Angle Constraints Research Articles

High-precision computational guidance in terminal phase with impact angle, lead angle and lateral acceleration constraints

This paper proposes a high-precision three-dimensional nonlinear optimal computational guidance law in the terminal phase of an interceptor that ensures near-zero miss-distance as well as the desired impact angle. Additionally, it achieves these ambitious objectives while ensuring that the lead angle and lateral acceleration constraints are not violated throughout its trajectory. This ensures (i) the target does not escape the field of view of its seeker at any point in time (a state constraint) and (ii) it does not demand unreasonable lateral acceleration that cannot be generated (a control constraint). The guidance problem is formulated and solved using newly proposed Path-constrained Model Predictive Static Programming (PC-MPSP) framework. All constraints, both equality and inequality, are equivalently represented as linear constraints in terms of the errors in the control history, thereby reducing the complexity and dimensionality of the problem significantly. Coupled with a quadratic cost function in control, the problem is then reduced to a standard quadratic optimization problem with linear constraints, which is then solved using the computationally efficient interior-point method. Results clearly demonstrate the advantage of the proposed guidance scheme over the conventional Biased PN as well as the recently proposed GENeralized EXplicit (GENEX) guidance techniques. Numerical simulations with variation in initial conditions and Monte–Carlo simulations with parametric uncertainty demonstrate the robustness of the proposed guidance scheme.

A Simultaneous Learning and Control Scheme for Redundant Manipulators With Physical Constraints on Decision Variable and Its Derivative

In this article, a simultaneous learning and control scheme built on the joint velocity level with physical constraints on the decision variable and its derivative, i.e., joint angle, joint velocity, and joint acceleration constraints, is proposed for the redundant manipulator control. The scheme works when the structure parameters involved in the forward kinematics are unknown or implicit. The learning and control parts are incorporated simultaneously in the scheme, which is finally formulated as a quadratic programming problem solved by a devised recurrent neural network (RNN). The convergences of learning and control abilities of the RNN are proved theoretically. Simulations and physical experiments on a 7-degrees of freedom (DOFs) redundant manipulator show that, aided with the proposed scheme and the related RNN solver, a redundant manipulator with unknown structure parameters can perform a given inverse kinematics task with high accuracy while satisfying physical constraints on the decision variable and its derivative.

Mechanism Design and Control of a Winged Hovering Robot With Flapping Angle Constraint

Abstract In this paper, we first presented a four-bar linkage mechanism for actuating the wings in a flapping wing flying robot. After that, given the additional constraints imposed by the four-bar linkage, we parameterized the wing kinematics to provide sufficient control authority for stabilizing the system during 3D hovering. The four-bar linkage allows the motors to spin continuously in one direction while generating flapping motion on the wings. However, this mechanism constrains the flapping angle range which is a common control parameter in controlling such systems. To address this problem, we divided each wingbeat cycle into four variable-time segments which is an extension to previous work on split-cycle modulation using wing bias but allows the use of a constant flapping amplitude constraint for the wing kinematic. Finally, we developed an optimization framework to control the system for fast recovery while guaranteeing the stability. The results showed that the proposed control parameters are capable of creating symmetric and asymmetric motions between the two wings and, therefore can stabilize the hovering system with minimal actuation and flapping angle amplitude constraint.

An ISB-consistent upper limb model based on the Denavit-Hartenberg convention for joint angle estimation during prolonged rehabilitation exercises

An accurate and robust joint kinematics description is a crucial prerequisite for the development of tele- rehabilitation applications. Miniaturized wearable sensors (IMUs), along with the use of efficient sensor fusion algorithms, represent a suitable solution. However, orientation drift can affect real-time joint kinematics over prolonged acquisition. In this work, we proposed an optimization kinematics framework which exploits a Denavit-Hartenberg (DH) model of the upper limbs, compliant with the guidelines of the International Society of Biomechanics. The accuracy of the estimated 3D shoulder and elbow kinematics was evaluated using data recorded by two IMUs attached to a robotic arm during a 20- minute planar exercise and compared with the errors obtained using a model-free approach. The upper limb was modelled as a three-segment chain including trunk, upper arm (UA), and the forearm (FA) (Fig. 1). Shoulder and elbow joints were modelled with three (φ1, φ2, φ3) and two degrees of freedom (φ4, φ6), respectively. The carrying angle (φ5) was introduced as a fixed subject-specific parameter to describe the physiological abduction of the FA with respect to the UA. The joint angles were computed in an optimization process which minimizes at each time step the difference between the orientation predicted using the DH model and the corresponding orientation estimated by a sensor fusion algorithm without the magnetometer [1]. In addition, joint angle constraints were set based on the maximum angular velocity, the physiological angular limits, and the specific range of movement when known a-priori . To validate the methods, two IMUs (Xsens – MTw) were attached to the UA and FA of a robotic arm (Kinova – Jaco2) programmed to mimic a shoulder flexion-extension (φ1, φ2, φ3), an elbow flexion-extension (φ4), and a forearm prono-supination (φ6), simultaneously, for 20 minutes (~150 cycles) [3]. The φ5 was equal to zero for the robot. IMU and reference data were collected at 100 Hz. The gyroscope offset was computed during a preliminary acquisition and then subtracted from the measurements. The accuracy was evaluated in terms of root mean square difference (RMSD) between the model-based optimized and robot reference joint angles. Furthermore, the RMSD corresponding to the Euler inversion of the FA-to-UA relative orientation (model-free) was also computed. The RMSD (deg) for the joint angles obtained with the optimization (model-free) process amounted to 1 (10.2), 0.4 (0.2), 0.9 (1.4), 3.0 (3.1), 0 (8.2), and 1 (6) for φ1, φ2, φ3, φ4, φ5, φ6, respectively. The proposed methods allowed to reduce joint angles errors of almost a factor 10 over long period compared to model-free approach (1.1 vs 8.9 deg on average). These results if further confirmed on human experiments can contribute to the design of tele-rehabilitation applications relying on the accurate upper limb joint kinematics estimates. Funded by Sardegna Ricerche (POR FESR 2014/2020).

Differentiator-Based Incremental Three-Dimensional Terminal Angle Guidance With Enhanced Robustness

In this article, an incremental guidancelaw with terminal angle constraint is proposed against maneuvering targets in the 3-D space. First, a sliding surface is constructed such that its first-order dynamics excludes the relative range and line-of-sight angles in the perturbation. This manipulation avoids unboundedperturbations induced by target maneuvers near collision. Then, a benchmark guidance law is derived via the nonlinear dynamic inversion (NDI) based sliding mode control (NDI-SMC). To further enhance guidance system robustness, an incremental nonlinear dynamic inversion (INDI) based SMC (INDI-SMC) 3-D guidance law is developed. The INDI-SMC guidance law exploits the first-order derivative of the sliding variable and guidance command output at the latest step, which leads to reduced perturbation and thus requires smaller gains than the NDI-SMC guidance law. A multivariable continuous differentiator is employed to estimate the sliding variable's first-order derivative for guidance law implementation. Moreover, the stability of the differentiator is analyzed and the guidance robustness under uncertainties is compared. Extensive numerical simulations and a Monte Carlo test are conducted to verify effectiveness and robustness of the proposed method.

Impact angle constrained fuzzy adaptive fault tolerant IGC method for Ski-to-Turn missiles with unsteady aerodynamics and multiple disturbances

An impact angle constrained fuzzy adaptive fault tolerant integrated guidance and control method for Ski-to-Turn (STT) missiles subject to unsteady aerodynamics and multiple disturbances is proposed. Unsteady aerodynamics appears when flight vehicles are in a transonic state or confronted with unstable airflow. Meanwhile, actuator failures and multisource model uncertainties are introduced. However, the boundaries of these multisource uncertainties are assumed unknown. The target is assumed to execute high maneuver movement which is unknown to the missile. Furthermore, impact angle constraint puts forward higher requirements for the interception accuracy of the integrated guidance and control (IGC) method. The impact angle constraint and the precise interception are established as the object of the IGC method. Then, the boundaries of the lumped disturbances are estimated, and several fuzzy logic systems are introduced to compensate the unknown nonlinearities and uncertainties. Next, a series of adaptive laws are developed so that the undesirable effects arising from unsteady aerodynamics, actuator failures and unknown uncertainties could be suppressed. Consequently, an impact angle constrained fuzzy adaptive fault tolerant IGC method with three loops is constructed and a perfect hit-to-kill interception with specified impact angle can be implemented. Eventually, the numerical simulations are conducted to verify the effectiveness and superiority of the proposed method.

Intelligent Vehicle Trajectory Tracking Control Based on VFF-RLS Road Friction Coefficient Estimation

This paper proposes an autonomous vehicle trajectory tracking system that fully considers road friction. When an intelligent vehicle drives at high speed on roads with different friction coefficients, the difficulty of its trajectory tracking control lies in the fast and accurate identification of road friction coefficients. Therefore, an improved strategy is designed based on traditional recursive least squares (RLS), which is utilized for accurate identification of the friction coefficient. First, the tire force and slip rate required for the estimation of the road friction coefficient by constructing the vehicle dynamics model and tire effective model are calculated. In this paper, a variable forgetting factor recursive least squares (VFF-RLS) method is proposed for the construction of the friction coefficient estimator. Second, the identified results are output to the model predictive controller (MPC) constructed in this paper as a way to improve tire slip angle constraints, to realize the trajectory tracking of the intelligent vehicle. Finally, the joint simulation test results of Carsim and Matlab/Simulink show that the trajectory tracking system based on the VFF-RLS friction coefficient estimator has outstanding tracking performance.

Communication-Aware Orbit Design for Small Spacecraft Swarms Around Small Bodies

Exploration of small Solar System bodies has traditionally been performed by monolithic spacecraft carrying several science instruments. However, instruments often cannot be operated simultaneously due to requirements including viewing angle, illumination, power, and data constraints. This has motivated interest in architectures in which a swarm of small spacecraft, each carrying one instrument, studies a small body after being deployed by a carrier spacecraft; such architectures hold promise to yield significant improvements in mission efficiency, increased data quality, and reduced mission duration. A key difficulty is the selection of orbits for the spacecraft, which must satisfy not only instrument requirements but also communication and data storage constraints. To address this, we propose a novel gradient-based optimization algorithm that simultaneously optimizes spacecraft orbits, observations, and communications; the approach captures instrument requirements, communication bandwidth, and memory usage, and it accommodates irregular gravity field models and surface geometries. Numerical simulations of a six-spacecraft swarm studying the 433 Eros asteroid show that the approach results in a 67.9% increase in data returned as compared to a communication-agnostic approach. Collectively, these results enable system designers to quickly assess the end-to-end performance of multispacecraft constellations, and represent a first step toward communication-aware design of multispacecraft missions for small Solar System body exploration.

Terminal angle constraint finite-time guidance law with input saturation and autopilot dynamics

This paper proposes a finite-time command filtered backstepping guidance law (FCFBGL) with the terminal angle constraint while accounting for the input saturation and the autopilot dynamics. To eliminate the adverse effect induced by the filtering errors and the acceleration saturation, a new finite-time error compensation mechanism is integrated in the guidance law design. The proposed FCFBGL not only guarantees the the line-of-sight (LOS) angle error to converge to a small neighborhood of the origin in finite time but also achieves the continuity of the input signal. in finite time. Moreover, with the aid of the fractional power extended state observer (FPESO), the proposed FCFBGL requires no information on the target acceleration and the acceleration derivative of the missile, which is preferable in the practical application. The finite-time stability of the proposed guidance law is derived with the Lyapunov methodology. Simulation results illustrate the effectiveness and superiority of the proposed guidance law.

Stabilizing and Maneuvering Angle Rigid Multiagent Formations With Double-Integrator Agent Dynamics

This article studies 2-D formation stabilization and maneuvering of mobile agents governed by double-integrator dynamics. The desired formation is described by a set of triple-agent interior angles. A carefully chosen such set of angle constraints guarantees that the desired formation is angle rigid. To achieve the desired angle rigid formation, a stabilization control law is proposed using only local velocity and direction measurements. We show that the closed-loop dynamics of the formation, when each agent is modeled by a double-integrator, are closely related to the corresponding one in single-integrator agent dynamics. Sufficient conditions are constructed to guarantee the closed-loop stability for identical and distinct velocity damping gains, respectively. To guide an angle rigid formation to move with the desired translational velocity, orientation, and scale, formation maneuvering laws are then proposed. Simulation examples are also provided to validate the results.

Linear Quadratic Guidance Laws with Intercept Angle Constraints and Varying Speed Adversaries

The paper proposes two linear quadratic guidance laws, which enable target interception while imposing a predetermined terminal intercept angle. Unlike previous solutions, which usually assume constant missile and target speeds, time-dependent known speed profiles of the adversaries are addressed. The guidance laws are derived for linear, arbitrary-order missile and target dynamics using optimal control and differential games theories. Specific closed-form results are provided for ideal missile and target dynamics with constant axial acceleration adversaries. The performance of the proposed guidance laws is investigated using a nonlinear two-dimensional simulation, and the results are compared to two state-of-the-art optimal control and differential-games-based guidance laws that can impose the intercept angle. It is shown that the proposed guidance laws can intercept the target with small miss distances and intercept angle errors and that they have better performance than the compared state-of-the-art guidance laws when the adversaries’ speeds vary. The selection of which guidance law to use depends on the scenario. When the target is predictable, the optimal-control-based guidance law is better suited; whereas when the target is intelligent, the differential-games-based guidance law is a more appropriate choice.

Optimal Look-Angle Guidance with Field-of-View and Impact Angle Constraints for Strapdown Munition

A strapdown seeker with limited field-of-view (FOV) can simplify and decrease cost of the guidance system for a munition. However, the inherent defect of the strapdown seeker is that it could not provide the necessary line-of-sight (LOS) angular information for typical guidance application. This paper proposed an optimal look-angle guidance law (OLAGL) which directly utilized seeker angle information and satisfies the constraints of FOV and terminal impact angle. The coefficient determination, effects of switching threshold, and gains for the guidance law are analyzed and detailed. The simulation results compared with typical trajectory shaping guidance for a ground target show that the presented guidance law can satisfy the impact angle constraint under the limitation of FOV and provide a well engineering reference.

Adaptive Super-Twisting Cooperative Guidance Law with Fixed-Time Convergence

For the guidance problem of multiple missiles cooperatively intercepting a maneuvering target, fixed-time cooperative guidance law is proposed with impact angle constraints. First, fixed-time consensus, integral sliding mode technique, and adaptive super-twisting algorithm are implemented to construct cooperative guidance law along the line-of-sight (LOS) direction. Second, based on fixed-time convergence observer and terminal sliding mode control, one fixed-time guidance law along the normal direction of LOS is designed to ensure that the missiles attack the target with expected angles. Finally, simulation results are carried out to demonstrate the effectiveness of the proposed fixed-time cooperative guidance law.

3D SLAM based on NDT matching and ground constraints for ground robots in complex environments

PurposeIn large-scale environments and unstructured scenarios, the accuracy and robustness of traditional light detection and ranging (LiDAR) simultaneous localization and mapping (SLAM) algorithms are reduced, and the algorithms might even be completely ineffective. To overcome these problems, this study aims to propose a 3D LiDAR SLAM method for ground-based mobile robots, which uses a 3D LiDAR fusion inertial measurement unit (IMU) to establish an environment map and realize real-time localization.Design/methodology/approachFirst, we use a normal distributions transform (NDT) algorithm based on a local map with a corresponding motion prediction model for point cloud registration in the front-end. Next, point cloud features are tightly coupled with IMU angle constraints, ground constraints and gravity constraints for graph-based optimization in the back-end. Subsequently, the cumulative error is reduced by adding loop closure detection.FindingsThe algorithm is tested using a public data set containing indoor and outdoor scenarios. The results confirm that the proposed algorithm has high accuracy and robustness.Originality/valueTo improve the accuracy and robustness of SLAM, this method proposed in the paper introduced the NDT algorithm in the front-end and designed ground constraints and gravity constraints in the back-end. The proposed method has a satisfactory performance when applied to ground-based mobile robots in complex environments experiments.

Novel Particle Swarm Optimization Guidance for Hypersonic Target Interception with Impact Angle Constraint

Considering that the terminal impact angle constraint can improve the interception performance of hypersonic target, a novel particle swarm optimization guidance (NPSOG) algorithm is proposed to satisfy the impact angle constraint. Two-dimensional dynamics engagement mode for hypersonic target interception is formulated. The performance index is positively correlated with the line-of-sight (LOS), LOS rate, and the relative distance between missile and target. The weight coefficients among the three are adaptively adjusted by the fuzzy logic controller. The particle swarm optimization (PSO) algorithm is utilized to generate the guidance commands. Numerical examples are given to verify the performance of the proposed guidance law in various engagement scenarios, and the performance of the algorithm is validated comparing with several heuristic guidance methods and nonheuristic guidance methods.

Adaptive improved super-twisting integral sliding mode guidance law against maneuvering target with terminal angle constraint

This paper investigates the maneuvering target interception problem considering terminal angle constraint, the input saturation and the second-order autopilot lag with the unavailable missile's acceleration. The considering problem is formulated as an output feedback control problem of a four-order nonlinear uncertain weakly observable system, which is challenging to address by general composite methods directly. Hence, the liner normal equivalent control model of the original guidance system is firstly derived to facilitate the extended state observer (ESO) based method design. Then, a nonlinear ESO is introduced to estimate the unmeasured system states and modeled disturbances as well as compensate for control saturation. Thereafter, the ESO-based guidance scheme is developed by integrating a novel four-order integral sliding mode manifold and an adaptive improved super-twisting algorithm. The main novelty is that a novel integral sliding mode manifold is proposed to replace the linear sliding mode manifold of super-twisting sliding mode to further reduce the convergent time of closed-loop system states. Besides, the conventional super-twisting algorithm is improved by modifying the reaching law and designing the adaptive gains to guarantee the continuity of guidance command and suppress the large constant gains and parameter uncertainties. Notably, only the output relative information is utilized in its design process. Numerical simulations validate the previous analyses and show the superiorities in reducing the energy consumption in high maneuvering target interception and achieving robustness to a certain margin under various uncertainties.

Reference-trajectory-planner–based integrated guidance and control under input saturation and impact angle constraint

This paper investigates the integrated guidance and control (IGC) problem for intercepting maneuvering targets subject to the impact angle and input saturation. In order to elegantly implement tracking control under constraints, the whole controller includes the reference trajectory planner for generating reference trajectory, and the reference trajectory tracking controller for tracking the generated reference trajectory. The trajectory tracking controller is based on the command filter backstepping design under the time-domain separation, and the reference trajectory planner with a kind of reference model governor takes into account the available regulation ability of the trajectory tracking controller, so as to improve the adaptability of the proposed control scheme. The two cooperate with each other to improve the stability of guidance interception system and come out a more reasonable interception path. The simulation comparison results are provided to illustrate the superiority of the reference-trajectory-planner–based IGC law.

Nonlinear Guidance Laws for Maneuvering Target Interception With Virtual Look Angle Constraint

For the problem of intercepting a maneuvering target with a desired terminal impact angle, we propose a guidance law in this article based on a nonlinear relative virtual guidance model in which the origin is attached to the target. In this way, the original maneuvering target is transformed to a stationary one. We introduce the idea of polynomial guidance in the range domain into the relative virtual guidance model, then the acceleration command is obtained considering the terminal line-of-sight angle constraint and the terminal virtual look angle constraint. After linearization, the proposed law turns to a similar structure with the trajectory shaping guidance law, which is the optimal guidance law in the linear system. Finally, the performance of the proposed guidance law is demonstrated through numerous nonlinear simulations <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</b>

Under-actuated USV path following control under multiple constraints

The path following control of an under-actuated unmanned surface vehicle (USV) under the constraints of rudder angle, rudder velocity, and rudder response time in the disturbing environment is studied, and a cascaded path following control system based on guidance law and heading control law is designed. First, the guidance law is designed on the basis of integral line-of-sight, while the tracking error state is introduced to design a variable gain disturbance observer, which not only ensures the stability of the convergence section but also takes into account the tracking accuracy of the stable section. The stability of the system is analyzed. Subsequently, the rudder maneuverability constraint and rudder effect delay are further imposed after fully considering the limited range of rudder angle, rudder velocity, and rudder response time in the process of path following. In addition, the heading control law is, therefore, designed on the basis of the rolling optimization strategy, which effectively reduces the oscillation while ensuring the convergence speed. The stability of the control law is further proved. Thereafter, a simulation experiment proves the effectiveness and advancement of the algorithm designed in this paper. In the end, based on the software and hardware design of the control system, “Sea Sturgeon” USV is used for the lake test of the proposed control algorithm to verify its feasibility in practical engineering applications.

Thermal buckling analysis of tapered laminated composite beam: Numerical and experimental investigation

AbstractThe present study focuses on the numerical modeling of the thermal buckling behavior of tapered laminated composite beams validated by experimentation. Lagrange's energy‐based governing differential expression was derived utilizing classical laminated plate theory and higher‐order shear deformation theory to analyze the tapered composite beam's thermal buckling property. The uniform temperature rise environment is employed to estimate the critical buckling temperature of the tapered laminated composite beam. The obtained results from the numerical approaches were validated with the experimental results and the previous results obtained from the literature associated with the fundamental frequencies of the structure and critical buckling temperature. The parametric study was incorporated in this present work to investigate the influence of the structural parameters and the geometrical parameters like taper angle, ply orientation, aspect ratio, and boundary constraints of the beam.