Trajectory Planning Research Articles

A method for simultaneously implementing trajectory planning and DAG task scheduling in multi-UAV assisted edge computing

UAV-assisted edge computing(UEC) as a new framework is able to provide computing services to remote areas. However, facing computationally intensive tasks with huge computation time forces them to hover near the user’s devices(UDs) for long periods of time. To better utilize the available arithmetic resources and reduce the computation time of UAVs, it is imperative to introduce directed acyclic graph (DAG) task scheduling into the UEC framework. Therefore, this article proposes a DAG-type task-driven trajectory planning (DAG-TDTP) model, which can plan UAV routes while scheduling DAG subtasks between UAVs that offload from UDs. To implement the DAG-TDTP model, we propose a distance-based heterogeneous earliest-finish-time (D-HEFT) algorithm and a time segmentation method based on the cooperative task offloading matrix. To stimulate the potential of the DAG-TDTP model in reducing energy consumption, we propose a genetic algorithm based on temporary key nodes (TKNGA) for the proposed model. Through simulation analysis, we verify the superiority of the proposed model in reducing UAV system energy consumption and the superiority of TKNGA compared to other algorithms.

A New Method for Displacement Modelling of Serial Robots Using Finite Screw

Kinematics is a hot topic in robotic research, serving as a foundational step in the synthesis and analysis of robots. Forward kinematics and inverse kinematics are the prerequisite and foundation for motion control, trajectory planning, dynamic simulation, and precision guarantee of robotic manipulators. Both of them depend on the displacement models. Compared with the previous work, finite screw is proven to be the simplest and nonredundant mathematical tool for displacement description. Thus, it is used for displacement modelling of serial robots in this paper. Firstly, a finite-screw-based method for formulating displacement model is proposed, which is applicable for any serial robot. Secondly, the procedures for forward and inverse kinematics by solving the formulated displacement equation are discussed. Then, two typical serial robots with three translations and two rotations are taken as examples to illustrate the proposed method. Finally, through Matlab simulation, the obtained analytical expressions of kinematics are verified. The main contribution of the proposed method is that finite-screw-based displacement model is highly related with instantaneous-screw-based kinematic and dynamic models, providing an integrated modelling and analysis methodology for robotic mechanisms.

Motion Planning for a Legged Robot with Dynamic Characteristics.

Legged soccer robots present a significant challenge in robotics owing to the need for seamless integration of perception, manipulation, and dynamic movement. While existing models often depend on external perception or static techniques, our study aims to develop a robot with dynamic and untethered capabilities. We have introduced a motion planner that allows the robot to excel in dynamic shooting and dribbling. Initially, it identifies and predicts the position of the ball using a rolling model. The robot then pursues the ball, using a novel optimization-based cycle planner, continuously adjusting its gait cycle. This enables the robot to kick without stopping its forward motion near the ball. Each leg is assigned a specific role (stance, swing, pre-kick, or kick), as determined by a gait scheduler. Different leg controllers were used for tailored tiptoe trajectory planning and control. We validated our approach using real-world penalty shot experiments (5 out of 12 successful), cycle adjustment tests (11 out of 12 successful), and dynamic dribbling assessments. The results demonstrate that legged robots can overcome onboard capability limitations and achieve dynamic mobility and manipulation.

Gaussian Pseudo-spectrum Optimization-Based Fuzzy Logic Parallel Parking Trajectory Planning

Gaussian Pseudo-spectrum Optimization-Based Fuzzy Logic Parallel Parking Trajectory Planning

A Multi-Model Architecture Based on Deep Learning for Longitudinal Available Overload Prediction of Commercial Subsonic Aircraft with Actuator Faults

Assessing the real-time longitudinal available overload onboard under fault conditions offers vital insights for the fault-tolerant reconfiguration and trajectory planning of commercial subsonic aircraft. After actuator failures in a commercial subsonic aircraft, its aerodynamic model undergoes changes. Traditional methods based on analytical models rely on precise aerodynamic models. However, due to the complexities of the flight environment and uncertainties in disturbances, establishing an accurate aerodynamic model after actuator failures is often challenging. Consequently, traditional methods can yield significant errors when evaluating the available overload under actuator faults. To address this, we introduce a multi-model architecture based on deep learning for the longitudinal available overload prediction of a commercial subsonic aircraft with actuator faults. For flight state data under different working conditions and different faults, Spearman correlation coefficient analysis and the gradient boosting decision tree (GBDT) algorithm are used to remove redundant feature parameters, thereby enhancing the training and prediction speed of the model while reducing the risk of overfitting. To meet prediction accuracy and speed demands, we employ the multi-layer perceptron (MLP) deep learning network to fully explore the environmental features, including uncertainties and disturbances, within the flight state, and the mapping relationships between the flight state and the available overload variations. We incorporate the light gradient boosting machine (LightGBM) and the categorical boosting (CatBoost) algorithms to enhance the model’s prediction speed and fuse it with a longitudinal available overload analytical model to elevate the model’s prediction accuracy, thereby achieving the real-time estimation of the commercial subsonic aircraft’s longitudinal available overload with actuator faults. The results demonstrate that the proposed method achieves a higher accuracy than traditional methods, with a relative error of less than 5%.

Research on the Safety Design and Trajectory Planning for a New Dual Upper Limb Rehabilitation Robot

The increasing utilization of upper limb rehabilitation robots in rehabilitation therapy has brought to light significant safety concerns regarding their mechanical structures and control systems. This study focuses on a six degrees of freedom (DOF) upper limb rehabilitation robot, which has been designed with an emphasis on safety through careful consideration of its mechanical structure and trajectory planning. Various parameter schemes for the shoulder joint angles were proposed, and the robotic arm’s structure was developed by analyzing the spatial motion trajectories of the shoulder joint motor. This design successfully achieves the objective of minimizing the installation space while maximizing the range of motion. Additionally, an enhanced artificial field method is introduced to facilitate the planning of self-collision avoidance trajectories for dual-arm movements. This approach effectively mitigates the risk of collisions between the robotic arm and the human body, as well as between the two robotic arms, during movement. The efficacy of this method has been validated through experimental testing.

Research on Trajectory Planning and Tracking Algorithm of Crawler Paver

The implementation of unmanned intelligent construction on the concrete surfaces of an airport effectively improves construction accuracy and reduces personnel investment. On the basis of three known common tracked vehicle dynamics models, reference trajectory planning and trajectory tracking controller algorithms need to be designed. In this paper, based on the driving characteristics of the tracked vehicle and the requirements of the stepping trajectory, a quartic polynomial trajectory planning algorithm was selected with the stability of the curve as a whole and the end point as the optimization goal, combining the tracked vehicle dynamics model, collision constraints, start–stop constraints and other boundary conditions. The objective function of trajectory planning was designed to effectively plan the reference trajectory of the tracked vehicle’s step-by-step travel. In order to realize accurate trajectory tracking control, a nonlinear model predictive controller with transverse-longitudinal integrated control was designed. To improve the real-time performance of the controller, a linear model predictive controller with horizontal and longitudinal decoupling was designed. MATLAB 2023A and CoppeliaSim V4.5.1 were used to co-simulate the two controller models. The experimental results show that the advantages and disadvantages of the tracked vehicle dynamics model and controller design are verified.

Motion primitives and sample-based trajectory planning for fixed-wing unmanned aircraft

Navigating fixed-wing unmanned aircraft presents significant challenges, primarily stemming from the intricate dynamics involved and the demand for rapid planning. In this paper, we introduce an efficient approach that concurrently addresses nonlinear control and trajectory planning challenges. To tackle the control problem, we introduce a computationally efficient motion primitive that effectively maps feasible targets to control inputs. As for trajectory planning, we propose an enhanced, rapidly exploring, random tree algorithm capable of generating high-quality trajectories with minimal exploration. Our primary motivation is to seamlessly integrate the introduced motion primitive with a sample-based trajectory-planning technique, providing a comprehensive solution to the intricate challenges posed by nonlinear control and trajectory planning for fixed-wing unmanned aircraft. Experimental results showcase our approach’s superiority, delivering enhanced control precision, faster planning speeds, and improved planning quality.

Dynamic modeling and trajectory optimization for the rigid-flexible coupled spacecraft with the free-floating manipulator and solar panels

The rigid-flexible coupled spacecraft, composed of flexible solar panels and a multilink manipulator, has gained prominence in on-orbit servicing due to rapid advancements in space technology. However, the intricate effects of rigid-flexible coupling pose significant challenges for dynamic modeling, trajectory planning, and control. This paper aims to develop general dynamic approaches for modeling and trajectory planning in such spacecraft, considering large deformations. The main distinguishing feature is the use of the referenced nodal coordinate formulation to accurately describe the large-deformed solar panels rather than directly treating them as disturbance for the free-floating system. Additionally, the common recursive model for the multilink manipulator is integrated into the same framework. The modal reduction method with modal derivatives techniques is employed to address geometric nonlinearity resulting from large deformations. Polynomial trajectory parameters with different performance characteristics are obtained by defining various optimization objectives. The coupling analysis is conducted based on an accurate reduced-order dynamic model, the results of which can be used for designing manipulator tasks. Coupling values are defined as the objective for trajectory optimization, offering advantages such as insensitivity to dynamic model accuracy and a fast optimization process. After validating the accuracy of the proposed dynamic model through simulations, the performances of different optimized trajectories are demonstrated using numerical examples.

Space-time graph path planner for unsignalized intersection management with a V2V agent coordination architecture

Reducing traffic congestion and increasing passenger safety are important objectives for emerging automated transportation systems. Autonomous intersection management systems (AIMS) enable large scale optimization of vehicle trajectories with connected and autonomous vehicles (CAVs). We propose a novel approach for computing the fastest waypoint trajectory in intersections using graph search in a discretized space-time graph that produces collision-free paths with variable vehicle speeds that comply with traffic rules and vehicle dynamical constraints. To assist our planner algorithm in decentralized scenarios, we also propose a multi-agent protocol architecture for vehicle coordination for trajectory planning using a vehicle-to-vehicle (V2V) network. The trajectories generated allow a much higher evacuation rate and congestion threshold, with lower O(N) algorithm runtime compared to the state of the art conflict detection graph platoon path planning method, even for large scenarios with vehicle arrival rate of 1/s and thousands of vehicles.

Road adhesion coefficient Estimation: Physics-informed deep learning method with vehicle dynamics model

Road adhesion coefficient (RAC) is not only a significant basis for trajectory planning and decision-making of autonomous vehicles but also a critical parameter to determine the control potential of autonomous vehicles under complex operating conditions. Accurate, timely, and reliable estimation of RAC facilitates many function units of autonomous vehicles and improves driving safety. To address the issues of low accuracy and transparency of RAC estimation method based on road surface image recognition, a vehicle dynamics model-informed deep learning (VDMIDL) method for RAC estimation is proposed in this work. The physics information related to vehicle dynamics is integrated into a CNN-based deep learning model via the fusion of vehicle physical features and high-dimensional road surface image features to realize accurate estimation of RAC. The results of the model training show that the proposed VDMIDL model for RAC estimation possesses higher prediction accuracy compared with the conventional deep learning (CDL) model. The vehicle test results indicate that the proposed VDMIDL model can provide more prospective and precise RAC for trajectory planning, decision-making, and control of the vehicle in response to sudden variations in road conditions. The VDMIDL model is applicable to a wide range of road conditions. RAC estimated by the VDMIDL model is accurate and stable under poor road condition in particular. The proposed fusion estimation model incorporates more physics information into deep learning model, endowing more interpretability and transparency to the black-box model.

UAV path planning based on bird flock migration

Unmanned aerial vehicle, generally referred to as UAV, due to its high-performance and low-cost characteristics, it is particularly widely used in both military and civil applications, and is often used to perform a variety of complex missions. Trajectory planning is the basis for UAVs to realize autonomous flight, which ensures that UAVs avoid obstacles and threatening areas when performing tasks, and guarantees the safe execution of tasks. The operation of a UAV requires finding the safest and most efficient trajectory from a starting point to a specified end point based on several specific constraints. Current UAV trajectory planning algorithms, such as swarm algorithm, particle swarm algorithm, and ant colony algorithm, have been widely recognized, but still have many limitations when they are applied to complex and variable terrain. Therefore, this paper proposes an improved UAV trajectory planning algorithm based on simulated bird migration, and uses matlab for simulation and algorithm evaluation. The simulation results indicate that the improved search strategy is effective, the algorithm can find a better solution in each iteration, and the search strategy of the algorithm can effectively guide the algorithm towards a more optimized region. Overall, this algorithm has high research value in both military and civilian fields.

A Control System Design and Implementation for Autonomous Quadrotors with Real-Time Re-Planning Capability

Real-time (re-)planning is crucial for autonomous quadrotors to navigate in uncertain environments where obstacles may be detected and trajectory plans must be adjusted on-the-fly to avoid collision. In this paper, we present a control system design for autonomous quadrotors that has real-time re-planning capability, including the hardware pipeline for the hardware–software integration to realize the proposed real-time re-planning algorithm. The framework is based on a modified version of the PX4 Autopilot and a Raspberry Pi 5 companion computer. The planning algorithm utilizes minimum-snap trajectory generation, taking advantage of the differential flatness property of quadrotors, to realize computationally light, real-time re-planning using an onboard computer. We first verify the control system and the planning algorithm through simulation experiments, followed by implementing and demonstrating the system on hardware using a quadcopter.

Research on Trajectory Planning of Autonomous Vehicles in Constrained Spaces.

This paper addresses the challenge of trajectory planning for autonomous vehicles operating in complex, constrained environments. The proposed method enhances the hybrid A-star algorithm through back-end optimization. An adaptive node expansion strategy is introduced to handle varying environmental complexities. By integrating Dijkstra's shortest path search, the method improves direction selection and refines the estimated cost function. Utilizing the characteristics of hybrid A-star path planning, a quadratic programming approach with designed constraints smooths discrete path points. This results in a smoothed trajectory that supports speed planning using S-curve profiles. Both simulation and experimental results demonstrate that the improved hybrid A-star search significantly boosts efficiency. The trajectory shows continuous and smooth transitions in heading angle and speed, leading to notable improvements in trajectory planning efficiency and overall comfort for autonomous vehicles in challenging environments.

Fuzzy Logic-Based Autonomous Lane Changing Strategy for Intelligent Internet of Vehicles: A Trajectory Planning Approach

The autonomous lane change maneuver is a critical component in the advancement of intelligent transportation systems (ITS). To enhance safety and efficiency in dynamic traffic environments, this study introduces a novel autonomous lane change strategy leveraging a quintic polynomial function. To optimize the trajectory, we formulate an objective function that balances the time required for lane changes with the peak acceleration experienced during the maneuver. The proposed method addresses key challenges such as driver discomfort and prolonged lane change durations by considering the entire lane change process rather than just the initiation point. Utilizing a fifth-order polynomial for trajectory planning, the strategy ensures smooth and continuous vehicle movement, reducing the risk of collisions. The effectiveness of the method is validated through comprehensive simulations and real-world vehicle tests, demonstrating significant improvements in lane change performance. Despite its advantages, the model requires further refinement to address limitations in mixed traffic conditions. This research provides a foundation for developing intelligent vehicle systems that prioritize safety and adaptability.

The Effectiveness of Artificial Intelligence-based Pedicle Screw Trajectory Planning in Patients With Different Levels of Bone Mineral Density.

Retrospective cohort study. To evaluate the effectiveness of pedicle screw trajectory planning based on artificial intelligence (AI) software in patients with different levels of bone mineral density (BMD). AI-based pedicle screw trajectory planning has potential to improve pullout force (POF) of screws. However, there is currently no literature investigating the efficacy of AI-based pedicle screw trajectory planning in patients with different levels of BMD. The patients were divided into 5 groups (group A-E) according to their BMD. The AI software utilizes lumbar spine CT data to perform screw trajectory planning and simulate AO screw trajectories for bilateral L3-5 vertebral bodies. Both screw trajectories were subdivided into unicortical and bicortical modes. The AI software automatically calculating the POF and pullout risk of every screw trajectory. The POF and risk of screw pullout for AI-planned screw trajectories and AO standard trajectories were compared and analyzed. Forty-three patients were included. For the screw sizes, AI-planned screws were greater in diameter and length than those of AO screws (P<0.05). In groups B-E, the AI unicortical trajectories had a POF of over 200N higher than that of AO unicortical trajectories. POF was higher in all groups for the AI bicortical screw trajectories compared with the AO bicortical screw trajectories (P<0.05). AI unicortical trajectories in groups B-E had a lower risk of screw pullout compared with that of AO unicortical trajectories (P<0.05). AI unicortical screw trajectory planning for lumbar surgery in patients with BMD of 40-120mg/cm3 can significantly improve screw POF and reduce the risk of screw pullout.

Differential Difference Equations in Trajectory Planning and Control for Differential Drive Robots: A Comprehensive Exploration

This paper provides a thorough investigation into the utilisation of differential difference equations (DDEs) for the purposes of trajectory planning and control in the context of differential drive four-wheeled robots. The inclusion of sensor and control delays is crucial when developing navigation strategies that are both resilient and efficient for robots functioning in dynamic environments. Differential delay equations (DDEs) provide a robust mathematical framework for representing the dynamics of such systems, facilitating precise and reliable path tracking. In order to demonstrate the versatility and practicality of Delay Differential Equations (DDEs), we investigate three distinct scenarios: straight-line path tracking, circular path tracking, and path planning with obstacle avoidance. These scenarios serve as demonstrations of how Delay Differential Equations (DDEs) facilitate the robot's ability to adjust its motion by utilising previous information, thereby ensuring a trajectory tracking process that is both smooth and stable. The trajectory plots provide a visual representation of the robot's path and effectively illustrate the successful completion of various navigation objectives. This study highlights the importance of dynamic differential equations (DDEs) in the advancement of intelligent and adaptable robotic systems, thereby paving the way for future progress in the realm of robotics and autonomous systems.

Motion Prediction and Object Detection for Image-Based Visual Servoing Systems Using Deep Learning

This study primarily investigates advanced object detection and time series prediction methods in image-based visual servoing systems, aiming to capture targets better and predict the motion trajectory of robotic arms in advance, thereby enhancing the system’s performance and reliability. The research first implements object detection on the VOC2007 dataset using the Detection Transformer (DETR) and achieves ideal detection scores. The particle swarm optimization algorithm and 3-5-3 polynomial interpolation methods were utilized for trajectory planning, creating a unique dataset through simulation. This dataset contains randomly generated trajectories within the workspace, fully simulating actual working conditions. Significantly, the Bidirectional Long Short-Term Memory (BILSTM) model was improved by substituting its traditional Multilayer Perceptron (MLP) components with Kolmogorov–Arnold Networks (KANs). KANs, inspired by the K-A theorem, improve the network representation ability by placing learnable activation functions on fixed node activation functions. By implementing KANs, the model enhances parameter efficiency and interpretability, thus addressing the typical challenges of MLPs, such as the high parameter count and lack of transparency. The experiments achieved favorable predictive results, indicating that the KAN not only reduces the complexity of the model but also improves learning efficiency and prediction accuracy in dynamic visual servoing environments. Finally, Gazebo software was used in ROS to model and simulate the robotic arm, verify the effectiveness of the algorithm, and achieve visual servoing.

Stratospheric airship trajectory planning in wind field using deep reinforcement learning

Stratospheric airships, with their long endurance, high flight altitude, and large payload capacity, show promise in earth observation and mobile internet applications. However, challenges arise due to their low flight speed, limited maneuverability and energy constraints when planning trajectories in dynamic wind fields. This paper proposes a deep reinforcement learning-based method for trajectory planning of stratospheric airships. The model considers the motion characteristics of stratospheric airships and environmental factors like wind fields and solar radiation. The soft actor-critic (SAC) algorithm is utilized to assess the effectiveness of the method in various scenarios. A comparison between time-optimized and energy-optimized trajectories reveals that time-optimized trajectories are smoother with a higher speed, while energy-optimized trajectories can save up to 10% energy by utilizing wind fields and solar energy absorption. Overall, the deep reinforcement learning approach proves effective in trajectory planning for stratospheric airships in deterministic and dynamic wind fields, offering valuable insights for flight design and optimization.

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.