Trajectory Generation Method Research Articles

An Online Generation Method of Terminal-Area Trajectories for Wave-Rider Using Deep Neural Networks

This paper presents a deep neural network-based online trajectory generation method for the aerodynamic characteristic description and terminal-area energy management of wave-rider aircrafts. First, the flight dynamics equations in the energy domain are linearized and discretized to generate numerous aircraft trajectory samples with sequential convex optimization (SCO) methods. Then, an optimization objective function is designed to promote the smoothness of the control variables and improve the trajectory similarity. Compared to the nonlinear programming (NLP), the proposed trajectory sample generation method is more suitable for the training of deep neural networks (DNNs). Finally, deep neural networks are formulated and trained for the control variables and state variables, using the generated obtained trajectory samples, so that the reference trajectories can be obtained online during the energy management process of the wave-rider’s terminal phase. Numerical simulations validate the high accuracy of the trajectories generated with the deep neural network. Meanwhile, this proposed method enables smaller storage usage, which is highly suitable for integration into on-board flight control systems.

Adaptive Prescribed Performance Control of Unmanned Aerial Manipulator With Disturbances

This article presents the problem of autonomous control of an unmanned aerial manipulator (UAM) developed for operation with unknown disturbances, wherein the disturbances from the coupling effect between the UAM and the external environment need to be considered. Regarding the coupling force as a disturbance to the entire UAM system, an adaptive prescribed performance control (APPC) scheme utilizing the knowledge of prescribed performance is proposed to guarantee the transient and steady-state performance responses. Also, an adaptive law is designed to estimate the upper boundary parameters of the UAM system uncertainties and disturbances, wherein the restrictive constant boundary assumptions and the prior information of the upper bound are not required in the controller design. Furthermore, to enable safe manipulation in a realistic situation, an end-effector trajectory generation method is presented satisfying the joint angle limitation. For the validation of the proposed method, the simulation results of numerical simulation comparisons are shown. Moreover, experimental scenarios including stable flight and simulated co-work with humans in complex environments are designed to verify the proposed method. <i>Note to Practitioners</i>&#x2014;This article is motivated by the problem of aerial manipulation under unknown disturbances, which may be caused by the wide movement of the manipulator and the sudden loading or unloading of an object. Existing approaches for aerial manipulation often require the assumption of a constant or slowly varying external disturbance. However, a priori bounded disturbance might impose a priori bound on the system state before obtaining closed-loop stability. In this article, the proposed controller with an adaptive law is designed to estimate the upper boundary parameters of the overall disturbances and ensure the predefined performance, so that the prior information of the upper bound of disturbances is not required. The performance of the proposed control strategy is demonstrated via numerical simulation comparisons and experiments, including stale flight and simulated co-work with humans in a complex environment.

PateGail: A Privacy-Preserving Mobility Trajectory Generator with Imitation Learning

Generating human mobility trajectories is of great importance to solve the lack of large-scale trajectory data in numerous applications, which is caused by privacy concerns. However, existing mobility trajectory generation methods still require real-world human trajectories centrally collected as the training data, where there exists an inescapable risk of privacy leakage. To overcome this limitation, in this paper, we propose PateGail, a privacy-preserving imitation learning model to generate mobility trajectories, which utilizes the powerful generative adversary imitation learning model to simulate the decision-making process of humans. Further, in order to protect user privacy, we train this model collectively based on decentralized mobility data stored in user devices, where personal discriminators are trained locally to distinguish and reward the real and generated human trajectories. In the training process, only the generated trajectories and their rewards obtained based on personal discriminators are shared between the server and devices, whose privacy is further preserved by our proposed perturbation mechanisms with theoretical proof to satisfy differential privacy. Further, to better model the human decision-making process, we propose a novel aggregation mechanism of the rewards obtained from personal discriminators. We theoretically prove that under the reward obtained based on the aggregation mechanism, our proposed model maximizes the lower bound of the discounted total rewards of users. Extensive experiments show that the trajectories generated by our model are able to resemble real-world trajectories in terms of five key statistical metrics, outperforming state-of-the-art algorithms by over 48.03%. Furthermore, we demonstrate that the synthetic trajectories are able to efficiently support practical applications, including mobility prediction and location recommendation.

Ideal trajectory generation method of missile formation based on Gaussian pseudo-spectrum method

With the increasingly complex combat environment and the diversity of combat tasks, important military targets are surrounded by multi-layer defense. Modern information warfare pays more attention to system confrontation and multi-system cooperative operations,and missile formation to attack targets is the main research content of this paper. For missile wing ideal trajectory generation problems, ensure the attack Angle of time and meet the design requirements, Gaussian pseudo-spectral method is used to generate guarantee missile attacks within the specified time shot on target, at the same time meet the attack Angle constraint at the end of the ideal trajectory, the more missiles cooperative engagement problems into the ideal trajectory tracking problem, avoid the estimate of the remaining time of flight.The main contents of this paper are as follows:(1) Gaussian pseudo-spectral method is used to generate the ideal trajectory model.(2)Use Matlab to simulate the established model.

Digital twin-based excavation trajectory generation of Uncrewed excavators for autonomous mining

As modern large-capacity excavators, cable shovels provide payload capacities of more than 100-tons per scoop. The presence of a high dynamic payload combined with the self-weight may result in severe stress loading of the whole shovel front-end components during excavation. Structural performance analysis based on numerical simulations typically demands a prohibitively heavy computation, so conventional optimization-based excavation trajectory generation methods generally do not consider structural performance constraints, which may cause sudden component failure or unanticipated costly downtime. Herein, a shape–performance integrated digital twin was constructed to analyze the shape and structural performance of an uncrewed cable shovel (UCS) in real time, which was further used to support optimal excavation trajectory generation. The proposed procedure presents salient features that the time-consuming structural performance response was taken as an additional constraint, which could effectively prevent the sudden structural failures. The effectiveness and applicability were demonstrated via field tests with a UCS prototype (1:7 scale model of the WK-55 type).

A general method of trajectory generation based on point-cloud structures in automatic fibre placement

In the process of manufacturing fibre reinforced composite components with automatic fibre placement(AFP), trajectory generation is the core technology that determines the quality and efficiency of fibre placement and the performance of formed components. This study overcome the limitation that traditional algorithms only consider parameter surfaces or mesh surfaces and study a general method of AFP trajectory generation based on point-cloud structures. Firstly, we proposed a directed projection providing a theoretical guarantee for the subsequent trajectory generation on moulds represented by point-clouds; Secondly, we provided two different solvers named numerical and direct approach to generate initial trajectories and subsequent offsetting trajectories. Our numerical simulations and error analyses show that proposed tactics are well suitable for point-cloud structures and could generate full coverage trajectories within a tiny error without gaps and overlaps. The proposed method is absolutely different from the traditional method and does not need to mesh or reconstruct the point-cloud, but it can directly generate trajectories on point-clouds, thus avoid errors in surface reconstruction and reduce processes of AFP trajectory generation.

A Trajectory Generation Method for Multi-Rotor UAV Based on Adaptive Adjustment Strategy

In order to fly safely and autonomously in complex environments, UAVs need to be able to plan their trajectories in real-time. This paper proposes an improved B-spline-based trajectory generation method that can generate safe, smooth, and kinodynamically feasible trajectories in real-time. This paper firstly introduces the principle of error upper bound of the B-spline curve and proposes a new trajectory safety assurance method; then, the loss function of trajectory is constructed based on safety, smoothness, and flight time; finally, a parameter adaptive trajectory optimization method is proposed, so that obtain the safe trajectory. Compared with the existing methods, the proposed method has two important improvements: (1) it solves the problem of overly conservative safety distance estimation at control points, improves the trajectory smoothness, and reduces the required flight time; (2) it proposes a trajectory optimization method with adaptive adjustment of safety distance parameters, which improves the quality and success rate of the planned trajectory. We validate our proposed method in simulation and real-world tasks, and the test results show that the method proposed in this paper can significantly improve the quality of the generated trajectory.

Heel-strike and toe-off walking of humanoid robot using quadratic programming considering the foot contact states

Heel-strike and toe-off (heel-toe) walking has been studied to increase step length, reduce the torque of the leg joints, or make robots walk similarly to humans. To realize heel-toe walking, it is necessary to determine the foot angle and ensure contact between the ground and the heel and toe. The foot angle for heel-toe walking can be analytically calculated considering the position of the center of mass (CoM) before the foot lands or rises. Therefore, the trajectory of the CoM of one cycle of walking must be known in advance. However, this method cannot be easily incorporated with model predictive control (MPC) to generate the trajectory of CoM in real time. This paper proposes a heel-toe walking method that can be used with the CoM trajectory generated using the MPC scheme. The CoM trajectory generation method that reduced the velocity fluctuation using MPC, which was proposed in a previous study, was used. The stability of the MPC scheme is proved in this paper. The quadratic programming is used to generate the heel-toe walking by considering the foot contact states as the constraints. The increase in step length and the decrease in singularity occurrence due to heel-toe walking were compared and analyzed in the simulation. The experiment verified the proposed heel-toe method.

A Trajectory Generation Algorithm for a Re-Entry Gliding Vehicle Based on Convex Optimization in the Flight Range Domain and Distributed Grid Points Adjustment

Optimal trajectory generation for the guidance of re-entry glide vehicles is of great significance. To realize a faster generation speed and consistency with the guidance mechanism, an improved convex optimization trajectory generation algorithm based on the flight range domain for the re-entry glide vehicles is proposed in this paper. Firstly, according to the definition of the range-to-go, the projected range-to-go of the re-entry glide vehicle is presented when the dynamic model is converted to the flight range domain. Then, the attack angle and bank angle are expanded to the state variables and the change rate, which is designed as a new control variable. When the dynamic models and constraints are convexificated and discretized, the vehicle trajectory discrete convex model in the flight range domain is proposed. In order to further improve the generation speed and accuracy, an initial trajectory generation method that is close to the guidance requirements is proposed by the landing points of different control laws. In addition, by analyzing the nonlinear illegal degree of grid points, the probability density of grid points and the adjustment strategy of grid points are proposed. Finally, the ablation experiment shows that the initial trajectory generation and distributed grid points method works. With different target points, different no-fly zones, different initial states, and the Monte Carlo experiment, our method can effectively and robustly complete the generation. The lateral and longitudinal generation error is less than 1 km. And compared with the Gaussian pseudo-spectral method, our method obtained comparable accuracy and faster speed.

A UAV-based explore-then-exploit system for autonomous indoor facility inspection and scene reconstruction

Traditional indoor facility inspections on pipelines and boilers are conducted manually and can be logistically challenging, labor-intensive, costly, and dangerous for the inspectors. With the maturity of unmanned technology, the unmanned aerial vehicle (UAV) is becoming a promising alternative to the problematic manual inspection. However, due to the lack of GPS signal indoor, the localization of UAVs is a big challenge to achieve fully autonomous inspection. Moreover, the narrow and complex indoor environment makes it difficult to guarantee flight safety. This paper presents a UAV-based explore-then-exploit system to tackle these problems for autonomous indoor facility data collection and scene reconstruction. The proposed system consists of a hardware description and integration of two UAVs, a two-step simultaneous localization and mapping (SLAM) method for UAV localization and 3D environmental mapping, a safety-guaranteed coverage path planning algorithm for inspection and data collection, as well as an obstacle-aware trajectory generation method. The proposed system is examined in GPS-denied and cluttered indoor environment and 3D scene reconstruction is conducted. The quantitative analysis shows that the positioning accuracy is centimeter-level and the reconstruction error is within 3 cm. The performance analysis demonstrates the robustness and feasibility of our system in reconstructing and inspecting complex indoor environments for high-efficiency and low-cost facility management.

DMP-Based Reactive Robot-to-Human Handover in Perturbed Scenarios

While seemingly simple, handover requires joint coordinate efforts from both partners, commonly in dynamic collaborative scenarios. Practically, humans are able to adapt and react to their partner’s movement to ensure seamless interaction against perturbations or interruptions. However, literature on robotic handover usually considers straightforward scenarios. We propose an online trajectory generation method based on Dynamic Movement Primitives to enable reactive robot behavior in perturbed scenarios. Thus, the robot is able to adapt to human motion (stopping should the handover be interrupted while persisting through minor disturbances on the partner’s trajectory). Qualitative analysis is conducted to demonstrate the capability of the proposed controller with different parameter settings and against a non-reactive implementation. This analysis shows that controllers with reactive parameter settings produce robot trajectories that can be deemed as more coordinated under perturbation. Additionally, a randomized trial with participants is conducted to validate the approach by assessing the subject perception through a questionnaire while measuring task completion and robot idle time. Our method has been shown to significantly increase the subjective perception of the interaction with no statistically significant deterioration in task performance metrics under one of the two sets of parameters analyzed. This paper represents a first step towards the introduction of reactive controllers in handover tasks that explicitly consider perturbations and interruptions.

Nonlinear Path Generation and Tracking Control Design for a Mobile Robot*

This paper proposes trajectory generation and tracking control methods for a differential drive wheel mobile robot. The reference trajectory is generated as a polynomial function in time variable while the tracking control algorithm is constructed using Lyapunov's stability criteria. Experimental results are reported to show the good performance of the proposed trajectory generation and tracking control algorithms.

Accurate TCP Position and Orientation Trajectory Generation in 6DOF Robotic Manipulators and CNC Machine Tools using FIR Filtering and Haversine Synchronisation

The use of robotics in manufacturing is rapidly growing. One promising application in particular is the use of robots as machining platforms. Robotic machining offers many advantages such as large operating envelopes, flexibility in operations and low installation and running costs. Robotic machining platforms much like computer numerically controlled (CNC) machine tools are commanded by numerical controllers (NCs) using the well established G-code part programming language (ISO-6983). Toolpaths are defined in the work piece coordinate system (WCS) as a series of discrete tool centre point (TCP) positions and tool orientations. The role of the NC is to generate smooth feed drive or robot joint commands such that the tool or end effector travels along the commanded toolpath whilst satisfying TCP position and orientation tolerances and robot/machine tool kinematic constraints. Interpolating tool orientations directly in the WCS requires complex real-time spherical interpolation computations. Overcoming this challenge, this paper introduces a C4 continuous tool path trajectory generation method for 6DOF motion. The tool centre point position is smoothed in the WCS, however, the tool orientation is smoothed directly in the rotary coordinate system without the requirement for spherical interpolation. The interpolated tool orientation trajectory follows the path of the great circle arc using the modified Haversine method eliminating non-linear interpolation errors present in linear interpolation of rotary axis positions (machine coordinate system interpolation). The proposed method is validated by simulation of a 6DOF robotic manipulator.

Online and Real-Time Trajectory Generation Method for Unforeseen Events Using a Modified Spline Approach

This letter focuses on the problem of online and instantaneous generation of smooth trajectories and their analytical time derivatives, where future reference signals provided by a trajectory planner or a user are a-priori unknown. For this purpose, we propose a modified cubic spline polynomial which transforms the instantaneous piecewise references into smooth and continuous functions for digital control systems. The resulting reference signals are not only smooth and continuous in time but also analytically differentiable. The inferred derivative values could then be used in a variety of linear and non-linear controllers such as, Proportional-Integral-Derivative (PID), sliding mode, and backstepping. We also provide optimum and boundary values for the parameters used in the proposed technique. In addition, we present a lightweight implementation (a few lines of code) of the algorithm by which real-time computations are rapidly performed using a microcontroller. Both simulation and real experiments demonstrate that for the plants having different degrees of complexities, the proposed approach with a PD / PID controller outperforms the conventional filtered derivative-based one in terms of overshoot in the step response, robustness against noise, and trajectory tracking error.

Computer-vision-guided semi-autonomous concrete crack repair for infrastructure maintenance using a robotic arm

Engineering inspection and maintenance technologies play an important role in safety, operation, maintenance and management of buildings. In project construction control, supervision of engineering quality is a difficult task. To address such inspection and maintenance issues, this study presents a computer-vision-guided semi-autonomous robotic system for identification and repair of concrete cracks, and humans can make repair plans for this system. Concrete cracks are characterized through computer vision, and a crack feature database is established. Furthermore, a trajectory generation and coordinate transformation method is designed to determine the robotic execution coordinates. In addition, a knowledge base repair method is examined to make appropriate decisions on repair technology for concrete cracks, and a robotic arm is designed for crack repair. Finally, simulations and experiments are conducted, proving the feasibility of the repair method proposed. The result of this study can potentially improve the performance of on-site automatic concrete crack repair, while addressing such issues as high accident rate, low efficiency, and big loss of skilled workers.

Extensively Explored and Evaluated Actor-Critic With Expert-Guided Policy Learning and Fuzzy Feedback Reward for Robotic Trajectory Generation

Trajectory generation for redundant manipulators based on inverse kinematics (IK) still faces some restraints, as it lacks universal IK calculation or specific trajectory generation methods that are suitable for robots with arbitrary degrees of freedom. In this article, the IK-free trajectory generation for robot manipulators is formulated as a Markov decision process and implemented by a general method based on deep reinforcement learning. First, an extensively explored and evaluated actor-critic (E3AC) algorithm that can make diverse action explorations and comprehensive evaluations is designed to solve the trajectory generation problem. Second, a dual-memory structure with expert-guided policy learning strategy is proposed to further enhance the performance of the algorithm in the early training period by additional successful experiences and performing an increasingly unbiased data sampling. Third, a fuzzy feedback reward mechanism that can directly establish a mapping from the abundant state variables to the self-tuning reward is constructed, instead of puzzling out an explicit function to feature the complex relations among the control objects. Finally, the comparative experimental results show that, the proposed approach is more efficient in algorithm convergence and reward calculation, and is more qualified for complex tasks with strong randomness.

Receding Horizon Trajectory Generation of Stratospheric Airship in Low-Altitude Return Phase

The contribution of this paper is the proposal of a new receding horizon trajectory generation method for stratospheric airships’ return phase. Since the energy consumption, wind field and path constraints are restrictions during the return phase of airships at low altitude, it is crucial to develop novel trajectory optimization methods to ensure that the airship returns to the landing site. In this article, optimization objects and conditions of the return trajectory were constructed, considering the energy consumption and wind field. Then, a modified interior point method (MIP) was used to transform the inequality constraint, which is a simple and adaptable method used to improve the solving efficiency on the basis of a modified multiple shooting method (MMS). In addition, an adaptive gradient descent regulator was improved to reduce the influence on the optimization result due to different selections of the initial search point, and the convergence was made faster and more stable. Finally, considering the performance and path constraints of the airship, the effectiveness of the scheme was verified by numerical experiments under wind effects and a comparison of different methods.

Convex Optimization for Trajectory Generation: A Tutorial on Generating Dynamically Feasible Trajectories Reliably and Efficiently

Reliable and efficient trajectory generation methods are a fundamental need for autonomous dynamical systems. The goal of this article is to provide a comprehensive tutorial of three major convex optimization-based trajectory generation methods: lossless convexification (LCvx) and two sequential convex programming algorithms, successive convexification (SCvx) and guaranteed sequential trajectory optimization (GuSTO). Trajectory generation is defined as the computation of a dynamically feasible state and control signal that satisfies a set of constraints while optimizing key mission objectives. The trajectory generation problem is almost always nonconvex, which typically means that it is difficult to solve efficiently and reliably onboard an autonomous vehicle. The three algorithms that we discuss use problem reformulation and a systematic algorithmic strategy to nonetheless solve nonconvex trajectory generation tasks using a convex optimizer. The theoretical guarantees and computational speed offered by convex optimization have made the algorithms popular in both research and industry circles. The growing list of applications includes rocket landing, spacecraft hypersonic reentry, spacecraft rendezvous and docking, aerial motion planning for fixed-wing and quadrotor vehicles, robot motion planning, and more. Among these applications are high-profile rocket flights conducted by organizations such as NASA, Masten Space Systems, SpaceX, and Blue Origin. This article equips the reader with the tools and understanding necessary to work with each algorithm and know their advantages and limitations. An open source tool called the SCP Toolbox accompanies the article and provides a practical implementation of every numerical example. By the end of the article, the reader will not only be ready to use the lossless convexification and sequential convex programming algorithms, but also to extend them and to contribute to their many exciting modern applications.

Kinematic Orienteering Problem With Time-Optimal Trajectories for Multirotor UAVs

In many unmanned aerial vehicle (UAV) applications for surveillance and data collection, it is not possible to reach all requested locations due to the given maximum flight time. Hence, the requested locations must be prioritized and the problem of selecting the most important locations is modeled as an Orienteering Problem (OP). To fully exploit the kinematic properties of the UAV in such scenarios, we combine the OP with the generation of time-optimal trajectories with bounds on velocity and acceleration. We define the resulting problem as the Kinematic Orienteering Problem (KOP) and propose an exact mixed-integer formulation together with a Large Neighborhood Search (LNS) as a heuristic solution method. We demonstrate the effectiveness of our approach based on Orienteering instances from the literature and benchmark against optimal solutions of the Dubins Orienteering Problem (DOP) as the state-of-the-art. Additionally, we show by simulation \color{black} that the resulting solutions can be tracked precisely by a modern MPC-based flight controller. Since we demonstrate that the state-of-the-art in generating time-optimal trajectories in multiple dimensions is not generally correct, we further present an improved analytical method for time-optimal trajectory generation.

Spline-Based Optimal Trajectory Generation for Autonomous Excavator

In this paper, we propose a novel trajectory generation method for autonomous excavator teach-and-plan applications. Rather than controlling the excavator to precisely follow the teaching path, the proposed method transforms the arbitrary slow and jerky trajectory of human excavation into a topologically equivalent path that is guaranteed to be fast, smooth and dynamically feasible. This method optimizes trajectories in both time and jerk aspects. A spline is used to connect these waypoints, which are topologically equivalent to the human teaching path. Then the trajectory is reparametrized to obtain the minimum time-jerk trajectory with the kinodynamic constraints. The optimal time-jerk trajectory generation method is both formulated using nonlinear programming and conducted iteratively. The framework proposed in this paper was integrated into a complete autonomous excavation platform and was validated to achieve aggressive excavation in a field environment.