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This paper aims to focus on solving the path optimization problem by modifying the probabilistic roadmap (PRM) technique as it suffers from the selection of the optimal number of nodes and deploy in free space for reliable trajectory planning.

Traditional PRM is modified by developing a decision-making strategy for the selection of optimal nodes w.r.t. the complexity of the environment and deploying the optimal number of nodes outside the closed segment. Subsequently, the generated trajectory is made smoother by implementing the modified Bezier curve technique, which selects an optimal number of control points near the sharp turns for the reliable convergence of the trajectory that reduces the sum of the robot’s turning angles.

The proposed technique is compared with state-of-the-art techniques that show the reduction of computational load by 12.46%, the number of sharp turns by 100%, the number of collisions by 100% and increase the velocity parameter by 19.91%.

The proposed adaptive technique provides a better solution for autonomous navigation of unmanned ground vehicles, transportation, warehouse applications, etc.

This study aims to propose and evaluate the progress in the basic-pixel (a strategy to generate continuous trajectories that fill out the entire surface) algorithm towards performance gain. The objective is also to investigate the operational efficiency and effectiveness of an enhanced version compared with conventional strategies.

For the first objective, the proposed methodology is to apply the improvements proposed in the basic-pixel strategy, test it on three demonstrative parts and statistically evaluate the performance using the distance trajectory criterion. For the second objective, the enhanced-pixel strategy is compared with conventional strategies in terms of trajectory distance, build time and the number of arcs starts and stops (operational efficiency) and targeting the nominal geometry of a part (operational effectiveness).

The results showed that the improvements proposed to the basic-pixel strategy could generate continuous trajectories with shorter distances and comparable building times (operational efficiency). Regarding operational effectiveness, the parts built by the enhanced-pixel strategy presented lower dimensional deviation than the other strategies studied. Therefore, the enhanced-pixel strategy appears to be a good candidate for building more complex printable parts and delivering operational efficiency and effectiveness.

This paper presents an evolution of the basic-pixel strategy (a space-filling strategy) with the introduction of new elements in the algorithm and proves the improvement of the strategy’s performance with this. An interesting comparison is also presented in terms of operational efficiency and effectiveness between the enhanced-pixel strategy and conventional strategies.

Imitation learning is a powerful tool for planning the trajectory of robotic end-effectors in Cartesian space. Present methods can adapt the trajectory to the obstacle; however, the solutions may not always satisfy users, whereas it is hard for a nonexpert user to teach the robot to avoid obstacles in time as he/she wishes through demonstrations. This paper aims to address the above problem by proposing an approach that combines human supervision with the kernelized movement primitives (KMP) model.

This approach first extracts the reference database used to train KMP from demonstrations by using Gaussian mixture model and Gaussian mixture regression. Subsequently, KMP is used to modulate the trajectory of robotic end-effectors in real time based on feedback from its interaction with humans to avoid obstacles, which benefits from a novel reference database update strategy. The user can test different obstacle avoidance trajectories in the current task until a satisfactory solution is found.

Experiments performed with the KUKA cobot for obstacle avoidance show that this approach can adapt the trajectories of the robotic end-effector to the user’s wishes in real time, including trajectories that the robot has already passed and has not yet passed. Simulation comparisons also show that it exhibits better performance than KMP with the original reference database update strategy.

An interactive learning approach based on KMP is proposed and verified, which not only enables users to plan the trajectory of robotic end-effectors for obstacle avoidance more conveniently and efficiently but also provides an effective idea for accomplishing interactive learning tasks under constraints.

The purpose of this paper is to design a new trajectory error compensation method to improve the trajectory tracking performance and compliance of the knee exoskeleton in human–exoskeleton interaction motion.

A trajectory error compensation method based on admittance-extended Kalman filter (AEKF) error fusion for human–exoskeleton interaction control. The admittance controller is used to calculate the trajectory error adjustment through the feedback human–exoskeleton interaction force, and the actual trajectory error is obtained through the encoder feedback of exoskeleton and the designed trajectory. By using the fusion and prediction characteristics of EKF, the calculated trajectory error adjustment and the actual error are fused to obtain a new trajectory error compensation, which is feedback to the knee exoskeleton controller. This method is designed to be capable of improving the trajectory tracking performance of the knee exoskeleton and enhancing the compliance of knee exoskeleton interaction.

Six volunteers conducted comparative experiments on four different motion frequencies. The experimental results show that this method can effectively improve the trajectory tracking performance and compliance of the knee exoskeleton in human–exoskeleton interaction.

The AEKF method first uses the data fusion idea to fuse the estimated error with measurement errors, obtaining more accurate trajectory error compensation for the knee exoskeleton motion control. This work provides great benefits for the trajectory tracking performance and compliance of lower limb exoskeletons in human–exoskeleton interaction movements.

Research on same-sex marriage has suggested that the transition to marriage is a symbolically meaningful experience that significantly changes sexual minority lives. This chapter draws upon semi-structured, in-depth interviews with 28 married gay men and lesbians to examine how the life course trajectories they took en route to marriage shaped their experiences transitioning to marriage. A description of the short and direct and long and winding trajectories to marriage is provided. Subsequently, it is demonstrated that, although those who took the former report experiences much like those documented by research thus far, those who took the latter had smaller wedding ceremonies to which they attach relatively little meaning, and they report that getting married has done little to change their family relationships. These findings paint a more nuanced picture of the transition to same-sex marriage than has been documented to-date, and point to important directions for future research.

This chapter focuses on the heterogeneous pathways (including marital and cohabiting union and parenting histories) through which people navigate their family life courses from adolescence through mid-life, and their implications for union dissolution in middle and later life. The analyses draw on data (retrospective, cross-sectional) from the 2011 and 2017 Canadian General Social Surveys. The study sample includes individuals aged 50 and over (n = 14,547) who were in a union at age 50. Sequence analyses are used to identify the most common family life course trajectories among these individuals from adolescence through midlife (ages 15–50). Logistic regression analyses then address the implications of these trajectories for union dissolution in middle and later life (ages 50+). The results reveal four main family trajectories that characterize the earlier years of the adult life course: married with children, cohabiting with children, single or cohabiting without children, and married without children. These family trajectories, together with their level of complexity, play an important role in relation to both marital and cohabiting union dissolution outcomes in later life.

Many existing trajectory optimization algorithms use parameters like maximum velocity or acceleration to formulate constraints. Due to the ignoring of the quadrotor actual tracking capability, the generated trajectories may not be suitable for tracking control. The purpose of this paper is to design an online adjustment algorithm to improve the overall quadrotor trajectory tracking performance.

The authors propose a reference trajectory resampling layer (RTRL) to dynamically adjust the reference signals according to the current tracking status and future tracking risks. First, the authors design a risk-aware tracking monitor that uses the Frenét tracking errors and the curvature and torsion of the reference trajectory to evaluate tracking risks. Then, the authors propose an online adjusting algorithm by using the time scaling method.

The proposed RTRL is shown to be effective in improving the quadrotor trajectory tracking accuracy by both simulation and experiment results.

Infeasible reference trajectories may cause serious accidents for autonomous quadrotors. The results of this paper can improve the safety of autonomous quadrotor in application.

This paper aims to study the motion trajectory of the oil seal for shaft in eccentric state and derive equation of lip motion trajectory.

This paper analyzes the force during the motion of the eccentric lip by considering the material viscoelasticity, and a cam-plate mechanism is established as an equivalent model for the motion between the shaft and the lip; according to this, the equation of lip motion trajectory is derived.

The trajectory of the lip lags that of the shaft in the eccentric state because the viscoelasticity-affected lip recovery velocity is lower than the shaft recovery speed. The lip trajectory enters the lag phase earlier and the lag phase’s duration is longer with the increase of the eccentricity and rotational speed, because the deviation of the recovery velocities between the lip and the shaft will be exacerbated.

Innovatively, by considering the viscoelasticity of the material, the cam-plate mechanism is used to equivalent the motion of the shaft-lip to derive the equation for the radial motion trajectory of the eccentric lip. The regularity of lip motion is the key to determining the performance of oil seals, and the eccentric lip trajectory research method revealed in this paper provides a research basis for the performance research and optimization of eccentric oil seals.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2023-0161/

In the digital assembly system of large aircraft components (LAC), the docking trajectory of LAC is an important factor affecting the docking accuracy and stability of the LAC. The main content of docking trajectory planning is how to move the LAC from the initial posture and position to the target posture and position (TPP). This paper aims to propose a trajectory planning method of LAC based on measured data.

First, the posture and position error model of the wing is constructed according to the measured data of the measurement points (MPs) and the fork lug joints. Second, the particle swarm optimization algorithm based on the dynamic inertia factor is used to optimize the TPP of the wing. Third, to ensure the efficiency and stability of posture adjustment, the S-shaped curve is used as the motion trajectory of LAC, and the parameters of the trajectory are solved by the generalized multiplier method. Finally, a series of docking experiments are carried out.

During the process of posture adjustment, the motion of the numerical control locator (NCL) is stable, and the interaction force between the NCLs is always within a reasonable range. After the docking, the MPs are all within the tolerance range, and the coaxiality error of the fork lug hole is less than 0.2 mm.

In this paper, the measured data rather than the theoretical design model is used to solve the TPP, which improves the docking accuracy of LAC. Experiment results show that the proposed trajectory method can complete the LAC docking effectively and improve the docking accuracy.

This paper aims to propose an online local trajectory planner for safe and fast trajectory generation that combines the jerk-limited trajectory (JLT) generation algorithm and the particle swarm optimization (PSO) algorithm. A trajectory switching algorithm is proposed to improve the trajectory tracking performance. The proposed system generates smooth and safe flight trajectories online for quadrotors.

First, the PSO algorithm method can obtain the optimal set of target points near the path points obtained by the global path searching. The JLT generation algorithm generates multiple trajectories from the current position to the target points that conform to the kinetic constraints. Then, the generated multiple trajectories are evaluated to pick the obstacle-free trajectory with the least cost. A trajectory switching strategy is proposed to switch the unmanned aerial vehicle (UAV) to a new trajectory before the UAV reaches the last hovering state of the current trajectory, so that the UAV can fly smoothly and quickly.

The feasibility of the designed system is validated through online flight experiments in indoor environments with obstacles.

The proposed trajectory planning system is integrated into a quadrotor platform. It is easily implementable onboard and computationally efficient.

The proposed local planner for trajectory generation and evaluation combines PSO and JLT generation algorithms. The proposed method can provide a collision-free and continuous trajectory, significantly reducing the required computing resources. The PSO algorithm locally searches for feasible target points near the global waypoint obtained by the global path search. The JLT generation algorithm generates trajectories from the current state toward each point contained by the target point set. The proposed trajectory switching strategy can avoid unnecessary hovering states in flight and ensure a continuous and safe flight trajectory. It is especially suitable for micro quadrotors with a small payload and limited onboard computing power.