Null-space Projection Research Articles

Revisiting the traffic flow observability problem: A matrix-based model for traffic networks with or without centroid nodes

This study introduces a graph theory-based model that addresses the link flow observability problem in traffic networks by optimizing passive sensor deployment. The model aims to determine the minimal number of sensors and their optimal placement. It constructs a virtual network and uses isomorphic graph theory to map between the original and virtual networks, ensuring consistency in nodes, links, and link directions. Two formulas are proposed to calculate the minimum number of observable links required across different networks, factoring in links, ordinary nodes, centroid nodes, and added links. Key concepts such as chords, cut sets, and loops, along with their matrices, are analyzed. A matrix-based framework is developed to consider flow conservation conditions. Results show that solving the full link flow observability problem using node flow conservation equations yields a fixed number of sensors with non-unique deployment schemes, Additionally, a resource-constrained sensor network optimization (RSNO) model is presented, employing null space projection (NSP) as an objective function to quantify the impact of budget constraints particularly under the condition if all the link flows cannot be observed. Numerical examples demonstrate the RSNO model's applications.

Multi-Section Magnetic Soft Robot with Multirobot Navigation System for Vasculature Intervention.

Magnetic soft robots have recently become a promising technology that has been applied to minimally invasive cardiovascular surgery. This paper presents the analytical modeling of a novel multi-section magnetic soft robot (MS-MSR) with multi-curvature bending, which is maneuvered by an associated collaborative multirobot navigation system (CMNS) with magnetic actuation and ultrasound guidance targeted for intravascular intervention. The kinematic and dynamic analysis of the MS-MSR's telescopic motion is performed using the optimized Cosserat rod model by considering the effect of an external heterogeneous magnetic field, which is generated by a mobile magnetic actuation manipulator to adapt to complex steering scenarios. Meanwhile, an extracorporeal mobile ultrasound navigation manipulator is exploited to track the magnetic soft robot's distal tip motion to realize a closed-loop control. We also conduct a quadratic programming-based optimization scheme to synchronize the multi-objective task-space motion of CMNS with null-space projection. It allows the formulation of a comprehensive controller with motion priority for multirobot collaboration. Experimental results demonstrate that the proposed magnetic soft robot can be successfully navigated within the multi-bifurcation intravascular environment with a shape modeling error and a tip error of under the actuation of a CMNS through invitro ultrasound-guided vasculature interventional tests.

Impedance-based null-space control of redundant torque-controlled robot

PurposeThe null-space projection method is commonly adopted for controlling redundant robots, which undoubtedly requires the robot Jacobian matrix inverse. This paper aims to provide a novel control scheme, which enables null-space control of redundant robots without conflict with the main task space.Design/methodology/approachIn this paper, an impedance-based null-space control approach for redundant robots is proposed. The null-space degrees of freedom are separated from the primary task space by using the eigenvalue decomposition. Then, a joint impedance controller spans the null space and is reflected into the joint space to manage the redundancy. Finally, several experiments have been conducted to evaluate and validate the performance of the proposed approach in comparison with the null-space projection method under various situations.FindingsExperiment results show that no significant differences were observed between the different filling eigenvalues in the proposed approach under different null-space dimensions and motion velocity. Besides, comparative experiment results demonstrate that the proposed method can achieve comparable results to the null-space projection method. Nevertheless, the suggested approach has benefits regarding the quantity of control parameters in addition to not requiring a Jacobian inverse. Notably, the performance of the proposed method will improve as the null-space dimension increases.Originality/valueThis study presents a new control method for redundant robots, which has advantages for dealing with the problems of controlling redundant robots compared to the existing methods.

Joint Hybrid Beamforming Design for Millimeter Wave Amplify-and-Forward Relay Communication Systems

Hybrid beamforming (HBF) has been regarded as one of the most promising technologies in millimeter Wave (mmWave) communication systems. In order to guarantee the communication quality in non-line-of-sight (NLOS) scenarios, joint HBF design for the mmWave amplify-and-forward (AF) relay communication system is studied in this paper. The ideal case is first considered where the mmWave half-duplex (HD) AF relay system operates with channel state information (CSI) accurately known. In order to tackle the non-convex problem, a manifold optimization (MO)-based alternating optimization algorithm is proposed, where an optimization problem containing only constant modulus constraints in Euclidean space can be converted to an unconstrained optimization problem in a Riemann manifold. Furthermore, considering more practical cases with estimation errors of CSI, we investigate the robust joint HBF design with the system operating in full-duplex (FD) mode to obtain higher spectral efficiency (SE). A null-space projection (NP) based self-interference cancellation (SIC) algorithm is developed to attenuate the self-interference (SI). Different from the traditional SI suppression algorithm, there’s no limit on the number of RF chains. Numerical results reveal that our proposed algorithms has a good convergence and can effectively deal with the influence of different CSI estimation errors. A significant performance improvement can be achieved in contrast with other approaches.

Detection and Mitigation of GNSS Spoofing with Nullspace Projection

Detection and Mitigation of GNSS Spoofing with Nullspace Projection

Anti-Jamming Null Space Projection Beamforming Based on Symbiotic Radio

Anti-Jamming Null Space Projection Beamforming Based on Symbiotic Radio

A differential-algebraic extended Kalman filter with exact constraint satisfaction

This work proposes an Augmented Manifold Differential-Algebraic Extended Kalman Filter for state and input estimation for multibody systems described by a set of differential algebraic equations. The proposed Kalman Filter allows for exact constraint satisfaction and does not require reformulation of the multibody system equations. The approach consists of two main steps: (i) elimination of the Lagrange multipliers from the system state via a nullspace projection and (ii) an additional correction step that constrains the a-posteriori estimated system state to lie on the constraint manifold. The latter is achieved by solving a constrained optimization problem using a Euclidean descent approach and projection on the constraint manifold, i.e. manifold optimization. The proposed approach is numerically validated on both open and closed kinematic chain rigid multibody models and is shown to be robust and indifferent to the type of kinematic chain being considered. Furthermore, an experimental validation is carried out where the forces and torques acting on the wheel center of a McPherson car suspension test setup are successfully estimated using a flexible multibody model and the proposed Kalman Filter.

Null-Space-Based Time-Varying Formation Control of Uncertain Nonlinear Second-Order Multiagent Systems With Collision Avoidance

In this paper, the time-varying formation control problem with collision avoidance is addressed for uncertain nonlinear second-order multi-agent systems in a null-space-based behavioral control architecture. To guarantee the tracking and coordination performance simultaneously, a novel and flexible time-varying formation task strategy is designed where only neighborhood information is necessary. Moreover, the agent radius and a sine function are introduced such that the collision avoidance task function describes collision risk more accurately in contrast to existing results. Then, two fixed-time sliding mode controllers with constant and variable exponent coefficients, respectively, are proposed to track the desired trajectory generated by null space projection. Also, the theoretical results for the task design and trajectory tracking are obtained by using the Lyapunov stability theory. Numerical simulation and practical experiments are finally conducted to illustrate the effectiveness and superiority of the proposed method.

Null Space Projection-Based Design of Multibeam for Joint Communication and Sensing Systems

This paper proposes a multibeam combining method for joint communication and sensing (JCAS) systems. A sensing beamforming (BF) vector is designed to have components only in the orthogonal subspace of the communication BF vector by using a null space projection. In addition, a sensing beam-centric coherence combining is adopted to align the phases of the communication beam and the sensing beam at the sensing beam direction. The proposed approach allows the communication channel to remain stable while scanning the region of interest with the combined beams. The sensing BF gain is also improved by making the sidelobe of the communication beam contribute to increasing the BF gain of the sensing beam. Simulation results are provided to verify the effectiveness of the proposed method.

Two Low-Complexity Efficient Beamformers for an IRS- and UAV-Aided Directional Modulation Network

As excellent tools for aiding communication, an intelligent reflecting surface (IRS) and an unmanned aerial vehicle (UAV) can extend the coverage area, remove the blind area, and achieve a dramatic rate improvement. In this paper, we improve the secrecy rate (SR) performance of directional modulation (DM) networks using an IRS and UAV in combination. To fully explore the benefits of the IRS and UAV, two efficient methods are proposed to enhance the SR performance. The first approach computes the confidential message (CM) beamforming vector by maximizing the SR, and the signal-to-leakage-noise ratio (SLNR) method is used to optimize the IRS phase shift matrix (PSM), which is called Max-SR-SLNR. To reduce the computational complexity, the CM, artificial noise (AN) beamforming, and IRS phase shift design are independently designed in the following method. The CM beamforming vector is constructed based on the maximum ratio transmission (MRT) criteria along the channel from Alice-to-IRS, the AN beamforming vector is designed by null-space projection (NSP) on the remaining two channels, and the PSM of the IRS is directly given by the phase alignment (PA) method. This method is called the MRT-NSP-PA. The simulation results show that the SR performance of the Max-SR-SLNR method outperforms the MRT-NSP-PA method in the cases of small-scale and medium-scale IRSs, and the latter approaches the former in performance as the IRS tends to a larger scale.

Half-duplex and full-duplex interference mitigation in relays assisted heterogeneous network.

In a multicell environment, the half-duplex (HD) relaying is prone to inter-relay interference (IRI) and the full-duplex (FD) relaying is prone to relay residual-interference (RSI) and relay-to-destination interference (RDI) due to Next Generation Node B (gNB) traffic adaptation to different backhaul subframe configurations. IRI and RDI occur in the downlink when a relay is transmitting on its access link and interfering with the reception of a backhaul link of another victim relay. While the simultaneous transmission and reception of the FD relay creates the RSI. IRI, RDI, and RSI have detrimental effects on the system performance, leading to lower ergodic capacity and higher outage probability. Some previous contributions only briefly analysed the IRI, RSI, and RDI in a single cell scenario and some assumed that the backhaul and access subframes among the adjacent cells are perfectly aligned for different relays without counting for IRI, RSI and RDI. However, in practise the subframes are not perfectly aligned. In this paper, we eliminate the IRI, RSI, and RDI by using the hybrid zeroforcing and singular value decomposition (ZF-SVD) beamforming technique based on nullspace projection. Furthermore, joint power allocation (joint PA) for the relays and destinations is performed to optimize the capacity. The ergodic capacity and outage probability comparisons of the proposed scheme with comparable baseline schemes corroborate the effectiveness of the proposed scheme.

Optimal Control of Dielectric Elastomer Actuated Multibody Dynamical Systems.

In this work, a simulation model for the optimal control of dielectric elastomer actuated flexible multibody dynamics systems is presented. The dielectric elastomer actuator (DEA) behaves like a flexible artificial muscle in soft robotics. It is modeled as an electromechanically coupled geometrically exact beam, where the electric charges serve as control variables. The DEA-beam is integrated as an actuator into multibody systems consisting of rigid and flexible components. The model also represents contact interaction via unilateral constraints between the beam actuator and, for example, a rigid body during the grasping process of a soft robot. With a mathematically concise and physically representative formulation, a reduced free energy function is developed for the electromechanically coupled beam. In the optimal control problem, an objective function is minimized while the electromechanically coupled dynamic balance equations for the multibody system have to be fulfilled together with the complementarity conditions for the contact and boundary conditions. The optimal control problem is solved via a direct transcription method, transforming it into a constrained nonlinear optimization problem. The electromechanically coupled geometrically exact beam is firstly semidiscretized with one-dimensional finite elements and then the multibody dynamics is temporally discretized with a variational integrator leading to the discrete Euler-Lagrange equations, which are further reduced with the null space projection. The discrete Euler-Lagrange equations and the boundary conditions serve as equality constraints, whereas the contact constraints are treated as inequality constraints in the optimization of the discretized objective. The constrained optimization problem is solved using the Interior Point Optimizer solver. The effectiveness of the developed model is demonstrated by three numerical examples, including a cantilever beam, a soft robotic worm, and a soft robotic grasper.

Null-Space Minimization of Center of Gravity Displacementof a Redundant Aerial Manipulator

Displacements of the base during trajectory tracking are a common issue in the control of aerial manipulators. These are caused by reaction torques transferred to the base due to the manipulator motion and, in particular, to the motion of its center of gravity. We present a novel approach to reduce base displacements of a kinematically redundant aerial manipulator by using null-space projection in the inverse kinematic control. A secondary objective function minimizes the horizontal displacement of the manipulator center of gravity. We test this algorithm on different trajectories for both three and four degrees of freedom (DOF) manipulators in a simulation environment. The results comparing our algorithm with inverse kinematic control without the null-space projection show up to an 80% reduction in the end-effector position error and an average of about 56% reduction in maximum base displacement. The simulation implementation also runs faster than in real-time in our code implementation. We provide a workspace analysis based on multiple stopping criteria such as excessive base displacement, joint velocities and end-effector position error for the 3 and 4 DOF manipulators. As expected, the 4 DOF manipulator has a larger workspace.

Virtual Stiffness: A Novel Biomechanical Approach to Estimate Limb Stiffness of a Multi-Muscle and Multi-Joint System

In recent years, different groups have developed algorithms to control the stiffness of a robotic device through the electromyographic activity collected from a human operator. However, the approaches proposed so far require an initial calibration, have a complex subject-specific muscle model, or consider the activity of only a few pairs of antagonist muscles. This study described and tested an approach based on a biomechanical model to estimate the limb stiffness of a multi-joint, multi-muscle system from muscle activations. The "virtual stiffness" method approximates the generated stiffness as the stiffness due to the component of the muscle-activation vector that does not generate any endpoint force. Such a component is calculated by projecting the vector of muscle activations, estimated from the electromyographic signals, onto the null space of the linear mapping of muscle activations onto the endpoint force. The proposed method was tested by using an upper-limb model made of two joints and six Hill-type muscles and data collected during an isometric force-generation task performed with the upper limb. The null-space projection of the muscle-activation vector approximated the major axis of the stiffness ellipse or ellipsoid. The model provides a good approximation of the voluntary stiffening performed by participants that could be directly implemented in wearable myoelectric controlled devices that estimate, in real-time, the endpoint forces, or endpoint movement, from the mapping between muscle activation and force, without any additional calibrations.

Hybrid Beamforming Design for Self-Interference Cancellation in Full-Duplex Millimeter-Wave MIMO Systems with Dynamic Subarrays.

Full-duplex (FD) millimeter-wave (mmWave) multiple-input multiple-output (MIMO) communication is a promising solution for the extremely high-throughput requirements in future cellular systems. The hybrid beamforming structure is preferable for its low hardware complexity and low power consumption with acceptable performance. In this paper, we introduce the hardware efficient dynamic subarrays to the FD mmWave MIMO systems and propose an effective hybrid beamforming design to cancel the self-interference (SI) in the considered system. First, assuming no SI, we obtain the optimal fully digital beamformers and combiners via the singular value decomposition of the uplink and downlink channels and the water-filling power allocation. Then, based on the obtained fully digital solutions, we get the dynamic analog solutions and digital solutions using the Kuhn-Munkres algorithm-aided dynamic hybrid beamforming design. Finally, we resort to the null space projection method to cancel the SI by projecting the obtained digital beamformer at the base station onto the null space of the equivalent SI channel. We further analyze the computational complexity of the proposed method. Numerical results demonstrate the superiority of the FD mmWave MIMO systems with the dynamic subarrays using the proposed method compared to the systems with the fixed subarrays and the half-duplex mmWave communications. When the number of RF chains is 6 and the signal-to-noise ratio is 10 dB, the proposed design outperforms the FD mmWave MIMO systems with fixed subarrays and the half-duplex mmWave communications, respectively, by 22.4% and 47.9% in spectral efficiency and 19.9% and 101% in energy efficiency.

Shaping Impedances to Comply With Constrained Task Dynamics

Humans are capable of managing multiple tasks simultaneously. It is widely assumed that human motor control can be emulated by impedance control. To achieve human-like behavior, however, the impedance parameters of multiple tasks may vary during task execution. We propose an algorithm that shapes task impedance as a function of the robot’s time-varying inertial properties. These properties involve virtually constrained masses and virtually constrained inertias that counteract a task in order to comply with a given constraint. In this work, we not only detect task conflicts, but also show how to handle them. Our method is able to control kinematically redundant robots. We developed a damping-design method that does not interfere with our desired Cartesian task-space behavior. The control approach was verified in experiments on a real robot. We compared our impedance shaping method with two alternative control approaches: simple impedance superposition and nullspace projection. Our method preserved the passivity while improving the Cartesian task performance of an impedance controller. The method has computational advantages, beneficial to control robots with many degrees of freedom.

Probing Word Syntactic Representations in the Brain by a Feature Elimination Method

Neuroimaging studies have identified multiple brain regions that are associated with semantic and syntactic processing when comprehending language. However, existing methods cannot explore the neural correlates of fine-grained word syntactic features, such as part-of-speech and dependency relations. This paper proposes an alternative framework to study how different word syntactic features are represented in the brain. To separate each syntactic feature, we propose a feature elimination method, called Mean Vector Null space Projection (MVNP). This method can remove a specific feature from word representations, resulting in one-feature-removed representations. Then we respectively associate one-feature-removed and the original word vectors with brain imaging data to explore how the brain represents the removed feature. This paper for the first time studies the cortical representations of multiple fine-grained syntactic features simultaneously and suggests some possible contributions of several brain regions to the complex division of syntactic processing. These findings indicate that the brain foundations of syntactic information processing might be broader than those suggested by classical studies.

Cancellation of streak artifacts in radial abdominal imaging using interference null space projection.

In radial abdominal imaging, it has been commonly observed that signal from the arms cause streaks due to system imperfections. We previously introduced a streak removal technique (B-STAR), which is inherently spatially variant and limited to work in image space. In this work, we propose a spatially invariant streak cancellation technique (CACTUS), which can be applied in either image space or k-space and is compatible with iterative reconstructions. Streak sources are typically spatially localized and can be represented using a low-dimensional subspace. CACTUS identifies the streak subspace by leveraging the spatial redundancy of receiver coils and projects the data onto the streak null space to eliminate the streaks. When applied in k-space, CACTUS can be combined with iterative reconstructions. CACTUS was tested in phantoms and in vivo abdominal imaging using a radial turbo spin-echo pulse sequence. In phantoms, CACTUS improved T2 estimation in comparison to previous de-streaking methods. In vivo experiments showed that CACTUS reduced streaks and yielded T2 estimation, in regions affected by streaks, closer to a streak-free reference. Evaluation using a clinical abdominal dataset (n=20) showed that CACTUS is comparable to B-STAR and yields significantly better signal preservation and streak cancellation than coil removal and suppression methods. CACTUS provides superior signal preservation and streak reduction performance compared to coil removal and suppression methods. As a clear advantage over B-STAR, CACTUS can be integrated with iterative reconstruction methods. In abdominal T2 mapping, CACTUS improves the accuracy of parameter estimation in areas affected by streaks.

Beamforming Design for IRS-Aided Decode-and-Forward Relay Wireless Network

As a low-cost and low-power-consumption passive reflector, intelligent reflecting surface (IRS) can make a significant rate improvement by building a programmable wireless environment. To improve the rate performance and coverage range of wireless networks, an IRS-aided decode-and-forward (DF) relay network is proposed with multiple antennas at relay station (RS). To achieve a high rate, an alternately iterative structure (AIS) of maximizing receive power (Max-RP) at RS is proposed to jointly optimize the beamforming vectors at RS and phase shifts at IRS. Considering its high-complexity, two low-complexity Max-RP schemes of null-space projection (NSP) plus maximum ratio combining (MRC) and IRS element selection (IRSES) plus MRC are presented to reduce this complexity, respectively. For the former, NSP is used to separate the reflected signal from IRS and the direct transmitted signal from source and MRC is adopted to combine the two signals at RS. For the latter, the basic concept of IRSES is as follows: IRS is partitioned into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M}$ </tex-math></inline-formula> subsets of elements and adjusting the phases of all elements per subset make all reflected signals and the direct signal from source phase alignment (PA) at the corresponding antenna of relay. Simulation results show that the proposed three methods perform much better than the existing network with single-antenna relay in terms of rate performance. In particular, a 85% rate gain over existing scheme is achieved in the high signal-to-noise ratio region. Moreover, it is verified that the positions of RS and IRS have a substantial impact on rate performance, and there exists an optimal positions of RS and IRS.

Hovering control of an underwater robot with tilting thrusters using the decomposition and compensation method based on a redundant actuation model

Six-degree-of-freedom (6-DOF) hovering control is important for underwater robots to perform various tasks. Our previous underwater robot study, which used tilting thrusters, could not control 6-DOF motion simultaneously owing to several mechanical and control problems. In this study, we developed a new robot with tilting thrusters and improved 6-DOF hovering performance. The maneuverability of the robot was evaluated by analyzing the force and moment of the thrust vector. Based on this, a redundant tilting mechanism without constraints was designed to solve structural problems. A proportional–integral–derivative (PID)-based control design using the decomposition and compensation method (PID-DC) that is appropriate for this mechanism, was derived. The decomposition method was used to overcome the nonlinearity of the thrust vector caused by the tilting mechanism, and the null-space projection technique was applied to minimize the thrust force and avoid the boundary of the tilting angle. A compensator based on the empirical model of the tilting thruster transferred the control input to the system with regulation. Simulation and experimental results verified the validity of the controller for the 6-DOF hovering motion of the robot, and the hovering performance was significantly improved. Furthermore, the stability of the hovering performance under tidal currents was demonstrated through disturbance experiments.