非線形計画法に基づく軌道計画のためのスプライン法

抄録

When we plan a trajectory of robot arm, we often use a method drawing smooth curve between given points. In this computation of the trajectory, spline method is used such as parametric spline. By using spline method we easily guess the approximate trajectory from given data points and function characterizing each coordinate. However since piecewise power series are mainly used as spline function, we need much capacity for memorizing the obtained curve. This is unsuitable for robot arm path planning.
Fourier series are sometimes used as one of curve drawing method. Fourier series method has two advantages: one is that Fourier series are differentiable arbitrary times, another is ease of memorizing curves. It has been pointed out as demerit that notable oscillation exists according to harmonics and data points. By appointing regions instead of points, freedom of trajectory increases and optimal trajectory is obtained under the given conditions.
When we plan a path, in some cases it suffice to give arbitrary regions instead of passing points without starting point and destination. Spline method with concept of passing region appointment is useful in robot path planning of this type.
This paper deals with a new spline method for planning robot arm trajectory. We appoint starting point and destination point exactly. We appoint some regions which the robot arm goes through, instead of appointing obstacles. The trajectory is assumed by a straight line and odd functions of Fourier series. The coefficients of Fourier series are decided so that the cost function is minimal by using nonlinear programming. The cost functions are given by sum of square of Fourier coefficients. Some examples are shown by using this method.