A Novel Cost Calculation Method for Manipulator Trajectory Planning.

It is worthwhile to calculate the execution cost of a manipulator for selecting a planning algorithm to generate trajectories, especially for an agricultural robot. Although there are various off-the-shelf trajectory planning methods, such as pursuing the shortest stroke or the smallest time cost, they often do not consider factors synthetically. This paper uses the state-of-the-art Python version of the Robotics Toolbox for manipulator trajectory planning instead of the traditional D-H method. We propose a cost function with mass, iteration, and residual to assess the effort of a manipulator. We realized three inverse kinematics methods (NR, GN, and LM with variants) and verified our cost function's feasibility and effectiveness. Furthermore, we compared it with state-of-the-art methods such as Double A* and MoveIt. Results show that our method is valid and stable. Moreover, we applied LM (Chan λ = 0.1) in mobile operation on our agricultural robot platform.

Time-Optimal Trajectory Planning and Tracking for Autonomous Vehicles.

This article presents a hierarchical control framework for autonomous vehicle trajectory planning and tracking, addressing the challenge of accurately following high-speed, at-limit maneuvers. The proposed time-optimal trajectory planning and tracking (TOTPT) framework utilizes a hierarchical control structure, with an offline trajectory optimization (TRO) module and an online nonlinear model predictive control (NMPC) module. The TRO layer generates minimum-lap-time trajectories using a direct collocation method, which optimizes the vehicle's path, velocity, and control inputs to achieve the fastest possible lap time, while respecting the vehicle dynamics and track constraints. The NMPC layer is responsible for precisely tracking the reference trajectories generated by the TRO in real time. The NMPC also incorporates a preview algorithm that utilizes the predicted future travel distance to estimate the optimal reference speed and curvature for the next time step, thereby improving the overall tracking performance. Simulation results on the Catalunya circuit demonstrated the framework's capability to accurately follow the time-optimal raceline at an average speed of 116 km/h, with a maximum lateral error of 0.32 m. The NMPC module uses an acados solver with a real-time iteration (RTI) scheme, to achieve a millisecond-level computation time, making it possible to implement it in real time in autonomous vehicles.

Planning Socially Expressive Mobile Robot Trajectories.

Many mobile robotics applications require robots to navigate around humans who may interpret the robot's motion in terms of social attitudes and intentions. It is essential to understand which aspects of the robot's motion are related to such perceptions so that we may design appropriate navigation algorithms. Current works in social navigation tend to strive towards a single ideal style of motion defined with respect to concepts such as comfort, naturalness, or legibility. These algorithms cannot be configured to alter trajectory features to control the social interpretations made by humans. In this work, we firstly present logistic regression models based on perception experiments linking human perceptions to a corpus of linear velocity profiles, establishing that various trajectory features impact human social perception of the robot. Secondly, we formulate a trajectory planning problem in the form of a constrained optimization, using novel constraints that can be selectively applied to shape the trajectory such that it generates the desired social perception. We demonstrate the ability of the proposed algorithm to accurately change each of the features of the generated trajectories based on the selected constraints, enabling subtle variations in the robot's motion to be consistently applied. By controlling the trajectories to induce different social perceptions, we provide a tool to better tailor the robot's actions to its role and deployment context to enhance acceptability.

A Multistage Hemiplegic Lower-Limb Rehabilitation Robot: Design and Gait Trajectory Planning.

Most lower limb rehabilitation robots are limited to specific training postures to adapt to stroke patients in multiple stages of recovery. In addition, there is a lack of attention to the switching functions of the training side, including left, right, and bilateral, which enables patients with hemiplegia to rehabilitate with a single device. This article presents an exoskeleton robot named the multistage hemiplegic lower-limb rehabilitation robot, which has been designed to do rehabilitation in multiple training postures and training sides. The mechanism consisting of the thigh, calf, and foot is introduced. Additionally, the design of the multi-mode limit of the hip, knee, and ankle joints supports delivering therapy in any posture and training sides to aid patients with hemiplegia in all stages of recovery. The gait trajectory is planned by extracting the gait motion trajectory model collected by the motion capture device. In addition, a control system for the training module based on adaptive iterative learning has been simulated, and its high-precision tracking performance has been verified. The gait trajectory experiment is carried out, and the results verify that the trajectory tracking performance of the robot has good performance.

Reducing Tyre Wear Emissions of Automated Articulated Vehicles through Trajectory Planning.

Effective emission control technologies and eco-friendly propulsion systems have been developed to decrease exhaust particle emissions. However, more work must be conducted on non-exhaust traffic-related sources such as tyre wear. The advent of automated vehicles (AVs) enables researchers and automotive manufacturers to consider ways to further decrease tyre wear, as vehicles will be controlled by the system rather than by the driver. In this direction, this work presents the formulation of an optimal control problem for the trajectory optimisation of automated articulated vehicles for tyre wear minimisation. The optimum velocity profile is sought for a predefined road path from a specific starting point to a final one to minimise tyre wear in fixed time cases. Specific boundaries and constraints are applied to the problem to ensure the vehicle's stability and the feasibility of the solution. According to the results, a small increase in the journey time leads to a significant decrease in the mass loss due to tyre wear. The employment of articulated vehicles with low powertrain capabilities leads to greater tyre wear, while excessive increases in powertrain capabilities are not required. The conclusions pave the way for AV researchers and manufacturers to consider tyre wear in their control modules and come closer to the zero-emission goal.

Variable Time-Step Physics Engine with Continuous Compliance Contact Model for Optimal Robotic Grinding Trajectory Planning.

In the transition from virtual environments to real-world applications, the role of physics engines is crucial for accurately emulating and representing systems. To address the prevalent issue of inaccurate simulations, this paper introduces a novel physics engine uniquely designed with a compliant contact model designed for robotic grinding. It features continuous and variable time-step simulations, emphasizing accurate contact force calculations during object collision. Firstly, the engine derives dynamic equations considering spring stiffness, damping coefficients, coefficients of restitution, and external forces. This facilitates the effective determination of dynamic parameters such as contact force, acceleration, velocity, and position throughout penetration processes continuously. Secondly, the approach utilizes effective inertia in developing the contact model, which is designed for multi-jointed robots through pose transformation. The proposed physics engine effectively captures energy conversion in scenarios with convex contact surface shapes through the application of spring dampers during collisions. Finally, the reliability of the contact solver in the simulation was verified through bouncing ball experiments and robotic grinding experiments under different coefficients of restitution. These experiments effectively recorded the continuous variations in parameters, such as contact force, verifying the integral stability of the system. In summary, this article advances physics engine technology beyond current geometrically constrained contact solutions, enhancing the accuracy of simulations and modeling in virtual environments. This is particularly significant in scenarios wherein there are constant changes in the outside world, such as robotic grinding tasks.

Trajectory Analysis of 6-DOF Industrial Robot Manipulators by Using Artificial Neural Networks.

Robot manipulators are robotic systems that are frequently used in automation systems and able to provide increased speed, precision, and efficiency in the industrial applications. Due to their nonlinear and complex nature, it is crucial to optimize the robot manipulator systems in terms of trajectory control. In this study, positioning analyses based on artificial neural networks (ANNs) were performed for robot manipulator systems used in the textile industry, and the optimal ANN model for the high-accuracy positioning was improved. The inverse kinematic analyses of a 6-degree-of-freedom (DOF) industrial denim robot manipulator were carried out via four different learning algorithms, delta-bar-delta (DBD), online back propagation (OBP), quick back propagation (QBP), and random back propagation (RBP), for the proposed neural network predictor. From the results obtained, it was observed that the QBP-based 3-10-6 type ANN structure produced the optimal results in terms of estimation and modeling of trajectory control. In addition, the 3-5-6 type ANN structure was also improved, and its root mean square error (RMSE) and statistical R2 performances were compared with that of the 3-10-6 ANN structure. Consequently, it can be concluded that the proposed neural predictors can successfully be employed in real-time industrial applications for robot manipulator trajectory analysis.

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.

Safe Trajectory Planning for Incremental Robots Based on a Spatiotemporal Variable-Step-Size A* Algorithm.

In this paper, a planning method based on the spatiotemporal variable-step-size A* algorithm is proposed to address the problem of safe trajectory planning for incremental, wheeled, mobile robots in complex motion scenarios with multiple robots. After constructing the known conditions, the spatiotemporal variable-step-size A* algorithm is first used to perform a collision-avoiding initial spatiotemporal trajectory search, and a variable time step is utilized to ensure that the robot completes the search at the target speed. Subsequently, the trajectory is instantiated using B-spline curves in a numerical optimization considering constraints to generate the final smooth trajectory. The results of simulation tests in a field-shaped, complex, dynamic scenario show that the proposed trajectory planning method is more applicable, and the results indicate higher efficiency compared to the traditional method in the incremental robot trajectory planning problem.

Trajectory-Aware Offloading Decision in UAV-Aided Edge Computing: A Comprehensive Survey.

Recently, the integration of unmanned aerial vehicles (UAVs) with edge computing has emerged as a promising paradigm for providing computational support for Internet of Things (IoT) applications in remote, disaster-stricken, and maritime areas. In UAV-aided edge computing, the offloading decision plays a central role in optimizing the overall system performance. However, the trajectory directly affects the offloading decision. In general, IoT devices use ground offload computation-intensive tasks on UAV-aided edge servers. The UAVs plan their trajectories based on the task generation rate. Therefore, researchers are attempting to optimize the offloading decision along with the trajectory, and numerous studies are ongoing to determine the impact of the trajectory on offloading decisions. In this survey, we review existing trajectory-aware offloading decision techniques by focusing on design concepts, operational features, and outstanding characteristics. Moreover, they are compared in terms of design principles and operational characteristics. Open issues and research challenges are discussed, along with future directions.

Research on Lane-Changing Decision Making and Planning of Autonomous Vehicles Based on GCN and Multi-Segment Polynomial Curve Optimization.

This paper considers the interactive effects between the ego vehicle and other vehicles in a dynamic driving environment and proposes an autonomous vehicle lane-changing behavior decision-making and trajectory planning method based on graph convolutional networks (GCNs) and multi-segment polynomial curve optimization. Firstly, hierarchical modeling is applied to the dynamic driving environment, aggregating the dynamic interaction information of driving scenes in the form of graph-structured data. Graph convolutional neural networks are employed to process interaction information and generate ego vehicle's driving behavior decision commands. Subsequently, collision-free drivable areas are constructed based on the dynamic driving scene information. An optimization-based multi-segment polynomial curve trajectory planning method is employed to solve the optimization model, obtaining collision-free motion trajectories satisfying dynamic constraints and efficiently completing the lane-changing behavior of the vehicle. Finally, simulation and on-road vehicle experiments are conducted for the proposed method. The experimental results demonstrate that the proposed method outperforms traditional decision-making and planning methods, exhibiting good robustness, real-time performance, and strong scenario generalization capabilities.

Cooperative Safe Trajectory Planning for Quadrotor Swarms.

In this paper, we propose a novel distributed algorithm based on model predictive control and alternating direction multiplier method (DMPC-ADMM) for cooperative trajectory planning of quadrotor swarms. First, a receding horizon trajectory planning optimization problem is constructed, in which the differential flatness property is used to deal with the nonlinear dynamics of quadrotors while we design a relaxed form of the discrete-time control barrier function (DCBF) constraint to balance feasibility and safety. Then, we decompose the original trajectory planning problem by ADMM and solve it in a fully distributed manner with peer-to-peer communication, which induces the quadrotors within the communication range to reach a consensus on their future trajectories to enhance safety. In addition, an event-triggered mechanism is designed to reduce the communication overhead. The simulation results verify that the trajectories generated by our method are real-time, safe, and smooth. A comprehensive comparison with the centralized strategy and several other distributed strategies in terms of real-time, safety, and feasibility verifies that our method is more suitable for the trajectory planning of large-scale quadrotor swarms.

Coordinated Decision Control of Lane-Change and Car-Following for Intelligent Vehicle Based on Time Series Prediction and Deep Reinforcement Learning.

Adaptive cruise control and autonomous lane-change systems represent pivotal advancements in intelligent vehicle technology. To enhance the operational efficiency of intelligent vehicles in combined lane-change and car-following scenarios, we propose a coordinated decision control model based on hierarchical time series prediction and deep reinforcement learning under the influence of multiple surrounding vehicles. Firstly, we analyze the lane-change behavior and establish boundary conditions for safe lane-change, and divide the lane-change trajectory planning problem into longitudinal velocity planning and lateral trajectory planning. LSTM network is introduced to predict the driving states of surrounding vehicles in multi-step time series, combining D3QN algorithm to make decisions on lane-change behavior. Secondly, based on the following state between the ego vehicle and the leader vehicle in the initial lane, as well as the relationship between the initial distance and the expected distance with the leader vehicle in the target lane, with the primary objective of maximizing driving efficiency, longitudinal velocity is planned based on driving conditions recognition. The lateral trajectory and conditions recognition are then planned using the GA-LSTM-BP algorithm. In contrast to conventional adaptive cruise control systems, the DDPG algorithm serves as the lower-level control model for car-following, enabling continuous velocity control. The proposed model is subsequently simulated and validated using the NGSIM dataset and a lane-change scenarios dataset. The results demonstrate that the algorithm facilitates intelligent vehicle lane-change and car-following coordinated control while ensuring safety and stability during lane-changes. Comparative analysis with other decision control models reveals a notable 17.58% increase in driving velocity, underscoring the algorithm's effectiveness in improving driving efficiency.

Optimising trajectory planning for stereotactic brain tumour biopsy using artificial intelligence: a systematic review of the literature.

PURPOSE: Despite advances in technology, stereotactic brain tumour biopsy remains challenging due to the risk of injury to critical structures. Indeed, choosing the correct trajectory remains essential to patient safety. Artificial intelligence can be used to perform automated trajectory planning. We present a systematic review of automated trajectory planning algorithms for stereotactic brain tumour biopsies. METHODS: A PRISMA adherent systematic review was conducted. Databases were searched using keyword combinations of 'artificial intelligence', 'trajectory planning' and 'brain tumours'. Studies reporting applications of artificial intelligence (AI) to trajectory planning for brain tumour biopsy were included. RESULTS: All eight studies were in the earliest stage of the IDEAL-D development framework. Trajectory plans were compared through a variety of surrogate markers of safety, of which the minimum distance to blood vessels was the most common. Five studies compared manual to automated planning strategies and favoured automation in all cases. However, this comes with a significant risk of bias. CONCLUSIONS: This systematic review reveals the need for IDEAL-D Stage 1 research into automated trajectory planning for brain tumour biopsy. Future studies should establish the congruence between expected risk of algorithms and the ground truth through comparisons to real world outcomes.

A Deep Learning Model with a Self-Attention Mechanism for Leg Joint Angle Estimation across Varied Locomotion Modes.

Conventional trajectory planning for lower limb assistive devices usually relies on a finite-state strategy, which pre-defines fixed trajectory types for specific gait events and activities. The advancement of deep learning enables walking assistive devices to better adapt to varied terrains for diverse users by learning movement patterns from gait data. Using a self-attention mechanism, a temporal deep learning model is developed in this study to continuously generate lower limb joint angle trajectories for an ankle and knee across various activities. Additional analyses, including using Fast Fourier Transform and paired t-tests, are conducted to demonstrate the benefits of the proposed attention model architecture over the existing methods. Transfer learning has also been performed to prove the importance of data diversity. Under a 10-fold leave-one-out testing scheme, the observed attention model errors are 11.50% (±2.37%) and 9.31% (±1.56%) NRMSE for ankle and knee angle estimation, respectively, which are small in comparison to other studies. Statistical analysis using the paired t-test reveals that the proposed attention model appears superior to the baseline model in terms of reduced prediction error. The attention model also produces smoother outputs, which is crucial for safety and comfort. Transfer learning has been shown to effectively reduce model errors and noise, showing the importance of including diverse datasets. The suggested joint angle trajectory generator has the potential to seamlessly switch between different locomotion tasks, thereby mitigating the problem of detecting activity transitions encountered by the traditional finite-state strategy. This data-driven trajectory generation method can also reduce the burden on personalization, as traditional devices rely on prosthetists to experimentally tune many parameters for individuals with diverse gait patterns.

Trajectory Planning of Autonomous Underwater Vehicles Based on Gauss Pseudospectral Method.

This paper aims to address the obstacle avoidance problem of autonomous underwater vehicles (AUVs) in complex environments by proposing a trajectory planning method based on the Gauss pseudospectral method (GPM). According to the kinematics and dynamics constraints, and the obstacle avoidance requirement in AUV navigation, a multi-constraint trajectory planning model is established. The model takes energy consumption and sailing time as optimization objectives. The optimal control problem is transformed into a nonlinear programming problem by the GPM. The trajectory satisfying the optimization objective can be obtained by solving the problem with a sequential quadratic programming (SQP) algorithm. For the optimization of calculation parameters, the cubic spline interpolation method is proposed to generate initial value. Finally, through comparison with the linear fitting method, the rapidity of the solution of the cubic spline interpolation method is verified. The simulation results show that the cubic spline interpolation method improves the operation performance by 49.35% compared with the linear fitting method, which verifies the effectiveness of the cubic spline interpolation method in solving the optimal control problem.

A Novel Vectorized Curved Road Representation Based Aerial Guided Unmanned Vehicle Trajectory Planning.

Unmanned vehicles frequently encounter the challenge of navigating through complex mountainous terrains, which are characterized by numerous unknown continuous curves. Drones, with their wide field of view and ability to vertically displace, offer a potential solution to compensate for the limited field of view of ground vehicles. However, the conventional approach of path extraction solely provides pixel-level positional information. Consequently, when drones guide ground unmanned vehicles using visual cues, the road fitting accuracy is compromised, resulting in reduced speed. Addressing these limitations with existing methods has proven to be a formidable task. In this study, we propose an innovative approach for guiding the visual movement of unmanned ground vehicles using an air-ground collaborative vectorized curved road representation and trajectory planning method. Our method offers several advantages over traditional road fitting techniques. Firstly, it incorporates a road star points ordering method based on the K-Means clustering algorithm, which simplifies the complex process of road fitting. Additionally, we introduce a road vectorization model based on the piecewise GA-Bézier algorithm, enabling the identification of the optimal frame from the initial frame to the current frame in the video stream. This significantly improves the road fitting effect (EV) and reduces the model running time (T-model). Furthermore, we employ smooth trajectory planning along the "route-plane" to maximize speed at turning points, thereby minimizing travel time (T-travel). To validate the efficiency and accuracy of our proposed method, we conducted extensive simulation experiments and performed actual comparison experiments. The results demonstrate the superior performance of our approach in terms of both efficiency and accuracy.

Deep Reinforcement Learning for Joint Trajectory Planning, Transmission Scheduling, and Access Control in UAV-Assisted Wireless Sensor Networks.

Unmanned aerial vehicles (UAVs) can be used to relay sensing information and computational workloads from ground users (GUs) to a remote base station (RBS) for further processing. In this paper, we employ multiple UAVs to assist with the collection of sensing information in a terrestrial wireless sensor network. All of the information collected by the UAVs can be forwarded to the RBS. We aim to improve the energy efficiency for sensing-data collection and transmission by optimizing UAV trajectory, scheduling, and access-control strategies. Considering a time-slotted frame structure, UAV flight, sensing, and information-forwarding sub-slots are confined to each time slot. This motivates the trade-off study between UAV access-control and trajectory planning. More sensing data in one time slot will take up more UAV buffer space and require a longer transmission time for information forwarding. We solve this problem by a multi-agent deep reinforcement learning approach that takes into consideration a dynamic network environment with uncertain information about the GU spatial distribution and traffic demands. We further devise a hierarchical learning framework with reduced action and state spaces to improve the learning efficiency by exploiting the distributed structure of the UAV-assisted wireless sensor network. Simulation results show that UAV trajectory planning with access control can significantly improve UAV energy efficiency. The hierarchical learning method is more stable in learning and can also achieve higher sensing performance.

Multi-Objective Optimal Trajectory Planning for Robotic Arms Using Deep Reinforcement Learning.

This study investigated the trajectory-planning problem of a six-axis robotic arm based on deep reinforcement learning. Taking into account several characteristics of robot motion, a multi-objective optimization approach is proposed, which was based on the motivations of deep reinforcement learning and optimal planning. The optimal trajectory was considered with respect to multiple objectives, aiming to minimize factors such as accuracy, energy consumption, and smoothness. The multiple objectives were integrated into the reinforcement learning environment to achieve the desired trajectory. Based on forward and inverse kinematics, the joint angles and Cartesian coordinates were used as the input parameters, while the joint angle estimation served as the output. To enable the environment to rapidly find more-efficient solutions, the decaying episode mechanism was employed throughout the training process. The distribution of the trajectory points was improved in terms of uniformity and smoothness, which greatly contributed to the optimization of the robotic arm's trajectory. The proposed method demonstrated its effectiveness in comparison with the RRT algorithm, as evidenced by the simulations and physical experiments.

Path Planning for Obstacle Avoidance of Robot Arm Based on Improved Potential Field Method.

In medical and surgical scenarios, the trajectory planning of a collaborative robot arm is a difficult problem. The artificial potential field (APF) algorithm is a classic method for robot trajectory planning, which has the characteristics of good real-time performance and low computing consumption. There are many variants of the APF algorithm, among which the most widely used variants is the velocity potential field (VPF) algorithm. However, the traditional VPF algorithm has inherent defects and problems, such as easily falling into local minimum, being unable to reach the target, poor dynamic obstacle avoidance ability, and safety and efficiency problems. Therefore, this work presents the improved velocity potential field (IVPF) algorithm, which considers direction factors, obstacle velocity factor, and tangential velocity. When encountering dynamic obstacles, the IVPF algorithm can avoid obstacles better to ensure the safety of both the human and robot arm. The IVPF algorithm also does not easily fall into a local problem when encountering different obstacles. The experiments informed the RRT* algorithm, VPF algorithm, and IVPF algorithm for comparison. Compared with the informed RRT* and VPF algorithm, the result of experiments indicate that the performances of the IVPF algorithm have significant improvements when dealing with different obstacles. The main aim of this paper is to provide a safe and efficient path planning algorithm for the robot arm in the medical field. The proposed algorithm can ensure the safety of both the human and the robot arm when the medical and surgical robot arm is working, and enables the robot arm to cope with emergencies and perform tasks better. The application of the proposed algorithm could make the collaborative robots work in a flexible and safe condition, which could open up new opportunities for the future development of medical and surgical scenarios.