Trajectory Planning Strategy Research Articles

A Hybrid Control Approach Integrating Model-Predictive Control and Fractional-Order Admittance Control for Automatic Internal Limiting Membrane Peeling Surgery

As the prevalence of related diseases continues to rise, a corresponding increase in the demand for internal limiting membrane (ILM) peeling surgery has been observed. However, significant challenges are encountered in ILM peeling surgery, including limited force feedback, inadequate depth perception, and surgeon hand tremors. Research on fully autonomous ILM peeling surgical robots has been conducted to address the imbalance between medical resource availability and patient demand while enhancing surgical safety. An automatic control framework for break initiation in ILM peeling is proposed in this study, which integrates model-predictive control with fractional-order admittance control. Additionally, a multi-vision task surgical scene perception method is introduced based on target detection, key point recognition, and sparse binocular matching. A surgical trajectory planning strategy for break initiation in ILM peeling aligned with operative specifications is proposed. Finally, validation experiments for automatic break initiation in ILM peeling were performed using eye phantoms. The results indicated that the positional error of the micro-forceps tip remained within 40 μm. At the same time, the contact force overshoot was limited to under 6%, thereby ensuring both the effectiveness and safety of break initiation during ILM peeling.

Design and Testing of a Four-Arm Multi-Joint Apple Harvesting Robot Based on Singularity Analysis

The use of multi-joint arms in a high-spindle environment can solve complex problems, but the singularity problem of the manipulator related to the structure of the serial manipulator is prominent. Therefore, based on the general mathematical model of fruit spatial distribution in high-spindle apple orchards, this study proposes two harvesting system architecture schemes that can meet the constraints of fruit spatial distribution and reduce the singularity of harvesting robot operation, which are four-arm dual-module independent moving scheme (Scheme A) and four-arm single-module parallel moving scheme (Scheme B). Based on the link-joint method, the analytical expression of the singular configuration of the redundant degree of freedom arm group system under the two schemes is obtained. Then, the inverse kinematics solution method of the redundant arm group and the singularity avoidance picking trajectory planning strategy are proposed to realize the judgment and solution of the singular configuration in the complex working environment of the high-spindle. The singularity rate of Scheme A in the simulation environment is 17.098%, and the singularity rate of Scheme B is only 6.74%. In the field experiment, the singularity rate of Scheme A is 26.18%, while the singularity rate of Scheme B is 13.22%. The success rate of Schemes A and B are 80.49% and 72.33%, respectively. Through experimental comparison and analysis, Scheme B is more prominent in solving singular problems but still needs to improve the success rate in future research. This paper can provide a reference for solving the singular problems in the complex working environment of high spindles.

Precision Position Servo PMSM Fast-Response Control Based on Trajectory Planning and ADRC

Trajectory planning and tracking control strategies have a significant impact on the fast and stable operation of high-precision position servo permanent magnet synchronous motors (PMSMs). Therefore, this paper proposes an active disturbance rejection control (ADRC) strategy for high-precision position servo PMSMs based on jerk- and time-optimal trajectory planning. Firstly, in order to meet the requirement of continuous jerk in the positioning process of precision loads, the seventh-degree Chebyshev polynomial is adopted to establish the point-to-point trajectory planning function. Based on the dynamic boundary conditions under the short-term overload of PMSMs, and with the positioning time as the optimization objective, the optimal coefficient of the polynomial is solved through the fast particle swarm optimization (FPSO) algorithm to obtain the trajectory planning function that takes into account both jerk and time performance. Then, the trajectory plan is used as the position loop reference signal to construct a non-cascade second-order ADRC strategy, leading to a position servo PMSM control strategy that combines a second-order disturbance observer and feedback control law. Finally, the experimental platform is set up to verify the proposed method. The results show that, compared with the traditional control methods, the steady-state positioning time of the control strategy proposed under typical working conditions is reduced by 12.5%, and the jerk continuity during the positioning process has also been significantly improved.

Safe trajectory planning and tracking for tractor semi-trailers in steering collision avoidance scenarios

Collision avoidance technology provides an effective solution for improving vehicle driving safety. However, current research primarily focuses on passenger cars and small commercial vehicles, neglecting tractor semi-trailers, which have elongated body lengths and complex dynamic characteristics. There is still a significant research gap in the application of collision avoidance control technology for tractor semi-trailers. To address this, this paper proposes a safe trajectory planning and tracking strategy for steering collision avoidance scenarios, aimed at enhancing the driving safety of tractor semi-trailers. To tackle the challenge of accurately predicting the pose of the semi-trailer during collision avoidance trajectory planning, a real-time trajectory planning method combining model predictive control and artificial potential field is proposed. Then, a tracking error model considering both lateral and yaw errors of the tractor semi-trailer is established to address the off-tracking phenomenon, and a linear quadratic regulator control strategy is proposed. Finally, static and dynamic collision avoidance scenarios are designed to validate the proposed strategy. Simulation and experimental results show that the proposed control strategy effectively ensures the safe collision avoidance maneuver of the tractor semi-trailer.

Analytical Modeling, Virtual Prototyping, and Performance Optimization of Cartesian Robots: A Comprehensive Review

A comprehensive literature review on the kinematics and dynamics modeling and virtual prototyping (V.P) of the Cartesian robots with a flexible configuration is presented in this paper. Different modeling approaches of the main components of the Cartesian robot, which includes linear belt drives and structural components, are presented and discussed in this paper. Furthermore, the vibrations modeling, trajectory planning, and control strategies of the Cartesian robot are also presented. The performance optimization of the Cartesian robot is discussed here, which is affected by the highly flexible configuration of the robot incurred due to high-mix, low-volume production. The importance of virtual prototyping techniques, like finite element analysis and multi-body dynamics, for modeling Cartesian robots or its components is presented. Design and performance optimization methods for robots with a flexible configuration are discussed, although their application to Cartesian robots is rare in the literature and it presents an exciting opportunity for future research in this area. This review paper focuses on the importance of further research on the virtual prototyping tools for flexibly configured robots and their integration with experimental validation. The findings offer useful insights to industries looking to maximize their production processes while keeping the customization, reliability, and efficiency.

Jump Control Based on Nonlinear Wheel-Spring-Loaded Inverted Pendulum Model: Validation of a Wheeled-Bipedal Robot with Single-Degree-of-Freedom Legs.

Jumping is a fundamental capability for wheeled-bipedal robots (WBRs) navigating unstructured terrains, with jump height and stability serving as indicators of the robot's environmental adaptability. However, existing trajectory planning methods demand high output capacity from the joints and fail to balance computational load with trajectory tracking performance. This limitation hinders most robots from experimental validation. To address these challenges, this study presents an optimized virtual model, trajectory planning strategy, and control method. These solutions enhance both the height and stability of jumps while ensuring real-time execution on physical robots. Firstly, inspired by the human jumping mechanism, a Nonlinear Wheel-Spring-Loaded Inverted Pendulum (NW-SLIP) model was originally proposed as the virtual model for trajectory planning. The jump height is increased by 3.4 times compared to the linear spring model. Then, cost functions are established based on this virtual model, and the trajectory for each stage is iteratively optimized using Quadratic Programming (QP) and a bisection method. This leads to a 21.5% increase in the maximum jump height while reducing the peak joint torque by 14% at the same height. This significantly eases execution and enhances the robot's trajectory-tracking ability. Subsequently, a leg statics model is introduced alongside the kinematics model to map the relationship between the virtual model and joint space. This approach improves trajectory tracking performance while circumventing the intricate calculation of the dynamics model, thereby enhancing jump consistency and stability. Finally, the proposed trajectory planning and jump control method is validated through both simulations and real-world experiments, demonstrating its feasibility and effectiveness in practical robotic applications.

Stable distance regression via spatial–frequency state space model for robot-assisted endomicroscopy

PurposeProbe-based confocal laser endomicroscopy (pCLE) is a noninvasive technique that enables the direct visualization of tissue at a microscopic level in real time. One of the main challenges in using pCLE is maintaining the probe within a working range of micrometer scale. As a result, the need arises for automatically regressing the probe–tissue distance to enable precise robotic tissue scanning.MethodsIn this paper, we propose the spatial frequency bidirectional structured state space model (SF-BiS4D) for pCLE probe–tissue distance regression. This model advances traditional state space models by processing image sequences bidirectionally and analyzing data in both the frequency and spatial domains. Additionally, we introduce a guided trajectory planning strategy that generates pseudo-distance labels, facilitating the training of sequential models to generate smooth and stable robotic scanning trajectories. To improve inference speed, we also implement a hierarchical guided fine-tuning (GF) approach that efficiently reduces the size of the BiS4D model while maintaining performance.ResultsThe performance of our proposed model has been evaluated both qualitatively and quantitatively using the pCLE regression dataset (PRD). In comparison with existing state-of-the-art (SOTA) methods, our approach demonstrated superior performance in terms of accuracy and stability.ConclusionOur proposed deep learning-based framework effectively improves distance regression for microscopic visual servoing and demonstrates its potential for integration into surgical procedures requiring precise real-time intraoperative imaging.

AoI-Minimal Task Assignment and Trajectory Optimization in Multi-UAV-Assisted Wireless Powered IoT Networks

This paper investigates the energy transfer and data collection problem of multiple unmanned aerial vehicle (UAV)-assisted wireless-powered Internet of Things (IoT) networks. To ensure information freshness for IoT devices and reduce UAVs’ energy consumption, we minimize the average Age of Information (AoI) of IoT devices by jointly optimizing the energy harvesting (EH) and data collection time for IoT devices, the selection of data collection points (DCPs), DCP-IoT associations, and task assignment, flight speed, and trajectories of UAVs, subject to the limited endurance of UAVs. As this problem is nonconvex, we propose a novel DCP association and trajectory-planning scheme that seeks age-optimal solutions through an iterative three-step process. First, we calculate the EH and data collection time for IoT devices using Karush–Kuhn–Tucker (KKT) conditions. Then, we introduce an optimal hovering time allocation-based affinity propagation (OHTAP) clustering algorithm to determine optimal DCP locations and establish DCP-IoT associations. Finally, we develop two algorithms to optimize UAVs’ trajectories: an improved partheno-genetic algorithm with enhancement mechanisms (EIPGA) and a hybrid algorithm that combines improved MinMax k-means clustering with EIPGA. Numerical results confirm that our scheme consistently outperforms benchmark schemes in AoI performance and solution stability across diverse scenarios.

Longitudinal Perching Trajectory Planning for a Fixed-Wing Unmanned Aerial Vehicle at High Angle of Attack Based on the Estimation of Region of Attraction

In this paper, a method for planning the perching trajectory of a fixed-wing unmanned aerial vehicle (UAV) based on the estimation of the region of attraction (ROA) is proposed, to expand the feasible domain of a UAV in the presence of aerodynamic performance degradation and landing-limited conditions with high angle of attack (AOA). According to the aerodynamic characteristics of the system, the perching process is first decomposed into flight and landing segments, and the corresponding flight dynamic model and structural dynamic model are established, based on the Lagrange function, while the continuity of the two models is proved. Then, the structural dynamic model is analyzed for asymptotic stability based on the ROA estimation results from the Lyapunov function. On this basis, a fixed-wing UAV perching trajectory planning strategy is proposed. This strategy enables the UAV to achieve stable perching with a reasonable flight trajectory, as it fully considers the flight dynamic constraints of the UAV and the structural dynamic constraints of the landing gear. Our simulation results show that flight trajectory planning considering the ROA can significantly increase the number of available trajectories for fixed-wing UAVs during high AOA perching, which also greatly enhances its flexibility in trajectory selection.

Trajectory planning strategy for obstacle avoidance based on D-APF

Trajectory planning strategy for obstacle avoidance based on D-APF

Planning Aggressive Drone Manoeuvres: A Geometric Backwards Integration Approach

This paper addresses the problem of performing aggressive manoeuvres by using multirotor vehicles that include passing through any specific point within the full state space of the vehicle. To this end, the design of optimal trajectories considers the dynamical model of the vehicles by numerically integrating it backwards in time, in the manifold where the dynamics evolve, and dividing the manoeuvres into three distinct phases to accommodate any combination of initial, desired, and final states. In the first phase, the vehicles fly from an initial to a launch configuration to achieve the necessary momenta to reach the desired one in the second phase. To ensure the feasibility of executing the second phase, the relation between snap and body torques is exploited by commanding the vehicles to track geodesic curves on SO(3) during the backwards integration. The vehicles are then driven to a final configuration in the third phase. Most existing solutions to execute aggressive and precise manoeuvres with these rotorcraft focus either on the attitude control problem, leaving the position in open-loop, or use different controllers for different sections of the manoeuvre. In this work, a single tracking controller is considered to validate the proposed trajectory planning strategy in a realistic simulation environment, which involves the PX4 firmware, and in a controlled experimental setup. The results demonstrate that accurate tracking of the designed trajectories enables the vehicles to perform 360-degree loops at great speed and manoeuvres that facilitate the exchange of a parcel between two multirotor vehicles during flight.

Multi-objective trajectory planning of segment erector considering error uncertainty

To meet the requirements for automation and precision in segment assembling and enhance the quality and efficiency of assembly, a multi-objective trajectory planning method considering error uncertainty is proposed for the trajectory planning strategy for segment erector under the conditions of heavy load and low-speed assembly. Based on the forward kinematics model of segment erector, the working space of segment erector is determined by Monte Carlo method, and the key track points are determined according to the actual operation requirements. The kinematic mapping relationship between Cartesian space and joint space is established based on the inverse kinematics model of segment erector, and the trajectory planning is carried out by using 5th-degree B-spline and 5th-degree polynomial respectively. Considering uncertainty errors caused by structural parameters, environmental factors, and joint space, the time, energy, and impact objective functions are established, and the comprehensive optimal trajectory is obtained based on the elite non-dominated sorting genetic algorithm II (NSGA-II). The results show that this method is an effective trajectory planning solution, which ensures that the segment erector moves smoothly, and has obvious advantages in reducing time, energy, and impact during the moving process.

Fuel‐Saving Postcapture Detumbling by Dual‐Arm Space Robot

After the dual‐arm space robot captures a noncooperative target, a closed‐chain multibody system is formed, making dynamic modeling and detumbling trajectory planning particularly challenging. This paper proposes a novel trajectory planning strategy that guides the combined system into a uniaxial rotational state about its maximum principal inertia axis. Unlike prior work that focuses solely on eliminating the target’s relative motion, our approach additionally drives the closed‐chain system into a dynamically favorable uniaxial rotation. This configuration avoids multiaxis coupling and simplifies subsequent stabilization, requiring only unidirectional thruster torque. By reducing the number of required control directions and eliminating complex angular momentum interactions, the subsequent attitude stabilization becomes more fuel‐efficient. As a result, the fuel required for postdetumbling control can be significantly reduced. The detumbling process is executed solely by actuating the joints of the dual manipulators without consuming any base thruster fuel. Numerical simulations validate that the proposed strategy effectively establishes the desired rotational mode and that the joint‐space tracking controller enables accurate execution of the planned trajectory.

An Integrated Trajectory Planning and Motion Control Strategy for Autonomous Berthing of Underactuated Unmanned Surface Vehicles

An Integrated Trajectory Planning and Motion Control Strategy for Autonomous Berthing of Underactuated Unmanned Surface Vehicles

Collision Avoidance Trajectory Planning Based on Dynamic Spatio-Temporal Corridor Search in Curvy Road Scenarios for Intelligent Vehicles

To avoid collisions and ensure driving safety, comfort, and efficiency, in this study, we propose a trajectory planning strategy for intelligent vehicles navigating curvy road scenarios. This strategy is based on a dynamic spatio-temporal corridor search. First, an obstacle space expansion module is constructed using a critical safety distance model to generate a searchable spatio-temporal corridor. Next, a dynamic step expansion is performed to improve the traditional hybrid A* search algorithm by the discretization of front-wheel steering angles and acceleration. The bisection method is applied to iteratively optimize the child nodes at each step, and the child node with the lowest cost is selected as the rough search node. Subsequently, a locally weighted dual-regression fitting algorithm is employed for segment trajectory fitting, and the optimal trajectory is generated. Finally, the performance of the proposed trajectory planning strategy is validated on the Carla simulation platform. The results show the effectiveness and efficiency of our strategy in three typical scenarios.

Study on Trajectory Optimization for a Flexible Parallel Robot in Tomato Packaging

Currently, flexible robots, exemplified by parallel robots, play a crucial role in the automated packaging of agricultural products due to their rapid, accurate, and stable characteristics. This research systematically explores trajectory planning strategies for parallel robots in the high-speed tomato-grabbing process. Kinematic analysis of the parallel robot was conducted using geometric methods, deriving the coordinates of each joint at various postures, resulting in a kinematic forward solution model and corresponding equations, which were verified with data. To address the drawbacks of the point-to-point “portal” trajectory in tomato grabbing, a 3-5-5-3 polynomial interpolation method in joint space was proposed to optimize the path, enhancing trajectory smoothness. To improve the efficiency of the tomato packaging process, a hybrid algorithm combining particle swarm optimization (PSO) and genetic algorithms (GA) was developed to optimize the operation time of the parallel robot. Compared to traditional PSO, the proposed algorithm exhibits better global convergence and is less likely to fall into local optima, thereby ensuring a smoother and more efficient path in the robot-grabbing tomato process and providing technical support for automated tomato packaging.

Time-Delay-Based Sliding Mode Tracking Control for Cooperative Dual Marine Lifting System Subject to Sea Wave Disturbances

Dual marine lifting systems are complicated, fully actuated mechatronics systems with multi-input and multi-output capabilities. The anti-swing cooperative lifting control of dual marine lifting systems with dual ships’ sway, heave, and roll motions is still open. The uncertainty regarding system parameters makes the task of achieving stable performance more challenging. To adjust both the attitude and position of large distributed-mass payloads to their target positions, this paper presents a time-delay-based sliding mode-tracking controller for cooperative dual marine lifting systems impacted by sea wave disturbances. Firstly, a dynamic model of a dual marine lifting system is established by using Lagrange’s method. Then, a kinematic coupling-based cooperative trajectory planning strategy is proposed by analyzing the coupling relationship between the dual marine lifting system and dual ship motion. After that, an improved sliding mode tracking controller is proposed by using time-delay estimation technology, which estimates unknown system parameters online. The finite-time convergence of full-state variables is rigorously proven. Finally, the simulation results verify the designed controller in terms of anti-swing control performance. The hardware experiments revealed that the proposed controller significantly reduces the actuator positioning errors by 83.33% compared with existing control methods.

Time Series Classification for Predicting Biped Robot Step Viability.

The prediction of the stability of future steps taken by a biped robot is a very important task, since it allows the robot controller to adopt the necessary measures in order to minimize damages if a fall is predicted. We present a classifier to predict the viability of a given planned step taken by a biped robot, i.e., if it will be stable or unstable. The features of the classifier are extracted from a feature engineering process exploiting the useful information contained in the time series generated in the trajectory planning of the step. In order to state the problem as a supervised classification one, we need the ground truth class for each planned step. This is obtained using the Predicted Step Viability (PSV) criterion. We also present a procedure to obtain a balanced and challenging training/testing dataset of planned steps that contains many steps in the border between stable and non stable regions. Following this trajectory planning strategy for the creation of the dataset we are able to improve the robustness of the classifier. Results show that the classifier is able to obtain a 95% of ROC AUC for this demanding dataset using only four time series among all the signals required by PSV to check viability. This allows to replace the PSV stability criterion, which is safe, robust but impossible to apply in real-time, by a simple, fast and embeddable classifier that can run in real time consuming much less resources than the PSV.

Trajectory optimization and obstacle avoidance of autonomous robot using Robust and Efficient Rapidly Exploring Random Tree.

One of the key challenges in robotics is the motion planning problem. This paper presents a local trajectory planning and obstacle avoidance strategy based on a novel sampling-based path-finding algorithm designed for autonomous vehicles navigating complex environments. Although sampling-based algorithms have been extensively employed for motion planning, they have notable limitations, such as sluggish convergence rate, significant search time volatility, a vast, dense sample space, and unsmooth search routes. To overcome the limitations, including slow convergence, high computational complexity, and unnecessary search while sampling the whole space, we have proposed the RE-RRT* (Robust and Efficient RRT*) algorithm. This algorithm adapts a new sampling-based path-finding algorithm based on sampling along the displacement from the initial point to the goal point. The sample space is constrained during each stage of the random tree's growth, reducing the number of redundant searches. The RE-RRT* algorithm can converge to a shorter path with fewer iterations. Furthermore, the Choose Parent and Rewire processes are used by RE-RRT* to improve the path in succeeding cycles continuously. Extensive experiments under diverse obstacle settings are performed to validate the effectiveness of the proposed approach. The results demonstrate that the proposed approach outperforms existing methods in terms of computational time, sampling space efficiency, speed, and stability.

Obstacle Avoidance in Distributed Optimal Coordination of Multirobot Systems: A Trajectory Planning and Tracking Strategy

Obstacle Avoidance in Distributed Optimal Coordination of Multirobot Systems: A Trajectory Planning and Tracking Strategy