Jacobian Control Research Articles

HybridOctree_Hex: Hybrid octree-based adaptive all-hexahedral mesh generation with Jacobian control

We present a new software package, “HybridOctree_Hex,” for adaptive all-hexahedral mesh generation based on hybrid octree and quality improvement with Jacobian control. The proposed HybridOctree_Hex begins by detecting curvatures and narrow regions of the input boundary to identify key surface features and initialize an octree structure. Subsequently, a strongly balanced octree is constructed using the balancing and pairing rules. Inspired by our earlier preliminary hybrid octree-based work, templates are designed to guarantee an all-hexahedral dual mesh generation directly from the strongly balanced octree. With these pre-defined templates, the sophisticated hybrid octree construction step is skipped to achieve an efficient implementation. After that, elements outside and around the boundary are removed to create a core mesh. The boundary points of the core mesh are connected to their corresponding closest points on the surface to fill the buffer zone and build the final mesh. Coupled with smart Laplacian smoothing, HybridOctree_Hex takes advantage of a delicate optimization-based quality improvement method considering geometric fitting, Jacobian and scaled Jacobian, to achieve a minimum scaled Jacobian that is higher than 0.5. We empirically verify the robustness and efficiency of our method by running the HybridOctree_Hex software on dozens of complex 3D models without any manual intervention or parameter adjustment. We provide the HybridOctree_Hex source code, along with comprehensive results encompassing the input and output files and statistical data in the following repository: https://github.com/CMU-CBML/HybridOctree_Hex.

High-speed polarization tracking using thin film lithium niobate integrated dynamic polarization controller.

Dynamic polarization controllers (DPCs) are essential devices in various optical applications. We develop a thin film lithium niobate (TFLN) integrated DPC driven by the real-time implemented Jacobian control algorithm for fast polarization tracking. Experimental results demonstrate a high polarization tracking speed of 100 krad/s when targeting a specific linear state of polarization, with a low control loop delay of 420 ns, half-wave control voltages of 2.75 V, and a fast polarization restoring time of 1.6 us. Compared to previously reported integrated DPCs, the TFLN-based DPC achieves significantly higher tracking speed and lower loop delay. The results highlight the effectiveness of the Jacobian method and the outstanding performance of TFLN-based DPCs. The study opens up possibilities for further advancements in DPC solutions using TFLN technology.

Finite‐time control of mobile manipulators subject to unknown/unstructured external disturbances

AbstractA robust finite‐time control law is proposed for mobile manipulators with uncertain both kinematic and dynamic equations. Moreover, the following external disturbances are allowed to act on the system: unstructured forces exerted on the end‐effector, slip reaction forces affecting the platform wheels, unknown friction forces coming from joints directly driven by the actuators and undesirable unstructured forces caused by singular configurations. In order to cope with both parametric uncertainties and unknown/unstructured external disturbances, we first transform the original control problem whose non‐holonomic constraints are violated into a steering one in an extended space of generalized coordinates with extended non‐holonomic constraints of the Pfaffian form and then introduce a task space non‐singular terminal sliding manifold. Based on the Lyapunov stability theory, a new class of estimated extended transposed Jacobian control laws is derived which both effectively counteract the external forces and significantly reduce the slipping phenomena. A second order sliding technique is involved in our control law to eliminate undesirable chattering effect. An illustrative example of a mobile manipulator control demonstrates the advantages of the approach. Moreover, numerical comparisons with other representative controllers well‐known in the literature are also given.

Mapping Pediatric Spinal Cord Development with Age.

Pediatric spinal cord morphometry has been relatively understudied because of non-optimal image quality due to the difficulty of spine imaging, rarity of post-mortem analysis, motion artifacts, and pediatric MR imaging research focus on understanding spinal injury or pathology. The pediatric brain has been comparatively well-studied with white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF) differences observed with age and gender. Therefore, a greater understanding of pediatric cervical and thoracic spinal cord morphometry would be beneficial for developing clinically relevant cord growth models. We focused on retrospectively characterizing cervical and thoracic spinal cord growth and morphometry changes in a healthy pediatric population. High resolution multi-echo gradient echo (mFFE) images were acquired from pediatric spinal cord scans from 63 patients (mean: 9.24 years, range: 0.83-17.67 years). The mFFE scans were then registered to the template space for uniform viewing and analysis by using a customized semi-automatic processing pipeline involving Spinal Cord Toolbox (SCT). Jacobian control determinants were calculated, and subsequent WM, GM, dorsal column, lateral funiculi, and ventral funiculi scalar averaging was conducted. Random effects models were used to model age-related Jacobian scalar differences. Observing the growth of cord matter by patient age and vertebral level suggests that the upper cervical spinal cord, specifically C2-C3, and mid-thoracic spinal cord, T3-T8, grow faster than other cervical levels and thoracic levels, respectively. This knowledge will facilitate clinical decision making when considering spine interventions and conducting radiological analysis in children with cervical and thoracic spine abnormalities.

Adaptive fuzzy Jacobian control of spacecraft combined attitude and Sun tracking system

PurposeThe paper aims to address the combined attitude control and Sun tracking problem in a flexible spacecraft in the presence of external and internal disturbances. The attitude stabilization of a flexible satellite is generally a challenging control problem, because of the facts that satellite kinematic and dynamic equations are inherently nonlinear, the rigid–flexible coupling dynamical effect, as well as the uncertainty that arises from the effect of actuator anomalies.Design/methodology/approachTo deal with these issues in the combined attitude and Sun tracking system, a novel control scheme is proposed based on the adaptive fuzzy Jacobian approach. The augmented spacecraft model is then analyzed and the Lyapunov-based backstepping method is applied to develop a nonlinear three-axis attitude pointing control law and the adaptation law.FindingsNumerical results show the effectiveness of the proposed adaptive control scheme in simultaneously tracking the desired attitude and the Sun.Practical implicationsReaction wheels are commonly used in many spacecraft systems for the three-axis attitude control by delivering precise torques. If a reaction wheel suffers from an irreversible mechanical breakdown, then it is likely going to interrupt the mission, or even leading to a catastrophic loss. The pitch-axis mounted solar array drive assemblies (SADAs) can be exploited to anticipate such situation to generate a differential torque. As the solar panels are rotated by the SADAs to be orientated relative to the Sun, the pitch-axis wheel control torque demand can be compensated by the differential torque.Originality/valueThe proposed Jacobian control scheme is inspired by the knowledge of Jacobian matrix in the trajectory tracking of robotic manipulators.

Tracking the Kinematically Optimal Trajectories by Mobile Manipulators

This paper addresses the kinematically optimal control problem of the mobile manipulators. Dynamic equations of the mobile manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the mobile manipulator when tracking the trajectory by the end-effector. A computationally simple class of the Jacobian transpose control algorithms is proposed for the end-effector trajectory tracking. Such controllers apply a new non-singular Terminal Sliding Mode (TSM) manifold defined by a non-linear integral equality of the second order with respect to the task space tracking error. Based on the Lyapunov stability theory, the proposed Jacobian transpose control schemes are proved to be finite-time stable provided that some well-founded assumptions are fulfilled during the mobile manipulator movement. The performance of the proposed control strategies is illustrated through computer simulations for a mobile manipulator that attains trajectory tracking by the end-effector in a two-dimensional task space and simultaneously minimises some objective function.

Modified transpose Jacobian control of a tractor-trailer wheeled robot

Tractor-trailer wheeled robot (TTWR) is a modular robotic system that consists of a tractor module towing a trailer. Control of these systems started from motion aid facilities in human-driven vehicles, to fully autonomous mobile robots in recent years. The mobility of such highly nonlinear systems is restricted due to the presence of nonholonomic constraints of wheels, also the system severe underactuated nature. Trajectory tracking is one of the challenging problems focused in the context of Wheeled mobile robots (WMRs) that has been discussed in this paper. First, kinematic equations of TTWR are obtained. Then, reference trajectories for tracking problem are produced. Subsequently, a non-model-based controller based on Modified transpose jacobian (MTJ) method is designed to steer the TTWR asymptotically follow reference trajectories. Obtained simulation and experimental comparison results show the effectiveness of the proposed controller.

Control of Mobile Manipulators in a Task Space $ $

This note addresses the problem of position control of mobile manipulators operating in the task space with state constraints. A relatively simple class of task space regulators consisting of a generalized transpose Jacobian controller with a nonlinear quasi-velocity term, an integral term including a function of manipulator coordinates and the task error plus the gradient of a kinematic criterion function, is proposed. The Lyapunov stability theory is used to derive the control scheme. Through the use of the gradient of the criterion function, an optimal solution to the mobile manipulator task is ensured. The performance of the proposed control strategy is illustrated through computer simulations for a mobile manipulator operating in a three-dimensional task space.

Prediction Error Based Adaptive Jacobian Tracking for Free-Floating Space Manipulators

The work presented here investigates task-space trajectory tracking control for free-floating space robots with uncertain kinematics and dynamics. To deal with these two kinds of uncertainties, we propose a prediction error based adaptive Jacobian controller, which includes a modified task-space computed torque controller and two modified least-squares estimators. By defining a new variable that is termed as the estimate of the spacecraft angular acceleration, the proposed controller can work without requiring measurement of the spacecraft angular acceleration. The kinematic and dynamic parameter adaptations are driven by prediction errors. Using input-output stability analysis, we obtain explicit stability results of the closed-loop system and show the asymptotic convergence of the end-effector motion tracking errors of the free-floating manipulator. Furthermore, it is shown that the performance of the proposed controller has a tight relationship with the estimated generalized Jacobians of free-floating manipulators. Simulation results are presented to show the performance of the proposed controller, and in addition some implementation issues of the proposed control algorithm are discussed.

OpenMP-based parallel transient stability simulation for large-scale power systems

This paper provides an OpenMP-based parallel Very Dishonest Newton (VDHN) algorithm with variable step size, running transient stability simulations (TSA) on multi-core computers. Under the framework of simultaneous solution method of TSA, the step-size control strategy is used according to the local truncation error theory firstly. Then, computation of the generation units, which is the most time-consuming part of the simulation, is dynamically dispatched to several cores using an α dynamic scheduling scheme to obtain workload balancing based on OpenMP. Due to the convergence of Newton-type iterations, an adaptive Jacobian update control strategy is applied to reduce the sequential part of the simulation and the overhead generated by OpenMP. Several large scale test cases verify the validity and practicability of the proposed parallel algorithm, showing that the proposed approach achieves high speed-up and a considerable reduction in parallel overheads.

Investigations on the dynamic coupling in AUV-manipulator system and the manipulator trajectory errors using bond graph method

This article presents the modelling and simulation of the dynamic coupling in an autonomous underwater vehicle (AUV)-manipulator system, used for subsea intervention tasks. Bond graph, a powerful tool in multi-domain dynamic system modelling, is used for the first time to model the coupled dynamics of the AUV-manipulator system. This method enables the development of the system model in a modular form by creating sub-system models and connecting these models together at energy interactions ports, thus overcoming many of the computational difficulties encountered in conventional modelling methods. The effects of gravity, buoyancy, added mass and fluid drag on the dynamics of a 3 degrees of freedom (DoF) manipulator mounted on a 6 DoF AUV are analysed. The manipulator trajectory errors due to the interaction forces and moments between the vehicle and the manipulator have also been investigated and the results are presented. The dynamic model predicts the reaction forces on the vehicle under various operating conditions of the manipulator and their influence on the manipulator trajectory. The percentage errors of manipulator tip trajectory for different initial configurations and operating conditions are analysed. The estimation of resulting errors in the manipulator path due to dynamic coupling effect on the manipulator trajectory helps in the design of suitable trajectory controller for the system. Cartesian space transpose Jacobian controller for trajectory control of manipulator has been implemented and results are presented.

Uncalibrated eye‐in‐hand visual servoing: an LMI approach

PurposeThe purpose of this paper is to present the control of six degrees of freedom (PUMA560) robotic arm using visual servoing, based upon linear matrix inequality (LMI). The aim lies in developing such a method that neither involves camera calibration parameters nor inverse kinematics. The approach adopted in this paper includes transpose Jacobian control; thus, inverse of the Jacobian matrix is no longer required. By invoking the Lyapunov's direct method, closed‐loop stability of the system is ensured. Simulation results are shown for three different cases, which exhibit the system stability and convergence even in the presence of large errors.Design/methodology/approachThe paper presents LMI‐based visual servo control of PUMA560 robotic arm.FindingsThe proposed method is implementable in the dynamic environment due to its independence to camera and object model.Research limitations/implicationsVisibility constraint is not included during servoing – this may cause features to leave the camera field of view (fov).Originality/valueLMI optimization is employed for visual servo control in an uncalibrated environment. Lyapunov's direct method is utilized which ensures system stability and convergence.

CARTESIAN APPROACH FOR GAIT PLANNING AND CONTROL OF BIPED ROBOTS ON IRREGULAR SURFACES

Biped robots possess higher capabilities than other mobile robots for moving on uneven environments. However, due to natural postural instability of these robots, their motion planning and control become a more important and challenging task. This article presents a Cartesian approach for gait planning and control of biped robots without the need to use the inverse kinematics and the joint space trajectories, thus the proposed approach could substantially reduce the processing time in both simulation studies and online implementations. It is based on constraining four main points of the robot in Cartesian space. This approach exploits the concept of Transpose Jacobian control as a virtual spring and damper between each of these points and the corresponding desired trajectory, which leads to overcome the redundancy problem. These four points include the tip of right and left foot, the hip joint, and the total center of mass (CM). Furthermore, in controlling biped robots based on desired trajectories in the task space, the system may track the desired trajectory while the knee is broken. This problem is solved here using a PD controller which will be called the Knee Stopper. Similarly, another PD controller is proposed as the Trunk Stopper to limit the trunk motion. Obtained simulation results show that the proposed Cartesian approach can be successfully used in tracking desired trajectories on various surfaces with lower computational effort.

Prediction Error Based Adaptive Jacobian Tracking of Robots With Uncertain Kinematics and Dynamics

In this note, we have proposed a prediction error based adaptive Jacobian controller to solve the problem of concurrent adaptation to both uncertain kinematics and dynamics. This controller is composed of a modified computed torque controller and two cushion floor least-square estimators, and in ideal case of perfect knowledge of the robot parameters it leads to linear and decoupled error dynamics. The kinematic and dynamic parameters adaptations are driven by prediction errors. Using input-output stability analysis, we show that the end-effector motion tracking errors converge asymptotically. We have also derived an alternative adaptive Jacobian controller that does not require the invertibility of the estimated inertia matrix. Simulation results are presented to show the performance of the proposed controllers.

Pseudo-inverse Jacobian control with grey relational analysis for robot manipulators mounted on oscillatory bases

Interest in complex robotic systems is growing in new application areas. An example of such a robotic system is a dexterous manipulator mounted on an oscillatory base. In literature, such systems are known as macro/micro systems. This work proposes pseudo-inverse Jacobian feedback control laws and applies grey relational analysis for tuning outer-loop PID control parameters of Cartesian computed-torque control law for robotic manipulators mounted on oscillatory bases. The priority when modifying controller parameters should be the top ranking importance among parameters. Grey relational grade is utilized to investigate the sensitivity of tuning the auxiliary signal PID of the Cartesian computed-torque law to achieve desired performance. Results of this study can be feasible to numerous mechanical systems, such as mobile robots, gantry cranes, underwater robots, and other dynamic systems mounted on oscillatory bases, for moving the end-effector to a desired Cartesian position.

Neural Network Control of Multifingered Robot Hands Using Visual Feedback

It is interesting to observe that humans are able to manipulate an object easily and skillfully without the exact knowledge of the object, contact points, or kinematics of our fingers. However, research so far on multifingered robot control has assumed that the kinematics and contact points of the fingers are known exactly. In many applications of multifingered robot hands, the kinematics and contact points of the fingers are uncertain and structures of the Jacobian matrices are unknown. In this paper, we propose an adaptive neural network (NN) Jacobian controller for multifingered robot hand with uncertainties in kinematics, Jacobian matrices, and dynamics. It is shown that using NNs, the uniform ultimate boundedness of the position error can be achieved in the presence of the uncertainties. Simulation results are presented to illustrate the performance of the proposed controller.

Passivity based adaptive Jacobian tracking for free-floating space manipulators without using spacecraft acceleration

Most research so far on trajectory tracking of free-floating space manipulators has assumed that the kinematics of the space manipulator is exactly known. However, when a space manipulator picks up different tools of unknown lengths or unknown gripping points, its kinematics and dynamics change and are difficult to derive exactly. Thus, in this paper, we have proposed a passivity based adaptive Jacobian controller for free-floating space manipulators. The proposed controller consists of a transposed Jacobian feedback and a dynamic compensation term, and the parameter adaptation laws are derived by Lyapunov-like stability analysis tools. It is shown that the end-effector motion tracking errors converge asymptotically. To avoid using spacecraft acceleration, we define a new reference velocity, which is called spacecraft reference velocity. In addition, we have also conducted passivity interpretation of the proposed controller to obtain some physical insight into its properties. Simulation results are presented to show the performance of the proposed controller.

Adaptive Jacobian Force/Position Tracking Control of Robotic Manipulators in Compliant Contact with an Uncertain Surface

Most research so far on force/position tracking control of robots has assumed that the kinematics and dynamics are exactly known. In this work, we deal with force/position tracking under uncertainties arising from robot kinematics, dynamics, surface stiffness and position with an emphasis on uncertain kinematics. A robot with uncertain kinematics and dynamics in contact with a compliant surface is considered. A new adaptive Jacobian controller has been designed to cope with the uncertain robot kinematics, dynamics, environmental stiffness and position. It is shown that the controller can achieve force and position tracking via Lyapunov stability analysis. Simulation results demonstrate the performance of the controller.

On Sensor Switching Visual Servoing

This article investigates dynamic camera switching during visual servoing tasks using multi-camera systems considering image-based and position-based Jacobian transpose control schemes. Stability is discussed using a common Lyapunov function assuming ideal target and camera models and multiple Lyapunov functions under parameter perturbations. It is shown that asymptotic stability cannot be achieved for arbitrary switching under parameter perturbations. Therefore, an energy supervised switching scheme is introduced guaranteeing asymptotic stability. The contributions are stable visual servoing strategies which facilitate instantaneous adjustments of control performance and dynamical device switches in case of task requirements or sensor breakdown.

Adaptive Jacobian position/force tracking control of free-flying manipulators

This paper solves the problem of position/force tracking control of a free-flying space manipulator with uncertain kinematics and dynamics. A free-flying manipulator interacting with an uncertain compliant surface is considered. To cope with the uncertainties arising from free-flyer’s kinematics, dynamics and surface stiffness and position, an adaptive Jacobian controller is devised. The convergence of the force and position tracking errors is proved based on Lyapunov stability analysis. Numerical simulation is presented to show the performance of the controller.