Trajectory Planning Approach Research Articles

A Unified Collision Avoidance Trajectory Planning with Dual Variables for Collaborative Aerial Transportation Systems

As an essential application of unmanned aerial vehicle (UAV) systems, payload transportation has garnered significant attention in recent years. Collaborative payload transportation utilizing multiple UAVs can effectively increase the payload capacity of the transportation system. Nevertheless, the incorporation of multiple UAVs makes the dynamic model of the transportation system more complex due to the coupled UAV and payload states. In the immediate disaster relief response, the collaborative system is often required to promptly deliver supplies to the target site while avoiding obstacles to ensure the system’s safety. Consequently, devising fast delivery trajectories that avoid collisions for such complicated systems poses a considerable challenge. To this end, a novel trajectory planning method is presented for collaborative transportation systems. Specifically, the dynamic model of the collaborative transportation system is derived by utilizing the Euler–Lagrange method. Then, the trajectory planning problem is formulated as an optimization problem with considerations of dynamics, actuation, safety, and formation constraints. To expedite the optimization process, the collision avoidance safety constraint is constructed using dual variables. The efficacy of this trajectory planning approach is confirmed through multiple real-world flight experiments involving collaborative aerial transportation systems of two and three UAVs.

Trajectory Planning Design for Parallel Parking of Autonomous Ground Vehicles with Improved Safe Travel Corridor

In this paper, the concept of symmetry is utilized to design the trajectory planning for parallel parking of autonomous ground vehicles—that is, the construction and the solution of the optimization-based trajectory planning approach are symmetrical. Parking is the main factor that troubles most drivers for their daily driving travel, and it can even lead to traffic congestion in severe cases. With the rise of new intelligent and autonomous vehicles, automatic parking seems to have become a trend. Traditional geometric planning methods are less adaptable to parking scenarios, while the parking paths planned by graph search methods may only achieve local optimality. Additionally, significant computational time is often required by numerical optimization methods to find a parking path when a good initial solution is not available. This paper presents a hierarchical trajectory planning approach for high-quality parallel parking of autonomous ground vehicles. The approach begins with a graph search layer to roughly generate an initial solution, which is refined by a numerical optimization layer to produce a high-quality parallel parking trajectory. Considering the high dimensionality and difficulty of finding an optimal solution for the path planning optimization problem, this paper proposes an improved safe travel corridor (I-STC) with the construction of collision constraints isolated from surrounding environmental obstacles. By constructing collision constraints of the I-STC based on the initial solution, the proposed method avoids the complexities and non-differentiability of traditional obstacle avoidance constraints, and simplifies the problem modeling the subsequent numerical optimization process. The simulation results demonstrate that the I-STC is capable of generating parallel parking trajectories with both comfort and safety.

Trajectory planning and tracking of dynamic lane change for autonomous buses considering vehicle stability in dynamic traffic scenarios

Trajectory planning and tracking of lane change are critical technologies for autonomous buses. Characteristics of the buses susceptible to stability problems resulting from the high height, large passenger capacity and long lengths, coupling the dynamic traffic with the dynamic changes in the states of adjacent vehicles and road adhesion coefficient, put forward great challenges in lane change for autonomous buses (ABs). To cope with the foregoing challenges, a framework is proposed to achieve the trajectory planning and tracking of dynamic lane change for ABs. For trajectory planning approach, the trajectory planning and replanning is optimized in the safe range of longitudinal length of the lane-changing trajectory to obtain the real-time reference trajectory, combining consideration of vehicle yaw, roll stability and lane-changing efficiency. The minimum longitudinal length of lane-changing trajectory determined by the yaw stability and roll stability of ABs, combined with the maximum length formed by the adjacent vehicles with dynamic states, form the real-time safe range for lane-changing trajectory planning. For trajectory tracking approach, a tracking approach using model predictive control based on multipoint preview is proposed to achieve the real-time planned trajectory tracking considering buses stability. The effectiveness of the proposed strategy is evaluated by simulating an experimentally validated Trucksim model in different dynamic traffic scenarios to demonstrate the capability of the strategy in trajectory planning and tracking, and guaranteeing vehicle stability for dynamic lane change of ABs.

Industrial Robot Trajectory Optimization Based on Improved Sparrow Search Algorithm

This paper proposes an enhanced multi-strategy sparrow search algorithm to optimize the trajectory of a six-axis industrial robot, addressing issues of low efficiency and high vibration impact on joints during operation. Initially, the improved D-H parametric method is employed to establish both forward and inverse kinematic models of the robot. Subsequently, a 3-5-3 mixed polynomial interpolation trajectory planning approach is applied to the robot. Building upon the conventional sparrow algorithm, a two-dimensional Logistic chaotic system initializes the population. Additionally, a Levy flight strategy and nonlinear adaptive weighting are introduced to refine the discoverer position update operator, while an inverse learning strategy enhances the vigilante position update operator. These modifications boost both the local and global search capabilities of the algorithm. The improved sparrow algorithm, based on 3-5-3 hybrid polynomial trajectory planning, is then used for the time-optimal trajectory planning of the robot. This is compared with traditional sparrow search algorithm and particle swarm algorithm optimization results. The findings indicate that the proposed enhanced sparrow search algorithm outperforms both the standard sparrow algorithm and the particle swarm algorithm in terms of convergence speed and accuracy for robot trajectory optimization. This can lead to the increased work efficiency and performance of the robot.

Theoretical and experimental investigations on a data-driven trajectory planning scheme for dynamic shape control of piezo-actuated compliant morphing structures

Piezo-actuated compliant morphing structures can transmit motion and force via elastic deformation with lower weight, simplified design, and higher accuracy, a typical example is the variable camber wing. However, the rapid shape change of compliant structures is a challenging control problem because it often results in a high level of vibration due to the structural flexibility necessary to achieve the morphing requirement. This study presents a model-free data-driven trajectory planning approach based on spline curves and surrogate-based optimization (SBO) to obtain smooth “rest-to-rest” morphing trajectories. The macro-fiber composite (MFC) patches are used for piezoelectric actuators to generate elastic deformation. The flexible beam and variable camber wing are used for both linear numerical simulation and experimental tests with various nonlinearities and uncertainties. An optimization criterion is proposed to minimize both transient and residual vibrations during the “rest-to-rest” motion. An extraordinarily terminal displacement error function is added to eliminate the effects of the hysteresis and creep of the actuator. The control inputs, i.e., voltage profiles for the MFCs, are defined using cubic spline curves via only a few control points. Then, the optimization problem is solved by employing a Kriging surrogate model-based algorithm integrated with the expected improvement (EI) infilling-sampling criterion, which constructs an efficient algorithm similar to reinforcement learning. The optimal morphing trajectories can be highly efficiently obtained by using only 4 control points and less than 150 samplings. The experimental results of both the plate model and the variable camber wing model show that the proposed method can not only achieve a smooth dynamic morphing trajectory with minimized vibration but also automatically compensate for hysteresis and creep. The proposed method provides an effective means for the rapid realization of an optimized morphing trajectory for compliant morphing structures.

A multi-objective trajectory planning approach for vibration suppression of a series–parallel hybrid flexible welding manipulator

Although the series–parallel hybrid welding manipulator has advantages over the traditional series manipulator, its must run continuously and smoothly according to a specific trajectory at the rated velocity. Considering a flexible manipulator with a complex series–parallel hybrid structure as the research object, this paper proposes a multi-objective approach to indirectly suppress the vibration. In view of the complex flexible mechanism with a multi-kinematic pair arrangement and a multi-motor drive, a system comprehensive elastodynamics model is established, and the effectiveness of the model is verified through the hammer test method. To achieve synchronous and coordinated planning of the end position and attitude, the spatial arc welding trajectory is planned on the basis of the synchronous planning controller and the dual-S velocity profile interpolation function. Then, a multi-objective optimization model considering the travel time, energy consumption and terminal amplitude fluctuations is proposed, the trajectory planning problem is transformed into a parameter optimization problem in the interpolation function, and then the elite non-dominated sorting genetic algorithm (NSGA-II) is employed to determine the optimal trajectory. The optimal trajectory thus obtained effectively suppresses the vibration of the system. Finally, compared with the classic fifth-degree polynomial trajectory planning method, the system vibration suppression effect is significant, which verifies the effectiveness and feasibility of the proposed method and provides a theoretical basis for further realizing real-time control.

A Deep Reinforcement Learning Algorithm for Trajectory Planning of Swarm UAV Fulfilling Wildfire Reconnaissance

Wildfires have long been one of the critical environmental disasters that require a careful monitoring system. An intelligent system has the potential to both prevent/extinguish the fire and deliver urgent requirements postfire. In recent years, unmanned aerial vehicles (UAVs), with the ability to detect missions in high-risk areas, have been gaining increasing interest, particularly in forest fire monitoring. Taking a large-scale area involved in a fire into consideration, a single UAV is often insufficient to accomplish the task of covering the whole disaster zone. This poses the challenge of multi-UAVs optimum path planning with a key focus on limitations such as energy constraints and connectivity. To narrow down this issue, this paper proposes a deep reinforcement learning-based trajectory planning approach for multi-UAVs that permits UAVs to extract the required information within the disaster area on time. A target area is partitioned into several identical subareas in terms of size to enable UAVs to perform their patrol duties over the subareas. This subarea-based arrangement converts the issue of trajectory planning into allowing UAVs to frequently visit each subarea. Each subarea is initiated with a risk level by creating a fire risk map optimizing the UAV patrol route more precisely. Through a set of simulations conducted with a real trace of the dataset, the performance outcomes confirmed the superiority of the proposed idea.

Beyond Static Obstacles: Integrating Kalman Filter with Reinforcement Learning for Drone Navigation

Autonomous drones offer immense potential in dynamic environments, but their navigation systems often struggle with moving obstacles. This paper presents a novel approach for drone trajectory planning in such scenarios, combining the Interactive Multiple Model (IMM) Kalman filter with Proximal Policy Optimization (PPO) reinforcement learning (RL). The IMM Kalman filter addresses state estimation challenges by modeling the potential motion patterns of moving objects. This enables accurate prediction of future object positions, even in uncertain environments. The PPO reinforcement learning algorithm then leverages these predictions to optimize the drone’s real-time trajectory. Additionally, the capability of PPO to work with continuous action spaces makes it ideal for the smooth control adjustments required for safe navigation. Our simulation results demonstrate the effectiveness of this combined approach. The drone successfully navigates complex dynamic environments, achieving collision avoidance and goal-oriented behavior. This work highlights the potential of integrating advanced state estimation and reinforcement learning techniques to enhance autonomous drone capabilities in unpredictable settings.

Trajectory planning of a free-floating dual-arm space robot with minimal base disturbance in obstacle environments

This paper addresses the issue of trajectory planning for a free-floating dual-arm space robot, considering the constraints of collision avoidance while simultaneously minimizing the base position and attitude disturbance during on-orbit tasks. One arm is designated as the mission arm, tracking a prescribed path to complete specific goals, while the other serves as the balance arm, compensating for any base attitude disturbance. A collision-free path planning approach is presented for the mission arm, which utilizes a hybrid map, improved artificial potential field (IAPF) and adaptive coupling guidance method. The hybrid map in the mission arm joint space contains the coupling relationship between the deviation of the base position and the motion of the dual arms, along with obstacles transformed from Cartesian space. Then, to address the problem of the goals nonreachable with obstacles nearby (GNRON) of the artificial potential field (APF), a novel repulsive potential field is incorporated into the IAPF. To minimize the base position disturbance, a coupling guidance method is presented that enables the mission arm to move in areas with lower coupling factors on the hybrid map. Finally, simulations are conducted to demonstrate the effectiveness and superiority of the proposed hybrid map and coordinated trajectory planning approach.

An automatic driving trajectory planning approach in complex traffic scenarios based on integrated driver style inference and deep reinforcement learning.

As autonomous driving technology continues to advance and gradually become a reality, ensuring the safety of autonomous driving in complex traffic scenarios has become a key focus and challenge in current research. Model-free deep reinforcement learning (Deep Reinforcement Learning) methods have been widely used for addressing motion planning problems in complex traffic scenarios, as they can implicitly learn interactions between vehicles. However, current planning methods based on deep reinforcement learning exhibit limited robustness and generalization performance. They struggle to adapt to traffic conditions beyond the training scenarios and face difficulties in handling uncertainties arising from unexpected situations. Therefore, this paper addresses the challenges presented by complex traffic scenarios, such as signal-free intersections. It does so by first utilizing the historical trajectories of adjacent vehicles observed in these scenarios. Through a Variational Auto-Encoder (VAE) based on the Gated Recurrent Unit (GRU) recurrent neural network, it extracts driver style features. These driver style features are then integrated with other state parameters and used to train a motion planning strategy within an extended reinforcement learning framework. This approach ultimately yields a more robust and interpretable mid-to-mid motion planning method. Experimental results confirm that the proposed method achieves low collision rates, high efficiency, and successful task completion in complex traffic scenarios.

An Efficient Trajectory Planning Approach for Autonomous Ground Vehicles Using Improved Artificial Potential Field

In this paper, the concept of symmetry is utilized in the promising trajectory planning design of autonomous ground vehicles—that is, the construction and the solution of improved artificial potential field-based trajectory planning approach are symmetrical. Despite existing artificial potential fields (APF) achievements on trajectory planning in autonomous ground vehicles (AGV), applying the traditional approach to dynamic traffic scenarios is inappropriate without considering vehicle dynamics environment and road regulations. This paper introduces a highly efficient approach for planning trajectories using improved artificial potential fields (IAPF) to handle dynamic road participants and address the issue of local minima in artificial potential fields. To begin with, potential fields are created with data obtained from other sensors. By incorporating rotational factors, the potential field will spin when the obstacle executes a maneuver; then, a safety distance model is also developed to limit the range of influence in order to minimize the computational burden. Furthermore, during the planning process, virtual forces using the gradient descent method are generated to direct the vehicle’s movement. During each timestep, the vehicle will assess whether it is likely to encounter a local minimum in the future. Once a local minimum is discovered, the method will create multiple temporary objectives to guide the vehicle toward the global minimum. Consequently, a trajectory that is both collision-free and feasible is planned. Traffic scenarios are carried out to validate the effectiveness of the proposed approach. The simulation results demonstrate that the improved artificial potential field approach is capable of generating a secure trajectory with both comfort and stability.

A New Trajectory Planning Approach With Motion Duration Control for Kinematic Constrained Systems

A New Trajectory Planning Approach With Motion Duration Control for Kinematic Constrained Systems

A Platoon-Based Approach for AGV Scheduling and Trajectory Planning in Fully Automated Production Systems

A Platoon-Based Approach for AGV Scheduling and Trajectory Planning in Fully Automated Production Systems

Enhancing UAV Path Planning Efficiency through Adam-Optimized Deep Neural Networks for Area Coverage Missions

Efficient Unmanned Aerial Vehicle (UAV) trajectory generation is crucial for successful area coverage missions, aiming to maximize coverage while minimizing resource consumption. In this research, we present a comprehensive study on optimizing UAV trajectory generation using Deep Neural Networks (DNNs) with the Adam optimization algorithm. The DNNs are trained on historical data to produce smooth and continuous trajectories, thereby reducing abrupt changes in direction and enhancing overall efficiency during the mission. To evaluate the performance of the proposed approach, we conducted experiments comparing different activation functions, namely tanh, sigmoid, and ReLU, with the Adam-optimized DNN model. The trajectories generated by each activation function were analyzed using key metrics, including Mean Squared Error (MSE), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and R-squared (R2) scores for both X and Y coordinates. The results of the comparative analysis revealed that the DNN model with the Adam optimizer exhibited superior performance over the other activation functions. It achieved lower MSE, MAE, and RMSE values, indicating better trajectory accuracy and smoother paths. Additionally, the R2 scores demonstrated a higher correlation between the generated trajectories and the actual trajectories, highlighting the model's ability to capture underlying patterns effectively. The findings underscore the significance of leveraging the Adam-optimized DNN approach for UAV trajectory planning, offering promising opportunities for resource optimization, increased mission success, and further advancements in autonomous aerial systems. This research contributes to the ongoing efforts in UAV path planning, optimization, and intelligent control strategies, paving the way for enhanced autonomous systems in various real-world applications.

Trajectory planning of vibration suppression for hybrid structure flexible manipulator based on differential evolution particle swarm optimization algorithm

A differential evolution particle swarm optimization algorithm is proposed to address the vibration problem of a hybrid structure flexible manipulator after motion and stop. Firstly, the errors in the modeling process of the flexible manipulator were corrected, and its state variables were decomposed to establish dynamic and kinematic models. A sliding mode controller was then designed to track the trajectory. To find the optimal trajectory, a mapping function was constructed, and non-uniform interpolation points were selected. A normal distribution function was used to select discrete interpolation points, and the cubic spline interpolation was used to fit the trajectory. To prevent the particle swarm optimization algorithm from falling into local optima, the mutation and crossover operators of the differential evolution algorithm are incorporated into the algorithm, thereby expanding the search range. The effectiveness of this improved method was verified by comparing it with traditional particle swarm optimization algorithms. This study provides a new trajectory planning approach for the motion control of a hybrid structured flexible manipulator and has important practical significance.

A suggestion-based hierarchical energy efficient control framework for connected and automated vehicles in mixed stream urban road networks

Connected and automated vehicles (CAVs) and their advanced control systems have the ability to improve energy efficiency and mobility of the transportation system, but hundred percent market penetration of CAVs will not happen in the near future. CAVs are thus expected to share the road with human-driven vehicles (HDVs), which can act in suboptimal manners. Since vehicles on road constitute an interactive system, where actions of one vehicle influence the actions of its surrounding vehicles, suboptimal behavior of HDVs affect all their surrounding vehicles including the CAVs. This paper thus focuses on the development of a suggestion-based control framework for CAVs in interactive mixed traffic environments. Our mixed traffic environment includes both CAVs and connected HDVs that have vehicle-to-vehicle (V2V) communication capabilities. In this suggestion-based control framework, a CAV is considered to provide velocity and lane-change suggestions to multiple surrounding HDVs to follow. These suggestions are the velocities and lane-change actions the CAV wants the HDVs to follow to improve its own and the group’s energy efficiency and mobility. To take into account the interactive nature of the environment, the CAV is considered to jointly plan its own trajectory, evaluate the suggestions to the surrounding HDVs, and predict the actions of its surrounding vehicles. The joint planning requires solving the problem in joint state- and action-space, and in this paper, we develop a Monte Carlo Tree Search (MCTS)-based trajectory planning approach for the CAV. Since the joint action- and state-space grows exponentially with the number of agents and can be computationally expensive, we propose an adaptive action-space by pruning the actions resulting in unsafe trajectories for each agent. The trajectory planning approach is followed by a low-level model predictive control (MPC)-based motion controller, which aims at tracking the reference trajectory in an optimal fashion. Simulation studies show the proposed control strategy’s efficacy compared with existing baseline methods. Simulation studies show improvements in fuel efficiency ranging from 4% to 50% for HDVs and from 1% to 30% for the CAV compared to the baseline.

Time-optimal trajectory planning for a rigid formation of nonholonomic mobile platforms

AbstractThis paper presents a method for planning time-optimal trajectories for a formation of multiple nonholonomic (heavy duty) platforms (HDPs) to cooperatively transport an object to a specified pose. The first part addresses the mobile platforms themselves while the second part provides a trajectory planning approach derived from the well-known virtual leader approach. In order to ensure proper transport of the shared payload, the vehicles are modeled individually, resulting in a formation control problem. The goal of the optimization process is to minimize a cost function that balances time optimality, smooth control signals, and formation rigidity. The optimal control problem (OCP) takes into account the kinematics of the vehicles as well as their physical limitations. It is solved by using a multiple shooting method, which yields the desired trajectories for all vehicles while ensuring smooth control signals. The paper includes optimization results for several scenarios involving two and three HDPs together with various target poses, demonstrating the effectiveness of the proposed method.

An enhanced coupling optimal trajectory planning for bridge cranes

For the bridge crane system, the control objective is to deliver the cargo to the target location quickly, accurately, and with the smallest possible swing. Therefore, this paper proposes a novel signal-based trajectory planning approach and designs the corresponding tracking control strategy. The approach ensures that the payload can be transported smoothly in the shortest time and effectively suppresses and eliminates payload swing throughout the process. Specifically, a novel signal with enhanced coupling is first constructed, and then the system model is transformed into the system represented by the signal. The system is further discretized into critical control points, the trajectories are designed, and the optimization problem is formulated using the constraints obtained from the discrete system. Moreover, the proposed method enhances the coupling between the trolley motion and the payload swing angle, which reduces computational accuracy loss and improves the transient performance of the system. Additionally, a tracking controller is designed to verify the feasibility of the trajectory and enhance the tracking effect of the trajectory. Finally, the effective control performance of the proposed method is verified by comparing it with existing methods.

Trajectory planning approach for autonomous electric bus in dynamic environment

Path planning is a challenging task to achieve vehicle autonomy, and it becomes even more difficult in handling dynamic situations and big vehicle sizes. Its performance is affected by the accuracy of mapping and vehicle localization. Many path planning algorithms have been developed to address static environments, however, these do not accurately reflect real-world scenarios which are dynamic in nature. This paper introduces a new planning architecture consisting of a global planner that plans a path in an occupancy grid map generated using LIDAR and odometry data. The local planner uses this global plan and plans a local plan on a section of the map that takes into consideration dynamic obstacles. Both the local and global plans are used to calculate the optimum velocity profile, providing a feasible and comfortable trajectory. The trajectory is then fed to a predictive Stanley controller, and both the calculated steering angle and the optimum velocity are achieved by low-level controllers. The performance of the proposed architecture was tested on a golf bus in a constrained environment and compared to different manual driving attitudes using a key performance indicator. The results of the proposed architecture show that it has a better KPI, with an average of 37% better than manual driving.

Trajectory planning for unmanned surface vehicles in multi-ship encounter situations

Unmanned surface vehicles (USVs) can encounter traffic ships while navigating toward the target location. For the USVs, collision avoidance (CA) trajectories need to be planned according to the international regulations for preventing collisions at sea (COLREGS). A novel trajectory planning approach is proposed for the collision-free trajectories planning of USVs in the case of multiship encounters. Unlike the existing trajectory planning approaches, the proposed approach uses the holistic thinking to simplify the analysis of encounter situations. Ships approaching from all sides of the USV are treated as one or two equivalent obstacles based on consistent offset velocity direction (COVD) method. Furthermore, planned velocity is designed using the proposed CA strategy and kinematic constraints. This strategy is compliant with COLREGS and includes an emergency CA module to further ensure a safe distance between the USV and traffic ships. The performance of the proposed trajectory planning approach is verified through physical simulations using an existing simulator. The simulation results show that the proposed trajectory planning approach can implement multiple USVs to simultaneously avoid collisions and reach their respective target positions. Moreover, the approach remains effective when other USVs do not follow the COLREGS protocols.