Angle Constraints Research Articles

Impact angle, speed and acceleration control guidance via polynomial trajectory shaping

An Impact Angle, Speed and Acceleration Control Guidance (IASAG) law against the stationary target is proposed, which is critical for the effectiveness of the air-to-surface guided weapons. It is hard to address multiple terminal constraints problem for unpowered missile, especially including terminal speed constraint, which is uncontrollable state. Based on Line-of-Sight (LOS) angle, a fourth-order polynomial function is designed to make the number of coefficients of the function equal to number of boundary conditions. Through analytic calculation and transformation, the relation between the specified boundary conditions and the coefficients are established. The coefficient equations are reduced to a univariate nonlinear equation whose solution is determined by terminal speed constraint. Based on the characteristic of the nonlinear equation, we propose a Particle Swarm Optimization(PSO) method to find the coefficient that satisfies terminal speed constraint. According to Lyapunov stability theory, an asymptotically stable trajectory tracking controller is designed to track the reference leading angle with respect to range-to-go to guarantee the impact angle, speed and acceleration constraints. The effectiveness of the proposed guidance law is verified through numerical simulations.

Three-dimensional impact-angle-constrained cooperative guidance strategy against maneuvering target

In order to improve the multiple-missile cooperative attack capability and penetration capability, this paper investigates two three-dimensional impact-angle-constrained cooperative guidance strategies against maneuvering target for controllable thrust missiles. First, a three-dimensional nonlinear guidance model is established that does not assume small missile lead angles in the guidance process. Second, in the line-of-sight (LOS) direction of the cluster cooperative guidance strategy, the proposed guidance algorithm transforms the simultaneous attack problem into a second-order multiagent consensus problem, which effectively solves the practical problem of low guidance precision provoked by the time-to-go estimation. Then, by combining second-order sliding mode control (SMC) and nonsingular terminal SMC theory, the guidance algorithms in the normal and lateral directions to the LOS are designed, respectively, so that the multi-missile can accurately attack a maneuvering target while satisfying the impact angle constraints. Finally, by utilizing the second-order multiagent consensus tracking control in the leader-following cooperative guidance strategy, a novel leader-following time consistency algorithm is investigated to ensure that the leader and followers can attack the maneuvering target simultaneously. Moreover, the stability of the investigated guidance algorithms is proved mathematically. The effectiveness and superiority of the proposed cooperative guidance strategies are verified by numerical simulations.

Impact angle constraint guidance law using fully-actuated system approach

Aiming at the terminal impact-angle constraint in the interception of large maneuvering targets, this paper proposes a three-dimensional (3D) interception guidance law combined with the high-order fully-actuated system approach and the cascaded linear extended state observer (LESO). First, a complete second-order nonlinear model with full actuated characteristics is developed for the missile-target relative dynamics without small-angle assumption. Subsequently, the nonlinear system is transformed into a quasi-feedback system, and then, a high-order fully-actuated model is developed. A cascaded LESO able to estimate the system state and target maneuver information is introduced, and the controller is designed to convert the closed-loop system into a linear time-invariant closed-loop system with the desired characteristic structure, which makes the closed-loop system have the desired closed-loop poles. Finally, the controller parameter matrix is solved using the desired closed-loop poles, and the convergence is validated by the Lyapunov stability theory. Consequently, the linearization of the 3D nonlinear system is realized, and the channel coupling is eliminated. The effectiveness of the proposed method is verified by simulation and analysis.

Stress-based topology optimization of thermoelastic structures considering self-support constraints

A thermoelastic topology optimization method considering stress and manufacturing constraints is developed for engineering structures under thermo-mechanical coupled field in this paper. A design dependent non-uniform temperature field is considered for the heat conduction and the thermoelastic analysis during the topology optimization. Based on the solid isotropic material with penalization (SIMP), a topology optimization model is formulated to minimize the structural compliance under stress and overhang angle constraints. The overhang angle constraint to achieve the self-support property in additive manufacturing is established by connecting the elemental density values between the printing element and the corresponding support elements in the lower layer. The stress aggregation function is built to approximate the maximum stress value and an improved adaptive normalization scheme is applied to deal with the highly nonlinearity of the optimization. The sensitivity of the objective function and constraints with respect to the design variables are derived by the adjoint method, and the design variables are updated by the gradient-based optimization method. Moreover, a robustness scheme is proposed for the thermoelastic topology optimization to eliminate possible manufacturing issues such as “single node connection” and “thin rod” phenomena. Several typical numerical examples are provided to demonstrate the effectiveness of the proposed method in stress value reduction and overhang angle control. Meanwhile, the topology optimization with robustness scheme is also proved to result in more robust designs for manufacturing.

Three-dimensional event-triggered fixed-time cooperative guidance law against maneuvering target with the constraint of relative impact angles

In order to improve the flexibility and reduce the energy consumption of cooperative guidance laws considering the impact angle constraint, this paper proposes a three-dimensional event-triggered fixed-time cooperative guidance law with the constraint of relative impact angles. First, for the purpose of avoiding the precision degradation due to the estimation error of time-to-go especially facing a maneuvering target, the range-to-go and velocity along the line-of-sight (LOS) are taken as the coordination variables for achieving time-cooperative guidance. Secondly, instead of assigning specific desired impact angles for each missile, only the consensus errors of relative impact angles are utilized as the coordination variables for achieving space-cooperative guidance, which can avoid continually maneuvering for maintaining the constant desired impact angles, thus reducing the fuel consumption. Next, the guidance laws along the LOS and perpendicular to the LOS are developed, and the event-triggering mechanisms are designed to reduce the update frequency of cooperative guidance commands, thus further reducing the energy consumption. To guarantee the convergence rate, the fixed-time control theory is adopted and the stability of proposed event-triggered cooperative guidance laws are rigorously proved. In addition, it is also proved that there is no Zeno behavior when implementing the proposed event-triggered cooperative guidance laws. Finally, numerical simulations indicate that the strictly simultaneous attack is achieved and the constraint of relative impact angles is satisfied. Comparative studies demonstrate that the computation burden of cooperative guidance commands is relaxed and the fuel consumption is reduced by the proposed event-triggered cooperative guidance laws with the constraint of relative impact angles.

Rapid Detection and Orbital Parameters’ Determination for Fast-Approaching Non-Cooperative Target to the Space Station Based on Fly-around Nano-Satellite

Non-cooperative targets, such as space debris, defunct spacecrafts and LEO constellation satellites, have brought serious risks to the space station. The rapid detection and orbital parameters’ determination of the fast-approaching non-cooperative target can greatly improve the protection ability of the space station. In this paper, a novel rapid detection and orbital parameters’ determination method based on the collaborative observation of the space station, and a fly-around nano-satellite is developed. The early-warning region of the space station is established, and considering the observation constraints of the nano-satellite, the non-cooperative target detection strategy is provided, which includes a collaborative observation configuration as well as the attitude variation of the cameras, and the detection efficiency is analyzed. Then, the orbital parameters’ filtering model of the non-cooperative target based on the collaborative observation is constructed, and the Unscented Kalman filter method is utilized to determinate the orbital parameters of the non-cooperative target. Considered the observability of the initial collaborative observation configuration, this paper analyzes the observation configuration with low observability in different scenarios, and proposes an optimal orbital maneuver algorithm for the nano-satellite. This algorithm can realize a fuel-optimal orbital maneuver that satisfies the minimum line-of-sight angle constraint of the collaborative observation.

Retrieval dynamics and control for approach of tethered on-orbit service satellite

Approach and docking with space tether system has the advantages of less system complexity and lower cost compared with conventional rendezvous and docking which are usually essential operations in on-orbit service of spacecraft. This paper deals with the relative dynamics and control of the tethered on-orbit service satellite for the process of approach and docking by retrieving tether. Considering the system safety, it is necessary to keep the pitch angle constant or it varying in a small range during the approach. Therefore, we propose a control law for tether retrieval. Specifically, the relative dynamics equations are established to analyze the effects of orbit eccentricity, orbit altitude, and tether length rate on the system dynamics as well as investigate the property of pitch motion. Then the retrieval control law with constant pitch angle constraint is proposed using the dynamic inverse method based on the dynamics analyses. We further discuss the feasible region of orbit eccentricity and constant pitch angle for the control law to retrieve the tether. The numerical simulation experiments show that the proposed law can realize stable retrieval while maintaining a constant pitch angle.

Adaptive platoon finite-time control for marine surface vehicles with connectivity preservation and collision avoidance

This paper addresses finite-time platoon formation control scheme for vessel train problem subject to modeling uncertainties and external disturbances. The line-of-sight range and angle constraints are proposed to satisfy the collision avoidance and connectivity maintenance. Barrier Lyapunov function is introduced in the kinematic design such that each vehicle follows its leader within the required distance. To compensate for the uncertain model dynamics, the adaptive scheme is incorporated into the decentralized design to estimate nonlinear functions. Furthermore, a disturbance observer is developed to handle time-varying external disturbances. All closed-loop states are guaranteed bounded by Lyapunov theory, and the errors can be regulated to the small neighborhood around zero in finite time. Finally, simulation results are presented to illustrate the effectiveness of the proposed approach with a group of marine surface vessels.

Design of finite time cooperative mid-course guidance law for unmanned target drone aircrafts

For cooperative mid-course guidance problem of multiple unmanned target drone aircrafts(UTDA), a novel cooperative guidance law with impact angle constraints is proposed in this study. Firstly, the relative motion equation of UTDAs and target, and the multiple-UTDA cooperative guidance model with impact angle constraints are constructed. Then, the process of cooperative guidance law design is divided into two stages. In the first stage, the acceleration command on the LOS direction is designed based on the fixed-time consensus theory, the speed dimension is introduced which can guarantee the consensus of all UTDAs' impact times in fixed time. In the second stage, an impact-angle-control guidance law is proposed based on the approaches of variable coefficients sliding mode control and finite-time convergence theory to reach the virtual targets, the acceleration command on the direction of perpendicular to the LOS is developed, which can ensure that all the LOS angles converge to the desired terminal LOS angle in finite-time and some mobility when approaching the virtual targets is achieved, and the Lyapunov stability is adopted. Finally, numerical simulations express that the cooperative mid-course guidance law designed in this study can make each UTDA reach the virtual target at the same time with small miss distance and meet the LOS constraint, and demonstrate the effectiveness of the proposed mid-course guidance law.

Design space analysis for supercritical CO2 radial inflow turbine stators

Radial inflow turbines(RITs) play a vital role in power generation due to their small size, compact construction and large power density, especially when applying to supercritical CO2(sCO2) power cycles. Correct preliminary design of the RITs is important for enhancing the efficiency of cycles. Most preliminary design studies for RITs simply impose empirically developed angle constraints for the rotor inlet conditions instead of giving much attention to the stators. In addition, the previous design procedure can only calculate one geometry at a time, which does not allow the selection of the most suitable geometry that fits the cycle parameters and constraints. Hence, this paper presents a workflow to correctly size a stator for achieving a desired rotor inflow conditions. Then a stator design-space analysis with utilising an existing 500 kW sCO2 rotor is conducted. Based on a number of given stator radius ratio(r3/r4), blade number(Zs) and blade trailing edge thickness(t3), the obtained design map contains a total number of Nr3/r4×NZs×Nt3 preliminary design cases. New insights are discussed, including that the workflow is functional; the blade angles need to adjust between no-loss and loss cases; the rotor–stator interaction loss will increase the stator inlet/outlet operational parameter when guaranteeing the target rotor inlet conditions; and including of the stator losses in turbine design is significant.

A Three-Phase Dual-Output T-Type Three-Level Converter

A novel three-phase dual-output T-type three-level converter (DO-T-TLC) topology is proposed in this article. The proposed topology has the dc-link and two sets of three-phase ac voltage output terminals. The topology of DO-T-TLC is introduced. Then, the operating principle of multiplexing switches and the available switching states of converter are analyzed, including current path, output phase voltage level, and blocking voltage of different switching states. The phase disposition pulsewidth modulation scheme with dc offsets is discussed in detail, and the key problems of the modulation scheme under both the common frequency and different frequency operation modes, such as voltage level selection, displacement angle constraint, and modulation index range, are studied. For the imbalance of two series capacitors in the dc-link, the mechanism is first revealed, and then a dc-link capacitor voltage balance method to control the average neutral point current is proposed. When DO-T-TLC is used in different operation modes, the ability and effect of this method to balance capacitor voltages are summarized. A low-power three-phase prototype is built, and the experimental results are given to verify the feasibility of the proposed topology and the effectiveness of the modulation scheme to control the voltage balance.

Platoon formation control of autonomous underwater vehicles under LOS range and orientation angles constraints

A new controller design is presented on the basis of the dynamic surface control (DSC) method for the constrained platoon formation control of the underactuated autonomous underwater vehicles (AUVs) in the presence of model uncertainties with limited field-of-view (FOV) constraints. An asymmetric barrier Lyapunov function (BLF) is applied to prevent both the line-of-sight (LOS) range and orientation angles from violating limited FOV constraints. Lyapunov method is adopted to reveal that all signals of the closed-loop control system are bounded and the constrained platoon formation tracking errors are semi-globally uniformly ultimately bounded (SGUUB). An adaptive neural network technique is employed to compensate uncertain parameters and unmodeled dynamics of the vehicles. Compared with existing works in the literature, the proposed control scheme not only forces both the range and orientation angles between AUVs to their desired values in the presence of FOV constraints in the fixed-time, but also decrease the safety hazard by avoiding any possible collision between the vehicles, increase the tracking error convergence rate and improve the transient performance of the tracking controller for all AUVs. The computer simulation results demonstrate the efficiency of this newly proposed constrained platoon formation controller for the AUVs.

New PWM inverter control based on optimal pulse pattern computation without phases symmetry constraints

The control of inverters has degrees of freedom that open the way to improve the output harmonic spectrum. Numerous works dealing with this objective have been proposed in the literature, particularly within the definition of switching angles. Among them, the well-known PWM techniques such as Quarter Wave Symmetry (QWS), Half Wave Symmetry (HWS), and Full Wave Symmetry (FWS) are based on Optimal Pulse Patterns (OPP) computation using symmetries angles constraints. In this paper to improve the harmonic quality, the symmetry angles constraints are not considered leading to a new OPP method: Phases Symmetry Relaxation (PSR). To highlight the interest in the proposed PSR method, an evaluation in terms of Weighted Total Harmonic Distortion (WTHD) is performed. Simulation and experimental tests are conducted in comparison with the well known FWS, highlighting the interest in the proposed PSR strategy.

Cross-Source Point Cloud Registration Algorithm Based on Angle Constraint

Cross-Source Point Cloud Registration Algorithm Based on Angle Constraint

Analysis of Line-of-Sight Angle Characteristics for Intercepting a Non-Maneuvering Target With Impact Angle Constraints

With the widespread informationization in modern warfare, higher requirements are required for monitoring the high-value target’s movement state and the corresponding attack conditions. Since the impact-angle constraint guidance law can improve the striking effect of a missile, the study of the hitting conditions and corresponding angle range of the attack angle constraint guidance law has become particularly important. This paper proposes a relationship between the missile’s line-of-sight and flight-path angle under terminal conditions and defines the line-of-sight selection region. Then, we analyze the selection method of the line-of-sight restriction at the end of the missile’s terminal phases. Additionally, Cauchy’s inequality is used to derive the mathematical expressions for line-of-sight selection region under extreme and ideal conditions when employing the developed guidance law to intercept non-maneuvering targets. Finally, a thorough analysis and numerous simulations demonstrate that the line-of-sight angle always falls within the extreme selection region during the entire flight and before hitting the target at the expected impact angle. Compared with a head-on interception, the line-of-sight selection region of the tail-chase case is broader, and the selection region range increases with the upward trend of the acceleration limit.

Minimizing Look Angle Rate Guidance Law Considering Impact Angle and Field-of-View Limit

This study proposes a look angle rate minimizing optimal guidance law with impact angle control and look angle limit. The optimal control theory is adopted to solve the look angle rate minimization problem which has the state inequality on the look angle limit and constraint for impact angle control at the final time. The performance of the proposed guidance law is shown demonstrated by simulations for engagement scenarios of several look angle limits and impact angle constraints. The comparative study shows that the proposed guidance law outperforms on the energy and look angle managing ability.

Unsaturated Optimal Guidance Law for Impact Angle and Acceleration Constraints

Unsaturated Optimal Guidance Law for Impact Angle and Acceleration Constraints

Dynamic Line of Sight Shaping for Impact Time and Angle Control Guidance

This paper presents a novel guidance law enabling to control together of the impact time and angle for planar engagement scenarios. The developed guidance command has a form of biased proportional navigation, and the bias term employs the angle and time constraints at the terminal phase. Specifically, the bias term with nonlinear expression contains the second derivative of the line of sight angle. Thus, shaping a Bézier curve with the C2 continuity guarantee allows us to meet final constraints. Besides, one extra design variable is needed to remove the impact time error related to angle error arising from nonlinearity. Control point locations of resulting 4th degree Bézier curve are determined by boundary conditions, except one being determined using an offline Newton iteration method to eliminate the error. Simulation studies, including a comparison study, are conducted to show the effectiveness of the proposed ITACG law.

Piecewise Trajectory and Angle Constraint Based Fractional-order Sliding Mode Control

This paper proposes an approach for piecewise trajectory planning and fractional-order sliding-mode guidance of a two-stage launched miniature munition with the laser beam riding steered guidance technology. In the proposed approach, firstly, the polynomial description is used as an expected trajec- tory. Then consider the random external disturbances/parametric uncertainties and other factors deteriorate the tracking control performances of the miniature munition. To reduce the chatter- ing caused by modeling errors and external disturbances and achieve fast speed and high accuracy tracking performances for miniature munition, based on adaptive multi-power reaching strategy, an integrated guidance and control (IGC) method with the fractional-order sliding-mode guidance law (FOSMGL) is introduced. The designed fractional-order sliding surfaces ultimately and successively allow both the trajectory and the attitude angle converge to expected value in a finite time. In addition, considering the case of a moving target, a feedfor- ward compensation mechanism, which decreases the lag of the guidance system, is imposed using an additional compensated term obtained from the attitude angle error. The convergence and reachability of the proposed algorithm in finite-time are analyzed using the Lyapunov function method. The validity and practicability of the proposed method are verified by a numerical example.

Visual Odometry With Point and Line Features Based on Underground Tunnel Environment

Compared with the interior environment, there exists a lot of noise and dust in an underground tunnel, and the light is unstable, which is difficult to track by the direct method. Moreover, errors in line segment projection and line feature drift under the influence of light can lead to significant deviations in the odometry. Consequently, to improve the accuracy and robustness of visual odometry, a point-line feature stereo visual odometry system is proposed in this paper. The system combines ORB features and LSD line features; using the angle relationship of line projection, we propose a new method for calculating the reprojection error of line features, reconstruct the reprojection model based on line features, and construct a new reprojection error model based on point-line features, which adds an angle constraint to the reprojection of line features and solves the instability caused by line projection error. It is shown in our experiments on the KITTI, New College dataset, that the translation error of our system is reduced by about 40% on average compared to PLVO, with a reduction in relative positioning error. Experiments in the hallway and underground tunnel environments have shown that the maximum positioning error of our system has been reduced by 75% in hallways and by 56.7% in an underground tunnel. Therefore, our algorithm effectively improves the localization accuracy and is more advantageous in low-texture environments.