Trajectory Planning Process Research Articles

Automatic unberthing for underactuated unmanned surface vehicle: Model-based planning and control approaches in constricted harbors

Due to limitations in maneuverability, Unmanned Surface Vehicle (USV) often struggles to achieve automatic unberthing through a single cohesive operation in constricted harbors. To address this problem, this paper proposed a novel Two-Layer Trajectory Planning Method (TL-TPM) and two Model Predictive Control (MPC) methods. Throughout the trajectory planning process, the TL-TPM considers the USV dynamic constraints along with the cumulative risk in viable areas. It incorporates the residual velocity and yaw angle deviation from the backward phase to derive the USV’s retreating trajectory and optimizes sailing time in the forward phase for a smooth forward trajectory, forming a complete automatic unberthing trajectory. The Efficiency-Priority MPC (EP-MPC) and Accuracy-Priority MPC (AP-MPC) are designed for trajectory tracking, considering tracking positional deviations, yaw angle deviations and surge force variations. The proposed EP-MPC demonstrates high computational efficiency and robustness, while AP-MPC shows superior control accuracy under various environmental disturbances. Extensive simulations validate the effectiveness of these methods in achieving automatic unberthing under wind and current impacts.

A semi-analytical approach to wire arc additive manufacturing simulation for deposition sequence optimisation

ABSTRACT Categorised as a directed energy deposition process, wire arc additive manufacturing (WAAM) is a promising technology for fabricating large-scale structures and components across various industries. However, the quality of WAAM parts depends on the tool trajectory, as it affects the temperature distribution. Ideally, temperature-related issues, such as overheating, are minimised by choosing an optimal deposition sequence. Selecting the deposition sequence solely on intuition is an unreliable approach, particularly when dealing with complex and irregular parts. This paper introduces a simplified WAAM simulation (SWS) model, which was embedded into an optimisation procedure for determining the optimal deposition sequence of thin-walled WAAM parts. The proposed method is based on a semi-analytical function, which was calibrated and validated using thermal histories obtained from finite element simulations. The findings showed that the proposed SWS model can reproduce the average thermal history at predefined positions within a sample part with minimal computational effort. Moreover, the optimisation successfully identified optimal deposition sequences for producing the sample part regarding a given optimisation criterion. The outcomes of this research contribute to the tool trajectory planning process for WAAM parts. An optimal deposition sequence improves WAAM part quality, increasing the usability of WAAM technology in the production industry.

Real-Time Trajectory Smoothing and Obstacle Avoidance: A Method Based on Virtual Force Guidance.

In dynamic environments, real-time trajectory planners are required to generate smooth trajectories. However, trajectory planners based on real-time sampling often produce jerky trajectories that necessitate post-processing steps for smoothing. Existing local smoothing methods may result in trajectories that collide with obstacles due to the lack of a direct connection between the smoothing process and trajectory optimization. To address this limitation, this paper proposes a novel trajectory-smoothing method that considers obstacle constraints in real time. By introducing virtual attractive forces from original trajectory points and virtual repulsive forces from obstacles, the resultant force guides the generation of smooth trajectories. This approach enables parallel execution with the trajectory-planning process and requires low computational overhead. Experimental validation in different scenarios demonstrates that the proposed method not only achieves real-time trajectory smoothing but also effectively avoids obstacles.

Trajectory Planning Research Based on Rapidly-exploring Random Trees (RRT) Algorithm and Modified Forms

With the rapid advancement of computer technology, robots have become indispensable in various fields. Trajectory planning plays a crucial role in optimizing robot performance by enhancing work efficiency and reducing operational costs. While the widely used Rapidly-exploring Random Trees (RRT) algorithm is effective in path planning, it often generates non-optimal paths with poor smoothness. By incorporating elements from RRT-Connect and reverse optimization, the algorithm can efficiently navigate through intricate and dynamic surroundings. Furthermore, the utilization of cubic polynomial interpolation in optimizing path curves adds a layer of sophistication to the trajectory planning process. This interpolation technique allows for the creation of smoother and more natural path trajectories, reducing jerky movements and enhancing overall motion control precision. The paths produced by the enhanced RRT algorithm demonstrate increased continuity and visual attractiveness, crucial for tasks necessitating accurate and elegant robotic motions. The improved algorithm showcases reduced path length and time consumption, as well as enhanced path smoothness. Particularly, relative to the traditional RRT approach, the time consumption has dropped by 69.15% and the median duration of the paths has fallen by 21.11%. These improvements signify a substantial advancement in trajectory planning for robots, offering more efficient and smoother paths for robotic operations across various applications.

Efficient and precise docking trajectory optimization for the ship block assembly

The assembly of the ship block is an extremely important stage of the shipbuilding process. Nevertheless, currently, the manual assembly efficiency is low, the accuracy is poor, and collision is very easy to occur. Therefore, there is an urgent need to conduct technical research on the automatic docking of ship blocks. The core of the automated docking technology is the attitude estimation and the trajectory planning of the posturing equipment. However, current data measurement and point set matching methods lead to large attitude-estimation errors, and it is difficult to meet the accuracy requirements of the assembly. Moreover, the current ship block trajectory planning methods pay more attention to single metrics, for example, time or energy consumption, while omitting the shock degree. In response to the above, this study first proposes a high-precision matching method for measuring point sets, in order to estimate the exact attitude of the ship block. Subsequently, trajectory translation for the block is performed using the seventh-degree polynomial. On this basis, a nonlinear weighted improved particle swarm optimization (IPSO) method is proposed to optimize the time, energy consumption and shock degree in the ship block trajectory planning process. Finally, the accuracy of the matching optimization is validated by simulation analysis and it is concluded that the seventh-degree polynomial leads to less shock than other polynomials. Furthermore, the shock force does not change abruptly even when the ship block is poised in steps. Through IPSO, the energy consumption and shock degree performance indices are optimized by 37.07% and 50.06%, respectively, in the ship block translation process.

Optimizing Port Multi-AGV Trajectory Planning through Priority Coordination: Enhancing Efficiency and Safety

Efficient logistics and transport at the port heavily relies on efficient AGV scheduling and planning for container transshipment. This paper presents a comprehensive approach to address the challenges in AGV path planning and coordination within the domain of intelligent transportation systems. We propose an enhanced graph search method for constructing the global path of a single AGV that mitigates the issues associated with paths closely aligned with obstacle corner points. Moreover, a centralized global planning module is developed to facilitate planning and scheduling. Each individual AGV establishes real-time communication with the upper layers to accurately determine its position at complex intersections. By computing its priority sequence within a coordination circle, the AGV effectively treats the high-priority trajectories of other vehicles as dynamic obstacles for its local trajectory planning. The feasibility of trajectory information is ensured by solving the online real-time Optimal Control Problem (OCP). In the trajectory planning process for a single AGV, we incorporate a linear programming-based obstacle avoidance strategy. This strategy transforms the obstacle avoidance optimization problem into trajectory planning constraints using Karush-Kuhn-Tucker (KKT) conditions. Consequently, seamless and secure AGV movement within the port environment is guaranteed. The global planning module encompasses a global regulatory mechanism that provides each AGV with an initial feasible path. This approach not only facilitates complexity decomposition for large-scale problems, but also maintains path feasibility through continuous real-time communication with the upper layers during AGV travel. A key advantage of our progressive solution lies in its flexibility and scalability. This approach readily accommodates extensions based on the original problem and allows adjustments in the overall problem size in response to varying port cargo throughput, all without requiring a complete system overhaul.

Consistent Solution Strategy for Static Equilibrium Workspace and Trajectory Planning of Under-Constrained Cable-Driven Parallel and Planar Hybrid Robots

This paper presents a consistent solution strategy for static equilibrium workspaces of different types of under-constrained robots. Considering the constraint conditions of cable force and taking the least squares error of the static equilibrium equation as the objective, the convex optimization solution is carried out, and the static equilibrium working space of the under-constrained system is obtained. A consistent solution strategy is applied to solve the static equilibrium workspaces of the cable-driven parallel and planar hybrid robots. The dynamic models are presented and introducing parameters that are applied to make the system stable for point-to-point movements. Based on this model, the traditional polynomial-based point-to-point trajectory planning algorithm is improved by adding unconstrained parameters to the kinematic law function. The constraints of the dynamics model are incorporated into the trajectory planning process to achieve point-to-point trajectory planning for the under-constrained cable-driven robots. Finally, under-constrained cable-driven parallel robots with three cables and planar hybrid robot with two cables are taken as examples to carry out numerical simulation. The final results show that the point-to-point trajectory planning algorithm introducing parameters is effective and feasible and can provide theoretical guidance for the design of subsequent under-constrained robots.

Contour Tracking Control for Mobile Robots applicable to Large-scale Assembly and Additive Manufacturing in Construction

In the construction industry, as well as during the assembly of large-scale components, the required workspaces usually cannot be served by a stationary robot. Instead, mobile robots are used to increase the accessible space. Here, the problem arises that the accuracy of such systems is not sufficient to meet the tolerance requirements of the components to be produced. Furthermore, there is an additional difficulty in the trajectory planning process since the exact dimensions of the pre-manufactured parts are unknown. Hence, existing static planning methods cannot be exerted on every application. Recent approaches present dynamic planning algorithms based on specific component characteristics. For example, the latest methods follow the contour by a force-controlled motion or detect features with a camera. However, in several applications such as welding or additive manufacturing in construction, no contact force is generated that could be controlled. Vision-based approaches are generally restricted by varying materials and lighting conditions, often found in large-scale construction. For these reasons, we propose a more robust approach without measuring contact forces, which, for example, applies to large-scale additive manufacturing. We based our algorithm on a high-precision 2D line laser, capable of detecting different feature contours regardless of material or lightning. The laser is mounted to the robot’s end-effector and provides a depth profile of the component’s surface. From this depth data, we determine the target contour and control the manipulator to follow it. Simultaneously we vary the robot’s speed to adjust the feed rate depending on the contour’s shape, maintaining a constant material application rate. As a proof of concept, we apply the algorithm to the additive manufacturing of two-layer linear structures made from spray PU foam. When making these structures, each layer must be positioned precisely on the previous layer to obtain a straight wall and prevent elastic buckling or plastic collapse. Initial experiments show improved layer alignment within 10 % of the layer width, as well as better layer height consistency and process reliability.

Probabilistic Situation Assessment for Intelligent Vehicles with Uncertain Trajectory Distribution

Situation assessment is crucial for intelligent vehicles, enabling detection of potential risks to dynamic and complex traffic environments. In this paper, we propose a unified framework that tackles the coupling relationships between traffic participants and quantifies the possible range of vehicle trajectory generation and the expected losses caused by risk source attributes in the driving process. We first apply the state space trajectory planning scheme based on a sampling algorithm to generate the path candidates; each feasible path is designed through a parametric cubic spline. Then, to evaluate the risk range in the driving process, we quantify the interaction of traffic participants, and employ the principle of least action to calculate the cost of each feasible path when achieving the destination. The probability distribution map, namely the possible range of driving trajectories, can be obtained based on the path cost. Furthermore, the vehicle-to-vehicle interaction is calculated based on the equivalent force, which estimates the expected accident losses. Finally, the vehicle trajectory prediction and the expected loss are combined to output the probabilistic situation assessment of intelligent vehicles. The algorithm is implemented in different scenarios and applied to the trajectory planning process. Results demonstrate that, compared with the classical situation assessment metric, the developed method can determine and accurately identify the influence range of driving risk in real-time, predict a dangerous situation earlier, and ensure the vehicle avoids obstacles in advance.

Eco-driving-based cooperative adaptive cruise control of connected vehicles platoon at signalized intersections

Vehicle driving patterns greatly impact the sustainability of the transportation system. Based on V2X communication, the ecological cooperative adaptive cruise control (Eco-CACC) is proposed combing the advantages of eco-driving and car-following to minimize the energy consumption of the connected automated vehicles platoon. Herein, the vehicle platoon behavior in the scenario of driving through a signalized intersection exhibits great benefits for sustainability which is even improved along corridors with more traffic lights. In the velocity trajectory planning process, a modified dynamic programming algorithm is formulated with the switching logic gate of two types of optimal control problems to increase the computational speed. By testing in the real-world scenario, the results of the proposed Eco-CACC demonstrate excellent energy performance which improves 8.02% compared to manual driving with the constant acceleration policy. Moreover, energy can be further improved by 2.02% and 1.55% when the car-following strategy is selected with MPC and IDM algorithm.

A Time Optimal Trajectory Planning Method for Double-Pendulum Crane Systems With Obstacle Avoidance

For a crane system, when the payload is too large to be seen as a mass point, or the hook mass cannot be directly ignored, it performs more like a double-pendulum crane system, instead of a single-pendulum crane system. Due to many factors, the working environment of the industrial crane system is complex. Obstacles sometimes appear in the movement path of the payload, which affects the normal operation of the crane system and may cause accidents like collisions. To handle this issue, we propose a time optimal trajectory planning method for the double-pendulum crane system with obstacle avoidance, which ensures the objective of obstacle avoidance by the payload hoisting/lowering. During the trajectory planning process, a series of physical constraints, including the trolley velocity constraints, the trolley acceleration constraints, the payload’s swing angle constraints and the hook’s swing angle constraints are considered. It can improve the safety of the crane system during the entire working process and the transportation efficiency is also improved at the same time. Finally, the effectiveness of the proposed method is verified by simulations.

Solving Inverse Kinematics of the Shotcrete Manipulator Based on the Plane Two-Link Model and Trajectory Planning

Traditionally, the construction of tunnel support is to manually move the manipulator through the remote control. During the manual construction process, there is a large rebound rate and a reduction in the compactness of the concrete. Skilled operators can obtain better shot blasting quality, but training of a skilled worker is costly. In this study, an automatic shotcrete manipulator is proposed to complete spraying and improve the spraying quality. The model of the manipulator is simplified into a planar two-link manipulator, solved the inverse kinematics of the shotcrete manipulator, and implemented the automatic trajectory planning process. By simplifying the complex mechanical arm structure model into a simple planar two-link manipulator model, the inverse kinematics of the shotcrete manipulator is solved, and automatic trajectory planning software is developed, which can better help construction and reduce injury to personnel’s health and can also help the construction party save materials and improve economic efficiency and construction efficiency.

A Bisection Algorithm for Time-Optimal Trajectory Planning Along Fully Specified Paths

The time-optimal trajectory planning problem involves minimizing the time required to follow a path defined in space, subject to kinematic and dynamic constraints. Here, we introduce a novel technique, called the bisection algorithm (BA), which is fully implemented in C++ and extends dynamic programming approaches to the problem. These approaches, which rely on dividing the global problem into a series of simpler subproblems, become increasingly advantageous compared to direct transcription methods as the number of problem constraints increases. In contrast to nearly all other dynamic programming approaches, BA does not rely on finding a maximum-velocity curve or explicitly finding acceleration switching points during the trajectory planning process. Additionally, only one forward and one backward integration are used, during which all constraints are imposed. This approach is made feasible through careful control of the numerical integration process and the use of a bisection algorithm to resolve constraint violations during integration. BA is shown to be significantly simpler, faster, and more robust than recently proposed algorithms: a direct comparison is made for a series of paths to be followed by a serial manipulator, subject to kinematic constraints. The wide applicability of BA is then established by solving the time-optimal problem for a parallel manipulator following a complex path, subject to both kinematic and dynamic constraints.

Simulation and Experimental Validation of Novel Trajectory Planning Strategy to Reduce Vibrations and Improve Productivity of Robotic Manipulator

This paper aims at investigating vibrational behaviors of the industrial manipulator Racer 7-1.4, designed and manufactured by COMAU S.p.A., with the target of new trajectory planning strategies to improve productivity rate without any loss of positioning accuracy. Starting from the analysis of a 9DoF multi-body system with lumped parameter, the first natural frequency of the robot was calculated in seven reference positions. Then, static and dynamic simulations were run by applying saturated ramp input and large motions to analyze the vibrational behavior of the manipulator. This research underlines that the optimal way to design the robot move is to set its duration at twice a period of free oscillation according to the first vibrational mode. Due to strong analogy of dynamic response of both 1DoF and 9DoF robot models, the closed-form solution of the 1DoF undamped system—featured by natural frequency equal to the first frequency of the 9DoF system—may be successfully adopted by the real-time trajectory planning process to predict residual vibration at move end-condition. This strategy was confirmed by experimental tests, allowing either residual vibration decrease and execution time reduction as well.

Modeling and Clinical Application of Incision Space in Facial Contour Surgery.

Virtual simulation surgical system is a good way to develop surgical instruments, make surgical plan, and train surgeons. At present, due to the deformation of intraoperative soft tissue after retraction and the lack of effective data collection, the surgical simulation of facial contour surgery can only be conducted according to the preoperative computed tomography data. Due to the difficulty of obtaining real operative spatial data, it is difficult for the virtual surgery trajectory planning process to yield a good effect on surgeon training. In this study, an optical tracking device was used to record the actual posture of surgical instruments, patient position, and incision space in the surgical environment, so as to construct a more accurate actual surgical space. The clinical data obtained in this study can be used for virtual simulation of surgical instrument movement and osteotomy, as well as selection, planning, and teaching purposes of surgical programs.

High speed blending motion trajectory planning using a predefined absolute accuracy

Motion trajectory commands are usually generated using CAD/CAM software and a specified motion controller. At the CAD/CAM stage, the motion commands are generated with respect to the constrains on the contouring error and the application. These commands are also related to the motion controller, which incorporates an advanced blending interpolation method in its function core. Although, high-speed motion can be achieved using blending interpolation, the accuracy of the trajectory is decreased. This study proposes a new blending method that uses a predefined absolute accuracy to optimize both the speed and the accuracy of the generated motion trajectory. The proposed method uses two strategies: the first accelerates or decelerates the velocity profile and the second inserts an arc trajectory command and the corresponding blending accuracy in a critical segment, in order to achieve the speed and the contouring error that is predefined by the user. Four cases are used to determine the performance of the proposed method: (a) line-to-line, (b) line-to-arc, (c) arc-to-arc, and (d) arc-to-line interpolations. The experiments use a predefined speed and accuracy for the motion trajectory. The results demonstrate that the proposed motion trajectory planning process satisfies the needs of industrial applications such as laser cutting and dispensing.

A dynamic lane-changing trajectory planning model for automated vehicles

This paper focuses on the lane-changing trajectory planning (LTP) process in the automatic driving technologies. Existing studies on the LTP algorithms are primarily the static planning method in which the states of the surrounding vehicles of a lane-changing vehicle are assumed to keep unchanged in the whole lane-changing process. However, in real-world traffic, the velocities of the surrounding vehicles change dynamically, and the lane-changing vehicle needs to adjust its velocity and positions correspondingly in real-time to maintain safety. To address such limitations, the dynamic lane-changing trajectory planning (DLTP) model is proposed in the limited literature. This paper proposes a novel DLTP model consisting of the lane-changing starting-point determination module, trajectory decision module and trajectory generation module. The model adopts a time-independent polynomial trajectory curve to avoid the unrealistic assumptions on lane-changing velocities and accelerations in the existing DLTP model. Moreover, a rollover-avoidance algorithm and a collision-avoidance algorithm containing a reaction time are presented to guarantee the lane-changing safety of automated vehicles, even in an emergent braking situation. The field lane-changing data from NGSIM data are used to construct a real traffic environment for lane-changing vehicles and verify the effectiveness of the proposed model, and CarSim is applied to investigate the traceability of the planned lane-changing trajectories using the proposed model. The results indicate that an automated vehicle can complete the lane-changing process smoothly, efficiently and safely following the trajectory planned by the proposed model, and the planned velocity and trajectory can be well-tracked by automated vehicles.

An offline path planning method for autonomous vehicles

Abstract Driving a road vehicle is a very complex task in terms of controlling it, substituting a human driver with a computer is a real challenge also from the technical side. An important step in vehicle controlling is when the vehicle plans its own trajectory. The input of the trajectory planning are the purpose of the passengers and the environment of the vehicle. The trajectory planning process has several parts, for instance, the geometry of the path-curve or the speed during the way. Furthermore, a traffic situation can also determine many other parameters in the planning process. This paper presents a basic approach for trajectory design. To reach the aim a map will be given as a binary 2204 x 1294 size matrix where the roads will be defined by ones, the obstacles will be defined by zeros. The aim is to make an algorithm which can find the shortest and a suitable way for vehicles between the start and the target point. The vehicle speed will be slow enough to ignore the dynamical properties of the vehicle. The research is one of the first steps to realize automated parking features in a self-drive car.

Re-entry guidance for hypersonic vehicle satisfying no-fly zone constraints

Re-entry guidance is one of the primary tasks of a global strike mission. Hypersonic and common aero vehicles are currently being investigated for missions like this. This paper proposes a guidance law considering not only the constraints of terminal status and flight process, but also the avoidance of no-fly zones, to meet the requirements of a global strike mission. An improved A* algorithm is proposed first to achieve a real-time trajectory planning process. Then a dynamic optimization guidance law based on the model of a hypersonic vehicle considering single and multiple no-fly zones is founded. Numerical simulations show the robustness and rapidity of this optimization method.

A Robot Trajectory Optimization Approach for Thermal Barrier Coatings Used for Free-Form Components

This paper is concerned with a robot trajectory optimization approach for thermal barrier coatings. As the requirements of high reproducibility of complex workpieces increase, an optimal thermal spraying trajectory should not only guarantee an accurate control of spray parameters defined by users (e.g., scanning speed, spray distance, scanning step, etc.) to achieve coating thickness homogeneity but also help to homogenize the heat transfer distribution on the coating surface. A mesh-based trajectory generation approach is introduced in this work to generate path curves on a free-form component. Then, two types of meander trajectories are generated by performing a different connection method. Additionally, this paper presents a research approach for introducing the heat transfer analysis into the trajectory planning process. Combining heat transfer analysis with trajectory planning overcomes the defects of traditional trajectory planning methods (e.g., local over-heating), which helps form the uniform temperature field by optimizing the time sequence of path curves. The influence of two different robot trajectories on the process of heat transfer is estimated by coupled FEM models which demonstrates the effectiveness of the presented optimization approach.