Velocity Constraints Research Articles

Convex and Nonconvex Sweeping Processes with Velocity Constraints: Well-Posedness and Insights

Convex and Nonconvex Sweeping Processes with Velocity Constraints: Well-Posedness and Insights

Vertical deformation analysis based on combined adjustment for GNSS and leveling data

A method is proposed to fuse the velocity data of the global navigation satellite system (GNSS) and leveling height via combined adjustment with constraints. First, stable GNSS–leveling points are uniformly selected, and the constraints of the geodetic height change velocity and normal height change velocity are given. Then, the GNSS vertical velocities and leveling height difference are used as observations of combined adjustment, and robust least-squares estimation are used to estimate the velocities of the unknown points. Finally, a vertical movement model is established with the GNSS vertical velocities and leveling vertical velocities obtained via combined adjustment. Data from the second-order leveling network and GNSS control points in Shandong Province are taken as test data, and eight calculation schemes are used for discussion. One of the schemes, the bifactor robust combined adjustment method based on variance component estimation with two kinds of vertical velocity constraints achieves the optimal results. The method applied in the scheme can be recommended for data fusion of GNSS and leveling, further improving the reliability of vertical crustal movement in Shandong Province.

Multirobot Transport of Deformable Objects With Collision Avoidance

In the problem of autonomous transport of deformable objects, we propose a multirobot approach for steering a large object to a target configuration (object dimensions, orientation, and position). Firstly, we present a deformation model based on the evolution over time of the dimensions and rotation of the object's bounding box (BB). We consider the object is grasped by a set of mobile robots with double-integrator dynamics. Then, we propose a set of nominal controllers that allows reaching a desired configuration of the BB that models the deformable object. In order to prevent collisions of the object with static or dynamic obstacles, we formulate a control barrier function (CBF) that exploits our deformation model. Finally, we integrate the nominal controllers and the CBF into a quadratic-programming controller, which includes overstretching avoidance and velocity constraints. We report simulation results to show the performance of this approach in different test scenarios.

Unified Mapping Function-Based Neuroadaptive Control of Constrained Uncertain Robotic Systems.

For the existing adaptive constrained robotic control algorithms, the demanding "feasibility conditions" on virtual controller is normally inevitable and the extra limits on constraining functions have to be imposed, making the corresponding approaches more demanding and less user friendly in control development. Here, we develop a new neuroadaptive constrained control strategy for uncertain robotic manipulators in the presence of position and velocity constraints. First, a novel unified mapping function (UMF) is constructed so that the restriction on constraining boundaries is removed and more kinds of constraining forms can be handled. Second, by integrating the UMF-based coordinate transformation with the "universal" approximation characteristic of neural networks over some compact set, the developed neuroadaptive control completely obviates the complicated yet undesired "feasibility conditions." Furthermore, it is proven that all closed-loop signals are semiglobally bounded and the constraints are not violated. The effectiveness of the proposed control is validated via a two-link rigid robotic manipulator.

Underactuated Mechanical Systems With Both Actuator and Actuated/Unactuated State Constraints: A Predictive Control-Based Approach

Underactuated systems are widely used in practice. Due to actuator saturation and transient performance requirements, it is necessary to keep the control inputs and system states within safe limits. However, with fewer control inputs, the state constraints, especially for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unactuated</i> states, are usually difficult to guarantee. Model predictive control (MPC), as a method that can handle constraints naturally, unfortunately, still struggles to deal with unactuated variable constraints directly. To this end, this article proposes a general MPC algorithm <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">for a class of underactuated systems</i> . First, an MPC method considering actuator saturation constraints is designed, based on which, different velocity constraint-related matrices are constructed to convert both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">actuated</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unactuated</i> velocity constraints into control input constraints. Then, by delicately analyzing the coupling relationship between actuated and unactuated variables, the displacement/angle constraints of unactuated variables are theoretically ensured. To our best knowledge, it is the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> MPC approach designed for a class of underactuated systems with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">both</i> actuated and unactuated state constraints as well as actuator saturation. Finally, the proposed MPC approach is applied to two typical underactuated systems, i.e., tower cranes and boom cranes, and a series of experiments are investigated to verify the effectiveness and superiority of this approach.

Adaptive Neural Control of Connected Vehicular Platoons With Actuator Faults and Constraints

This paper focuses on the adaptive neural control problem for a connected vehicles platoon system with external disturbances, actuator fault and constraints. Then, the tangent barrier Lyapunov function is introduced into the control design to solve the time-varying position and velocity constraints in a vehicle platoon. Since the selected engine dynamics model is nonlinear, the neural network is adopted to approximate the unknown internal vehicle dynamics. Moreover, the actuator fault effect is addressed by the designed adaptive law designed based on the projection operator. It can be eventually confirmed that all the involved closed-loop signals are bounded based on the Lyapunov stability theory. Finally, a comparative simulation shows the effectiveness of the proposed control scheme.

Minimum-Time Transient Response Guaranteed Control of Servo Motor Systems With Modeling Uncertainties and High-Order Constraint

Practical servo motor systems are generally subject to various modeling uncertainties and actuating constraints. It is challenging to guarantee a minimum-time transient response when modeling uncertainties and constraints present simultaneously. As such, a two-loop control algorithm, which integrates a smooth projection based saturated adaptive robust controller (SARC) and a third-order minimum-time trajectory planner (TOMTTP) seamlessly, is proposed. Specifically, the smooth projection based SARC synthesized in the inner loop mainly handles the modeling uncertainties and feedback constraint, while the TOMTTP in the outer loop generates a time-optimal trajectory under the low-order constraints (velocity and feedforward constraints) and high-order constraint (feedforward rate constraint) simultaneously. Consequently, the transient response is achieved in a minimum-time manner. Simulations on a typical servo motor system are conducted, and the comparative results confirm the superiorities of the proposed approach.

Containment Control With Different Constraints

This paper addresses a containment control problem for discrete-time multi-agent systems when position, velocity and input constraints coexist. A nonlinear distributed containment control algorithm is presented. The main difficulty is how to decouple the nonlinearities caused by the three kinds of constraints. To prove the convergence of the containment control problem, the distances from the followers to the convex hull spanned by the leaders are analyzed by removing the errors caused by the projection operators and the stochasticities of the equivalent system matrices are explored to show nonincreasing property of the maximum distance. It is shown that containment control can be achieved as long as the convex hull is contained in each position constraint set. Numerical simulations are given to illustrate the obtained theoretical results.

Decentralized Robust Collision-Avoidance for Cooperative Multirobot Systems: A Gaussian Process-Based Control Barrier Function Approach

Data-based Machine Learning methods have been successfully applied to control system design in recent years. However, safety during the learning and control process is difficult to guarantee due to the inherent uncertainties. In this work, we propose a barrier function-based robust cooperative collision avoidance control framework for heterogeneous multirobot systems with model learning. First, a new control barrier function (CBF) design is proposed for cooperative collision avoidance, which leads to less conservativeness of the feasible control actions. Then, decentralized robust CBF conditions are derived which incorporate the estimation of the individual model uncertainty using Gaussian Process models such that each robot can guarantee safety with a high probability. Finally, a quadratic programming problem is formulated to obtain a controller which is minimally invasive to the nominal controller and satisfies the CBF and velocity constraints simultaneously. The decentralized implementation of the robust collision avoidance control strategy is explicitly shown and proven. Two simulation examples are given to demonstrate the effectiveness of the proposed control framework.

Nussbaum-based finite-time containment control for multi-UAVs with input saturation and velocity constraints

This paper devotes to addressing the finite-time containment control for the multi-UAVs with input saturation and velocity constraints. A novel smooth function is presented to estimate the saturation function with adjustable estimate errors. By utilizing the mean-value theorem, the containment control for UAVs with input saturation can be turned into a variable gain control problem. To address this issue, the Nussbaum-based method is used to design the controller in this paper. Besides, based on the backstepping method, the controller can constrain the velocity states of UAVs within a desired time-varying asymmetric region by limiting the values of virtual velocity commands and the Lyapunov function. Finally, the finite-time convergence of the errors and the practicability of the control law are verified by Lyapunov stability analysis and numerical simulations.

Safe Reinforcement Learning for Transition Control of Ducted-Fan UAVs

Ducted-fan tail-sitter unmanned aerial vehicles (UAVs) provide versatility and unique benefits, attracting significant attention in various applications. This study focuses on developing a safe reinforcement learning method for back-transition control between level flight mode and hover mode for ducted-fan tail-sitter UAVs. Our method enables transition control with a minimal altitude change and transition time while adhering to the velocity constraint. We employ the Trust Region Policy Optimization, Proximal Policy Optimization with Lagrangian, and Constrained Policy Optimization (CPO) algorithms for controller training, showcasing the superiority of the CPO algorithm and the necessity of the velocity constraint. The transition trajectory achieved using the CPO algorithm closely resembles the optimal trajectory obtained via the well-known GPOPS-II software with the SNOPT solver. Meanwhile, the CPO algorithm also exhibits strong robustness under unknown perturbations of UAV model parameters and wind disturbance.

M2C-GVIO: motion manifold constraint aided GNSS-visual-inertial odometry for ground vehicles

Visual-Inertial Odometry (VIO) has been developed from Simultaneous Localization and Mapping (SLAM) as a low-cost and versatile sensor fusion approach and attracted increasing attention in ground vehicle positioning. However, VIOs usually have the degraded performance in challenging environments and degenerated motion scenarios. In this paper, we propose a ground vehicle-based VIO algorithm based on the Multi-State Constraint Kalman Filter (MSCKF) framework. Based on a unified motion manifold assumption, we derive the measurement model of manifold constraints, including velocity, rotation, and translation constraints. Then we present a robust filter-based algorithm dedicated to ground vehicles, whose key is the real-time manifold noise estimation and adaptive measurement update. Besides, GNSS position measurements are loosely coupled into our approach, where the transformation between GNSS and VIO frame is optimized online. Finally, we theoretically analyze the system observability matrix and observability measures. Our algorithm is tested on both the simulation test and public datasets including Brno Urban dataset and Kaist Urban dataset. We compare the performance of our algorithm with classical VIO algorithms (MSCKF, VINS-Mono, R-VIO, ORB_SLAM3) and GVIO algorithms (GNSS-MSCKF, VINS-Fusion). The results demonstrate that our algorithm is more robust than other compared algorithms, showing a competitive position accuracy and computational efficiency.

Rudder/fin joint anti-rolling control system based on interference model predictive control and sliding mode observer

To overcome the difficulties of time-varying disturbance, model mismatch, and frequent operation in the rudder/fin joint control system, an interference model predictive control (I-MPC) rudder/fin joint control system with sliding mode observer is proposed. Considering that the model mismatch problem occurs when the ship is sailing, the model mismatch and external disturbance are regarded as the total disturbance. A discrete 3-degree-of-freedom ship disturbance mathematical model is established. The rudder angle and fin angle are selected as the system inputs, then a sliding mode observer is designed to observe the time-varying disturbance and system output in real time. Different from traditional MPC and feedforward compensation, I-MPC will predict the output based on the disturbance observation value, and the control law is solved under rudder/fin angle and angular velocity constraints. Simulation results show that the proposed method improves the tracking performance and anti-disturbance performance of the rudder/fin system. The observer has high observation accuracy for constant, sinusoidal, and time-varying disturbances. Mechanism wear and energy loss caused by frequent operation are avoided.

A yaw correction method for pedestrian positioning using two low-cost MIMUs

In pedestrian inertial navigation system, the traditional zero-velocity update (ZUPT) method establishes a velocity constraint. Based on the Kalman filter algorithm, the velocity error is utilized to correct the position drift. However, the yaw error cannot be observed. In this study, two low-cost magnetometers/inertial measurement units (MIMUs) are tied to the foot and shank, respectively. To improve the positioning accuracy, two error correction methods are developed. Firstly, the yaw angle coordinate is chosen as a Kalman filter measurement vector. Secondly, a geometric constraint is proposed. It includes degree of freedom constraint, angle constraint, and position vector constraint. Finally, different indoor and outdoor experiments are employed to verify the effectiveness of the proposed method. The average distance error percentage of the proposed method is less than 2%, and the heading bias is less than 5° within 5.05 min. Thus, the estimated paths are more in line with the actual trajectories.

Trajectory Estimation of a Flying Robot With a Single Ranging Beacon and Derived Velocity Constraints

The performance of the trajectory estimation with a single beacon highly depends on the observability of the system, which is further determined by the excitation patterns of the robot. Because the desired excitation patterns regarding specific observability conditions cannot always be guaranteed in real-time, the trajectory estimation may casually fail with divergence. To tackle this issue, indirectly derived velocity constraints are first introduced in this work, and their effects on improving the performance of trajectory estimation are comparatively investigated. Considering the geometric evolution equation and using the state augmentation technique, seven different velocity constraints are evaluated. The comparative results indicate that the trajectory estimation divergence can be most effectively avoided with a pure velocity magnitude constraint. On this basis, a velocity-constrained moving horizon estimation algorithm is implemented and verified in an indoor experimental testbed to accurately estimate the trajectory of the flying robot with a single ultra-wideband beacon in a long time interval. The results also quantitatively illustrate that the overall performance of the proposed approach outperforms that of the latest benchmark approach in both estimation precision and computational efficiency. In particular, with approximately the same estimation precision, the computational time cost of the proposed approach is less than 1/10 of that of existing approaches.

Trajectory planning for mechanical systems in the presence of dynamic obstacles

This paper deals with an optimal motion planning method for mechanical systems subjected to velocity and acceleration constraints in the presence of dynamical geometric obstacles. Using a state parametrization method based on time polynomials the trajectory planning problem is reformulated as a constrained nonlinear optimization problem which is solved using a numerical optimization toolbox. Quadrotor motion planning in the horizontal plane is considered as an illustration example.

Research on Covert Directional Spoofing Method for INS/GNSS Loosely Integrated Navigation

To meet the task requirements of using GNSS spoofing signals to achieve directional spoofing of unmanned target platforms, this paper proposes an INS/GNSS integrated navigation covert directional spoofing method, which can be used in key place security defense and public security protection scenarios. Taking the steady-state gain matrix as a breakthrough, this paper firstly studies the influence mechanism of GNSS spoofing signals on the position output of INS/GNSS integrated navigation, and then deduces the feasibility of directional spoofing by using exponential spoofing signal with two adjustable parameters in INS/GNSS integrated navigation mode. Then, the influence of spoofing signals on the attitude and speed of the integrated navigation output is analyzed, and the relevant constraints of velocity and attitude errors are introduced to determine the exponential GNSS spoofing signals model that meets the requirements of covertness, and finally the task of covert directional spoofing of the target unmanned platform is realized. Simulation and experiments verify the effectiveness and correctness of INS/GNSS covert directional spoofing method.

Path Following of Underactuated Autonomous Surface Vessels With Surge Velocity Constraint and Asymmetric Saturation

Path Following of Underactuated Autonomous Surface Vessels With Surge Velocity Constraint and Asymmetric Saturation

Finite element dynamic modeling and attitude control for a slender flexible spacecraft

This paper aims to study the dynamic modeling and attitude control of a kind of slender flexible spacecraft. The basic structure of this kind of spacecraft is different from the traditional structure of a center rigid body with flexible appendages, but rigid bodies at both ends, which are connected by a flexible truss structure. Firstly, the finite element modeling method is adopted to establish the dynamic model of this kind of spacecraft, and the vibration frequency and damping of the flexible structure are obtained. The unconstrained modes of the flexible spacecraft are obtained through mathematical analysis, finite element analysis and frequency domain analysis. In addition, a nonlinear sliding surface with angular velocity constraint is designed. On this basis, an adaptive sliding mode (ASM) controller is proposed, stability of the close-loop system under the controller is proved, and the dynamic model is verified through mathematical simulation.

TECHNICAL AND ECONOMIC SUBSTANTIATION OF THE AIR LAUNCH AEROSPACE SYSTEM PARAMETERS

The substantiation of the technical and economic parameters of the air launch aerospace system, which consists of a reusable unmanned aerial vehicle and integrated launch vehicle, is given. A combination of a turbofan engine and a ramjet engine is used as the unmanned aerial vehicle propulsion system. The considered vehicle is capable of delivering a payload into low-Earth orbits without the use of a spaceport. We have developed the methodology of the technical and economic substantiation of the parameters of the air launch aerospace system. The results were obtained by searching for the minimum of the objective function, which established the relationship between the technical and economic parameters of the aerospace system. For the objective function solution, the design parameters of the integrated launch vehicle and unmanned aerial vehicle were determined, as well as the limitation of the total acceleration velocity of the aerospace system. The methods used allowed us to determine the velocity constraints provided by the operation of the turbofan engine, ramjet engine, and the three solid propellant motors of integrated launch vehicle stages, as well as maximum dynamic pressure and maximum permissible temperature on the unmanned aerial vehicle surface. We determined the scheme for estimating the cost of launching the spacecraft into Earth orbit by the air launch aerospace system. The result of the substantiation is the determination of the technical and economic parameters of the integrated launch vehicle, unmanned aerial vehicle, and the aerospace system as a whole. The influence of the maximum temperature on the surface of the unmanned aerial vehicle and the specific impulse of the ramjet engine on the parameters of the aerospace system was also evaluated. The substantiation is the first step towards the creation of the Ukrainian aerospace air launch system.