Trajectory Generation Algorithm Research Articles

Universal and Automated Approaches for Optimising the Processing Order of Geometries in a CAM Tool for Redundant Galvanometer Scanner-Based Systems

The combination of highly dynamic systems with a limited work envelope with a less dynamic system with a larger working envelope promises to combine the advantages of both systems while eliminating the disadvantages. For these systems, separation algorithms determine the trajectories based on the target geometries. However, arbitrary processing orders of these result in inefficient trajectories because successive geometries may be geometrically far apart. This causes the dynamic system to operate below its potential. Current planning tools do not optimise the processing order for such redundant systems. The aim is to design and implement a planning tool for the application of laser marking. The tool considers the processing order of the 2D geometries from a geometric point of view. The resulting sequenced path data can then be used by trajectory generation algorithms to make full use of the potential of redundant systems. The approach analyses literature on Travelling Salesman Problems (TSP), which is then transferred to the given application. A heuristic and a genetic algorithm are developed and integrated into a planning tool. The results show the heuristic algorithm being faster while still producing solutions whose total path length is similar to that of the genetic algorithm. Even though the solutions don’t meet any optimality standards, the presented automated approaches are superior to manual approaches and are to be seen as a starting point for further research.

A variable step and multi-constraint vehicle’s trajectory generation algorithm based on deep deterministic policy gradient network

Abstract Aiming at the problem that the traditional vehicle’s trajectory generation method takes a long time and is difficult to calculate in real time, a variable step and multi-constraint trajectory generation algorithm based on a deep deterministic policy gradient (DDPG) network is proposed. Firstly, the dynamic model and constraint conditions of the vehicle are analyzed. On this basis, the reinforcement learning training model is constructed based on DDPG, and the state, action, and reward design of the training model are defined. At the same time, the variable step is introduced into the action model to improve the generated trajectory’s navigation precision. Finally, the proposed method is verified under different cases, and according to the results, the proposed method can realize quick generation of multi-constraint guidance trajectories.

Unpredictable trajectories on quadcopters by infusing hyperchaotic generated velocities on its 3 axes of movement

This article aims to adapt the chaotic trajectory generation algorithm, as originally presented by Cetina-Denis et al. in 2022 for quadcopters. This adaptation opens possibilities for various applications, including search and rescue operations and the handling of hazardous objects, within a three-dimensional exploration space. To accomplish this, hyperchaotic behavior is introduced into the linear displacement velocities along the three axes of motion by using the four-dimensional hyperchaotic Méndez–Arellano–Cruz–Martínez system. The article also delves into the potential applications of these aerial robots in patrolling designated spaces. It presents and analyzes both numerical and experimental findings, along with quantitative tests to assess the level of hyperchaos inherent in the generated trajectories. Furthermore, the article examines the scenario where two quadcopters simultaneously patrol the same workspace, exploring both numerical simulations and experimental outcomes.

Vision-based trajectory generation and tracking algorithm for maneuvering of a paddy field robot

In this study, we propose a novel visual-based autonomous trajectory-tracking control method for steering a wheeled robot following the lines of crop row in paddy field. A rice crop rows detection method, based on the region growth sequential clustering − random sample consensus (RANSAC) algorithm, is developed to generate trajectory. Concurrently, a dynamics predictive controller is employed to compute the command for the desired steering angle. The controller leverages a model that incorporates slip dynamics and operates on a low power consumption industrial computer. Experimental results show that the developed algorithm can successfully obtain the correct trajectory in more than 96.25 % of the cases, with the angle error consistently below 3°. Furthermore, the single-image processing time is notably swift at 13.98 ms, underscoring the commendable adaptability and real-time performance of the proposed methodology. During movement in the paddy field, the robot exhibits maximum lateral deviations of 4.55 cm, 5.65 cm, and 6.41 cm at speeds of 0.3 m/s, 0.6 m/s, and 0.9 m/s, respectively, accompanied by corresponding heading angle errors of 4.59°, 5.63°, and 7.39°. Notably, while adeptly tracking rice crop rows at all three speeds, the robot consistently maintains a maximum lateral error below one-fourth of the inter-row spacing of rice planting. This study assumes significance in enhancing the stability of ground-traversing agricultural robots, serving as a valuable reference for advancing the research and development of intelligent and efficient agricultural robotic systems.

Resolution Enhancement by Variable Zoom Trajectory in X-Ray Computed Tomography

Flat objects like electronic boards are challenging samples for high-resolution X-ray computed tomography scanning because their largest dimension significantly limits the magnification using circular trajectory scans. One way to improve spatial resolution for such samples is to utilize variable zoom trajectory. During variable zoom trajectory scanning, the source-to-object distance changes during the 360° rotation to maximize the magnification in the projections. Here, we propose an automatic variable zoom trajectory generation algorithm for arbitrary object and region of interest (ROI). We analyze how such a trajectory can enhance resolution in different cases and how isotropic is the resolution in the reconstructed volume. We demonstrate that the resolution can be improved without destroying the sample. However, the improvement is manifested mainly in directions in which we achieved the highest magnification in the projection.

Autonomous Trajectory Planning for Ultrasound-Guided Real-Time Tracking of Suspicious Breast Tumor Targets

Ultrasound image guidance could display the movement of soft tissue in real time, which provides an important basis for the operation path selection of tumor for examinations and interventions such as precise localization and puncture biopsy. However, factors such as tissue deformation, patient motion, and instrument contact pose great challenges for real-time smooth localization tracking of target tissues and maintaining a suitable acoustic window. Not only does it reduce the accuracy of ultrasound examination, but also may prolong the examination time. In this paper, a real-time autonomous ultrasound robot trajectory planning framework is proposed to achieve global scanning of breast tissue and real-time local tracking of suspicious tumor targets. In addition, an ultrasound suspicious tumor target next moment motion attitude and position estimation algorithm and an acceleration-continuous online trajectory generation (ACOTG) algorithm are proposed. Experiments on breast phantom showed that the fluctuation difference of both global scanning and tracking scanning force was less than 5 N <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm$</tex-math> </inline-formula> 15%, and ACOTG takes less than 1 microsecond to calculate the next moment state. The position, velocity, and acceleration of the tracking path did not change abruptly when the unknown target changed. The ultrasound image of the suspected tumor target could always be smoothly maintained in a suitable acoustic window, while the errors between the center of the suspected tumor target image and the center of the acoustic window in the horizontal direction and the depth direction were less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm$</tex-math> </inline-formula> 1 mm and 30 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm$</tex-math> </inline-formula> 10%, respectively. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this study was to solve the clinical problem of difficulty in keeping the suspected breast tumor target stably in the center of the field of view under the influence of tissue deformation, patient motion and instrument contact in ultrasound guidance. We proposed the idea of global conventional scanning and local online tracking to achieve the autonomous scanning, detecting and tracking of suspicious tumor targets within the global scope of the breast. ACOTG algorithm is proposed and implemented, which can make the ultrasound image of suspicious tumor target can be displayed stably in the center of the acoustic window. With the help of this system, the accuracy of ultrasound examination can be improved and the time of examination can be reduced. The proposed system can also be applied to ultrasound scanning of other parts of the body.

Three-dimensional variable center of mass height biped walking using a new model and nonlinear model predictive control

This paper presents a trajectory generation algorithm for a three-dimensional (3D) biped robot that can adjust the center of mass (CoM) according to the environment. We adopt a new abstract model that supports vertical motion and rotation. Differing from traditional abstract models, the proposed full centroid dynamics inverted pendulum model fully considers the robot’s movement and rotation. Unlike the zero moment point (ZMP), which only ensures the feet do not flip over, we also propose a new additional stability criterion, named zero frictional moment point (ZFMP), guaranteeing no yaw rotation while walking. Next, a nonlinear model predictive control is designed to generate the CoM trajectory, torso rotational angle, and adaptive footholds to induce various biped gaits. A full-dynamics 3D humanoid robot is simulated to test the proposed method while steering, walking underneath a low door, and walking with disturbances.

Real-Time On-the-Fly Motion Planning for Urban Air Mobility via Updating Tree Data of Sampling-Based Algorithms Using Neural Network Inference

In this study, we consider the problem of motion planning for urban air mobility applications to generate a minimal snap trajectory and trajectory that cost minimal time to reach a goal location in the presence of dynamic geo-fences and uncertainties in the urban airspace. We have developed two separate approaches for this problem because designing an algorithm individually for each objective yields better performance. The first approach that we propose is a decoupled method that includes designing a policy network based on a recurrent neural network for a reinforcement learning algorithm, and then combining an online trajectory generation algorithm to obtain the minimal snap trajectory for the vehicle. Additionally, in the second approach, we propose a coupled method using a generative adversarial imitation learning algorithm for training a recurrent-neural-network-based policy network and generating the time-optimized trajectory. The simulation results show that our approaches have a short computation time when compared to other algorithms with similar performance while guaranteeing sufficient exploration of the environment. In urban air mobility operations, our approaches are able to provide real-time on-the-fly motion re-planning for vehicles, and the re-planned trajectories maintain continuity for the executed trajectory. To the best of our knowledge, we propose one of the first approaches enabling one to perform an on-the-fly update of the final landing position and to optimize the path and trajectory in real-time while keeping explorations in the environment.

A Reduced-Complexity Trajectory Generation Algorithm for Three-Body Regimes With Minimum Predefined Data

A Reduced-Complexity Trajectory Generation Algorithm for Three-Body Regimes With Minimum Predefined Data

Position Control Using Trajectory Tracking and State Estimation of a Quad-rotor

Quad-rotor aircrafts are unmanned aerial vehicles that have gained significant popularity in recent years and have been developed for use in many areas. Such vehicles are capable of vertical take-off and landing and are used in various applications. To operate a quad-rotor aircraft efficiently and safely, fundamental issues such as mathematical modeling, control, and state estimation need to be studied. Mathematical modeling involves creating a holistic model of the various subsystems of the aircraft including aerody-namic, kinematic, dynamic and control systems. The control system is a mechanism used for the aircraft to perform the desired movements. State estimation techniques are used to obtain and predict information about the state of the aircraft. This study includes position control using a trajectory generation algorithm. Attitude estimation of the quad-rotor is improved with the Explicit Complementary Filter (ECF) and the state estimations is improved with the Extended Kalman Filter (EKF). Different from other studies, the results are obtained by feeding the model with a state estimation filter. The performances of the filters used for state estimation are compared.

Efficient and Collision-Free Human–Robot Collaboration Based on Intention and Trajectory Prediction

Human-Robot collaboration (HRC) is an important topic for manufacturing and household robotics. It is very challenging to ensure both efficiency and safety in HRC. This paper presents an HRC pipeline that generates efficient and collision-free robot trajectories based on predictions of the human arm and hand (AH) motions. We train a recurrent neural network for AH trajectory prediction based on observed initial trajectory segments. To increase the accuracy of target estimation at an early stage, the observed and the predicted hand palm trajectory are combined to predict the current AH motion target using Gaussian Mixture Models (GMMs). An optimization-based trajectory generation algorithm is proposed to ensure the safety of the human while collaborating with the robot. The proposed system is validated in a shared-workspace scenario with human pick-and-place motions. The task can be safely and efficiently completed. The results demonstrate that our proposed pipeline can predict the human AH trajectory and estimate the motion target intended by the human accurately and early.

Anti-Jamming Communication Using Imitation Learning.

The communication reliability of wireless communication systems is threatened by malicious jammers. Aiming at the problem of reliable communication under malicious jamming, a large number of schemes have been proposed to mitigate the effects of malicious jamming by avoiding the blocking interference of jammers. However, the existing anti-jamming schemes, such as fixed strategy, Reinforcement learning (RL), and deep Q network (DQN) have limited use of historical data, and most of them only pay attention to the current state changes and cannot gain experience from historical samples. In view of this, this manuscript proposes anti-jamming communication using imitation learning. Specifically, this manuscript addresses the problem of anti-jamming decisions for wireless communication in scenarios with malicious jamming and proposes an algorithm that consists of three steps: First, the heuristic-based Expert Trajectory Generation Algorithm is proposed as the expert strategy, which enables us to obtain the expert trajectory from historical samples. The trajectory mentioned in this algorithm represents the sequence of actions undertaken by the expert in various situations. Then obtaining a user strategy by imitating the expert strategy using an imitation learning neural network. Finally, adopting a functional user strategy for efficient and sequential anti-jamming decisions. Simulation results indicate that the proposed method outperforms the RL-based anti-jamming method and DQN-based anti-jamming method regarding solving continuous-state spectrum anti-jamming problems without causing "curse of dimensionality" and providing greater robustness against channel fading and noise as well as when the jamming pattern changes.

A numerically-stable trajectory generation and optimization algorithm for autonomous quadrotor UAVs

This paper introduces a novel trajectory generation and optimization algorithm (TGO) that enables agile and aggressive flight of quadrotor UAVs while considering various constraints associated with robot dynamics, actuator inputs, and flight environment. The TGO algorithm employs time-parametrized polynomial trajectories based on a predetermined sequence of waypoints to produce dynamically feasible and collision-free trajectories. This approach extends previous work that utilized differential flatness property and polynomial based trajectories by eliminating the need for iterative searching and computationally intensive sampling. One of the significant advantages of the TGO algorithm is its numerical stability for large number of waypoints and high-order polynomials. To address the ill-conditioned problem of Quadratic Programming (QP) based methods, the TGO algorithm reformulates the trajectory generation and optimization problem into an unconstrained quadratic programming (UCP) using the numerically stable null-space factorization method. The TGO algorithm produces minimum derivative trajectories and minimum waypoints arrival times, generating a wide range of aggressive trajectories that can leverage the full maneuvering capabilities of quadrotor robots. The proposed algorithm’s numerical stability and computational advantages are demonstrated through various scenarios and comparisons. An animated simulation of the TGO algorithm is available at: https://youtu.be/MvvhBG14iIg.

Real-time adaptive entry trajectory generation with modular policy and deep reinforcement learning

Recently, data-driven entry trajectory generation algorithms of hypersonic vehicles were highlighted for their high accuracy with low computational costs. Learning a unique black box model mapping the state to control variables is expected. However, insufficient adaptability remains a challenging problem when applying the algorithms in practice, especially for multi-missions. In this article, a real-time entry trajectory generation algorithm with modular policy is proposed to achieve adaptability to various missions, such as changing targets and emergency entry. Based on the modular idea, the entry trajectory problem is decomposed into two decision problems, i.e., adjusting the profile of the angle of attack (AOA) to determine the flight capability and planning the bank angle to ensure the satisfaction of task constraints, which correspond to AOA module and bank module respectively. Then, algorithms are developed by utilizing deep reinforcement learning (DRL) to train the two modules with which an intelligent entry trajectory generation algorithm is proposed to achieve real-time trajectory design in a wide range of reachable areas. Moreover, a non-uniform discretization approach with a state-related independent variable is proposed to deal with state misalignment and contradiction in stepsize settings. The simulation results demonstrate that the proposed algorithm can provide a reliable trajectory in a very short time and adapt to various tasks.

A collision-free visual servoing method for two space manipulators capturing tumbling satellites

A novel visual servoing method is proposed to synchronously capture a malfunctional satellite’s docking ring by two space manipulators. Due to the lack of conspicuous visual marks, structured light is implemented to estimate the ring’s pose. To ensure the capturing process’s security, two aspects are investigated. Spatially, capturing target points for two manipulators are planned together by considering the chaser’s orientation. As a consequence, collision risk between two manipulators is eliminated. Temporally, by adding duration parameters in trajectory generation algorithm, capturing synchronism for two manipulators is guaranteed. Experimental results show that, by the proposed method, a tumbling target was successfully captured by two space manipulators. Compared to existing methods, the collision risk between two manipulators is thoroughly eliminated and the capturing synchronism is improved remarkably.

Autonomous Drone Electronics Amplified with Pontryagin-Based Optimization

In the era of electrification and artificial intelligence, direct current motors are widely utilized with numerous innovative adaptive and learning methods. Traditional methods utilize model-based algebraic techniques with system identification, such as recursive least squares, extended least squares, and autoregressive moving averages. The new method known as deterministic artificial intelligence employs physical-based process dynamics to achieve target trajectory tracking. There are two common autonomous trajectory-generation algorithms: sinusoidal function- and Pontryagin-based generation algorithms. The Pontryagin-based optimal trajectory with deterministic artificial intelligence for DC motors is proposed and its performance compared for the first time in this paper. This paper aims to simulate model following and deterministic artificial intelligence methods using the sinusoidal and Pontryagin methods and to compare the differences in their performance when following the challenging step function slew maneuver.

MGV Obstacle Avoidance Trajectory Generation Considering Vehicle Shape

This study investigates the application of obstacle avoidance trajectory generation considering the vehicle shape of a micro ground vehicle by successive convexification and state-triggered constraints. The avoidance trajectory is generated by numerical computation and path-following experiments are conducted to assess the generated trajectory. The numerical computation results indicate that the trajectory obtained by the algorithm successfully avoids obstacles considering the vehicle shape and satisfies the constraints. The experiment includes the model predictive control to follow the generated trajectory. Numerical computations and experiments confirm the usefulness of the trajectory generation algorithm.

An online collision-free trajectory generation algorithm for human–robot collaboration

The premise of human–robot collaboration is that robots have adaptive trajectory planning strategies in hybrid work cell. The aim of this paper is to propose a new online collision avoidance trajectory planning algorithm for moderate dynamic environments to insure human safety when sharing collaborative tasks. The algorithm contains two parts: trajectory generation and local optimization. Firstly, based on empirical Dirichlet Process Gaussian Mixture Model (DPGMM) distribution learning, a neural network trajectory planner called Collaborative Waypoint Planning network (CWP-net) is proposed to generate all key waypoints required for dynamic obstacle avoidance in joint space according to environmental inputs. These points are used to generate quintic spline smooth motion trajectories with velocity and acceleration constraints. Secondly, we present an improved Stochastic Trajectory Optimization for Motion Planning (STOMP) algorithm which locally optimizes the generated trajectories of CWP-net by constraining the trajectory optimization range and direction through the DPGMM model. Simulations and real experiments from an industrial use case of human–robot collaboration in the field of aircraft assembly testing show that the proposed algorithm can smoothly adjust the nominal path online and effectively avoid collisions during the collaboration. • An online trajectory planning algorithm for dynamic obstacles avoidance is proposed. • A neural network CWP-net with multiple collision-free waypoints output is designed. • An improved STOMP algorithm is proposed for local trajectory optimization. • Continuous smooth trajectories are generated and satisfy joint constraints. • This work builds a bridge between advanced offline planners and online planning tasks.

Minimum-Time Trajectory Generation for Wheeled Mobile Systems Using Bézier Curves with Constraints on Velocity, Acceleration and Jerk.

This paper considers the problem of minimum-time smooth trajectory planning for wheeled mobile robots. The smooth path is defined by several Bézier curves and the calculated velocity profiles on individual segments are minimum-time with continuous velocity and acceleration in the joints. We describe a novel solution for the construction of a 5th order Bézier curve that enables a simple and intuitive parameterization. The proposed trajectory optimization considers environment space constraints and constraints on the velocity, acceleration, and jerk. The operation of the trajectory planning algorithm has been demonstrated in two simulations: on a racetrack and in a warehouse environment. Therefore, we have shown that the proposed path construction and trajectory generation algorithm can be applied to a constrained environment and can also be used in real-world driving scenarios.

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.