Trajectory Constraints Research Articles

An ETA-Based Tactical Conflict Resolution Method for Air Logistics Transportation

Air logistics transportation has become one of the most promising markets for the civil drone industry. However, the large flow, high density, and complex environmental characteristics of urban scenes make tactical conflict resolution very challenging. Existing conflict resolution methods are limited by insufficient collision avoidance success rates when considering non-cooperative targets and fail to take the temporal constraints of the pre-defined 4D trajectory into consideration. In this paper, a novel reinforcement learning-based tactical conflict resolution method for air logistics transportation is designed by reconstructing the state space following the risk sectors concept and through the use of a novel Estimated Time of Arrival (ETA)-based temporal reward setting. Our contributions allow a drone to integrate the temporal constraints of the 4D trajectory pre-defined in the strategic phase. As a consequence, the drone can successfully avoid non-cooperative targets while greatly reducing the occurrence of secondary conflicts, as demonstrated by the numerical simulation results.

A multi-segment multi-pulse maneuver control method for micro satellite

Aiming at the constraint due to micro satellite orbital maneuverability and relative navigation, a multi-segment multi-pulse maneuver control method is proposed for approaching a target satellite. Convert the along-track approaching trajectory into an impulsive control problem with fixed time and fixed distance. With time and distance from origin to destination as the optimization objectives, the time-distance optimal solution set is generated under the delta-v constraint and trajectory constraint. The planning function is obtained by fitting a segmented polynomial to the optimal solution set. In the approach mission, the maneuver time to reach the expected terminal is determined based on the planning function, and the approaching to the terminal is accomplished using fixed-time multi-pulse control. Based on the simulation scenario, a multi-segment maneuvering strategy is obtained according to the optimization result, and the mission simulation is completed using the three-pulse control. The results show that the proposed multi-segment multi-pulse maneuver control method can reliably complete the approach mission under the constraints.

Fault-tolerant practical tracking control for uncertain robotic system with general reference trajectory and output constraint

This paper is devoted to the fault-tolerant tracking control for a class of uncertain robotic systems under time-varying output constraints. Notably, both actuator fault and the disturbances are present while all the dynamic matrices are not necessarily to be parameterized by unknown parameters or have known nominal parts, and moreover, the reference trajectories as well as the output constraints functions are not necessarily twice continuously differentiable without any time derivatives of them being available for feedback. These remarkable characteristics greatly relax the corresponding assumptions of the related literature and in turn to bring the ineffectiveness of the traditional schemes on this topic. For this, a powerful adaptive control methodology is established by incorporating adaptive dynamic compensation technique into the backstepping framework based on Barrier Lyapunov functions. Then, an adaptive state feedback controller with the smart choices of adaptive law and virtual controls is designed which guarantees that all the states of the closed-loop system are bounded and the system output practically tracks the reference trajectory while not violates the output constraints.

Multiple UAV formations delivery task planning based on a distributed adaptive algorithm

In this paper, six-rotor UAVs are used in the field of distribution to realize the delivery of materials arriving the demand point by UAVs. Due to the small load capacity of the six-rotor UAV, in response to actual demand, the UAV group will be used to complete the delivery task. Considered to be close to the real requirements, trajectory constraints and dynamic obstacles are established in the trajectory planning based on group perception range. In order to better deal with dynamic obstacles and related constraints, this paper designs a distributed adaptive algorithm based on individual decision-making and group decision-making. Individual decision-making is embodied in the intelligence and adjustment of UAVs, involving actor-critic methods, artificial potential field method ideas and probability finite state machines; group decision-making is embodied in the leadership mechanism and joint decision-making; self-adaptation is embodied in the adaptive adjustment of UAV level in group. In order to avoid collisions between UAV groups, a conflict resolution algorithm is designed. Through simulation analysis, the distributed adaptive algorithm proposed in this paper can not only satisfy all constraints, avoid dynamic obstacles stably, and complete tasks with small fluctuations, but also obtain the most successful decision-making UAV in the group. This article further analyzes and discusses the relevant parameters in the algorithm, and obtains the optimal parameter ranges in individual decision-making and group decision-making.

Joint energy and throughput optimization for MEC-enabled multi-UAV IoRT networks

In this paper, we study an Unmanned Aerial Vehicle (UAV) enabled Mobile Edge Computing (MEC) service provisioning to the Internet of Remote Things (IoRT) devices spread randomly on the ground in a remote area. The data generated by the IoRT devices is collected by the UAVs, which immediately relay the data collected to an MEC device installed on the ground at a nearby location. The MEC device receives the data from the UAVs, and sends the results back to the UAVs, which in turn relay them to IoRT devices. We aim to minimize the energy consumption by the IoRT devices and the UAVs, while maximizing the system throughput subject to bandwidth, power, information-causality, and UAVs’ trajectory constraints. We formulate the problem as a Mixed Integer Non Linear Programming problem, which is a complex and non-convex optimization problem. To make the problem tractable, we use variable relaxation. We further develop an iterative algorithm based on Block Coordinate Descent method, to jointly optimize the connection scheduling, power control, bit transmission scheduling, bandwidth allocation, and trajectories of the UAVs. Numerical results demonstrate the convergence of the algorithm and superiority of the proposed model with respect to conventional methods. Our proposed system model of placing MEC at ground shows 9% improvement in energy consumption when compared to carrying out computations at MEC carried by UAV and a 99% improvement when compared to placing MEC at the satellite. The proposed system model shows a 0.2% lower system throughput on average, compared to placing MEC at UAV, which is tolerable considering gains in terms of energy consumption.

An Overlap-Free Calibration Method for LiDAR-Camera Platforms Based on Environmental Perception

Indoor environments are challenging for multi-sensor calibrations. Traditional calibration methods use the target structure for camera and LiDAR calibration. Those approaches not only require pre-processed data and offline calculations, but also face challenges in low-light and object-occluded indoor environments. We proposed an automatic calibration method using trajectory constraints on the LiDAR-Camera. The proposed method first obtains the accurate LiDAR trajectory by the LiDAR-SLAM algorithm. At the same time, the problem of visual SLAM trajectory drift in the indoor environment is improved by graphical optimization using the rigid relative position invariance between sensors during displacement. Thus, extrinsic calibration is achieved by using the relative relationship between sensor trajectories. This method has higher robustness than the target-based calibration methods. The experimental results show that our algorithm has higher accuracy than the target-based calibration in the underground environment. The rotation root-mean-square error (RMSE) improves from 6.637° to 0.564°, and the translation RMSE improves from 0.197 m to 0.082 m.

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.

Trajectory-Robust RFID Relative Localization Based on Phase Profile Correlation

Indoor localization systems based on radio frequency identification (RFID) technologies are widely adopted in the Internet of Things (IoT). Many of these applications prefer to obtain the relative position of the target object rather than the absolute position. Existing relative positioning methods are subject to strict trajectory constraints and cannot work under nonstraight trajectories. RFID mobile localization which has high accuracy can also be used for relative positioning, but they require the acquisition of precise moving trajectory coordinates. To overcome these challenges, we propose a trajectory-robust relative localization algorithm (TRL), based on phase profiles’ correlation in this article. The intuition of TRL is that the phase of the backscattered signal has a linear mapping relationship with the distance between the reader and the antenna, so the closer the tag is to each other, the higher the correlation of their phase curves is. We use the dynamic time warping (DTW) algorithm to calculate the correlation between the phase profiles of different tags and achieve relative localization of all the tags by sequentially determining their position intervals in the tag sequence. Compared with the state-of-the-art solutions, TRL gives greater flexibility to antenna movement and the demand for trajectory coordinates, and is it fully robust to trajectory error. A series of experimental results show that TRL has significant advantages over the current state-of-the-art schemes in terms of both accuracy and computation time.

Robust trajectory-constrained frequency control for microgrids considering model linearization error

Grid supportive modes integrated within inverter-based resources can improve the frequency response of renewable-rich microgrids. The synthesis of grid supportive modes to guarantee frequency trajectory constraints under a predefined disturbance set is challenging but essential. To tackle this challenge, a numerical optimal control (NOC)-based control synthesis methodology is proposed. Without loss of generality, a wind-diesel fed microgrid is studied, where we aim to design grid supportive functions in the wind turbine. In the control design, linearized models are used, and the linearization-induced errors are quantitatively analyzed by reachability and interval arithmetics and represented in the form of interval uncertainties. Then, the NOC problem can be formulated into a robust mixed-integer linear program. The control structure is strategically configured into two levels to realize online deployment. The proposed control is verified on the modified 33-node microgrid with a full-order three-phase nonlinear model in Simulink. The simulation results show the effectiveness of the proposed control paradigm and the necessity of considering linearization-induced uncertainty.

Optimal guidance for hypersonic vehicle using analytical solutions and an intelligent reversal strategy

This paper presents a novel three-dimensional guidance law to quickly generate optimal commands in the gliding phase. Owing to the complicated trajectory constraints and highly uncertain disturbances, the novel gliding profile is developed for the longitudinal plane. Subsequently, this longitudinal profile is utilized to obtain analytical equations of motion for performance index and path constraints prediction. Moreover, stringent terminal constraints, which comprise the altitude, the flight path angle, and the position of transition from gliding phase to terminal diving phase, are integrated into the longitudinal profile. The proposed analytical expressions simplify the onboard generation of optimal gliding trajectory as it does not involve complicated nonlinear programming problems. In addition, to regulate the terminal velocity onboard and simultaneously eliminate the heading error, two bank-reversal opportunities are used in the lateral profile and determined using a reinforcement learning algorithm. In the proposed guidance law, the terminal deviations are first predicted in real-time using the analytical expressions; and then the three-dimensional trajectory is regenerated by addressing a simple optimization problem and planning bank-reversal positions. The computation of the guidance law is facilitated using analytical solutions and a reinforcement learning method; therefore, the frequency of replanning facilitates the robustness, accuracy, and optimality. We evaluated the effectiveness of our method using some representative scenarios.

Human-Like Trajectory Planning for Autonomous Vehicles Based on Spatiotemporal Geometric Transformation

Human-driven vehicles and different levels of autonomous vehicles are expected to coexist on roads in the future. However, autonomous systems behave differently from their human-driver counterparts, these two behaviors are incompatible with one another, thereby negatively impacting traffic efficiency and safety. Herein, we present the construction of human-like trajectories for use in autonomous vehicles as a possible solution to this issue. We present a trajectory planning method based on the spatiotemporal geometric transformation of driving scenarios to generate human-like trajectories. Speed and safety redundancy data were collected through driving tests to understand human driving behaviors. Self-driving scenarios were abstracted as a Lorentz coordinate system under a three-dimensional Minkowski space-time. A surrounding-manifold tensor equation was established using differential geometry theory to depict the relationship between the trajectory constraints and the geometric spatiotemporal background. A metric tensor field can be solved from the equation to construct the corresponding “volcano space-time,” which is a three-dimensional general Riemannian space for placing the subject vehicle and the surroundings. The geodesics of the volcano space-time are solved using the geodesic equation and are projected back into the three-dimensional Minkowski space-time. Geodesic trajectories were fitted as Bézier curves in this study and corrected according to the vehicle dynamics constraints for trackability. In simulation and real vehicle tests, trajectories generated using the proposed algorithm exhibited collision avoidance and trackability, and the algorithm offered behaviors that were similar to those of human drivers under the same scenarios.

A Sampling-Based Motion Assignment Strategy With Multi-Performance Optimization for Macro-Micro Robotic System

This article proposes a sampling-based motion assignment strategy for coordinated motion planning of macro-micro robotic systems. It is used to achieve performance enhancements while solving joint trajectories. The sampling strategy is implemented by traversing a series of feasible sets generated by the trajectory constraints of the micro robot. Meanwhile, two kinds of performance index maps are introduced to achieve normalization and integration of multiple performance indices. They are used for iterative generation of trajectories and overall performance evaluation, respectively. Comparative numerical results prove the validity of the proposed strategy.

Small and dim infrared moving target detection based on spatial–temporal saliency

Infrared target detection is a significant work in military, high accuracy and high speed are the essential capabilities for precise guidance. With limited conditions, making full use of spatial–temporal information can really improve performance. This article studied small and dim infrared moving target detection based on sequence images. Quaternion Fourier Transform is an efficient method of visual saliency. To make this algorithm more accurate, we introduced four preprocessing feature map as input channels for quaternion. They are selective inter frame difference, fuzzy-based morphology filter, joint local gradient and gray contrast measure and temporal-constrained Gaussian curvature filter. All of them aim to highlight small-dim target and help to construct saliency map. Simultaneously, a trajectory constraint is introduced to reduce false alarm rate. Compared with single-frame based methods and multi-frames based methods, our novel algorithm performed better on balancing time consuming and detection precision.

An optimization for alleviating pilot workload during tilt rotor aircraft conversion and reconversion maneuvers

This work was focused on the conversion and reconversion maneuvers of XV-15 tilt rotor aircraft between helicopter and airplane modes. To alleviate pilot workload and improve safety, we proposed a multi-objective optimization method. Firstly, an augmented dynamics model has been developed and validated. Then, the transition maneuver was formulated as a proper optimization problem. The cost function consisted of several factors including transitional time, pilot workload, the power required, control allocation and pitch attitude. The constraints included not only the trajectory constraints and control rate limits, but also safety conditions of the conversion corridor and flight height. Finally, we analyzed the optimization results of two typical nacelle tilting schedules for both maneuvers using the wavelet analysis method to compare the pilot workload. Based on the results, in order to alleviate the pilot workload, it was recommended that during the conversion maneuver nacelles should initially tilt with much slower rate before aircraft reaches a certain forward speed at which the nacelle can tilt with normal rate. While during the reconversion maneuver nacelles were recommended to tilt under a normal rate. The nacelle tilting schedules in both maneuvers should be restricted inside the conversion corridors. As a result, the presented optimization method could identify the pros and cons between the two typical nacelle tilting schedules successfully. The obtained results could be used to provide a better reference for pilots and automatic conversion control systems.

A Novel Trajectory Planning Method for Parafoil Airdrop System Based on Geometric Segmentation Strategy

Reasonable trajectory planning is the precondition for the parafoil airdrop system to achieve autonomous accurate homing, and safe landing. To successfully realize the self-homing of the parafoil airdrop system, a new trajectory optimization design scheme is proposed in this paper. The scheme is based on the parafoil’s unique flight and control characteristics and adopts a segmented homing design. The current common trajectory design method faces a problem, whereby straight-line flight distance before landing is limited by the radius of the height-reducing area. The core feature of the proposed design scheme is its avoidance of this problem, thereby ensuring landing accuracy and safety. Firstly, the different starting states of the parafoil airdrop system and the landing requirements were comprehensively considered, and the homing trajectory reasonably segmented. Based on the requirements of energy control, stable flight, and landing accuracy, the optimal objective function of the trajectory was established, and the trajectory parameters, calculation methods, and constraints were given. Secondly, the cuckoo search algorithm was applied to optimize the objective function to obtain the final home trajectory. Finally, the trajectory planning under different airdrop conditions was simulated and verified. The results showed that the planned trajectories could reach the target point accurately and meet the flight direction requirements, proving the proposed scheme’s correctness and feasibility.

Classical Planning with Avoid Conditions

It is often natural in planning to specify conditions that should be avoided, characterizing dangerous or highly undesirable behavior. PDDL3 supports this with temporal-logic state trajectory constraints. Here we focus on the simpler case where the constraint is a non-temporal formula ? - the avoid condition - that must be false throughout the plan. We design techniques tackling such avoid conditions effectively. We show how to learn from search experience which states necessarily lead into ?, and we show how to tailor abstractions to recognize that avoiding ? will not be possible starting from a given state. We run a large-scale experiment, comparing our techniques against compilation methods and against simple state pruning using ?. The results show that our techniques are often superior.

Adaptive reinforcement learning in control design for cooperating manipulator systems

AbstractIn this paper, an optimal motion/force hybrid control strategy based on adaptive reinforcement learning (ARL) is proposed for cooperating manipulator systems. The optimal trajectory control and constraint force factor control, by using the Moore–Penrose pseudoinverse, are addressed to design the controller corresponding to the manipulator dynamic model. In addition, a frame of a different auxiliary term and an appropriate state‐variable vector are presented to address the non‐autonomous closed system with a time‐varying desired trajectory. The simultaneous actor/critic algorithm is implemented by optimizing the squared Bellman difference to be computed from the error of control policy and optimal control input. Moreover, the constraint force factor controller is discussed by a nonlinear technique after achieving the result of the constraint force factor. The tracking and convergence of ARL‐based optimal motion/force hybrid control strategy are validated in closed‐loop systems by a proposed Lyapunov function candidate. Finally, simulation results are implemented on a constrained system using three manipulators to verify the physical implementation of the presented optimal motion/force hybrid‐tracking control strategy.

Constrained control methods for lower extremity rehabilitation exoskeleton robot considering unknown perturbations

In this paper, trajectory tracking control is investigated for lower extremity rehabilitation exoskeleton robot. Unknown perturbations are considered in the system which are inevitable in reality. The trajectory tracking control is constructively treated as constrained control issue. To obtain the explicit equation of motion and analytical solution of lower extremity rehabilitation exoskeleton robot, Udwadia–Kalaba theory is introduced. Lagrange multipliers and pseudo-variables are not needed in Udwadia–Kalaba theory, which is more superior than Lagrange method. On the basis of Udwadia–Kalaba theory, two constrained control methods including trajectory stabilization control and adaptive robust control are proposed. Trajectory stabilization control applies Lyapunov stability theory to modify the desired trajectory constraint equations. A leakage type of adaptive law is designed to compensate unknown perturbations in adaptive robust control. Finally, comparing with nominal control and approximate constraint-following control, simulation results demonstrate the superiority of trajectory stabilization control and adaptive robust control in trajectory tracking control.

Robust trajectory and communication design for angle-constrained multi-UAV communications in the presence of jammers

This paper studies a multi-unmanned aerial vehicle (UAV) enabled wireless communication system, where multiple UAVs are employed to communicate with a group of ground terminals (GTs) in the presence of potential jammers. We aim to maximize the throughput overall GTs by jointly optimizing the UAVs' trajectory, the GTs' scheduling and power allocation. Unlike most prior studies, we consider the UAVs' turning and climbing angle constraints, the UAVs' three-dimensional (3D) trajectory constraints, minimum UAV-to-UAV (U2U) distance constraint, and the GTs' transmit power requirements. However, the formulated problem is a mixed-integer non-convex problem and is intractable to work it out with conventional optimization methods. To tackle this difficulty, we propose an efficient robust iterative algorithm to decompose the original problem be three sub-problems and acquire the suboptimal solution via utilizing the block coordinate descent (BCD) method, successive convex approximation (SCA) technique, and S-procedure. Extensive simulation results show that our proposed robust iterative algorithm offers a substantial gain in the system performance compared with the benchmark algorithms.

Parameters Estimation of Nutational Satellite Based on Sun Sensor

Estimation of the satellite’s kinematic parameters based on sun sensor is of great significance to tumbling satellite and can also be used as a backup method for the satellite’s raw attitude measurement. A method for estimating the kinematic parameters of the nutational satellite based on sun sensor is proposed in this article. The kinematic model of the sun vector is established by separating the nutational motion into two rotations. The kinematic parameters are calculated by vector decomposing and motion decoupling. The parameter estimation accuracy is ensured by trajectory constraints. Simulated and experimental results indicate that the algorithm is effective. For sun sensor with accuracy of 0.1°, the estimation accuracy of angular velocity is less than 0.2°/s. The estimation accuracy of nutational angle is about 0.7°–1°. Therefore, this method can be an effective way to estimate essential kinematic parameters of satellite when needed.