Setyamartana Parman

Polynomial joint angle arm robot motion planning in complex geometrical obstacles

This paper addresses a point-to-point of an arm robot motion planning in complex geometrical obstacle. It will govern a two-layer optimization strategy utilizing sixth degree polynomial as joint angle path. At the beginning of the motion planning process, the path planning starts with the optimization objective to minimize the joint angle travelling distance under collision detection rules as constraint. After the best path has been met, the associated time will be searched with the optimization objective to minimize the total travelling time and the torque under the maximum velocity, the maximum acceleration, the maximum jerk, and the maximum torque constraints. The performance of a Genetic Algorithm (GA) and a Particle Swarm Optimization (PSO) will be investigated in searching the feasible sixth degree polynomial joint angle path and the total travelling time that gives the optimal trajectories under kinodynamic constraints. A 3-Degree-Of-Freedom (3-DOF) planar robot will be utilized to simulate the proposed scenario.

Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity

Abstract In this paper, a new class of meshless methods based on local collocation and B-spline basis functions is presented for solving elliptic problems. The proposed approach is called as meshless local B-spline basis functions based finite difference (local B-FD) method. The method was straightforward to develop and program as it was truly meshless. Only scattered nodal distribution was required hence avoiding at all mesh connectivity for field variable approximation and integration. In the method, any governing equations were discretized by B-spline approximation in the spirit of FD technique using local B-spline collocation i.e. any derivative at a point or node was stated as neighboring nodal values based on the B-spline interpolants. In addition, as B-spline basis functions pose favorable properties such as (i) easy to construct to any arbitrary order/degree, (ii) have partition of unity property, and (iii) can be easily designed to pose the Kronecker delta property, the shape function construction as well as the imposition of boundary conditions can be incorporated efficiently in the present method. The applicability and capability of the present local B-FD method were demonstrated through several heat conduction problems with heat generation and spatially varying conductivity.

A new meshless local B-spline basis functions-FD method for two-dimensional heat conduction problems

Purpose – The purpose of this paper is to present a new approach of meshless local B-spline based finite difference (FD) method for solving two dimensional transient heat conduction problems. Design/methodology/approach – In the present method, any governing equations are discretized by B-spline approximation which is implemented in the spirit of FD technique using a local B-spline collocation scheme. The key aspect of the method is that any derivative is stated as neighbouring nodal values based on B-spline interpolants. The set of neighbouring nodes are allowed to be randomly distributed thus enhanced flexibility in the numerical simulation can be obtained. The method requires no mesh connectivity at all for either field variable approximation or integration. Time integration is performed by using the Crank-Nicolson implicit time stepping technique. Findings – Several heat conduction problems in complex domains which represent for extended surfaces in industrial applications are examined to demonstrate ...

A Meshfree Approach for Transient Heat Conduction Analysis of Nonlinear Functionally Graded Materials

In this paper, an alternative meshfree approach is presented for transient heat conduction analysis of nonlinear functionally graded materials (FGMs). The main idea behind the introduced approach is to use collocation in local domains containing of sets of regular or scattered nodes and approximating the solution by B-spline basis functions. It combines the favorable properties of B-spline basis functions in having arbitrary degree for better resolution of solution, partition of unity and the Kronecker delta properties with low computational effort of collocation. The method is called as local B-spline collocation method. It is mathematically simple, efficient to program and truly meshless. The method is applied for analyzing transient heat conduction in a wide range of FGMs with various material gradation models, in both 2D and 3D domains. The results obtained agree well with those computed by analytical solution and other well-known methods, confirming the suitability and efficacy of the presented scheme.

B-spline Collocation with Domain Decomposition Method

A global B-spline collocation method has been previously developed and successfully implemented by the present authors for solving elliptic partial differential equations in arbitrary complex domains. However, the global B-spline approximation, which is simply reduced to Bezier approximation of any degree p with C0 continuity, has led to the use of B-spline basis of high order in order to achieve high accuracy. The need for B-spline bases of high order in the global method would be more prominent in domains of large dimension. For the increased collocation points, it may also lead to the ill-conditioning problem. In this study, overlapping domain decomposition of multiplicative Schwarz algorithm is combined with the global method. Our objective is two-fold that improving the accuracy with the combination technique, and also investigating influence of the combination technique to the employed B-spline basis orders with respect to the obtained accuracy. It was shown that the combination method produced higher accuracy with the B-spline basis of much lower order than that needed in implementation of the initial method. Hence, the approximation stability of the B-spline collocation method was also increased.

Improving the modeling capacity of Volterra model using evolutionary computing methods based on Kalman smoother adaptive filter

This paper proposes three steps of improvements for identification of the nonlinear dynamic system, which exploits the concept of a state-space based time domain Volterra model. The first step is combining the forward and backward estimator in the original Volterra model; the second step is reformulating the Volterra model into a state-space model so that the Kalman Smoother (KS) adaptive filter can be used to estimate the kernel coefficients; the third step is optimization of KS parameters using evolutionary computing algorithms such as particle swarm optimization (PSO), genetic algorithm (GA) and artificial bee colony (ABC). The applicability of the proposed methods is tested in three simulated data and one experimental data. The results show that Volterra model with PSO–KS is preferable for fast identification process, while ABC–KS method is preferable for accurate identification process. However, in some cases, as the iteration number increases the result of PSO–KS method is comparable with ABC–KS method.

Continuous Path Planning of Kinematically Redundant Manipulator using Particle Swarm Optimization

This paper addresses a problem of a continuous path planning of a redundant manipulator where an end-effector needs to follow a desired path. Based on a geometrical analysis, feasible postures of a self-motion are mapped into an interval so that there will be an angle domain boundary and a redundancy resolution to track the desired path lies within this boundary. To choose a best solution among many possible solutions, meta-heuristic optimizations, namely, a Genetic Algorithm (GA), a Particle Swarm Optimization (PSO), and a Grey Wolf Optimizer (GWO) will be employed with an optimization objective to minimize a joint angle travelling distance. To achieve n-connectivity of sampling points, the angle domain trajectories are modelled using a sinusoidal function generated inside the angle domain boundary. A complex geometrical path obtained from Bezier and algebraic curves are used as the traced path that should be followed by a 3-Degree of Freedom (DOF) arm robot manipulator and a hyper-redundant manipulator. The path from the PSO yields better results than that of the GA and GWO.

B-spline collocation method for boundary value problems in complex domains

In this paper, an over-determined, global collocation method based upon B-spline basis functions is presented for solving boundary value problems in complex domains. The method was truly meshless approach, hence simple and efficient to programme. In the method, any governing equations were discretised by global B-spline approximation as the B-spline interpolants. As the interpolating B-spline basis functions were chosen, the present method also posed the Kronecker delta property allowing boundary conditions to be incorporated efficiently. The present method showed high accuracy for elliptic partial differential equations in arbitrary domain with Neumann boundary conditions. For coupled Poisson problems with complex Neumann boundary conditions, the boundary collocation approach was adopted and applied in a simple and less costly manner to further improve the accuracy and stability. Applications from elasticity problems were given to demonstrate the efficacy and capability of the present method. In addition, the relation between accuracy and stability for the method was better justified by the new effective condition number given in literature.

Study on structural deflection of flexible satellite during attitude maneuver using fuel-efficient input shaper

The paper investigates structural deflection of flexible satellite during attitude maneuvers. The satellite is consisted of a rigid main body and two flexible solar panels. Elastic motions of the flexible panels are discretized adhering the finite element method. The attitude maneuvers are equipped with feed-forward inputs in constant amplitude. The inputs are utilized to the satellite complying the fuel-efficient input shaper method. Several cases are investigated in the simulation in order to conclude the influence of fuelling duration with respect to the solar panel deflection, especially in the transient response.

B-Spline Collocation with Domain Decomposition Method and Its Application for Singularly Perturbed Convection-Diffusion Problems

Global collocation method using B-spline basis functions is shown to be capable for solving elliptic partial differential equations in arbitrary complex domains. The global B-spline collocation approach is effectively alleviating difficulties commonly associated to B-spline based methods in handling such domains. Nonetheless, the global method, which is simply reduced to Bezier approximation of degree p with C 0 continuity, has led to the use of B-spline basis of high order in order to achieve high accuracy. The need for B-spline bases of high order is also more prominent in domains of large dimension. In addition, it may also lead to the ill-conditioning problem for combination of the use of B-spline bases of high order and increasing number of collocation points. In this chapter, global B-spline collocation scheme with domain decomposition techniques is introduced for solving Poisson equations in arbitrary complex domains. Overlapping Schwarz multiplicative and additive domain decomposition techniques are examined in this study. It is shown that the combination method produces higher accuracy with the B-spline basis of much lower order than that needed in implementation of the global method. The B-spline collocation with domain decomposition method hence improves the approximation stability of the global B-spline collocation method. Numerical simulations of singularly perturbed convection-diffusion problems are presented to further show the method efficacy and capability.