities with regional pole placement constraints. Besides, the singularity avoidance steering law of a DGVSCMG by using MTQs is proposed. The applicability is demonstrated through numerical simulations of the proposed methods.