Path Tracking of an Underwater Snake Robot and Locomotion Efficiency Optimization Based on Improved Pigeon-Inspired Algorithm

This paper considers the tracking control of curved paths for an underwater snake robot, and investigates the methods used to improve energy efficiency. Combined with the path-planning method based on PCSI (parametric cubic-spline interpolation), an improved LOS (light of sight) method is proposed to design the controller and guide the robot to move along the desired path. The evaluation of the energy efficiency of robot locomotion is discussed. In particular, a pigeon-inspired optimization algorithm improved by quantum rules (QPIO) is proposed for dynamically selecting the gait parameters that maximize energy efficiency. Simulation results show that the proposed controller enables the robot to accurately follow the curved path and that the QPIO algorithm is effective in improving robot energy efficiency.

Numerical Method for Solving Nonlinear Equations Arising in Astrophysics

In this paper, a parametric cubic spline function was used to get the solution of a non-linear problem for an isothermal gas sphere. The quasi-linearization procedure was used to reduce the given problem to a sequence of linear problems, the resulting equations are modified at the singular point and are handled by using parametric cubic spline for determining the numerical results. All computations have been carried out by the Mathematica software program package. The findings of computational outcomes on those astrophysics problems confirmed that the technique is legitimate for the solution of these kinds of equations.

Numerical Method for a Class of Nonlinear Singularly Perturbed Delay Differential Equations Using Parametric Cubic Spline

In this paper, we study the numerical method for a class of nonlinear singularly perturbed delay differential equations using parametric cubic spline. Quasilinearization process is applied to convert the nonlinear singularly perturbed delay differential equations into a sequence of linear singularly perturbed delay differential equations. When the delay is not sufficiently smaller order of the singular perturbation parameter, the approach of expanding the delay term in Taylor’s series may lead to bad approximation. To handle the delay term, we construct a special type of mesh in such a way that the term containing delay lies on nodal points after discretization. The parametric cubic spline is presented for solving sequence of linear singularly perturbed delay differential equations. The error analysis of the method is presented and shows second-order convergence. The effect of delay parameter on the boundary layer behavior of the solution is discussed with two test examples.

Numerical analysis of two-parameter singularly perturbed boundary value problems via fitted splines

In this paper, we consider two-parameter singularly perturbed boundary value problems via fitted splines. We propose an exponentially fitting factor to the highest order derivative of the problem and discretize by parametric cubic spline functions on a uniform mesh. An error analysis of the method is presented. The efficiency of the method is demonstrated by test examples which support the theoretical results.

On Numerical Simulations of the Micro-Gears and their Cold Forging Process

In this paper, a parametric cubic spline function for generating gear profile is proposed. The spline function includes new gear design parameters such as pressure angle, number of teeth, module, and tooth tip circle modification. The proposed geometry can improve corner filling condition. Finally, the simulation software DEFORM is used to simulate the cold forging process of the micro-gears with different profiles.