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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.

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.

The purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation. Through our methods, we aim to provide accurate solutions and gain a deeper understanding of the intricate behaviors exhibited by these systems.

In this study, we use a dual technique that combines the Aboodh residual power series method and the Aboodh transform iteration method, both of which are combined with the Caputo operator.

We develop exact and efficient solutions by merging these unique methodologies. Our results, presented through illustrative figures and data, demonstrate the efficacy and versatility of the Aboodh methods in tackling such complex mathematical models.

Owing to their fractional derivatives and nonlinear behavior, these equations are crucial in modeling complex processes and confront analytical complications in various scientific and engineering contexts.