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.

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.

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.

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.

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.

Gradient-based autonomous obstacle avoidance trajectory planning for B-spline UAVs.

Unmanned aerial vehicles (UAVs) have become the focus of current research because of their practicability in various scenarios. However, current local path planning methods often result in trajectories with numerous sharp or inflection points, which are not ideal for smooth UAV flight. This paper introduces a UAV path planning approach based on distance gradients. The key improvements include generating collision-free paths using collision information from initial trajectories and obstacles. Then, collision-free paths are subsequently optimized using distance gradient information. Additionally, a trajectory time adjustment method is proposed to ensure the feasibility and safety of the trajectory while prioritizing smoothness. The Limited-memory BFGS algorithm is employed to efficiently solve optimal local paths, with the ability to quickly restart the trajectory optimization program. The effectiveness of the proposed method is validated in the Robot Operating System simulation environment, demonstrating its ability to meet trajectory planning requirements for UAVs in complex unknown environments with high dynamics. Moreover, it surpasses traditional UAV trajectory planning methods in terms of solution speed, trajectory length, and data volume.

Trajectory planning framework for autonomous vehicles based on collision injury prediction for vulnerable road users.

Due to the escalating occurrence and high casualty rates of accidents involving Electric Two-Wheelers (E2Ws), it has become a major safety concern on the roads. Additionally, with the widespread adoption of current autonomous driving technology, a greater challenge has arisen for the safety of vulnerable road participants. Most existing trajectory planning methods primarily focus on the safety, comfort, and dynamics of autonomous vehicles themselves, often overlooking the protection of vulnerable road users (VRUs), typically E2W riders. This paper aims to investigate the kinematic response of E2Ws in vehicle collisions, including the 15 ms Head Injury Criterion (HIC15). It analyzes the impact of key collision parameters on head injuries, establishes injury prediction models for anticipated scenarios, and proposes a trajectory planning framework for autonomous vehicles based on predicting head injuries of VRUs. Firstly, a multi-rigid-body model of two-wheeler-vehicle collision was established based on a real accident database, incorporating four critical collision parameters (initial collision velocity, initial collision position, and collision angle). The accuracy of the multi-rigid-body model was validated through verifications with real fatal accidents to parameterize the collision scenario. Secondly, a large-scale effective crash dataset has been established by the multi-parameterized crash simulation automation framework combined with Monte Carlo sampling algorithm. The training and testing of the injury prediction model were implemented based on the MLP + XGBoost regression algorithm on this dataset to explore the potential relationship between the head injuries of the E2W riders and the crash variables. Finally, based on the proposed injury prediction model, this paper generated a trajectory planning framework for autonomous vehicles based on head collision injury prediction for VRUs, aiming to achieve a fair distribution of collision risks among road users. The accident reconstruction results show that the maximum error in the final relative positions of the E2W, the car, and the E2W rider compared to the real accident scene is 11 %, demonstrating the reliability of the reconstructed model. The injury prediction results indicate that the MLP + XGBoost regression prediction model used in this article achieved an R2 of 0.92 on the test set. Additionally, the effectiveness and feasibility of the proposed trajectory planning algorithm were validated in a manually designed autonomous driving traffic flow scenario.

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.

Trajectory Planning on Rolling Locomotion of Spherical Movable Tensegrity Robots with Multi-Gait Patterns.

Spherical movable tensegrity robots, resorting to the intrinsic hallmark of being lightweight and resilient, have exhibited tremendous potential in exploring unpredictable terrains and extreme environments where traditional robots often struggle. The geometry of spherical tensegrities is suitable for rolling locomotion, which guarantees the system to react to changing demands, navigate unexplored terrain, and perform missions even after suffering massive damage. The objective of this article is to enrich the type of spherical movable tensegrity robots with multiple kinematic gait patterns and to gain superior motion paths that are in conformity with the intrinsic features of structural rolling locomotion. Aiming at this purpose, three 12-rod spherical tensegrities with multi-gait patterns are investigated, and the dynamic simulation on independent (or evolutionary) gait patterns is conducted and testified on ADAMS. The routing spaces and the blind zones formed by single kinematic gait are compared to assess the suitability of the assigned kinematic gait pattern. Accordingly, we develop a trajectory planning method with the embedding of the steering control strategy into a modified rapidly exploring random tree (MRRT) algorithm to produce qualified marching routes. In the meantime, two momentous evaluation indictors, applicable to multi-gaits tensegrities, are introduced in searching the corresponding optimal gait patterns that conform to specified needs. The techniques are illustrated and validated in simulation with comparisons on several prototypes of tensegrity robots, indicating that the proposed method is a viable means of attaining marching routes on rolling locomotion of spherical movable tensegrity robots.

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.

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.

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.

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.

Kinematics Analysis and Gait Study of Bionic Turtle Crawling Mechanism.

Longer distance water delivery culverts pose obstacles such as deposited silt, stones, and dead trees. In this paper, a crawling robot is designed to mimic the joint structure of a turtle using bionic design principles. The mechanism and gait of the robot are analyzed. The kinematics model of the robot is established using the D-H method and analytical approach, while the dynamics model is established using Lagrange's method. Based on kinematics and dynamics analysis theory, compound cycloid and cubic polynomial motion trajectories for the robot foot are planned along with a crawling gait resembling that of a turtle's abdomen. Simulation experiments and scale prototype experiments confirm that when gait parameters are identical, the energy consumption of compound cycloid trajectory exceeds that of cubic polynomial foot trajectory. When planning these two types of foot trajectories, it was observed that energy consumption ratio decreases with increasing step length but increases with increasing step height.

Motion planning framework based on dual-agent DDPG method for dual-arm robots guided by human joint angle constraints.

Introduction: Reinforcement learning has been widely used in robot motion planning. However, for multi-step complex tasks of dual-arm robots, the trajectory planning method based on reinforcement learning still has some problems, such as ample exploration space, long training time, and uncontrollable training process. Based on the dual-agent depth deterministic strategy gradient (DADDPG) algorithm, this study proposes a motion planning framework constrained by the human joint angle, simultaneously realizing the humanization of learning content and learning style. It quickly plans the coordinated trajectory of dual-arm for complex multi-step tasks. Methods: The proposed framework mainly includes two parts: one is the modeling of human joint angle constraints. The joint angle is calculated from the human arm motion data measured by the inertial measurement unit (IMU) by establishing a human-robot dual-arm kinematic mapping model. Then, the joint angle range constraints are extracted from multiple groups of demonstration data and expressed as inequalities. Second, the segmented reward function is designed. The human joint angle constraint guides the exploratory learning process of the reinforcement learning method in the form of step reward. Therefore, the exploration space is reduced, the training speed is accelerated, and the learning process is controllable to a certain extent. Results and discussion: The effectiveness of the framework was verified in the gym simulation environment of the Baxter robot's reach-grasp-align task. The results show that in this framework, human experience knowledge has a significant impact on the guidance of learning, and this method can more quickly plan the coordinated trajectory of dual-arm for multi-step tasks.

A trajectory planning method for a casting sorting robotic arm based on a nature-inspired Genghis Khan shark optimized algorithm.

In order to meet the efficiency and smooth trajectory requirements of the casting sorting robotic arm, we propose a time-optimal trajectory planning method that combines a heuristic algorithm inspired by the behavior of the Genghis Khan shark (GKS) and segmented interpolation polynomials. First, the basic model of the robotic arm was constructed based on the arm parameters, and the workspace is analyzed. A matrix was formed by combining cubic and quintic polynomials using a segmented approach to solve for 14 unknown parameters and plan the trajectory. To enhance the smoothness and efficiency of the trajectory in the joint space, a dynamic nonlinear learning factor was introduced based on the traditional Particle Swarm Optimization (PSO) algorithm. Four different biological behaviors, inspired by GKS, were simulated. Within the premise of time optimality, a target function was set to effectively optimize within the feasible space. Simulation and verification were performed after determining the working tasks of the casting sorting robotic arm. The results demonstrated that the optimized robotic arm achieved a smooth and continuous trajectory velocity, while also optimizing the overall runtime within the given constraints. A comparison was made between the traditional PSO algorithm and an improved PSO algorithm, revealing that the improved algorithm exhibited better convergence. Moreover, the planning approach based on GKS behavior showed a decreased likelihood of getting trapped in local optima, thereby confirming the effectiveness of the proposed algorithm.

Design and experimentation of multi-fruit envelope-cutting kiwifruit picking robot.

Currently kiwifruit picking process mainly leverages manual labor, which has low productivity and high labor intensity, meanwhile, the existing kiwifruit picking machinery also has low picking efficiency and easily damages fruits. In this regard, a kiwifruit picking robot suitable for orchard operations was developed in this paper for kiwifruit grown in orchard trellis style. First, based on the analysis of kiwifruit growth pattern and cultivation parameters, the expected design requirements and objectives of a kiwifruit picking robot were proposed, and the expected workflow of the robot in the kiwifruit orchard environment was given, which in turn led to a multi-fruit envelope-cutting kiwifruit picking robot was designed. Then, the D-H method was used to establish the kinematic Equations of the kiwifruit-picking robot, the forward and inverse kinematic calculations were carried out, and the Monte Carlo method was used to analyze the workspace of the robot. By planning the trajectory of the robotic arm and calculating critical nodes in the picking path, the scheme of trajectory planning of the robot was given, and MATLAB software was applied to simulate the motion trajectory as well as to verify the feasibility of the trajectory planning scheme and the picking strategy. Finally, a kiwifruit picking test bed was set up to conduct picking tests in the form of fruit clusters. The results show that the average time to pick each cluster of fruit was 9.7s, the picking success rate was 88.0%, and the picking damage rate was 7.3%. All the indicators met the requirements of the expected design of the kiwifruit-picking robot.

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.